Multi-wavelength Optical Kerr Effects
in High Nonlinearity Single Mode Fibers and Their
Applications in Nonlinear Signal Processing
KWOK Chi Hang
A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Philosophy in Electronic Engineering
© The Chinese University of Hong Kong
September 2006
The Chinese University of Hong Kong holds the copyright of this thesis. Any person(s) intending to use a part or whole of the materials in the thesis in a proposed publication must seek copyright release from the Dean of the Graduate School. M统系储書Ej |(j 1 OCT 1/ )l) ~university-遞 X^Xlibrary system Xn^ Abstract of dissertation entitled:
Multi-wavelength Optical Kerr Effects in High Nonlinearity Single Mode Fibers and Their Applications in Nonlinear Signal Processing Submitted by Chi Hang KWOK for the degree of Master of Philosophy in Electronic Engineering at The Chinese University of Hong Kong in June 2006
Abstract
Optical Kerr nonlinear effects originating from the intensity-induced refractive index change in a nonlinear medium are of much interest for high-speed optical signal processing owing to its ultra-fast response. The change of refractive index in a medium leads to a phase modulation to the light propagating in it. There are two types of intensity-induced nonlinear phase modulation known as self-phase modulation and cross-phase modulation (XPM) respectively for the phase modulation by an intense signal itself or by a separate intense signal co-propagating in the same medium. These two types of nonlinear phase modulation have a tremendous impact for nonlinear signal processing in optical communication networks.
Recent developments in highly nonlinear photonic crystal fibers and dispersion-shifted fibers opened up a new opportunity for fiber-based nonlinear optical signal processing. Such high nonlinearity fibers allow a short fiber length to be used to realize the nonlinear signal processing. Short fiber length not only makes the size of the processor more compact, but also improves the performance of wavelength flexibility and output signal quality because of small dispersion, dispersion variation and other external perturbations.
The dissertation summarizes the simulation and experimental results from the studies of various fiber-based nonlinear signal processing techniques in different types of nonlinear fibers. The studies on the impacts of the dispersion variation of the fibers and the polarization-dependence for XPM are also included in this dissertation.
i 摘要
基於在非錢性媒體中，由強度引起的折射率變化所產生的光克爾非綫性效應反應極快，這效應在高
速光信號處理中引起了很大的興趣。媒體中折射率的變化會導致在其傳輸中的光束產生相位調製。
當中有兩種由強度引起的非綫性相位調製，分別是由強信號自身引起的自相位調製和由同一媒體中
一起傳輸的不同強度信號造成的交叉相位調製。這兩種非綫性相位調製對光通信網絡中的非綫性信
號處理具有鉅大的影響。
近期在高非錢性光子晶體光纖及色散位移光纖的發展爲以光纖爲基礎的非綫性信號處理開啓了新篇
章。這種高非綫性光纖允許在非錢性信號處理中使用更短的光纖。這不僅使處理器的尺寸更爲精巧，
而且由於色散、色散變化和其他的外界干擾都很小，令這種以高非綫性光纖爲基礎的光信號處理器
在波長適應性和輸出信號的質量中都得到了改善。
本論文槪括了以不同種類的非錢性光纖構成之非綫性信號處理技術的模擬和實驗硏究結果，並研究
了光纖色散變化的影響以及交叉相位調製的偏振依賴性。
ii Acknowledgements
I would like to express my deepest and most sincere thanks to my supervisor, Prof. Chinlon LIN, for his guidance and advice. Prof. Lin's commitment and enthusiasm are instrumental in meeting the study objectives. I wish also to acknowledge Prof. H. K. Tsang for sharing his technical insights and comments with me. Special recognition goes to Dr. C. W. Chow and Dr. K. K. Chow for their continuous support, encouragement and discussions in guiding me throughout my study period.
Thanks also go to Prof. Alex P. K. Wai from the Hong Kong Polytechnic university and Dr. Kenneth K. Y.
Wong from the University of Hong Kong for their support and encouragement which make possible for a successful research collaboration among different universities in Hong Kong.
Finally thanks are extended to those who devoted their time and effort for providing stimulating ideas throughout the project. People deserving special mention for useful discussions include Ms. Emily P. S.
Chan, Dr. Simon L.Y. Chan, Dr. Dick W. H. Chung, Dr. Canny Y. H. Kwan, Miss S. H. Lee and Miss Y. Liu.
iii Claim of Originality
This dissertation is the result of my own work and includes nothing which is the outcome of work done from the third-party or in collaboration except where acknowledgements are made explicitly in the text.
iv Organization of Dissertation
Chapter One provides a general introduction from a communication system applications perspective for nonlinear optical signal processing, and introduces the fundamental concepts of optical nonlinearities being utilized for nonlinear optical signal processing. The advantages of using fiber as a potentially useful nonlinear medium for signal processing applications are outlined. The overall objectives of the dissertation are defined.
Chapter Two explains the basic fiber properties, including the origins of nonlinear refractive index change and the impact of fiber dispersion in the nonlinear interactions. Effects of the nonlinear phase shift for nonlinear signal processing are also introduced.
Chapter Three summarizes the measured fiber properties for three types of fiber to be used in developing the nonlinear optical signal processing applications. Basic fiber properties such as fiber dispersion, dispersion map, and nonlinear coefficient are experimentally measured for three types of fiber.
Chapter Four contains the major results in both experimental demonstrations and numerical simulations for two types of all-optical nonlinear signal processing applications. Performance of the developed devices with different types of nonlinear fiber is characterized. Both interferometric and noninterferometric structures are applied to utilize the ultra-fast nonlinear phase shift in fibers for all-optical nonlinear signal processing applications.
Chapter Five compares the proposed approaches with the existing schemes in performing all-optical signal processing, and concludes the dissertation by summarizing the performance of the devices developed and the results discovered in this dissertation. Future perspective on the relevant subject is also given.
Contributions of this dissertation to the multi-wavelength all-optical nonlinear signal processing techniques are discussed in this chapter.
V Appendix A lists the numerical model used for calculating the dispersion and zero-dispersion wavelength variation in a structural varying fiber.
Appendix B provides detailed description on the simulation model used in evaluating the performance of
XPolM-based wide band wavelength conversion.
Appendix C provides detailed description on the simulation model used in evaluating the performance of spectral filtering for modulation format conversion.
List of Publications summarizes both the journal and conference publications related to the work reported in this dissertation, and the work published in the study period.
vi Contents
Chapter 1 Introduction 1
1.1 All-Optical Signal Processing in Optical Communications 2 1.2 Fiber-Based Optical Kerr Nonlinear Switches 5 1.3 Highly Nonlinear Fibers 6 1.4 Obj ectives and Scope of Study 8 1.5 Summary 9
Chapter 2 Optical Nonlinearity 14
2.1 Fiber Nonlinearity 15 2.2 Dispersion 21 2.3 Cross-Phase Modulation 26 2.4 Cross-Polarization Modulation 29
Chapter 3 Fibers: The Nonlinear Media 47
3.1 Average Dispersion 48 3.2 Longitudinal Dispersion Map 53 3.3 Nonlinear Refractive Index and Nonlinear Coefficient 57 3.4 Electrostrictive Contribution 62 3.5 List of the Fiber Properties 66
Chapter 4 Multi-Wavelength Nonlinear Signal Processing 69
4.1 Challenge 70 4.2 Applications 72 4.3 Proposed System Application 110
Chapter 5 Conclusion and Future Work 114
5.1 Comparisons between Proposed and Existing Approaches 114 5.2 Conclusion of the Dissertation 115 5.3 Prospects and Directions of Future Work 117
Appdenix A Numerical Model for Dispersion Calculation I
Appdenix B Simulation Model of Wide Band Cross-Polarization Switch Ill
Appdenix C Simulation Model of Spectral Filtering under XPM VI
List of Publications IX
vii Chapter 1
Chapter 1 Introduction
The pioneering demonstration by P. A. Franken et al. in 1961 of optical second harmonic generation in quartz
using a ruby laser [1] started modem nonlinear optics. Since then, there has been a tremendous growth in the interest of utilizing the nonlinear effects in various optical applications over the past few decades [2-18].
Optical nonlinearities give rise to many unique effects in any dielectric material. Optical nonlinearities cover various nonlinear optical phenomena, and the definition of "optical nonlinearities" is used loosely in this dissertation to encompass any intensity-dependent effect that can change the optical waveguiding characteristics. This definition of optical nonlinearity includes but not limits to those effects normally covered by the term such as intensity-dependent refractive index, parametric effects, harmonic generation and nonlinear absorption. These effects are interesting in themselves as pure scientific researches, and they also have many useful applications. One of the well known optical nonlinearities commonly used in optical communications for all-optical nonlinear signal processing is optical Kerr effect. Kerr effect was reported by John Kerr in 1875 [19] and refers to an effect describing a change in the refractive index of a material in response to an intense applied electric field*. The Kerr effect was discovered long before the inventions of lasers and optical fibers in the 1960s. Optical nonlinearities can be prominent in optical fibers even for a small nonlinear index of silica because of the characteristics which is inherent in optical fibers. The core size and the length of the fiber can strongly enhance optical nonlinearities, with a ratio of the nonlinearities in bulk and confined-guiding silica expressed as [20]
明.(fiber)= A (1.1) /乂�“bulk ) m-.'a
* Note that the term "Kerr effect" refers to John Kerr's original discovery of refractive index change under a strong electric filed applied to the medium; while the "optical Kerr effect" is derived from this phenomenon in response to an intense applied electromagnetic field.
1 Chapter 1
where i" is the intensity (power per unit area) in the fiber and bulk, respectively; is the effective
length of guiding medium with a loss of a ； r� iths e radius of the fiber core; and A. is the wavelength of
the electromagnetic wave propagating in the medium. As a result, for a wavelength of 1550 nm propagating
in a fiber with a typical loss of 0.2 dB/km (a « 5x 10"^ m'') and a core radius of 4.5 ^m，the nonlinear
enhancement simply due to the small core and long interaction length can be of the order of 108. The
advance of doping technique for high—nonlinearity elements and complex core structure designs further
enhance the effective nonlinearity to reduce the power and shorten the fiber length required to achieve sufficient nonlinear effects for all-optical nonlinear signal processing. The fundamental restriction remained in all-optical nonlinear signal processing is the scalability of such nonlinear devices for the telecommunication applications. Typical optical fiber networks applying the wavelength-division multiplexing (WDM) technology operate with an order of tens of wavelengths resulting in a tremendous increase in the complexity at a network node no matter whether traditional optical-electrical-optical (OEO) conversion or all-optical nonlinear signal processing is applied. This concern of scalability of multi-channel operation is the major driving force for the advance of fiber-based all-optical nonlinear signal processing devices to handle multi-channel optical networks. Such devices are considered and developed in more detail later in this dissertation.
1.1 All-Optical Signal Processing in Optical Communications
Single-mode optical fibers now form a major part of the telecommunications network. Present transmission systems however only use a small fraction of the theoretical information carrying capacity of the fiber. The intensity modulation and direct detection systems currently employed can transmit at bit-rates up to 40 Gb/s per channel [21-23] whereas a single-mode fiber has a bandwidth of about 50000
GHz. There is an increasing need for larger information transmission capability in telecommunications, stemming from a demand for the provision of broadband transmission facilities for services such as
2 Chapter 1
high-definition television and Internet traffic. This demand cannot be met by present systems because the transmission bit-rates are limited by the speed of the electronic switching speeds.
All-optical nonlinear signal processing is undergoing extensive research and development because it can bypass the OEO conversions to unleash the large information processing potential of the existing WDM techniques. There are several different types of all-optical nonlinear signal processing approaches but they all share the basic element of optical nonlinearities of the guiding material.
Nonlinear effect relying on the second-order optical nonlinearity has been extensively researched and developed in the past three decades. Bulk-optics devices with strong second-order nonlinear effect are quite advanced and mature, and have been commercially available for years. Materials, like potassium titanyl phosphate (KTiOPO*)，barium borate (838204) or lithium niobate (LiNbOs), with strong second-order optical nonlinearity are commonly found in commercially available devices for all-optical nonlinear signal processing of light at different wavelength range. Fig. 1.1 shows the transparency range of different commonly used nonlinear crystals [24].
VV VIS IR ll.l 11.2 nj (l.-l (I.S ll.h 11.1 O.N I 2 4 H 丨f, 211
KTP LBO AGS KTA LB4 AGSe BBO LIS CLBO LlSe DLAP GaSc LiI03 KPb2CI5
Fig. 1.1 Transparency range of common nonlinear crystals.
3 Chapter 1
Owing to the power series nature of the optical nonlinear effects to the applied electric fields, the second-order nonlinear effects are the first observable and dominant effects in most materials with asymmetrical molecular structure. The third-order optical nonlinearity is, therefore, usually in negligible efficiency*. Only for material with symmetrical molecular structure does the third-order optical nonlinearity appear. Silica (Si02) as the core material in fabricating optical fiber is an amorphous solid which does not normally exhibit these second-order nonlinear effects as a result of averaging. As a consequence, the second-order nonlinear effects are averaged out to be approximately zero and the first observable nonlinear effects in optical fiber attribute to the third-order optical nonlinearity. Small material nonlinearity and high order effect make silica fiber to be less attractive as the nonlinear optical signal processing medium. Only after doping of various high nonlinearity elements in the fiber core and the advance design of the fiber structure can the fiber-based all-optical nonlinear signal processing become a reality.
These two classes of nonlinear processes have received much attention for a variety of applications.
Devices using second-order nonlinear crystal have comparatively high efficiency and short interaction length suitable for generation and detection applications; whereas the third-order nonlinear fiber-based devices are typically focused on the inline nonlinear signal processing for telecommunication signals.
While the choice between crystal-based and fiber-based devices depends on the applications and they have relative pros and cons, the author is inclined to support the use of fiber-based devices in telecommunication applications by avoiding the difficulty of mode coupling and matching faced for external waveguide devices.
Various applications based on fiber-based device have been developed over the years [25-30]. Yet, the processing remains in single channel operation. To explore the bandwidth potential of WDM techniques, devices serving multiple signals are favored to handle several signals with a single-device. The
* See Chapter 2 for a detailed discussion on the nonlinear properties of silica fiber.
4 Chapter 1
multi-channel capability has been investigated in this dissertation by minimizing the cross-talk in the
multi-wavelength operation, especially for implementation of all-optical functionalities in WDM networks.
1.2 Fiber-Based Optical Kerr Nonlinear Switches
All-optical nonlinear switching relying on the nonlinear refractive change from optical Kerr effect is one of
the main applications of optical nonlinearity. Nonlinear switching of light can be achieved through
interfering two identical copies of a signal with unbalanced phase shift between them. The unbalanced
phase shift is developed as a result of optically-induced nonlinear refractive index change. Signal splitting
and combining form an interferometer. Structures of the interferometers vary with the way the signal splits
and combines, and are generally classified as Mach-Zehnder interferometer, Sagnac interferometer and
Michelson interferometer, as shown in Fig. 1.2. Switching can also be realized with other noninterferometric approaches such as spectral filtering and polarization switching.
Mirrors
(a) (b) (c)
Fig. 1.2 Schematic of different interferometric switches: (a) Mach-Zehnder interferometer; (b) Sagnac interferometer; and (c) Michelson interferometer.
The cross-induced phase shift due to the refractive index change can be used for optical switching through an interferometer. A generic interferometer is designed so that a weak signal, divided equally in intensity and phase between its two arms, experiences a n phase difference between two arms and is not transmitted due to destructive interference. For a cross-induced nonlinear refractive index and phase change in one arm, the signal will be transmitted with the output power proportional to the amount of the phase difference between two arms because of the constructive interference. As a consequence, a signal can be gated by an intense signal through the optical Kerr effect in fiber.
5 Chapter 1
The phase modulation from either self-induced or cross-induced will lead to a broadening of the spectrum
owing to the time-varying phase shift under the relation co{t) =-d ^{t)/dt. The generated spectral
components correspond to different time instance of the signal. In general, the rising edge of a signal
contributes to the red-chirped components at the longer wavelength side of the carrier wavelength in a
broadened spectrum; and the falling edge of a signal contributes to the blue-chirped one at the shorter
wavelength side. Extraction of the nonlinear phase modulation broadened spectral components with an
optical bandpass filter can retrieve the time-domain information as the processed signal output. This
approach of spectral filtering provides a noninterferometric way to realize nonlinear switching based on
optical Kerr effect. Noninterferometric approach of nonlinear switch can also be realized by utilizing the
nonlinear polarization rotation characteristic of the optical Kerr nonlinear refractive index change. Fiber as
the nonlinear medium in a single-pass structure and a passive optical polarizer make up of this
noninterferometric switch.
All these nonlinear switching techniques will be applied in developing all-optical nonlinear signal
processing devices in this dissertation for telecommunication applications. In all cases, a gating signal is
used to switch or process another signal in the nonlinear switch allowing an "AND"-gate operation to be
performed all—optically with very fast response time,
1.3 Highly Nonlinear Fibers
In order to take the full advantages of the nonlinearities described above and to further enhance them, novel optical fibers have been designed and fabricated [31-33]. Equations in the later chapters will show that the parameters determining the strength of these nonlinearities are the effective area A^g-, the effective fiber length L订�，and the nonlinear refractive index ^^^^，besides the input power of the concerned fields.
Clearly, the nonlinearities become important when the effective length exceeds certain length relevant to the nonlinear length = x/yp for a fiber with a nonlinear coefficient of at a power P. The
6 Chapter 1
increase in fiber length will, however, eventually saturate this enhancement because of the finite fiber loss and dispersion that bounds the maximum l谓 achievable and voids the phase matching for parametric processes or introduces a large time-domain separation between the interacting signals for nonlinear refraction. In general, one should look for an ideal relation of « l�订 « L�with a dispersion length of
L^. Consequently, parameters for strengthening optical nonlinearities in fiber are limited to the effective area a^JJ- and the nonlinear refractive index n^^^.
Highly nonlinear fibers are, therefore in general, aimed at reducing the effective core area A^g-, and increasing the index contrast a« = n咖-，to confine the light more tightly in the core, or increasing nonlinear properties of the guiding medium for a larger �.Thes etwo ways consequently, lead to two main streams of highly nonlinear fiber designs. They are highly nonlinear photonic crystal fibers (PCFs) and doped highly nonlinear (dispersion-shifted)* fibers respectively, addressing the condition of reducing the effective core area and increasing the nonlinear properties of the guiding material.
PCFs fall into two basic categories. For one type, the index-guiding is formed by a solid core in the central region with defect region surround by multiple air holes in a regular lattice, and confines light by a total internal reflection like standard fibers [32]. For the other, guiding of light is achieved with a hollow-core photonic band-gap structure exhibiting a photonic band-gap effect at the operating wavelength in a low index core region [33]. Among these two classes of fiber structure, the term "PCF" is used in this dissertation to refer to the first type ofPCF with solid core to provide tight guiding of light. The advance in fiber fabrication techniques enables the size of the core guiding region to be reduced with high (silica core to air holes defect) index contrast for a substantial increase of the optical power density in the core [34, 35].
High nonlinearities can also be achieved by increasing the core doping level with high nonlinearity materials.
The heavily doped core multiplies the nonlinear refractive index n•^明 to reach a higher fiber nonlinearity.
* Dispersion-shifted is optional but preferred for a shorter l�i nthe interested wavelength region.
7 Chapter 1
Various dopants have been applied to increase the nonlinearity. For example, germanium-oxide (GeO?) typically used in increasing the core refractive index can have a nine-fold {y a 20 W'km"') increase in fiber nonlinearity compared with conventional silica fibers [36]; Pb-doped silica fibers have been fabricated with nonlinear coefficient y « 640 W"'km'' [37]. Bismuth-oxide, a newly-developed core dopant, can even boost the nonlinear coefficient to over thousands [38, 39].
From the above, it is clear that high nonlinearity fiber can be very useful for nonlinear signal processing applications. With careful design of the index profile, some of these fiber designs [35, 40, 41] can simultaneously achieve both high nonlinearity and low dispersion in the most common operating wavelength range of 1550 nm to realize the general goal of 丄肌 « z谈 « 乙.
1.4 Objectives and Scope of Study
The previous section introduced silica fiber as a nonlinear medium to be exploited for all-optical nonlinear signal processing. The primary objective of this dissertation is to evaluate the optical nonlinearities of three types of fibers: dispersion-shifted fiber (DSF), photonic crystal fiber (PCF), and highly nonlinear dispersion-shifted fiber (HNL-DSF) with the specific aim of implementing the nonlinear effects for optical signal processing in telecommunication applications. Since optical nonlinearities, apart from the optically-induced Kerr nonlinear refractive index change, are broad topics covering many nonlinear phenomena, the current study is focused only on the optically-induced Kerr nonlinear refractive index change and utilizing such nonlinearities in silica fibers for optical signal processing applications. This study will address but not attempt to investigate other fiber nonlinearity, such as four-wave-mixing (FWM), stimulated Raman/Brillouin scattering (SRS/SBS) and parametric amplification.
8 Chapter 1
1.5 Summary
All-optical nonlinear signal processing can potentially overcome the speed limitation of electronic components and utilize the full data processing capacity at the network nodes. Although various all-optical nonlinear signal processing techniques have already been demonstrated on the base of optical nonlinearities, such techniques need further development to make signal processing devices more efficient, reliable and economical.
All-optical nonlinear signal processing can be realized with all-optical nonlinear switch of different structures and approaches, in which fiber as the nonlinear medium, provides nonlinear phase shifts to the co-propagating signals through optically-induced nonlinear refractive index change. Regardless of the structure of this nonlinear switch, the nonlinear fiber plays a crucial role in the overall performance of the device. A key objective of this work is to evaluate the properties of different types of nonlinear fibers with the ultimate aim of realizing all-optical nonlinear signal processing. Scalable signal processing devices are explored to meet the increasing demand on the network capacity.
9 Chapter 1
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[35] K. P. Hansen, J. R. Folkenberg, C. Peucheret, and A. Bjarklev, "Fully dispersion controlled triangular-core nonlinear photonic crystal fiber," in Proc. Optical Fiber Conf, (OFC 2003), Atlanta, GA, Postdeadline Paper PD2-1, 2003.
[36] M. J. Holmes, D. L. Williams, and R. J. Manning, "Highly nonlinear optical fiber for all optical
processing applications," IEEE Photon. Technol Lett, vol. 7, no. 9, pp. 1045-1047, 1995.
12 Chapter 1
[37] P. Petropoulos, H. Ebendorff-Heidepriem, V. Finazzi, R. C. Moore, K. Frampton, D. J. Richardson, and T. M. Monro, "Highly nonlinear and anomalously dispersive lead silicate glass holey fibers," Opt. Express, vol. 11, no. 26, pp. 3568-3573，2003.
[38] T. Nagashima, T. Hasegawa, S. Ohara, N. Sugimoto, K. Taira, and K. Kikuchi, "Bi203-based highly nonlinear fiber with step index structure," in Proc. SPIE—Int. Society Optical Engineering, San Jose, CA, vol. 5350, pp. 50-57, 2004.
[39] K. Kikuchi, K. Taira, and N. Sugimoto, "Highly-nonlinear bismuth oxide-based glass fibers for all-optical signal processing," in Proc. Optical Fiber Conf., (OFC 2002), Anaheim, CA, Paper ThY6, 2002.
[40] K. -W. Chung, S. Kim, and S. Yin, "Design of a highly nonlinear dispersion-shifted fiber with a small effective area by use of the beam propagation method with the Gaussian approximation method," Opt. Lett,, vol. 28, no. 21, pp. 2031-2033,2003.
[41] M. Takahashi, R. Sugizaki, J. Hiroishi, M. Tadakuma, Y. Taniguchi, and T. Yagi, "Low-Loss and
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3615-3624, 2005.
13 Chapter 1
Chapter 2 Optical Nonlinearity
All-optical nonlinear signal processing in fibers relies on the nonlinear optical properties of the guiding material. The response of any dielectric material to light becomes nonlinear for intense electromagnetic fields as a result of anharmonic motion of bound electrons under the influence of an applied field [42, 43].
Optical nonlinearities can be elastic in the sense that no energy is exchanged between the electromagnetic field and the dielectric medium, or inelastic in which electromagnetic field transfers part of its energy to the nonlinear medium. Nonlinear effects，such as harmonic generation, wave-mixing and nonlinear refraction belong to elastic processes, whereas the vibrational excitations like stimulated Raman or Brillouin scattering belong to inelastic processes. Within this wide range of optical nonlinearity, nonlinear refraction in fibers is studied and utilized in this dissertation for system applications.
This chapter reviews the basic principles of the optically-induced nonlinear refraction in fibers, and their applications in nonlinear signal processing. Influence of dispersion variation on the nonlinear interaction is also studied.
14 Chapter 2
2.1 Fiber Nonlinearity
The advent of the laser and optical fiber made possible to study a wide variety of nonlinear optical effects.
Electric field applied to a dielectric medium is related to the induced polarization P, of the electric dipoles by
P = . E + : EE + ；IT�；EE +...E ) (2.1) where £•� iths e permittivity of vacuum; E is the electric field; and ；}；⑴，；；j ^ � and ；� are, respectively, the first-, second- and third-order susceptibility tensors. The first-order susceptibility tensor ；{；⑴ governs the linear response of the dielectric medium to an applied field E, at low power regime, whereas the dielectric medium reacts nonlinearly to a strong field with the higher-order susceptibility tensors. Structure of susceptibility tensors can be obtained with a classical anharmonic oscillator model of the dipole moment of a medium [43，44]. The constitutive equation between electric displacement D, and electric field E, can be written as
D = fo� E = foE + P (2.2)
where s^ is the relative permittivity.
Nonlinear responses of the medium to an applied strong electromagnetic field are governed by the higher-order susceptibility tensors (� ’ ；�•••） •For crystal structure with inversion symmetry, all even-order susceptibility tensors vanish [45]. Therefore, ；j；^ �is only present in crystals with particular symmetries, whereas ；^⑶ is present in all materials, including amorphous materials such as glass. The power series nature of (2.1) indicates that ；j； �effects dominate for low power of the applied field, and ；� effects can become significant only for this power to be large. As a result, ；^；⑵ effects are relatively easier to demonstrate for a given interaction length. Fibers, however, do not normally exhibit this second-order nonlinearity because of the amorphous structure of silica (SiO?) glass. Therefore, a larger power is required for the applied fields to reach the first observable nonlinear effects provided by third-order nonlinearity in
15 Chapter 1 fibers. Also because of the inefficient ；� effects in silica, ；j；^� effects can become dominate and more efficient in fibers. The third-order susceptibility ；{^⑶，governs elastic nonlinear effects related to the interplay between three electromagnetic fields of the same or different carrier frequency, such as third harmonic generation, FWM, and nonlinear refraction. It is also the origin of inelastic nonlinear effects of vibrational scattering (Raman and Brillouin). The third-order susceptibility in the cubic polarization
P�=；^⑶：EE Eis a fourth-rank tensor with 81 elements. In the isotropic medium, such as silica, the number of nonzero elements is reduced to 21 with 3 of them are independent. Different combinations of electric fields and their frequency correspond to different nonlinear phenomena. Among these nonlinear phenomena, the optically-induced nonlinear refractive index change is considered in this dissertation for fiber-based nonlinear signal processing.
Nonlinear refraction is a phenomenon referring to an intensity dependent refractive index resulting from the contribution of ；�.Considerin ugp to third-order susceptibility, the refractive index of a silica fiber can be generally written as
"="0+"2<#|五|2 (2.3) where n^ is the linear refractive index of the material at low optical power levels; n•^谓 is known as second-order nonlinear refractive index coefficient contributing to the intensity dependent refractive index change; and E ^ is the power of the applied field. The intensity dependent nonlinear refractive index change attributes to the optical Kerr effect and is one of the contributors for the refractive index modification other than the resonant-based electrostrictive contribution.
16 Chapter 1
In optical fibers, the two most important contributions to this nonlinear refractive index n^^^，are the nonresonant electronic polarization induction and the electrostriction, simply expressed as [4648]
ip, nu (氏 The first term in this equation attributes to the fast response optical Kerr nonlinearity and its efficiency varies with a polarization angle 0, between the electromagnetic fields and the ellipticity angle 炉，of the fiber eigenmodes owing to the tensorial properties of the electronic susceptibility. The second term relates to a slow and modulation frequency v^, dependent acoustical resonances in the fiber structure that are coupled to optical intensity modulation by electrostriction causing refractive index variations through the elasto-optics effect. Principles of these contributions are discussed in the following. Nonresonant Electronic Polarization Contribution The third-order susceptibility relates to the refractive index change through the definition [49，50] (2.5) where represents a third-order tensor combination of three coplanar electric waves with the same carrier frequency acting on the coplanar field itself, known as self-phase modulation (SPM). The nonresonant electronic polarization contribution ，known as the optical Kerr effect is governed by the third-order susceptibility. A general expression of this n.^^ is ⑷= + "(没，(2.6) illustrating a combined effect of self-induced and cross-induced refractive index change. Symbols are defined in (2.4) and (2.5). The former term of (2.6) governs the optically-induced refractive index change by the field itself; while the later one describes the optically-induced refractive index change seen by other co-propagating fiel(l(s) with a scaling factor ri{9,q))- This scaling factor and the effect of cross-induced 17 Chapter 1 refractive index change, known as cross-phase modulation (XPM) will be discussed in the subsequence sections. In short, this polarization-dependence arises from the tensorial properties of the nonlinear susceptibility between multiple fields. As the time response of the optical Kerr effect is of the order of femtoseconds [51], the effect from n^^ can therefore be considered to be independent of the signal bit-rate or the pulsewidth of the optical signal propagating in the fiber. In fused silica core fibers n^ is « 2.4x10"^° m^/w [52-59]. The nonlinear refractive indexes for fibers slightly doped with germanium (Ge), fluorine (F), or other elements deviate from this value. For example, germanium-oxide (GeO?), which is commonly used as dopant to modify the overall dispersion characteristic of a fiber, increases the nonlinear refractive index by 0.033x10"^° mVw per mole concentration [58]. The increase in nonlinear refractive index allows a higher nonlinearity to be reached at the same intensity level, and later leads to the design of high nonlinearity fibers [1.36，60]. Electrostrictive Contribution J I 1 I I I I I I I i I I I I I I I I I »- \ -0.5 ^ 4 -•I I • I I • _ I I • • • _ I •- 0 500 1000 1500 Modulation Frequency Vm (MHz) Fig. 2.1 Theoretical predictions of the electrostrictive frequency response for a fiber with a mode (intensity) radius of 3 nm. The solid curve includes the influence of acoustic reflections structurally damped by variations in the outer cladding diameter. The dashed curve is the intrinsic fiber response, equivalent to 100% damping of acoustic reflections. (After Buckland [66]) 18 Chapter 1 Electrostriction is a process in which the material density increases in response to the intensity of an applied electromagnetic field, creating a proportional change in the refractive index of the material [61-63]. The response time for the density change can be estimated as the time required for a sound wave to propagate across the fiber core and is equal to ~1 ns. The acoustic waves generated by this interaction propagate outward toward the cladding boundary and create echoes with a period of ~21 ns as they reflect back toward the core of the fiber [55，61, 64-66]. These waves can be long lived — the damping time of an acoustic wave in optical fibers has been shown to be of the order of 100 ns [55, 61, 64-66]. The electrostrictive frequency-response function includes an intrinsic contribution from the density variations that are driven locally by the optical intensity propagating in the fiber, and a contribution from the acoustic echoes. The intrinsic frequency response function [47] and the response function including damped acoustic reflections are shown in Fig. 2.1. In principle, the acoustic reflections can be arbitrarily reduced by structural variations in the cladding diameter or by increased acoustic coupling of the fiber to the external environment (i.e., as is accomplished by the fiber's polymer coating); the intrinsic response, however, is fundamental and cannot be eliminated. The magnitude of the electrostrictive contribution n^^，has been theoretically calculated as [47, 67] where y^ is the electrostrictive constant; Q is the isentropic compressibility; n^ is the weak-field refractive index; and c is the light speed in vacuum. Various techniques were developed to measure this electrostrictive contribution [52-59, 61-67]. For typical telecommunications optical fibers, » 0.5 X10—2�m^/ w[59, 67]. This value alters with different dopants and their concentrations [68] 19 Chapter 1 Nonlinear Coefficient of Fibers Nonlinear coefficient y, is commonly used in describing the fiber nonlinearity and is defined as =竺’. (2.8) ^々 This nonlinear coefficient expresses the amount of nonlinear phase shift acquired by a wave propagating in a fiber with an effective core area A^jj-，and effective nonlinear coefficient n^^^，at a given optical power, and relates the nonlinear phase shift 伞吼,to the optical field intensity I, by calculating the ratio between the optical power p = , and the effective core area a^.跃,through the expression K = YkffP 2. P , (2-9) Equation (2.9) illustrates a linear relationship among the nonlinear phase shift 中机,the optically-induced refractive index n^^jg-，the optical power ，which induces this refractive index change, and the interaction length L谓=(i_ e~'^)la (an effective interaction length under a fiber propagation loss a，equivalent to the length with constant power and zero propagation loss). The nonlinear coefficient provides a simple illustration of the amount of nonlinear phase shift which can be achieved for a given input power P, or an optical field intensity I，which can be customarily controlled for the ratio between the optical power P, and the effective core area A^^, to achieve a high nonlinear effect (such as the PCF with reduced core area). The wavelength dependence of this nonlinear coefficient is easily overlooked as it is easily understood that the power required to achieve the same nonlinear phase shift varies with the wavelength of the electromagnetic wave. Magnitude of all the variables in (2.9) except P and n^^jj-, varies with wavelength, and so does the power required to achieve a given amount of nonlinear phase shift. Hence, the use of this nonlinear coefficient is avoided in the following expressions where a wide range of input wavelength is considered. 20 Chapter 2 2.2 Dispersion Fiber dispersion is a result of the combined effects of material dispersion and waveguide dispersion. Material dispersion arises from the variation of the refractive index of the material as a function of wavelength which introduces a wavelength dependence of the group velocity; while waveguide dispersion occurs as a result of wavelength dependent core confinement of the guiding wave caused effective refractive index variation against the wavelength. The origin of fiber dispersion and its impacts on signal propagation had been extensive studied in various literature [69-72] and textbooks [73, 74], and will not be discussed in this dissertation. In short, dispersion degrades optical communication systems by limiting the maximum distance and/or data rate a signal can go without significant signal distortion as a result of signal time-spreading. In the nonlinear interaction, dispersion is also an important factor which restricts the processing signals from propagating at the same velocity. This group velocity mismatch voids the phase matching condition in wave-mixing processes [75], and introduces signal-to-signal walk-off, in nonlinear phase modulation processes. The signal-to-signal walk-off, or the walk-off, is the amount of time signals walked away from each other after propagating in a dispersive medium. While dispersion plays a crucial factor in the nonlinear interactions, the impact of dispersion variation along the fiber as a result of limited fiber uniformity has not been explored until the past few years because of the lack of nondestructive dispersion mapping techniques [76-80]. In FWM, the conversion efficiency, defined as the power ratio between the signal and the generated idler at the fiber output, depends significantly on the dispersion caused propagation constant difference [75, 81]. Because of this strong dependence, any change in the dispersion value in the longitudinal direction eventually changes the final output power of the idler and its conversion efficiency. Similar dispersion dependence is also observed in optical parametric amplification (OPA) process [82, 83]. In fact, these 21 Chapter 1 parametric processes are typically used for measuring the zero-dispersion variation along a fiber because of this strong dispersion dependence [76-80]. In contrast, nonlinear phase modulation has less sensitivity on this dispersion variation [84, 85]. This dissertation reports a systemic analysis on the impacts of dispersion variation in nonlinear phase modulation, and shows that XPM is indeed more robust to the dispersion variation. This robustness to the dispersion variation makes nonlinear phase modulation to be superior to those parametric processes. Causes of Dispersion Variation and its Model The cause of dispersion variation is fundamental. The physical properties of fibers vary along the length as the fiber is being drawn. Core diameter, core-to-cladding refractive index difference and their refractive index distributions influence all the optical properties, including fiber birefringence, nonlinearity and dispersion, and hence affect the performance of those fiber-based nonlinear effects. In here, this multi-dimensional problem is confined into a simple single-dimensional one concerning only the change of dispersion in the longitudinal direction, because of its unique time-relevant characteristic in the nonlinear interaction. rifTL ^^^^^ _ “ 一丨 Host: Fused silica Fig. 2.2 (a) Cross-section, and (b) three-dimensional refractive index profile for the DSF model. (After Keiser [74] and Dianov [86]) 22 Chapter 1 Property SiCV®) GeO: Unit Density 2.202 3.65 g/cm^ Refractive index at (b) 0.5893 ^rni 1.4584 1.6083 1.55 }im 1.4440 1.5871 Wavelength of zero material dispersion � 1.27 1.74 陣 Sellmeier coefficients (d-D A, 0.6961663 0.80686642 A in ^im A2 0.4079426 0.71815848 As 0.8974794 0.85416831 B, 0.0684043 0.06897261 B2 0.1162414 0.15396605 B3 9.896161 11.841931 � Fused silica (b) 25-100�C (c) Reported by Devyatykh et. al [87] and Polukhin [88] (d) Fitted range of 0.21-3.7 ^m for SiOz and 0.36-4.3 |im for GeOj (e) Valid at 20 °C for SiOz and 22-26 °C for GeOz ⑴ ⑷一l = _^+^i:^+_^,[89，90] A — A, — B2 义一 Bj Table 2.1 Properties of silica (SiO�）an germanium-oxidd e (GeO?) and glasses. 一 20 官—c Material dispersion ^^^^^ 5 15 • SiOs - GeOs ^^^^ £ 10 t 5 ^^ 一 0 Q 5 Fi^r dispersion (/) _i5 Waveguide O -20 L ‘ ‘ ‘ 1.2 1.3 1.4 1.5 1.6 Wavelength (|im) Fig. 2.3 Material, waveguide and the overall dispersion as a function of wavelength for the fiber design shown in Fig. 2.2. Ratio of SiOz and GeOj is 84.1:15.9 and the single-mode condition ( V < 2.405) is satisfied for wavelength longer than 1.48 |im . The combined dispersion is approximated by adding the material and waveguide dispersions. 23 Chapter 1 Fig. 2.2 shows cross-section and the three-dimensional refractive index profile for a DSF used in modeling the impact on the dispersion due to the change of its physical properties. The material properties of the fused silica and germanium-oxide are listed in Table 2.1. Ratio of the Si02 and GeO: are chosen to be 84.1:15.9 so that the zero-dispersion wavelength of the present design is 1550 nm as shown in Fig. 2.3. Dispersion variation is calculated by considering both the material dispersion and waveguide dispersion in this fiber with the core diameter and core refractive index being varied. Dispersion curves with different core diameter and core refractive index are plotted in Fig. 2.4. Numerical model used in the calculation is provided in the Appendix A. Insets of Fig. 2.4 show the concentric dispersion curves to the corresponding zero-dispersion wavelengths to visualize the variation of the dispersion slope. Based on these figures, one can conclude that the nonuniform fiber properties lead to both zero-dispersion wavelength and dispersion curve variations. Compare with the zero-dispersion wavelength variation, the dispersion curve variation, however, has less impact on the overall nonlinear interaction as it alters slightly from the predicted value within the interested wavelength range. The zero-dispersion wavelength variation, therefore, plays the dominate role in governing the group velocities in a nonlinear interaction. To simplify the situation, the fiber properties caused dispersion variation is modeled as a shift of the dispersion curve with a corresponding zero-dispersion wavelength A。，as = (2.10) where ；1�(z i)s the zero-dispersion wavelength in the longitudinal direction; and J^ = 义。is the 4) average zero-dispersion wavelength over a fiber length, L.义�(z )can be accurately measured from FWM or OPA spectra [76-80]. This assumption of constant dispersion curve will be used throughout the following discussion. 24 Chapter 1 (a) I % 0 1 4 Wavelength (^im) (b) E 1 ..... I 2 10 丫....營；一 一一.： ‘―^^1.7 \ 14 Wavelength (Jim) Fig. 2.4 Plots of the dispersion curve with (a) core radius and (b) core refractive index varying from its decided value. Insets show the corresponding concentric dispersion curves. 25 Chapter 2 2.3 Cross-Phase Modulation When two or more electromagnetic waves co-propagate in fibers, they interact with each other under the fiber nonlinearities. For instance, the optically-induced refractive index variation leads to a nonlinear phase change for the co-propagating fields at a different wavelength known as XPM. It is originated from a 义⑶ effect with the total elective field E, of two waves at different angular frequencies and ^y^ given by E =丄 叫'+£ 广'(2.11) 2 ‘ 2 where the two waves are polarized along the x—axis in a Cartesian coordinate with the propagation direction pointing toward the positive z-axis. The nonlinear polarization of the total elective field E, considered up to the third-order susceptibility evolved from (2.1) can be written as, P 4手;r£L4“|2 叫 勾 2 卜’ (2.12) The first two terms govern the self- and cross-induced nonlinear phase modulation at the input wavelengths and the terms relating the new oscillating frequencies 2Q)^ - co^ and - co^ are classified as FWM. By expending the third-order tensor for the two orthogonal components of one wave E�(denote das control), the nonlinear phase shift of the other wave E2 (denoted as probe) induced by this control wave, can be written as [91-93], ^ 〜ff where ；没，一 + + 叫 c� s没2 (2.14) ) \ 2 + cos>) \ 2 + cos>) 26 Chapter 1 is the scaling factor for an effective nonlinear refractive index for cross-induced refractive index change of a third-order susceptibility process. In (2.14), the polarization angle e, between two fields originated from the tensorial properties of the vector combination; while the ellipticity angle (p, depicts the cross-coupling effect between two orthogonal components of a particular eigenmode of the fiber. A more generally cross-coupling coefficient B, depending on the ellipticity angle cp, of the eigenmodes was developed in the classical paper in [91 ] and has an expression of 丑 _2“ + 2Z)sin> (2.15) 2a + bcos^ (p where a and b are material coefficients. In silica fibers, a = b, which is used in following discussion. The major axis of the polarization ellipse of E, is assumed to be aligned with one of the birefringent axes in (p，without loss of generality. The cross-coupling coefficient equals 2/3 for a linearly birefringent fiber and 2 for a circularly birefringent fiber. For most of the fibers, the state-of-polarization (SOP) is not preserved neither in linear nor in circular state along the entire fiber length. Because of the random evolution of the SOP of light in nonpolarization-maintaining fibers, the cross-coupling coefficient is time averaged value over the interaction length for a long enough fiber which has a beat length L^, much shorter than the length of fiber itself. Under this condition, coefficient of co-polarized and orthogonally-polarized coupling was reported to be 16/9 and 8/9 respectively [47, 92, 93]. Instead of having the two thirds reduction of the XPM—induced phase shift for the orthogonally-polarized component in an ideal linearly birefringent fiber, the reduction becomes a half in the nonpolarization-maintaining fiber with arbitrary birefringence. These XPM efficiencies for co-polarized and orthogonally-polarized components are important in the discussion of XPM—induced nonlinear polarization rotation and the fiber characterizations in the later sections. After taking into account of all these factors, the XPM efficiency in the general case comes to a very simple form as [48], 77(^)=4(3 + cos2^)/9 (2.16) 27 Chapter 1 for typical spoon fibers with low twist rate and short twisting-induced elliptical birefringent length, Lc « LB’ LorLf In the above illustration, the applied fields are assumed to be continuous wave with constant intensity. In the actually application, the input fields usually vary with time. For a control wave with modulation imprinted on the carrier, it is no longer monochromatic. Instead, the control signal becomes a narrowband wave. Under the assumption of slowly varying envelope of the interested wave, the above equations concerning the third-order susceptibility tensor caused nonlinear refractive index change in response to an applied monochromatic wave remain appropriate in modeling the same effect for an applied field with time-domain signal modulation. For the control signal with modulation, its electric field becomes a function of time and so does the nonlinear phase shift caused by this field. In a general case where the group velocity of the two interactive fields is different as a result of the dispersion inside the guiding medium, the effect ofXPM-induced nonlinear phase shift becomes time-averaged. After considering all the above factors, (2.13) can be written in a universal form for a time varying signal E^, as ‘(0 =字+[>c�s�+"丄宇 丫expf-� > (2.17) ^ Acff � o V ^ y V ^ y where M is the total walk-off between the two fields throughout the nonlinear interaction; and a is the propagation loss. 28 Chapter 2 2.4 Cross-Polarization Modulation Cross-polarization Modulation (XPolM) is a subsequence nonlinear phenomenon evolved from XPM by utilizing the difference in the cross-coupling efficiency in a noncircular birefringent fiber discussed in the previous section. This XPM-induced nonlinear polarization rotation of a co-propagating light is an emerging technique to realize high speed all-optical nonlinear signal processing, and has attracted much recent attention. With suitably chosen input SOPs of the control and the cw probe beam, the intensity dependent nonlinear phase shift of the probe beam will result in a change in its SOP. This XPM-induced nonlinear polarization rotation can be converted into intensity change through a noninterferometric structure consisting of a polarization controller (PC) and a polarizer. The PC, the polarizer and the nonlinear fiber form a nonlinear cross-polarization switch suitable for all signal gating applications. High conversion efficiency and output extinction ratio (ER), simple structure and high tolerance to the external perturbations make the cross-polarization switches advances over the traditional FWM-based and interferometric—based XPM switches. Contributions in the fiber-based XPolM for high speed all-optical nonlinear signal processing are reported in this dissertation [P-3, P-15, P-18]. The contributions include theoretical models presented in this section and applications (experimental demonstrations) developed in Chapter 4.2. The principle of the cross-polarization switching is shown in Fig. 2.5. A control signal and a cw probe beam are input to a nonlinear fiber with an angle of 45° between these two linearly polarized beams. At the output of the fiber, a polarizer is used to block the linearly polarized cw beam perpendicular to its transmission axis in the absence of nonlinear phase shift. The control signal introduces nonlinear phase shifts to the two orthogonal components of the cw beam with different XPM efficiencies. This difference in the overall phase shift of two orthogonal components leads to a change in the retardance of the cw beam as shown in Fig. 2.5(c-e). When passing through the polarizer, this change in the SOP will turn into a power change as the switched output. 29 Chapter 1 (a) \ 八 Polarizer PC (Constant retarder) | 1 義\ Nonlinear \ ^^ ,Intensity dependent change c 々>/ 々>/ 々>/ 、 A/ , 4/ /, :....>>rr ...... : ；^！：: 歉,晰 ^Probe 奴 (b) (C) (d) (e) Fig. 2.5 (a) Schematic illustrations of the XPM-induced polarization rotation, (b) Input components of the control signal and the cw beam, (c) and (d) XPM-induced phase lag for the cw beam, (e) Poincar^ sphere representation of the corresponding SOPs. Assuming the control signal to be a slowly varying function, the signal becomes a time-harmonic monochromatic plane wave traveling in a particular direction (say, z direction). This monochromatic plane wave allows a single-SOP to be used in considering a coherently monochromatic polarized wave. Such control signal with modulation imprinted on a carrier is a narrowband (nonmonochromatic) wave with continuous spectrum. The line broadening due to modulation, however, does not in itself alter the degree of polarization of the light [94] in finite linear birefringent system with low polarization-mode dispersion. Hence, the above monochromatic plane wave assumption for the slowly varying control signal holds when considering its SOP, and the XPolM process is modeled as an interplay between two monochromatic plane waves. Their general forms of the electronic field vector propagating in the fibers can be written as Jones vectors as, 30 Chapter 1 J. COSP )expyk 卜 M) (2.18) (sinpexpt/^yj for the control signal, and 彻=�n( 二 e+4/"�z ) (2.19) for the cw probe beam, where E, are electric fields; p, defined as tanp = , is the angle between the major axis of polarization ellipse of the control signal and the x—axis of the (x, y) plane; 0 is the angle between two major axes of the polarization ellipses; are the phase lags between two orthogonal components of a wave; ^y, are the carrier angular frequencies; and yfc. are the propagation constants. The subscripts c and p, respectively, represent the control signal and the cw probe beam. (a) Y • ’ 帖t) EpS'm(0+p) ： ^^ I 广t) Ec sin p ： 卜•••/…"^••••： I > I /^/：省⑶ ！ / i. “ 敌： h ； f \ 、一 j- \ t j p = 71/6，(f>c = 71/6 i.NyZ i \\ \ / jy = ；�CO S(和p) 31 Chapter 1 (b) Y 令 £:p(z’t) Ep sin 没 r I, ^ & (: t), i 美，：丨'J 71/4, (t>p = 71/6 cr> Fig. 2.6 Polar representations of the two input SOPs with respect to different coordinates. Insets show the corresponding SOPs in the Poincar6 sphere. Fig. 2.6(a) illustrates the polarization ellipses of the control signal and the cw probe beam in a (x, y) plane. In an axis-irrelevant cylindrical system (with the autocorrelation length much shorter than the birefringent-beat length in fiber, L^ « L^)’ (2.18) and (2.19) can be reduced to, without loss of generality, the following equations, EXzj)=E{\xpj{coJ-Kz) (2.20) for the control signal, and 彻(2.21) for the cw probe beam by setting = 0. Fig. 2.6(b) illustrates the same polarization ellipses of the control signal and the cw probe beam in the simplified system. 32 Chapter 1 Control signal, Xori PC I Nonlinear fiber — 、 /T\ ^ , 1 \ Polarizer CW hQ3m,Xprobe PC \ Combiner 力 PC ^_ ~• nno_^d：) \\/ ono _ / ⑴- Center wavelength = Converted output Fig. 2.7 Schematic structure of a fiber-based cross-polarization switch. Fig. 2.7 shows the simplified structure of cross-polarization switch. Control signal and cw probe beam are combined with a PC at each branch to control individually their input SOP. The combined signals are launched into a nonlinear fiber. At the output of the nonlinear fiber, a bandpass filter is used to select the cw wavelength which is blocked by the polarizer with an appropriate setting of the PC before it. Neglecting the constant polarization change caused by the finite fiber birefringence within the switch, output of the polarizer can be written as, 五〜•"層{sin(:)二 J—)("广^^^ _ with p _ ‘ cos^ s sin s cos s� (2 23) ^sin £ cos s sin^ e � ^J exp(ya)cosA： -exp(/沟sin/c) (2.24) l^exp(- jf3)sin k exp(- ja)cos k^ _ (expO^J 0 ) (2 25) "遍0 exp � J • where P is the projection matrix for the two orthogonal components projected onto the plane with angle e, with respect to the x-axis; U is the constant retardance with phase shifts of a and and coupling ratio of K，given by the PC before the polarizer to compensate the intrinsic fiber birefringence and to align perpendicularly with the principal (transmission) axis of the polarizer; 1；丽 is nonlinear phase shift acquired by the cw probe beam under XPM according to (2.17). The constant polarization rotation given by 33 Chapter 1 U can be absorbed in P by letting the principal axis of the polarizer to be always perpendicular to the input SOP of the cw probe beam in the absence ofXPM-induced nonlinear phase shift. The projection matrix P， can the rewritten as, CO 八e + Ttji) sin (没+ ;r/2)cos(没+ ;r/2)� ~[sin(^ + ;r/2)cos(^ + ;r/2) sin'(^ + ;r/2) J (2.26) _ sin^ ^ 一 sin 没 cos 没 、一 sin <9 cos 没 cos^ 6 ^ In most of the spoon fibers, except the polarization maintaining fibers, the overall birefringence is small and the birefringent axis is random because of the arbitrarily twisted nature of the fibers. As a result, the beat length, Lb is indeterminable and the SOP of a signal propagating inside evolves randomly. Under this assumption of arbitrary birefringent axis along the fiber, the cross-induced nonlinear phase shift of the two orthogonal components can be expressed as ^ 27116 |cos/7-£/ , Ik 8 \smp-2;r 16 |五<；「， o 27^ 9x —A- + —L^ff = n.———Lff 、丄丄” 义2 9 2 Ac双 ；I2 9 2 A时 欢义2 9 2 A吸愤 |sinp-£.expO-tf ^^^os^ (2.28) ‘^ 9 ‘ 々 9 ‘々9 々 respectively for the parallel and the perpendicular components. Simplifying (2.22) with the above assumptions and equations (2.26-2.28) yields, ( cos � \ I \ = P�.UxP M. “�exp(/A)J�exp;•(�"VO J sm'e -sin 如 OS 没丫 expCM) 0 丫 cos 没) .( x (2.29) "l-sin^cos^ cos20 )[ 0 explA^isin如xp(/ 34 Chapter 1 where (zJ�=九 一^y is the differential phase difference between the two orthogonal components of the cw probe beam; and 户。(2.30) - 3 « 1.2\ •....••”.... — Y . s . ..K 办 ^ -� 5 -0 5 Polarization Angle e (冗） Fig. 2.8 Plot of the switching efficiency against the polarization angle 6, and phase lag 於广 of the cw probe beam for a differential phase shift of n. The power switching efficiency n贼，of the cross-polarization switch can be found as the power ratio between the output and the input written as, 7]滅=2sin2 如os'Ml -cos( for any input SOP {6,命》with respect to the control signal. Fig. 2.8 plots the switching efficiency against the polarization angle 6, and phase lag of the cw probe beam 卢广 for a differential phase shift of n. The switching efficiency reaches its maximum when the input SOPs are aligned with a • polarization separation, while phase lag governs the maximum switching efficiency achievable. The result is obvious as it gives the maximum differential phase difference between the two orthogonal components throughout the 35 Chapter 1 nonlinear interaction. The plot also indicates that this cross-polarization switch can achieve 100% power switching efficiency of the input cw probe beam excluding the loss encountered in the setup. High conversion efficiency is one of the major advantages over the FWM-based approaches besides the dispersion tolerance. Ideally, the power of the cross-polarization switched output signal remains the same when the differential nonlinear phase shift between two orthogonal components is equal to n (|么卜 |么-卢少 | = ;r )• |Ec(z，t)丨•….1 r 门 J ^ J ^ |Eout(z,t)| Fig. 2.9 Illustrations of the inherent loss in incurred in the conversions. Fig. 2.9 illustrates the input and output power level of two types of control signal: the nonreturn—to-zero (NRZ), and return-to-zero (RZ). When the n differential nonlinear phase shift condition is satisfied, the maximum power switching efficiency is attained and the inherent conversion loss of the cross-polarization switch attributes to control signal modulation itself. With (2.31)’ one can determine the average power ratio between the converted output signal and the input cw signal as 2sin'没cos'9\i-cos[^i,{t)-(l>p\Ej\ -dt ^CK = — ^~• (2.32) \Ej\-dt -A 义r i M =2sin2 没cos'没 f[l-(/)-(f>p)\-dt -A where r is the bit period, and communication systems. 36 Chapter 1 .. ... Inherent loss Modulation and pulse format(a) Pulsewidth() w/o. transformation w. transformation NRZ - Super-Gaussian 0.60 x -3.9985 dB -3.9879 dB RZ - Gaussian (33%) 0.32 T -4.7410 dB -4.7831 dB RZ - Hyperbolic-Secant (33%) 0.26 T -4.8927 dB -4.9642 dB � All values are calculated with 25 dB extinction ratio and equal probability for mark and space. (b) Full-width-at-half-maximum, FWHM for a bit period of x. Table 2.2 List of inherent conversion loss for typical modulation formats. The time varying nonlinear differential phase shift acquired by the cw beam with the effects of group velocity mismatch and XPM can be written as [95], m = hU-^] 2 expf-^V (2.33) 〜乂^ 0 V L ) \ ^ J where bJ is the total walk-off throughout the nonlinear interaction. Using typical Taylor expansion technique on the propagation distance, z，we can obtain the differential phase shifts between two orthogonal components, (l>J^� 办(,)_ 8肪2乙r�/>�[Ar__ 1[(/+Arf"+i-/2"-� ‘T, (2m + l)[ r广J (2.34) 1 「(/+么『广-广-1"| _ 1 [“Ar广丨-广'1+……�> '2!(4w + l)[_ J一3!(6m + l)|_ J"……: for w-order super-Gaussian pulse fO)- 8肪2乙沾卜r 1�(/+Ary-/- 3�„>>^ 巾。�A3|_ r； J (2.35) +丄�t±^^Xzil1一丄土……’. 10[ T,' J 42 L r; � J for Gaussian pulse. 37 Chapter 1 Fig. 2.10 to Fig. 2.12 plot the normalized differential phase shifts with different walk-off values for different control pulse shapes. For the third-order (m = 3) super-Gaussian pulse shown in the plot, the overall waveform (pulse shape) is preserved and the maximum phase shift is maintained at the same level for a walk-off value as large as 0.3 t^丽 before the root-mean-square (rms) difference between two waveforms increases substantially. This large walk-off tolerance shows a possibility of wide band operation for NRZ signals. Similar walk-off tolerances for the XPM efficiency and pulse shape deformation are also observed in for picosecond pulses with Gaussian and hyperbolic-secant waveform as shown in Fig. 2.11 and Fig. 2.12 respectively. Applications based on this characteristic are developed in later chapter of this dissertation. 38 Chapter 2 ti 1.2 2 (a) _身 -3-2-10 1 2 Time (tfwhm) 1.6 1.2 (b) 3 - ！^ / 1 O i 1.4 ： s厂、rir^^ / 11 «c / s： S ® 芒 1.2 • / • 0.6 llS > X s i ？ 0 ^^ -0.4 g J o ifi 1 -rf ^^ 1 ^ p'"- 0.2 0.8 • ‘ 0 0 0.5 1 1.5 Walk-off (TFWHM) Fig. 2.10 Change of the signal waveform of a third-order (w = 3) super-Gaussian pulse with the presence of signal walk-off. (a) Plot of the normalized phase shift of the co-propagating field for 0 to 1.5r厂画 walk-off with 0.3 "酬 step size, (b) Plot of the (solid line to the left) full-width-at-half-maximum (FWHM) pulsewidth, (solid line to the right) normalized efficiency, (dashed line) normalized cross-correlation factor and (dotted line) rms difference of the resultant nonlinear phase shift against the walk-off. Values are normalized to the one with zero walk-off. 39 Chapter 2 ti 1.2 2 (a) -3-2-10 1 2 Time (tfwhm) 1.6 n 1.2 一 (b) / I 1.2 . • 0.6 III > 3 3 O 0 •0.4 S ^ I" 1 � 2 ;、 0.8 ‘ … '“‘ 0 0 0.5 1 1.5 Walk-off (TFWHM) Fig. 2.11 Change of the signal waveform of a Gaussian pulse with the presence of signal walk-off. (a) Plot of the normalized phase shift of the co-propagating field for 0 to 1.5 r蘭 walk-off with 0.3 顏 step size, (b) Plot of the (solid line to the left) FWHM pulsewidth, (solid line to the right) normalized efficiency, (dashed line) normalized cross-correlation factor and (dotted line) rms difference of the resultant nonlinear phase shift against the walk-off. Values are normalized to the one with zero walk-off. 40 Chapter 2 ti 1.2 2 (a) _-3-2-1 A0 1 2 Time (tfwhm) 1.6 — -7—1 1.2 一 (b) / •-III JH 1 一 ao - ...... r-^� 2 二、 0.8 ‘~ _ • 0 0 0.5 1 1.5 Walk-off (Tfwhm) Fig. 2.12 Change of the signal waveform of a hyperbolic-secant pulse with the presence of signal walk-off. 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Damask, Polarization optics in telecommunications, New York: Springer, 2005, Chapter 1. [95] G. P. Agrawal, P. L. Baldeck and R. R. Alfano, "Temporal and spectral effects of cross-phase modulation on copropagating ultrashort pulses in optical fibers," Phys. Rev. A, vol. 40, no. 9, pp. 5063-5072， 1989. 46 Chapter 1 Chapter 3 Fibers: The Nonlinear Media Fibers, as the major media in the nonlinear signal processing applications developed in this dissertation, have several major properties that significantly affect the performance of the fiber-based nonlinear signal processing devices. In order to optimize such devices for a particular nonlinear effect, one must need to know the basic parameters such as dispersion and nonlinearity of the fiber used. To explore the performance of the fibers in the signal processing applications, three different types of nonlinear fibers: standard DSF, HNL-DSF and dispersion-flattened PCF are used in developing the nonlinear signal processing schemes in this dissertation. Before developing their applications, this chapter summarizes the measured dispersion, zero-dispersion wavelength variation, nonlinear refractive index and electrostrictive contribution of these three different types of nonlinear fibers. The study of the basic properties of these fibers provides a better knowledge in determining an optimum operating condition. 47 Chapter 3 3.1 Average Dispersion All forms of dispersion degrade the signals transmitting inside the dispersive medium as well as limiting the signal at different wavelengths from propagating at the same velocity during the nonlinear interaction. In XPM, dispersion introduces walk-off between the interacting signals. Effects of dispersion to the nonlinear phase shift acquired by the co-propagating beam at the present of dispersion-induced walk-off are discussed in the previous chapter. Hence, the effects of the walk-off incurred in the XPM interaction can be characterized, once the dispersion profile of a fiber is known. The measurement methods used in obtaining the dispersion profile of the test fibers are standardized by Electronic Industries Alliance (EIA) and International Telecommunication Union (ITU) [96-99]. Among the proposed approaches, method for measuring the dispersion based on the time shift in a wavelength tunable modulated signal is used because of the simple configuration and high accuracy. Dispersion Measurement Based on Modulated Signal Time Shift •••••••• • ： ： i I i Ar i f \ Dispersive medium i / / I —~^Time ff\ I •Time I “ I \\) I ^r 1 • Wavelength | j • Wavelength | 1 i ^ Fig. 3.1 Schematic illustrate of time-domain shift of the signal for different input wavelengths. Principle of the measurement of fiber dispersion by a modulated signal time shift method is shown in Fig. 3.1. A monochromatic tunable optical source is intensity modulated and applied to the fiber under test. The transmitted signal is detected and the relative signal time delay is measured. The time delay measurement is repeated at intervals across the wavelength range of interest in C-band. From measurement at any 48 Chapter 1 wavelength, a curve of relative group delay can be constructed by accumulating these changes in group delay across the measurement wavelength range. The delay is denoted as "relative" because the measurement of dispersion does not require determination of absolute delay, and is vertical offset from an absolute propagation delay at the minimum value of zero. Under the definition of dispersion as the rate of change of the group delay with wavelength, the result remains valid for the relative group delay as, D =丄生 (3-1) L dA where D is the dispersion coefficient; Ar is the measured relative group delay; and L is the fiber length. Considering the physical characteristics of the fiber to be consistent along its length, the dispersion curve of the test fiber can be obtained from the second-order magnitude of the curve fitting function. Precision of this dispersion measurement is primarily determined by response time of the photodiode or its resolution and the accuracy in the measurement of the fiber length, while the wavelength accuracy of the optical source introduces uncertainty of the horizontal offset of the measured dispersion curve. Thermal transients in the measurement setup and the fiber under test also contribute significant measurement error. Spools of fiber are very sensitive to the temperature due to thermal expansion with a corresponding change in group delay Ar = rAL/L for a temperature-induced change in path length AL. Thus, measurement is conducted with the fiber being covered with polystyrene (as a thermal insulator) to form a micro-thermal-chamber. Finally, precision of the measured dispersion curve is significantly improved by appropriately choosing the modeling equation to fit the measured relative group delay data to minimize the accumulated measurement error [98, 99]. Depending on the magnitude of dispersion in the interested wavelength region, a three-term Sellmeier equation and a quadratic equation are commonly used to respectively measure the region without 49 Chapter 1 and with zero-dispersion point. In this dissertation, the cubic equation is used as the model to fit the relative group delay for fiber with zero-dispersion wavelength within the C-band. The Measurement Fiber under test PC (h ^I ~7lOOQ ["qH~^~^：^ Dso I —^— ©Trigger ： Fig. 3.2 Experimental setup for measuring the relative group delay with different input wavelengths. Experimental setup of the dispersion measurement based on modulation signal time shift is shown in Fig. 3.2. The coherence optical source used in the measurement is obtained from an external cavity tunable laser (HP8168F) with linewidth (3-dB spectral width) of 100 kHz. The cw beam is intensity modulated by an external electro-optic Mach-Zehnder-interferometer-based intensity modulator (MZ-IM) with a sinusoidal wave at 10 GHz generated from an rf synthesizer (Anritsu 69347B). The modulated signal is then launched into the fiber under test and its output is detected by a 30 GHz bandwidth unamplified InGaAs photodiodes (HP83440D) and a 50 GHz digital sampling oscilloscope (Agilent 86100A with HP547524A sampling module). The sampling oscilloscope is triggered by a synchronized 10 GHz rf signal tapped from the synthesizer. The fiber length is measured by optical time-domain reflectometer (Agilent E6003B) with a longitudinal resolution of- 0.5 m. Relative group delay is measured by changing the emitting wavelength of the tunable laser with a step size of 0.5 nm. Step size is chosen small enough to increase the number of sampling points for a more precise curve fitting to average out the measurement error. 50 Chapter 1 Measured Relative Group Delays and the Curve Fitted Dispersion Profiles Dispersion measurement is conducted with two spools of fiber: standard DSF and HNL-DSF. Fig. 3.3 shows the measured relative group delay for a unit fiber length of 1 km. The data points are fitted with the cubic equation ( T{X) = C-^^ + C^^ + Q/l + CQ ) using least square method to model up to the third-order dispersion (dispersion slope) and the dispersion curves are calculated from its derivative D�=华 = (3-2) CIA As far as the number of data points is larger than the order of the fitting curve and the solution converges, the coefficients obtained from the least square algorithm are very accurate. Indeed the R-square* value between the polynomial fit and the measured data is larger than 0.9999 in any of the measurements below. The dispersion curve of the dispersion-flattened PCF is not measured because of the short fiber length that limits the measurement accuracy. Instead, the dispersion curve of the dispersion-flattened PCF is quoted directly from the manufacturer without performing the measurement, and is shown on the same figure. R-square is defined as the ratio of the sum of squares of the regression and the total sum of squares. 51 Chapter 3 250 "55 200 . 64 m Dispersion-flattened PCF (calculated) Q g E 150 - 2乏 ^ g \ 3.2 km Standard DSF � a 100 - \ > \ 二 X JS 50 - X Z 0) 叫 \ 、、、、Z 1500 1520 1540 1560 1580 1600 Wavelength (nm) ？ 6 f^ 4 - g 3.2 km Standard DSF^^ 5 2 • CO ^^ 3 A 1 km HNL-DSF “ .2 A ^^^^ 64 m Dispersion-flattened PCF V ~ t 4 a -6 ‘ ‘ ‘ ‘ 1500 1520 1540 1560 1580 1600 Wavelength (nm) Fig. 3.3 Plot of (a) the measured (symbols) and cubic fitted (dotted lines) relative group delay per unit length and (b) the retrieved dispersion curve for different types of nonlinear fibers. Data for dispersion curve of the dispersion-flattened PCF are retrieved from the specification sheet supplied by manufacturer. 52 Chapter 3 3.2 Longitudinal Dispersion Map Dispersion curves measured in previous section are obtained under the assumption that physical characteristics of the fiber are consistent along the length. This assumption, however, does not hold for long fiber as the two main physical parameters that determine the fluctuation of optical properties (the core radius and the core-cladding refractive-index difference) are no longer to be uniform. The influence of these two parameters to the dispersion characteristics is discussed in the previous chapter. These changes affect both zero-dispersion wavelength 义。，and the dispersion slope. Numerical calculation in the previous chapter shows that the change of the dispersion slope is less significant when compared with the change of ；l。，and this characteristic is reported experimentally in a destructive measurement which shows a constant dispersion slope down to ±2% [100]. With the dispersion slope treated as a constant throughout the fiber, the dispersion map can be simplified as a shift of the dispersion curve with the corresponding ；1� ithn e longitudinal direction. Hence, one can map the dispersion using the model (2.10) with the measured zero-dispersion wavelength map along the fiber. Zero-Dispersion Wavelength Mapping using Parametric Amplification Method used in mapping the zero-dispersion wavelength is based on the phase mismatch caused gain variation in the parametric amplification [2.80]. Near the zero-dispersion wavelength, the parametric gain depends on the phase mismatch relation [101] 爲(义。•-人+2,户。 （3.3) where p�an d久 are respectively the third- and fourth-order dispersion terms; the and are respectively pump and signal wavelengths; y is the nonlinear coefficient; P� iths e pump power; and ；1� is the zero-dispersion wavelength. In a fiber-based OPA, longitudinal variations in zero-dispersion wavelength will sharply and locally modify the phase matching condition between the pump, the signal, and 53 ； Chapter 4 the idler. Thus, the phase-sensitive parametric gain spectrum will be modified in a short propagation length for high sensitivity zero-dispersion mapping measurements. In the measurement several experimental gain spectra at different around the zero-dispersion wavelength of the test fiber are obtained. The variations along the fiber are, then, mapped from these spectra by using a set of orthogonal polynomials (of successive orders, designed for polynomial regression [102]) whose coefficients are optimized with a Gauss-Newton iterative inversion algorithm. In this way, once the algorithm converges, the experimental gain spectra are accurately fitted from numerical simulations based on an extended nonlinear Schr5dinger equation (NLSE), which includes all known experimental parameters and the retrieved zero-dispersion wavelength map. The Measurement Fiber under test PC _^ Tl 000 PM ED^>—^^~0— OSA 2"-l(NR PRBZ Sformat at) 1 0 Gb/s Fig. 3.4 Experimental setup for measuring the OPA spectra at different pump wavelengths. The measurement setup is shown in Fig. 3.4. A cw pump beam obtained from an external cavity tunable laser (HP8168F) is phase modulated by a phase modulator with a 2^-1 bits pseudorandom bit sequence (PRBS) at 10 Gb/s to suppress the SBS by broadening its linewidth. The phase modulated cw pump beam is then amplified with a high power erbium-doped fiber amplifier (EDFA) (IPG EAU-2TB) and launched directly into the test fiber. At the output of the fiber a variable optical attenuator (VOA) is applied to reduce the input power before the OSA (ANDO AQ6317) which has a spectral resolution of 0.01 nm for spectral measurement. The pump wavelength is set from 1^ + 2 nm to 1^ + 7 nm for an average zero-dispersion wavelength of J^ in the test fiber. The measured spectra are fitted into a numerical program (originally developed by K. Uesaka [105]) to solve the inverse problem of interest. 54 ； Chapter 4 Measured Gain Spectra and the Retrieved Zero-dispersion Wavelength in the Longitudinal Direction -30 (a) 百-35 - m -40 • H 爹 1530 1540 1550 1560 1570 1580 1590 Wavelength (nm) 1556 ？ .(b) ^ 1555 • Q 1554 • ^^ Z 3 ： “：：^^^— TO E 1553 =~^ M^M W lu 1552 I I I I I I—I—I—i—i—I—I—I—I—I 0 12 3 Distance (km) Fig. 3.5 (a) Measured gain spectra at different pump wavelengths with a pump power of 0.5 W，and (b) the retrieved zero-dispersion wavelength map for the standard DSF. 55 ； Chapter 4 -30 —I i圆 -55 I I 1 1 1515 1525 1535 1545 1555 1565 1575 Wavelength (nm) 1542 I .(b) ^ 1541 • Q 1540 -— rrr^i^^^；^；^- "--- 13 E 1539 • W LU 1538 ‘ 1 ‘ " ~I ‘ ‘ ‘ 0 0.2 0.4 0.6 0.8 1 Distance (km) Fig. 3.6 (a) Measured gain spectra at different pump wavelengths with a pump power of 0.3 W, and (b) the retrieved zero-dispersion wavelength map for the HNL-DSF. 56 ； Chapter 4 3.3 Nonlinear Refractive Index and Nonlinear Coefficient In order to implement and utilize the fiber nonlinearities for signal processing applications, or accommodate nonlinearities, one must know the nonlinear coefficient for the fiber used. Two origins of fiber nonlinear refractive index change: nonresonant electronic polarization induction and electrostriction are discussed in the previous chapter. Nonlinear refractive index n^，contributed from fast optical Kerr effect in the nonresonant electronic polarization induction is measured in the section; while the electrostriction contribution n^^，will be characterized in the next section. Effects of the constituents of the fiber on the nonlinearity are well-known and readily determinable. This makes the measurement of the nonlinear refractive index possible with a reasonability high accuracy. Several methods of measuring n, that exploit different nonlinear effects, such as SPM by use of a pulsed laser [2.53, 2.54] or cw beams [2.58], XPM [2.55], modulation instability [2.56] and a technique based on FWM [2.52] have been proposed. Among these various schemes, the method using two cw beams for signal beating is applied in measuring the nonlinear refractive index contributed by the fast optical Kerr effect [2.58]. This method has advantages of using simple optical sources and conventional measurement apparatus to reach high accuracy and sensitive. Direct Continuous-wave Measurement of Nonlinear Refractive Index using a Dual-wavelength Beat Signal Method for measuring the nonlinear refractive index is based on the measurement of the nonlinear phase shift induced through the SPM effect with a cw dual-wavelength beat signal used as a pump source. Under the condition that, [2.58] 办co:L� \ (3.4) 57 ； Chapter 4 where k^=d^kldco'' is the dispersion of the fiber under test, the fiber dispersion can be neglected in the nonlinear interaction, and the nonlinear phase shift experienced by the beat signal propagating along the test fiber can be expressed as [2.55, 2.58, 2.93] £(/’ L) = lacos� (Aty/)]， (3 亏) where T is the average power of the signal; L 说 is the effective length of the fiber; is the effective nonlinear refractive index governing the SPM for random polarization; and A吸 is the effective area. The nonlinear coefficient of the fiber is determined by measuring experimentally the SPM nonlinear phase shift and the corresponding average power. The nonlinear phase shift is measured in the spectral domain. As the electric field E(t,L) in (3.5) is a periodic function in time, its spectrum is discrete, consisting of harmonics of the beat frequency as shown in Fig. 3.7. The nonlinear phase shift 么？似 is determined from the relative ratio of the spectral components. In the measurements, the ratio of intensities of the first-order sideband to the spectral intensity at the fundamental frequencies is used. By taking the Fourier transform of (3.5), one can analytically calculate this ratio in terms of Bessel functions as [2.58], /q V(“/2Wi2(“/2) (3.6) /2) where /�an d/ 丨 are the intensities of the zero- and first-order harmonics (Fig. 3.7) and 人 is the Bessel function of the n-th order. The nonlinear phase shift is a function of /� /丨，/ which can be readily measured. lo I, Wavelength Fig. 3.7 Schematic illustration of a typical SPM spectrum generated by the propagation of a beat signal in a fiber. 58 ； Chapter 4 The Measurement PC Fiber under test PC \ 3-dB coupler j. ^ ^ U j TL2 I OOP_OSA Fig. 3.8 Experimental setup for measuring the nonlinear refractive index at different input wavelengths. The experimental setup is shown in Fig. 3.8. The optical beat signal is derived from two cw external cavity tunable lasers (HP8168F and Agilent 8164A with HP 81689A module) operating near 1.55 ^m both have linewidth of around 100 kHz. They are combined with a 3-dB fused fiber coupler with a PC at each branch to individually control the input SOP so that that are co-polarized when propagation along the fiber. The co-polarized condition is guaranteed by maximizing the harmonics generated at the output using the fact that nonlinear phase shift has the maximum efficiency for the co-polarized state. Although the measurement result does not depend on either the frequency separation or the laser linewidths, the frequency separation is adjusted close enough («25 GHz, or 0.2 nm in this case) to permit a similar birefringent axis seen by the two cw beams. This frequency separation is far larger than the resonant frequency raised in the electrostrictive contribution of the nonlinear refractive index change discussed in the next section. The beat signal is then amplified with a high power EDFA (IPG EAU-2TB) and transmitted through a 2-nm tunable bandpass filter to suppress the amplified stimulated emission (ASE). The ASE level after the bandpass filter is typically less than 0.3% («25 dB) of the total output power and the signal-to-noise ratio is maintained by fixing the input conditions, while the power launched into the test fiber is controlled by a VOA. At the test fiber output, a high resolution optical spectrum analyzer (ANDO AQ6317) with a spectral resolution of 0.01 nm is used to measure the intensities ratio of the zero- and first-^rder harmonics. The transmitted power is closely monitored to avoid the SBS. 59 ； Chapter 4 Measured Nonlinear Phase Shift against the Power and the Nonlinear Coefficient Measurement is conducted with all three types of fiber used in this dissertation: standard DSF, HNL-DSF and dispersion-flattened PCF. Fig. 3.9 shows the measured nonlinear phase shift normalized to the corresponding effective fiber length against the input power. Measurements of the same fiber are repeated a number of times to ensure high repeatability of the results. All the measurements can be well interpolated by a linear fit, and the slope is determined with standard deviation of typically less than 5% between different independent trials due to the measurement errors. 3 o 3.2 km DSF • 1 km HNL-DSF ， A 64 m PCF 5 % 2 - T3 2 么” ifc ^ .-A-' -- ..-•'.JD--' A .O “®" Q .....O…T 1 1 0 10 20 30 40 50 60 Power (mW) Fig. 3.9 Plot of the measured the nonlinear phase shift against the input power for different types of nonlinear fibers. The nonlinear phase shifts are normalized to the effective fiber length for better comparison. Owing to the wavelength dependent nature of the effective core area A 时，and the linear proportion property as indicated in (2.8), the nonlinear coefficient y，varies against the wavelength; while the nonlinear refractive index depends only on the material properties and, in principle, remains the same for any input wavelength. For this reason, input wavelengths are varied from 1530 nm to 1560 nm with a step size of 10 nm in the measurement to estimate the wavelength dependence of �.Fig .3.10 plots the normalized nonlinear coefficient against the wavelength in C—band for different types of nonlinear fibers. 60 ； Chapter 4 1.2 }- O 3.2 km DSF S 0 1 km HNL-DSF •E 1 A A64mPCF 11 • 11 1 二:::::::: 二二一=二【::::::： 1= O ro O E 0.9 - oL. z 0.8 ‘ « ‘ ‘ “ ‘ « 1525 1530 1535 1540 1545 1550 1555 1560 1565 Wavelength (nm) Fig. 3.10 Plot of the nonlinear coefficient normalized to the one at 1550 nm against the wavelength for different types of nonlinear fibers. 61 ； Chapter 4 3.4 Electrostrictive Contribution Results of the measurements in the previous section are analyzed with the assumption that the origin of the nonlinearity is nonresonant electronic response caused by optical Kerr effect. This assumption leads to specific predictions regarding polarization properties and specifically precludes the possibility of time-scale effects. However, early reports showed that values obtained for the use of low frequency modulated control in a XPM experiments are consistently greater than values obtained in short-pulse SPM experiments [2.66]. This anomaly is mainly due to the electrostrictive response in fibers, in which the magnitude of the electrostrictive response is large enough to be observed in the presence of the optical Kerr nonlinearity, and this contribution is significant only if the time scale of the interaction is long enough to initiate the acoustic response [2.47]. Characterization of the electrostrictive contribution can be done with in a XPM for both frequency- and polarization-dependences of the nonlinear refractive index change. The measurement is based on direct measurements of the optical spectra with a wavelength meter. The high spectral resolution provides an accurate measurement of the frequency dependence of the induced nonlinear phase shift for different control and probe relative SOPs for a complete characterization of both the polarization-dependent optical Kerr and frequency-dependent electrostrictive contributions. Considering two monochromatic beams, control and probe, propagating in the same direction in a fiber, the intensity modulated control with a pure frequency modulation y^ will phase modulate the cw probe beam under XPM. The magnitude of induced XPM phase shift depends on the modulation frequency and relative SOP, and it is given by (2.17). After propagating through the fiber, the optical spectra of the cw probe beam, which is phase modulated by XPM, presents, in addition to the central peak, two symmetrical modulation sidebands with magnitudes that can be expressed as [2.48] 62 ； Chapter 4 \(L’v)= •S�(L)[V(“)4-vj - (3.7) ( where (f)舰 represents the peak-to-peak phase shift oscillating at frequency v^ ’ induced by XPM; and j” represents the Bessel function of order n. Ratio of these spectral components can be determined from the optical spectral. From these measured magnitudes the phase shift 伞雇 can be calculated according to (2.17), and the electrostrictive contributions for different modulation frequency y^ , and polarization conditions of the interacting beams can be derived from (2.4) with the value of n^ determined in previous section. The Measurement PC . __f TLl ^^^^D'' ^ Fiber under test m ^ ^^ PC 3-d B couple/rn II I TL 2 C^C^C)____—iC^ ？t—meter Fig. 3.11 Experimental setup for measuring the electrostrictive contributions at different modulation frequency y^. The measurement setup is shown in Fig. 3.11. The control is prepared by modulating the cw beam from an external cavity tunable laser (HP8168F) at 1550 nm with an electro-optic MZ-IM same as the setup used for dispersion measurement in Fig. 3.2. The rf synthesizer (Anritsu 69347B) generated a pure single-tone rf signal for the modulation with the frequency varied from 100 MHz to 2000 MHz. The control beam is amplified with a high power EDFA (IPG EAU-2TB) to deliver an average power of 17 dBm after the 2-nm tunable bandpass filter. The cw probe beam at 1551 nm is obtained from an external cavity tunable laser (Agilent 8164A with HP 81689A module). Two beams are combined with a 3-dB fused fiber coupler with a PC at each branch to individually control the input SOP to set the relative polarization between two beams to be co-polarized or orthogonally-polarized. The combined signal is then launched into the test fiber and a 63 ； Chapter 4 high resolution spectrometer (Agilent 83453B) with a spectral resolution of 0.008 pm («i MHZ) is used to measure the power of the carriers and their harmonics after the nonlinear interaction. Input and output powers are monitored to prevent the control from reaching the SBS threshold. Measured Nonlinear Induced Phase Shift against the Modulation Frequency -30 ^ -35 - 尝 （i) r -40 - I (iii) (iv) ^ I V •_ A f- ft (/) -45 - c 龙 50 - -55 ‘ ‘ ‘ 1549.98 1549.99 1550 1550.01 1550.02 Wavelength (nm) Fig. 3.12 Examples of the measured optical spectrum (overlaid) for four different modulation frequencies (i) 430 MHz, (ii) 820 MHz, (iii) 1.2 GHz and (iv) 1.8 GHz. 64 ； Chapter 4 An example of the complete measured output optical spectrum is reconstructed and shown in Fig. 3.12 with a noise level of around —55 dBm limited by the wavelength meter. The control spectrum shows amplitude modulation sidebands at the selected modulation frequency . The induced XPM effect can be clearly seen as symmetrical spectral components generated on the signal spectrum, which are separated by v^ from the central optical frequency Vp • FWM effect is also observed at - Vp • XPM dependence on v^ is shown in this figure, in which measured signal spectra are overlaid together for four different modulation frequencies corresponding to resonance maximum, resonance minimum, and electrostriction-free frequencies. Example of the measured values of induced phase shifts as a function of is shown in Fig. 3.13, for parallel and orthogonal relative SOP conditions of the HNL-DSF. The frequency step is 100 MHz («0.08 nm) which is limited by the resolution of the wavelength meter. The measurements match correctly with the theory predicted resonant peaks given by electrostriction at approximately 480 MHz [104] and vanished at approximately 1.4 GHz. Relation of "厕(0’0)="厕(;r’0) for XPM is also confirmed from the measurements in the electrostriction-free frequency range. I ^ ot ‘ 0 500 1000 1500 2000 Modulation Frequency (MHz) Fig. 3.13 Measured nonlinear induced phase shift for (i) parallel and (ii) orthogonal relative SOP conditions in a standard DSF. 65 ； Chapter 4 3.5 List of the Fiber Properties Table 3.1 summarizes the measured fiber properties of the three different types of nonlinear fibers obtained from the measurement in the previous sections and from the specification provided by the manufacturer. Dispersion- Property Standard DSF HNL-DSF flattened Unit PCF(a) Fiber length 3.247 1.024 0.064 km Zero-dispersion wavelength, ；1553.7 1540.2 - nm Group delay fit(b) C5 - -2.42x10"'° ps/nm^ C4 _ -1.95x10"^' ps/nm4 C3 一1.70x10—5 -1.32x10—5 -0.0063 ps/nm� C2 0.12 0.071 10.27 ps/nm' Ci -254.11 -123.47 -8362.64 ps/nm Co 165577.15 70935.41 - ps Dispersion slope at 1530 nm 0.0869 0.0199 0.0054 ps/nm\m 1540 nm 0.0858 0.0191 0.0031 1550 nm 0.0848 0.0183 0.0009 1560 nm 0.0838 0.0175 "0.0011 ZDWfit(c) D4 -2.42x10"'° -3.48x10-8 - nm/km^ D3 -1.32x10"' -1.70x10"' - nm/km3 D2 -0.0063 0.13 - nm/km' Di 10.27 -123.47 - nm/km Do 1553.28 1541.56 - nm Nonlinear refractive index, n^ 3.35x10-'° 3.28x10"'° 2.75x10"'° m^/W Nonlinear coefficient y, at 1550 nm 2.7 11.3 11.6 Effective area at(d) 1550 nm 51.1 n.8 6.2 ^im^ Electrostrictivecontribution(e)，0.50x10-'° 0.55x10"'° 0.62x10''° m^/W Resonance free frequency 1.38 1.45 1.10 GHz Stimulated Brillouin scattering threshold� 15.2 11.0 22.6 dBm 66 ； Chapter 4 Attenuation fit� Ls -136x10- 2.10x10- -431x10- dB/nnAm L2 6.34X10-3 4.51X10-^ 2.06X10—3 dB/nm\m Li 9.83 -0.017 -3.29 dB/nm.km Lo 5082.38 15.28 1765.01 dB/km Attenuation at 1530 nm 0.213 0.794 8.286 dB/km 1540 nm 0.206 0.779 8.194 1550 nm 0.190 0.764 8.117 1560 nm 0.174 0.751 8.051 Polarization dependent loss(h) ^ — � Values are from the specification sheet supplied by the manufacturer (Crystal Fibre A/S). (b) r(;i)+ C, A + Co, in nm. (c) Aot) = ZV + + + D,z + D�"inkm. � Estimated values. (')At resonance peak. �(^ M= + L^z' + in nm. � For a monochromatic electromagnetic cw with 100 kHz 3- Table 3.1 List of the typical fiber properties. 67 ； Chapter 4 References for Chapter 3 [96] TIA-455-228 (FOTP-228), Relative Group Delay and Chromatic Dispersion Measurement of Single-Mode Components and Devices by the Phase Shift Method, Feb. 2002. [97] TIA-455-175-B (FOTP-175), I EC 60793-1-42 Optical Fibres Part 1-42: Measurement Methods and Test Procedures - Chromatic Dispersion (ANSI/TIA-455-175-B-2003), May 2003. [98] TIA/TR-1028 (lEC 61280-7), Fibre Optic Communication System Design Guides - Part 7: Statistical Calculation for Chromatic Dispersion (ANSI/TWTR-l 028-2004), Feb. 2004. [99] ITU-T Recommendation G.650.1 ’ Definitions and test methods for linear, deterministic attributes of single-mode fibre and cable, Jun. 2004. [100] I. Brener, P. P. Mitra, D. D. Lee, D. J. Thomson, and D. L. Philen, "High-resolution zero-dispersion wavelength mapping in single-mode fiber," Opt. Lett., vol. 23, no. 19, pp. 1520-1522, 1998. [101] J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. Hedekvist, "Fiber-based optical parametric amplifiers and their applications," IEEE. J. Select. Topics Quantum Electron., vol. 8, no. 3，pp. 506-520, 2002. [102] B. Camahan, H. A. Luther, and J. O. Wilkes, Applied Numerical Methods, New York: Wiley, 1969. [103] Katsumi Uesaka, Senior Research Engineer, Innovation Core, Sumitomo Electric Industries, Ltd., [104] A. Melloni, M. Martinelli, and A. Fellegara, "Frequency Characterization of the Nonlinear Refractive Index in Optical Fiber," Fiber Integr. Opt., vol. 18, no. 1, pp. 1-13, 1999. 68 ； Chapter 4 Chapter 4 Multi-Wavelength Nonlinear Signal Processing Nonlinear signal processing in fibers has attracted much attention because of its unique characteristics of ultra-fast nonlinear response time and generally high nonlinear efficiency. The use of fibers for nonlinear application is easy as it does not require complicated mode coupling and matching problems as in the case of planar-lightwave-circuits or nonlinear crystals. The mature fiber fabrication processes for complex dopant-combination and core design also makes high nonlinearity fibers possible. These unique characteristics of fibers stimulated the development of fiber-based nonlinear signal processing for, mostly, optical communication applications. XPM, one of the nonlinear effects in fiber, is reviewed in the previous chapters of this dissertation and applications based on this nonlinear effect are developed in this chapter. This chapter is organized as follow. The technical difficulties ofXPM-based nonlinear switch are presented in the first section, and are addressed with various applications developed in the second section. Two classes of application, wavelength conversions and modulation format conversions, are demonstration in this dissertation with different approaches and fibers to explore the performance of different types of nonlinear fibers. A brief summary of the performance for the proposed schemes is given at the end of this chapter. 69 ； Chapter 4 4.1 Challenge Optically-controlled XPM in fibers had found many applications in ultra-fast signal processing of optical signals. In most telecommunication applications, signals carrying the transmitted data are intensity-modulated, although there are some advanced modulation formats being proposed and developed in recent years [105,106]. XPM finds applications through the interaction between the intensity-modulated signals by intensity-to-phase and phase-to-intensity conversions. A phase-modulated signal by XPM can be converted back into intensity modulation using either interferometric—based or noninterferometric-based approaches. Typical interferometric switches are shown in Fig. 1.2 in Chapter 1. Interferometric approach utilizes the interference property between two copies of an electromagnetic wave to determine the output intensity of a phase-modulated signal through a nonlinear relation />� =," P.„ [1 - cos((z5nl + (Z^al)]/^ . 丁he transmitted power ’ is governed by the phase difference between two copies, and the destructive interference condition in the absence of nonlinear phase shift •仇，is set by precisely controlling the constant phase difference 冷此，to be an integer multiple of IK . To address the difficulty of precise adjustment of the path difference, Sagnac-based interferometer is preferred for fiber-based XPM interferometric switch as the two copies of a signal share the same path in different directions. This difficulty of precise phase delay adjustment can also be overcome with the noninterferometric approaches like spectral filtering or nonlinear polarization switch. The single-pass structure of these noninterferometric approaches allows a path-length-independent operation which is more suitable for fiber-based nonlinear signal processing approaches as the fiber is usually sensitive to the external perturbations such as temperature fluctuation. 70 ； Chapter 4 In either approach, the signals co-propagating along the fiber in which nonlinear phase shift is built-up in the signal being processed generate new frequency components. As XPM and FWM are both originated from the ；^⑶ effect, an intense control beam in the XPM interaction will serve also as a pump in a partially degenerated FWM process to generate new frequency components. The generation of new frequency components not only degrades the performance of XPM as the control beam power is depleted in generating idlers but also limits the possibility of multi-wavelength operation in XPM. In the case of multi-wavelength operation, the XPM process relying on the optical Kerr nonlinearity will suffer inevitably from a finite in-band cross-talk by the undesirable FWM components, which cannot be removed at the output. These two technical difficulties (controlling the phase delay in the interferometric approaches and the multi-wavelength XPM operation) of the fiber-based XPM nonlinear signal processing are addressed individually with a series of studies on the structures and the fibers used. 71 ； Chapter 4 4.2 Applications Major achievements of this dissertation are presented in this section for wavelength conversion and modulation format conversion applications. Different schemes are proposed in the first part of this section for wavelength conversion applications, and in the second part for modulation format conversion applications. Applications of XPM-based nonlinear switches include but are not limited to these two types of signal conversion techniques. Wavelength Conversions Wavelength conversion is an important element in a wavelength-routed optical network to provide high flexibility and utilization of the wavelength allocation by preventing channel blocking during the wavelength routing. Such conversion can be achieved by converting the optical signal to electrical domain and then back to optical domain which is a costly and bit-rate dependent process. Hence, an all-optical wavelength conversion approach, in which the OE and EO conversion is avoided and the conversion is strictly in the optical domain, is favorable. All-optical wavelength conversion has been studied extensively because of the importance and a variety of applications. Examples of all-optical wavelength conversion include FWM in fiber [107, 108] and semiconductor optical amplifier [109], cross-absorption modulation in an electro-absorption modulator [110], terahertz optical asymmetric demultiplexer [111] and nonlinear optical loop mirror (NOLM) [1.16’ 112]. Approaches used in the early days are rather clumsy in structure and restrictive in operation conditions. One of the technical issues limiting the actual application of all-optical wavelength conversion is its tunability. An ideal all-optical wavelength converter is a generic device which is transparent to any input wavelength in a wide range of interest, so that it can be applied to convert from any input wavelength to any output wavelength within the communication band. 72 ； Chapter 4 For XPM-based all-optical wavelength conversion schemes like NOLM, the tunability is limited by the group-velocity-dispersion-induced walk-off between two signals during the XPM interaction. This walk-off caused operating range limitation can be solved with the idea of dispersion management similar to the one applied in signal transmission and a wavelength separation between the control signal and the converted signal as large as 120 nm was reported for -5.2 ns pulse (equivalent to -500 Mb/s) [113]. This dispersion managed approach, however, is too complicated to be implemented in achieving a small walk-off required in high bit-rate system as the dispersion managed interaction length cascades lot of short pieces of fibers with different dispersions. Instead of introducing any complex approach to minimize the walk-off for a wide wavelength separation, effort is made in this dissertation to study the fundamental limit of walk-off with different modulation formats. By appropriately choosing the nonlinear fiber, the dispersion characteristics and the fiber length, one can minimize the walk-off between two interacting signals to widen the conversion range. Two different approaches are proposed to achieve wide band wavelength conversion for RZ and NRZ signals. Single-channel wavelength conversion is demonstrated in a NOLM for RZ signal and in a cross-polarization switch for NRZ signal using the dispersion-flattened PCF with small negative dispersion and dispersion slope in the 1550 nm range to achieve this wide band operation. The conventional technique of matching the group velocity usually adopted in the XPM [1.25] is not required in the proposed scheme because of the flatness of dispersion which minimizes the walk-off between two signals. This allows the proposed schemes to be fully transparent to the input and converted wavelengths. In NOLM, the input signal acts as a control in the XPM interaction to provide nonlinear phase shift to the co-propagating cw beam which is split from a cw probe beam input to the NOLM. The unbalanced phase shift seen by two counter-propagating copies of a cw probe beam as a result of nonlinear phase shift leads to an intensity-dependent interferometric switch. Within the NOLM, an intense control signal introduces a time varying nonlinear phase shift to the co-propagating cw probe beam while the counter-propagating cw 73 ； Chapter 4 probe beam only acquires a nonzero constant nonlinear phase shift due to the averaged backward-XPM. When these two copies recombine, the unbalanced phase shift between two waves converts any phase difference into amplitude variation, and the finite constant nonlinear phase shift acquired by the counter-propagating cw probe beam leads to an ER degradation [114]. /T\ 64 m PCF 10 GHz < 讓麵“ > PPG VV) ：：纖 bits PRBS coupler i A i PC i PC J PC g DFB-LD y ^^ y/^ Wavelength converted RZ 1550 nm coupler M ^ signal at _____ PC / ^ ‘ TL I 000 Aprob, 3 Centered at Ap^, Fig. 4.1 Experimental setup of the PCF-based NOLM for widely tunable wavelength conversion of RZ signal. Inset shows the microscopic view of the PCF structure. The experimental setup of the NOLM-based widely tunable wavelength conversion scheme is shown in Fig. 4.1. The 10 Gb/s input RZ signal with a bits PRBS and a 20 ps full-width-at-half-maximum (FWHM) pulsewidth is prepared by externally modulating a gain-switched distributed feedback laser diode (DFB-LD) output at 1550 nm with a MZ-IM driven by a pulse pattern generator (PPG). The RZ signal is then amplified with a high power EDFA and launched into the NOLM through a 3-dB coupler. The average and the peak power of the amplified control signal are +22 dBm and 1.7 W respectively to achieve maximum switching efficiency in the NOLM. A wavelength tunable cw beam is launched into the NOLM through an optical circulator. The SOP of the RZ signal and the cw beam are individually controlled by the respective PC. The NOLM uses a 64 m dispersion-flattened PCF as nonlinear medium, and the output is filtered at the cw wavelength using a tunable bandpass filter with a 3-dB bandwidth of 2 nm. 74 ； Chapter 4 6 rr：：：- . ^—® i �� i 2 : ::: 2 i 一 0 •_-_�•».-'_ ' � ‘ - 0 O c ^ •2 a ^ ：^ (/) -2 •^kxxxxxxxxxLxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx^" ： -Z ^ 0 ••—"A/ —^ S" -4 - • -4 o _6 I 1 » _ ‘ -6 1520 1530 1540 1550 1560 1570 1580 Wavelength (nm) Fig. 4.2 Plot of (X) the average dispersion curve and (lines) the walk-off from 1530 nm, 1550 nm and 1565 nm for the 64 m dispersion-flattened PCF. Characteristics of the dispersion-flattened PCF are listed in Table 3.1. High nonlinear coefficient, small dispersion and dispersion slope allow a short fiber length to be used with the walk-off effect being minimized to within 5 ps over the entire C-band as shown in Fig. 4.2 regardless the input signal wavelength. The walk-off time against the wavelength separation between the control signal and the cw beam is a linear increase for this dispersion-flattened PCF, as compared with an exponential increase for the fiber without dispersion-flattened characteristic. For a 20 ps FWHM control pulse, the walk-off effect is considered to be insignificant as the walk-off is <0.3 or 6 ps over the spectral range of 1520 nm to 1570 nm. The R WTIM wavelength tuning range can be wider for a maximum walk-off tolerance of 0.3 r陋^^ or 6 ps as defined in Chapter 2. Hence, the estimated maximum possible wavelength tuning range without pulsewidth broadening is around 54 nm (1520-1575 nm) for any input signal wavelength within C-band (1530-1565 nm), and a larger wavelength tuning range of 109.5 nm (1493-1602.5 nm) is possible if a walk-off tolerance of 0.5 T陋M or 10 ps is employed. This large conversion range facilitates cross-band conversion such as C- to L- or 5-band. 75 ； Chapter 4 20 ； ,RZ signal input to PCF E ^ M ^ f Converted RZ signal I ：30 J \__ -50 L A , A 1545 1550 1555 1560 Wavelength (nm) Fig. 4.3 Measured optical spectra for the input signal at 1549.5 nm and the converted signal at 1555 nm. Spectral resolution: 0.01 nm. Fig. 4.3 shows the spectra of the input signal measured after the 3-dB coupler and the filtered NOLM output with 0.01 nm spectral resolution. The 20-dB spectral width of the cw beam is broadened from 0.06 nm to 0.36 nm after passing through the NOLM. This broadening is caused by XPM between the high power input RZ signal and the cw beam. The optical signal-to-noise ratio of the converted output after the bandpass filter is measured to be over 30 dB. The tunability of the wavelength converter is studied by measuring the ER and the FWHM pulsewidth of the converted output with different input cw wavelengths as shown in Fig. 4.4. The ER is defined as the power ratio of level "1" and level “0” of the RZ eye diagram measured in time-domain with a bandwidth-limited (3-dB bandwidth of 30 GHz) PIN photodiode. An ER of more than 13 dB is obtained over 60 nm with less than 2 dB variation. The small pulsewidth broadening and nearly constant ER ensure minimal distortion to the converted signal within this tuning range. Within the tuning range, the output pulsewidth of the converted signal, measured with a 30 GHz PIN photodiode (minimum measurable pulsewidth is 14 ps) is always <1.2 T函财 or 24 ps. Fig. 4.5 lists the measured output eye diagrams of the converted signal at different wavelengths. All the converted signals exhibit similar eye-opening indicating that a stable output signal quality is achieved over a wide band operation. 76 ； Chapter 4 25 r- 30 CQ ； __ _ 25 ? 20 I 一20 I 1 少，丨o��〜并少15 I - 丨 • O 1 i .E c ； Input signal (1549.5 nm) I 玄 ： “^ ^ lU 0 I I —ii 1 ‘ 0 1520 1530 1540 1550 1560 1570 1580 Wavelength (nm) Fig. 4.4 Plot of (o) the output ER of the converted signal and (x) its FWHM pulsewidth against the converted wavelength. tiiiiij Mil liitij \ ,：……： i ----•4' I --十 ！； i ： ！ ‘ . ？ . i ； , J ！ ！ - . • • - 1520 nm 1525 nm 1530 nm ^ I ； 丨- • i I I \kkkkk jMMi^MM .ill ： ] i 丨 ‘ …丨.i 1535 nm 1540 nm 1545 nm T . , ； ！; i 1 j ； ： • __ j I ： …...... I ； I…….I :.1 :_ …丨丄,i i ‘ 1555 nm 1560 nm 1565 nm i • - I i • • ; • i ”‘ 厂：：j j..厂 I • ;•.:.： . I1 ； , I I • \ • ； •： ： iii1 : i tiiiHii ] 1 ！ , ! i 1 . , • . - ！ - . 1570 nm 1575 nm 1580 nm Fig. 4.5 List of the measured eye diagrams of the converted signal at different wavelengths. Time base: 50 ps/div. 77 ； Chapter 4 碧 1� :WW 1 ？ 1�. 2 10-7 . \ \\\ S • WW -in-10 ^~^' ‘ lU -40 -38 -36 -34 -32 -30 -28 -26 Receiver Optical Power (dBm) Fig. 4.6 Plot of the measured BER performance for the (o) back-to-back RZ signal at 1549.5 nm, and the converted signal at (A) 1530 nm, (•) 1555 nm and (•) 1565 nm. Performance of the wide band wavelength converter is investigated and characterized with a 10 Gb/s bit error rate (BER) measurement. Fig. 4.6 plots the BER of different signals against the received optical power. The figure shows the BER performance of the converted signal for down-conversion of 20 nm and up-conversion of 5 nm and 25 nm. Similar BER performance of both up- and down-conversion is obtained and the power penalty incurred in the conversion is measured to be 2-4 dB at 10"^ BER level. Power penalty in the conversion is mainly due to the cross-talk from the SPM—broadened control spectrum and the ASE from the high power EDFA. Therefore, a higher power penalty is expected to be observed when the wavelength separation between the input control and the converted signal is small. 78 ； Chapter 4 The second approach proposed for wide band wavelength conversion is based on the cross-polarization switch. When the SOP of the control signal and the cw probe beam is aligned to be 45° with respect to each other, the intense control signal induces different nonlinear phase shifts to the two orthogonal components of the cw probe beam and leads to a nonlinear polarization rotation of the cw probe beam as explained in Chapter 2. A noninterferometric cross-polarization switch is formed by putting an optical polarizer after the nonlinear fibers so that the nonlinear polarization rotated light is converted into amplitude variation in the single-pass noninterferometric structure. As the conversion range of the RZ signal is studied in the previous demonstration with NOLM, NRZ modulation format is used to study the limit of walk-off-induced waveform degradation for NRZ signals in addition to the demonstration of the cross-polarization switch. (^) ^ PPG IC GHz bits PRBS PC � , PC DFB-LD ^ ^ — ED^ OCT) 知广 1550 nm pC 1 Combiner TL I ono V^ “ 64-mPCF „ Polarizer ^^ . Wavelength converted NRZ 丄 / signal at Centered at A^^e Fig. 4.7 Experimental setup of single-pass noninterferometric cross-polarization switch with a dispersion-flattened PCF for widely tunable wavelength conversion of NRZ signal. Fig. 4.7 shows the experimental setup of the cross-polarization switching. A 10 Gb/s NRZ signal at 1550 nm is amplified with an EDFA, and combined with a cw beam from a tunable laser through a 3-dB coupler or a wavelength-division-multiplexer respectively for in- or out-of-band conversions. The combined signals are launched into the 64 m dispersion-flattened PCF. The average power coupled into the PCF is estimated to be 29 dBm for the control signal, and 10 dBm for the cw beam. A tunable bandpass filter is used to select the cw wavelength, which is then blocked by the polarizer through adjusting the PC in the absence of control. 79 ； Chapter 4 � inn] pEsiB I I .�——�...... !.—：�.�_�...... - —^• n~！ r- I j r — ....丨..丨_ H i 一 — i . I : I :」...... ： ‘ I J ^ ' . • " i (0 fYYWi f^fyi^ Fig. 4.8 Simulation (left) and experimentally measured (right) eye diagrams of (a) the source signal at 1550 nm, and the converted signal at (b) 1480 nm, (c) 1560 nm and (d) 1600 nm. Time base: 50 ps/div. 10-5 I^ 0) \ I 10-6 • \ \ O 10-7- \ \ iS 10-:. \ \ ±i 10；® • \ \ m 10-10 • \ \ HO-11 LJ^ 么 丨 u -36 -34 -32 -30 -28 -26 Receiver Optical Power (dBm) Fig. 4.9 Plot of the measured BER performance for the (o) back-to-back NRZ signal at 1550 nm, and the converted signal at (A) 1560 nm. 80 ； Chapter 4 Fig. 4.8 shows both the simulation (details of the simulation are provided in Appendix B) and the measured eye diagrams of the source signal at 1550 nm and the converted signals at 1480 nm, 1560 nm and 1600 nm. The measured BERs of 1550 nm back-to-back signal and 1560 nm converted signal are shown in Fig. 4.9. BER measurements of the converted signals at 1480 nm and 1600 nm are not performed due to the lack of optical amplifier for these wavelengths. Nevertheless, clear and widely-open eye diagrams are obtained for all the converted signals with similar output signal quality and ER. Hence, a similar BER performance for the other two converted signals is expected. Due to the limited operating range of our tunable light source, the cw beam can only be tuned to the above wavelengths. A wider tuning range is expected for a maximum walk-off tolerance of 0.3 r before the converted waveform is distorted. As far as the result estimated FWHM from simulation as shown in Fig. 4.10，the conversion bandwidth for 10 Gb/s NRZ signals is �22 0nm (0.3 T,.遍=18 ps), and the conversion bandwidth at 40 Gb/s is �6 0nm (0.3 r,,,画=4.5 ps )• The inverse relation of the normalized efficiency against the wavelength in Fig. 4.10 comes from the inverse proportion of the nonlinear coefficient to the wavelength as expressed in (2.8). As phase matching is not required to accumulate the nonlinear phase change for polarization rotation, the proposed approach can have a larger tolerance to the high-order dispersion in fiber. Consequently, the conversion bandwidth using XPolM approach is larger than the FWM-based approach when the same nonlinear fiber is used [108]. The experimental conversion bandwidth is increased from 40 nm [108] to 120 nm for 10 Gb/s NRZ signals. 81 ； Chapter 4 0 1.5 r 1 1 r-j~ 100g jl-gg^il 1 1200 1300 1400 1500 1600 1700 1800 1900 z Wavelength (nm) (a) (b) (c) (d) (e) Fig. 4.10 (Upper) Plot of the calculated walk-off from 1550 nm control signal in a 64 m PCF, and its corresponding conversion efficiency for 10 Gb/s and 40 Gb/s signals normalized to the one with zero walk-off for the same input control power at 1550 nm. (Lower, a - e) Simulation eye diagrams of the converted output NRZ signal at different walk-off values from Wm/3 for every T酬 • 82 ； Chapter 4 A further improvement in XPM can be made by applying a Raman pump to the nonlinear fiber so that it acts as a distributed amplifier to lengthen the nonlinear interaction length. The counter-propagating Raman pump continuously enhances the nonlinear effects of the control signal in the XPM by amplifying its power. As a result, the effective fiber length , becomes, L粉驗 (4.1) for a Raman pump power of p^ . Fig. 4.11 illustrates the idea of a Raman-enhanced , which is longer than its physical length L. 产(0，0) “ 户(、0) > Distance Fig. 4.11 Schematic illustration of Raman-enhanced nonlinear interaction length. The Raman amplifier assists XPM in the fiber to enhance the effect of nonlinear phase shift by increasing the interaction length, so that the input control power required to achieve n phase shift is less than the one without Raman amplification. All-optical wavelength conversion demonstrated previously in a PCF—based cross-polarization switch is modified by applying a Raman pump to a similar cross-polarization switch with 1 km long HNL-DSF as the nonlinear medium. The experimental setup for the Raman-enhanced cross-polarization switching is shown in Fig. 4.12. A 10 Gb/s NRZ signal is prepared by modulating a cw beam at 1537 nm with a bits PRBS using a MZ-IM. The NRZ signal is amplified with a high power EDFA to serve as the control signal in the XPM, and combined with a cw probe beam at 1545 nm through a 3-dB coupler with a PC at each input to maximize the nonlinear effect by adjusting the input SOPs of the input beams. The combined signals are launched into a 83 ； Chapter 4 1 km HNL-DSF with the parameters listed in Table 3.1. This nonlinear fiber also serves as Raman gain medium by coupling the Raman pump at 1440 nm through the wavelength-division-multiplexers. The Raman pump counter-propagates with the combined signals to reduce the pattern-dependent pump depletion and the coupling of relative intensity noise of the laser diodes generally occurred in the case of co-propagating Raman amplification. A tunable bandpass filter is used at the fiber output to select the cw wavelength. A PC is placed before the polarizer to adjust the input SOP, so that the cw probe beam is blocked in the absence of the control signal. 10 GHz (^) > PPG bits PRBS PC PC DFB-LD — >U/=1537 nm ^ PG 3-dB coupler TL I QQQ~Vz^� =1545 nm 1 km HNL-DSF^<^ n , • Terminated p�ii!! 7 PC _^ y ^ —t —_ ~~ / [f WDM couplers Wavelength converted NRZ Centered at ；V^V. signal at ^robc Raman pump at 1440 nm Fig. 4.12 Experimental setup of the modified cross-polarization switch with Raman-enhancement for the wavelength conversion of NRZ signal. The Raman pump consists of two high power multi-mode laser diodes at 1440 nm whose powers are combined orthogonally with a polarization beam combiner (PBC) to deliver up to 420 mW power. The Raman gain spectrum of the 1 km HNL-DSF when applied with this Raman pump is shown in Fig. 4.13. The gain spectrum is obtained by calculating the on-off power difference between the output powers of a cw beam obtained from a tunable laser. Fig. 4.14(a) plots the measured nonlinear phase shifts acquired by the cw beam with the co-polarized control signal at different Raman pump powers. As the Raman pump power increases, the induced nonlinear phase shift increases for the same control power. It clearly shows that the 84 ； Chapter 4 Raman gain enhances the XPM process by increasing its nonlinear interaction length for a given input control power. In other words, with the presence of the Raman pump, one can use a smaller control power to achieve sufficient nonlinear phase shift. The effective nonlinear coefficient y^^，can be calculated by estimating the slope of each linearly-fitted curve in Fig. 4.14(a) with the same effective iteration length L对, and is plotted in Fig. 4.14(b). The effective nonlinear coefficient increases with the Raman pump power, and is doubled from the intrinsic nonlinear coefficient of the fiber when the Raman pump power is -350 mW. 8 ^^‘ ^ c 观谈 • MM TO 0 4 _ 撒你 Q 於*《似 1 2 • O 0 L 1 I I 1 1 1 1525 1530 1535 1540 1545 1550 1555 1560 Wavelength (nm) Fig. 4.13 Plot of the on-off Raman gain for the 1 km HNL-DSF fiber with 350 mW Raman pump power at 1440 nm. Input power of the cw beam is 0.25 mW. 85 ； Chapter 4 ^ \ ‘ •0 mW 云 4 - A • 35 mW W Romon m.mn * ^ A 82 RlW ^ Raman pump • • • W 二。 power = 420 mW ! i Y �12 8mW g £ 3 - \ X173 mW =5 A 5 i « +217mw £ o • \ $ o A X 260 mW 圣 $ 2 - M 6 § § •3�3mw ro • I A I ° • 344 mW f 1 - I I ° I A 382 mW I S 0 mW • 420 mW 0 1 1 “ 1 1 0 25 50 75 100 125 150 Instant Power - Control Signal (mW) 30 :~ 10 ！5 广（b) 善 g E 25 - Z � • 8 •su乂 ‘‘於 I CO c > 20 - ‘ Z广 ^ g 3 2 芒 15 _ Tt."^ QZ 10 •为 名 至=5 g St ,在 a 9L jg O 邊 •P<^ = -10dBm - 2 03 UJ ••必 oPcw = -20 dBm ^ 0 ——I 1 ” J- 0 0 100 200 300 400 500 Raman Pump Power (mW) Fig. 4.14 (a) Plot of the measured nonlinear phase shifts acquired by the co-polarized cw probe beam at different control and Raman pump powers, (b) Plot of the observed small signal Raman gain at (o with dashed linear fit line) -10 dBm and (• with dashed linear fit line) -20 dBm, and (• with dotted quadratic fit line) the effective nonlinear coefficient against the Raman pump power. 86 ； Chapter 4 B \ \ tS 10-6 • \ \ 2 10-: \\ 0-9. \ \ s ioio.[xra3\ \ 10-111 ^——^ 丨 u -36 -34 -32 -30 -28 -26 Receiver Optical Power (dBm) Fig. 4.15 Measured BER performance of (o) the back-to-back signal and (A) the converted signal at 10 Gb/s. Insets: measured input and output eye diagrams with 50 ps/div time scale. BER plots of the input back-to-back signal and output converted signal are shown in Fig. 4.15. The measured eye diagrams are shown in the same figure as insets. Widely-open eye is obtained for the converted signal. There is very little difference between the original and the converted eye diagrams. A small power penalty of � 1dB is measured for the converted signal at 1BER level when compared with the back-to-back signal. In addition, the Raman amplifier provided a 1.9 dB gain to the converted signal, which further increased the conversion efficiency, defined as the power ratio between the average output power of the converted signal and the input power of the cw probe beam, from -16.5 dB (the conversion efficiency without Raman amplification with a higher control power to achieve n phase shift) to -14.6 dB. 87 ； Chapter 4 NRZ^to-RZ Modulation Formation Conversions When a cw probe beam is replaced by a signal in the XPM process, the proposed devices become a signal processing gate to perform the logic operation. Modulation format conversion from NRZ signal to RZ signal is demonstrated as one of these applications for the XPM switching device in this dissertation. Future all-optical networks are likely to be a combined optical-time-division multiplexing (OTDM) and WDM networks by taking the advantages of both technologies. The NRZ modulation format usually employed in WDM networks requires less bandwidth per channel and has greater timing tolerance, while the RZ modulation format used in OTDM networks provides high bit-rate transmission with better tolerance to fiber nonlinearities and dispersion in the case of soliton transmission. Within the access networks, WDM systems with NRZ modulation format are desirable to provide optical communication between the optical line terminators in the central office and the optical network units at the subscriber side. To handle the increasing amount of the Internet traffic, high bit-rate OTDM systems may be considered in the core networks to increase the per-charmel capacity by time multiplexing different RZ channels with bit-interleaving. Hence, there may be a need for the conversion from a NRZ signal to a RZ signal, and an all-optical modulation format converter may be an essential function at the edge nodes of hybrid OTDM-WDM high speed optical communication systems [115-117]. In this dissertation, both interferometric approach of NOLM and noninterferometric approach of spectral filtering are applied for the modulation format conversion from a NRZ signal to a RZ signal. The idea of modulation format conversion is first demonstrated in a simple single-channel NOLM, and is extended to multi-channel case with the FWM-based cross-talk being suppressed in the multi-wavelength operation. Noninterferometric approach of spectral filtering is then introduced to overcome the polarization-dependent issue encountered in the NOLM. 88 ； Chapter 4 NRZ-ta-RZ Modulation Format Conversion in a NOLM I叩ut NRZ signal: J ^ ^^ Control pulse train: J^ ^^ J^ ^^ J^ Format converted output: J^ ^^ J^ Fig. 4.16 Schematic illustration of all-optical NRZ-to-RZ modulation format conversion. A schematic illustration of all-optical modulation format conversion from NRZ signal to RZ signal is shown in Fig. 4.16. NRZ signal is converted into RZ format ail-optically with a NOLM which performs an "AND" operation between the incoming NRZ signal and a clock recovered optical pulse train. This synchronized pulse train serves as a control in the NOLM to cross-phase modulate the NRZ signal, so that a pulse-like output whose logic is given by the input NRZ signal can be obtained at the output port of the NOLM as the converted RZ signal. 1 km HNL-DSF 10 GHz y > PPG � � fr\ pr Tv-dB pcf II ；^ coupler L DFB-LD ED^ (TX) J Format converted RZ 知"= 1550nm ^^ | p � coupler signal at ~7L|ooo[Q:|——• �rvbc = 1547.4 nm Centered at Aerobe Fig. 4.17 Experimental setup of the NOLM-based NRZ-to-RZ modulation format conversion for single-input channel. 89 ； Chapter 4 Firstly, the NRZ-to-RZ modulation format conversion is demonstrated for single-channel operation with the experimental setup shown in Fig. 4.17 which is similar to the one used for wavelength conversion. A synchronized optical pulse train with a repetition rate same as the bit-rate of the incoming NRZ signal is used as the control signal in the NOLM to cross-phase modulate the NRZ signal input to the NOLM. When the control pulse is aligned with the center of the NRZ bit slot as illustrated in Fig. 4.16，the NOLM gives a pulsed output only when the NRZ signal is a mark. In the demonstration, a 10 Gb/s NRZ signal is generated by modulating a cw beam at 1547.4 nm with an electro-optic MZ-IM. The PRBS bit length of the signal is 231-1. A synchronized 10 GHz optical pulse train is prepared by gain-switching a DFB-LD at 1550 nm followed by a 500 m dispersion-compensating fiber (DCF) for chirp compensation. The FWHM pulsewidth of this pulse train is 15 ps. This gain-switched pulse train is coupled into the loop through a 3-dB coupler and a polarizer to ensure the co-polarized operation between the control pulse train and the NRZ signal. PCs are used to maximize the XPM efficiency within the loop by co-polarizing the SOP between them. 90 ； Chapter 4 fP\ 1km HNL-DSF 10 GHz © H p:G I vU 500 m DCF 2^1 bits PRBS [ ^ NI ( K. PC PBC ~~ DFB-LD �� ED~ ^ 000 ^ 毛,,7=1浏細 ^nm J Vx PC 3-dB ‘ I TL |OnO � i 广pier PC r=>fOk PC fi ^ 知 丫启 m g coupler Format converted RZ PC signals at ？ PC • rt ……，. ^Y-y-. � T Optical delay line Ki DFB-LD ^ L� PC x=>foP ‘�dfb^LD Fig. 4.18 Experimental setup of the NOLM-based NRZ-to-RZ modulation format conversion for multiple input channels. Experimental setup of the multi-channel modulation format conversion modified from the one used in single-input channel is shown in Fig. 4.18. Two complementary 10 Gb/s NRZ signals with a PRBS of2^-1 bits are generated by modulating the cw beam at four wavelengths (1545 nm, 1547.4 nm, 1554.5 nm and 1557 nm) via two MZ-IMs. These two streams of NRZ signals are combined with a 3-dB coupler and launched into the NOLM through an optical isolator to block the reflected light from the NOLM. PCs before the 3-dB coupler are used to align the input SOPs, so that all four NRZ channels are co-polarized when launch into the NOLM. A fiber delay line is used at one of the input branches of the 3-dB coupler to align the time difference between these two streams of signals. Hence, all four 10 Gb/s channels are time— and polarization-aligned at the input of the NOLM. In the actual applications, these four 10 Gb/s NRZ data streams are independent and can be combined via an arrayed waveguide grating (AWG) with an optical delay line at each of its input branch to minimize the overall loss incurred in the couplers and to individually adjust 91 ； Chapter 4 the time shift. The optical pulse train is obtained as in the single-channel case to serves as a local gating signal to gate the incoming signals in the NOLM. In multi-wavelength operation with suppressed FWM components, a PBC is used instead of a 3-dB coupler to combine the NRZ signals with the control pulse train, which is amplified with an EDFA. A PC is used to align the input SOP of the control pulse train to maximize its power after the PBC. Hence, the control pulse train and the NRZ signals are orthogonal to each other throughout the nonlinear interaction. This orthogonal state between the intense control pulse train and the signals to be converted minimizes the generated FWM components in a randomized birefringent fiber [118-120]. The combined signals are launched into a 1 km HNL-DSF. After the nonlinear interaction, a thin-film band-stop filter (BSF) is used to filter out the control pulse train. The PC inside the NOLM is used to compensate the intrinsic fiber birefringence within the loop. An AWG with a S-dB bandwidth of 0.4 nm is used to separate each converted channel for characterization. ！^^ 1540 1545 1550 1555 1560 Wavelength (nm) Fig. 4.19 Measured optical spectra of the fiber output for (upper) co-polarized, and (lower) orthogonally-polarized control and signals for an individual conversion of four different channels. Each trace is shifted vertically by 30 dB for visualization. Spectral resolution: 0.01 nm. Fig. 4.19 shows the measured spectra of the four individually cross-phase-modulated signals at the output of the HNL-DSF for both co-polarized and orthogonally-polarized control and signals. A strong FWM component generated by the intense control pulse train and the NRZ signal is observed in the case of 92 ； Chapter 4 co-polarized experiment. In this scheme, control and signals are combined with a 3-dB coupler and a polarizer for the co-polarized operation. The FWM components observed in the co-polarized case can be significantly suppressed for the case with orthogonal control and signal as shown in Fig. 4.20. For instance, the idler power at-1554 nm generated by the FWM between the control pulse train and the NRZ signal at 1547.4 nm is suppressed from -37 dBm down to -63 dBm. Hence, the cross-talk of the XPM processed signal at 1554.5 nm, whose wavelength overlaps with the idler of channel 2, can be suppressed by 26 dB when the control and the NRZ signals are orthogonal to each other. 20 I • • JL I 2。 丄八 ！: J^^ 1540 1545 1550 1555 1560 Wavelength (nm) Fig. 4.20 Measured optical spectra of the fiber output for co-polarized and orthogonally-polarized control and signal of channel 2. Spectral resolution: 0.01 nm. 93 ； Chapter 4 )、 ！ ‘ ^ :(a) ‘ ！ [ i ？ ), , i. . 4... ..-, ：,,、• . f I ‘“ ‘ ‘ (b) i�—�4一，..：—女.. t ！ L.. ..i I .. .1— -i ’ - … ； i .,’...[ ： ‘ � J .丄一 i -i ；-- i - i^^iliitl ^uito, • .. .J . 1. i. ’. I - ’. L...... • ..…t..丨 ‘ • • Fig. 4.21 Measured output converted eye diagrams for (a) single-channel (b) and four-channel co-polarized operation at 1547.4 nm. (cHO converted outputs respectively at 1545 nm, 1547.4 nm, 1554.5 nm and 1557 nm for orthogonally-polarized operation. Time scale: 50 ps/div. In multi-wavelength operation, the generation of in-band FWM components between the five waves (one control and four signals) becomes severe. Fig. 4.21 shows the experimental output eye diagrams of the converted signals under different conditions. Under the multi-wavelength operation, the converted output at 1547.4 nm suffers severely from the FWM induced in-band cross-talk in the case of co-polarized control and signals. The in-band FWM component degrades the converted output as a result of signal beating, which contributes to a large amplitude fluctuation as shown in Fig. 4.21(b). Such signal degradation is avoided in the orthogonally-polarized experiment, where the intense control pulse train is orthogonally-polarized to the input NRZ signals. The signal quality of the converted outputs [Fig. 4.21(c>-(f)] under the multi-wavelength operation is thus restored and is similar to the one obtained in the single-wavelength operation. 94 ； Chapter 4 2 10-7 . ^^ \ ^ 10-8 • ^^ \ m 10-9 . W \ . 川-10 • V' ^ ^ lu -40 -38 -36 -34 -32 -30 Receiver Optical Power (dBm) Fig. 4.22 Plot of the measured BER performance for the back-to-back (o) RZ and (•) NRZ signals at 1550 nm, and (A symbols with dotted lines) the converted RZ signals at four different channels (1545 nm, 1547.4 nm, 1554.5 nm and 1557 nm). BER measurements are performed for the four format converted signals under the single- and multi-channel operations respectively for the scheme of co-polarized and orthogonally-polarized control and signals. Power penalties incurred in the format conversion are measured to be 0.5 dB and � 1dB (0.85 to 1.1 dB depending on the wavelength) at 10"^ BER level respectively for single- and multi-channel operations when compared to the RZ signal baseline with similar signal pulsewidth. Small power penalty resulted from signal degradation in the multi-channel case is achieved when the control pulse train and the NRZ signals are orthogonal in their SOPs. 95 ； Chapter 4 NRZ-to-RZ Modulation Format Conversion by Spectral Filtering of a XPM-Broadened Signal Spectrum The previous scheme of all-optical NRZ-to-RZ modulation format conversion assumes that the input SOP of the NRZ signal is constant. In practical systems, however, the SOP of an incoming signal varies with time due to the external perturbation of the transmission links. Such polarization fluctuation of the NRZ signal is seldom considered in previous reported schemes [121-128], and will turn into amplitude fluctuation after the conversion. For XPM-based nonlinear signal processing, the polarization-dependence encountered in XPM can be solved with twisted fiber as demonstrated by Lou et al. in [129, 130] and Tanemura et al. in [131] based on circular polarized fiber properties [132]. These schemes, however, require twisting of a long fiber (usually in hundreds of meters), which is rather clumsy compared with the polarization-diversity scheme typically used in addressing the polarization-dependent processes. In the second approach, an all-optical NRZ-to-RZ modulation format conversion based on spectral filtering of a XPM-broadened signal spectrum in DSF and PCF is proposed and demonstrated. A polarization-insensitive scheme is also developed using polarization-diversity loop. Polarization-sensitivity of the proposed schemes is investigated by comparing the polarization-dependent loss (PDL) incurred in the format conversion between single-pass and polarization-diversity loop configurations. The noninterferometric scheme of spectral filtering of a XPM-broadened signal spectrum has advantages of simple structure and robustness to the environmental perturbation compared with the interferometric scheme. The XPM efficiency is characterized by examining the PDL of the converted output with different polarization angles between two linearly polarized lights. The measured converted outputs of two different configurations illustrate the need for polarization-diversity scheme in the actual applications. 96 ； Chapter 4 <® » A � PBS (g) ^ c 众 /r\PC C ,^ \ \ \ C 0 Perpendicular to the paper j •*-> Parallel to the paper Nonlinear medium Fig. 4.23 Polarization-diversity loop. The scheme of polarization-diversity is shown in Fig. 4.23. Lights entering from input port A or port B of a 4—port polarization beam splitter (PBS) are separated into two orthogonal polarizations at the output ports C and D where the power ratio depends on the SOP of the input light. The polarization-diversity loop is formed with a nonlinear fiber connecting the two output ports (C and D) and a PC which is used to compensate the intrinsic fiber birefringence within the loop and to adjust the round trip polarization rotation of 90° or its odd multiple for reflection mode of operation as illustrated in Fig. 4.24. This extra 90° polarization rotation leads to an interchange of the SOPs of two counter-propagating orthogonal components of the control/signal. Hence, the two orthogonal components of an input light re-combine at its corresponding input port after traveling the diversity loop, denoted as reflection mode in contrast to the transmission mode where the net round trip polarization rotation is 180° or its integer multiple and the two Orthogonal components of an input light re-combine at the other input port (A->B and B->A). (a) 0 (g) (b) A I 亡 j-〜…；�(8 4<—— (g)<7 i 山 f i V i Ic tLhJ 丨 ILDJ � V J Fig. 4.24 Illustrations of polarization-diversity loop with extra 90�polarizatio rotation n for reflection mode operation at different input ports, (a) Control path, and (b) signal path within the loop. XPM between the co-propagating lights (clashed lines with black symbols in clockwise direction and dotted lines with gray symbols in counterclockwise direction) is considered in the format conversion. 97 ； Chapter 4 Polarization-insensitive XPM is achieved by launching a control beam at 45° with respect to the principle axis of the PBS into one input port and a polarization fluctuating signal into the other input port of a 4-port PBS. Inside the polarization-diversity loop, the co-propagating lights are always perpendicular to each other. As a consequence, the XPM effects seen by two orthogonal components of the signal are the same for a constant co-propagating XPM coefficient and an equally divided power of the control beam with 45° input SOP. In the reflection mode of operation, lights are reflected to their input ports after passing through the polarization-diversity loop, and the control beam and the NRZ signal are separated from each other by the PBS after the XPM interaction. However, the limited isolation of typically -25 dB of the PBS leads to a finite leakage of the control signal at the input port of the NRZ signal and vice versa. An optical filter is required to remove the leakage of the control signal power from the co-propagating spectral broadened NRZ signal at the output stage. By extracting the broadened parts of the NRZ signal near the carrier wavelength, red-chirped components at longer wavelength side or blue-chirped components at shorter wavelength side corresponding to the rising edge and the falling edge of the control signal respectively, RZ signal can be extracted as the converted output as illustrated in Fig. 4.25. In the case ofNRZ-to-RZ modulation format conversion considered in here, a periodic pulse train at a repetition rate same as the bit-rate of the NRZ signal is used as the control. This control pulse train and the NRZ signal are launched into two different input ports of the 3-dB coupler or the 4-port PBS respectively for single-pass or polarization-diversity loop configuration. 98 ； Chapter 4 (a) Input NRZ signal: J ^ (b) Control pulse train: J^ J^ 八 八 八 (c) XPM-induced frequency chirp: ^^A (d) Filtered output (blue-chirped): 上 ^^ ^^ (e) Filtered output (red-chirped): ^^ ^^ ^^ Fig. 4,25 Schematic illustration of the NRZ-to-RZ modulation format conversion by spectral filtering of the XPM-broadened signal, (a) Incoming NRZ signal to be converted, (b) Synchronization control pulse train, (c) XPM-induced frequency chirp as a derivative of the nonlinear phase shift. Time domain output of (d) the blue-chirped components and (e) the red-chirped components. Vertical scale: (a, b, d, and e) intensity, and (c) frequency. 10 GHz ^ > PPG SOO^CF 231 -1 bits PRBS ± (() PC DFB-LD � ED^QQQ^ ；U= 1549.255 nm | ^ PC � , 3-dB coupler DFB-LD CXX) ^ _I Pol. Scrambler ！ C 一)~^ 1551.065 nm 3.2 km DSF ff\ or 64 m PCF FBG ^ U i > Hllllllh- BPF Format converted RZ Centered at signal at Fig. 4.26 Experimental setup of the NRZ-to-RZ modulation format conversion by spectral filtering with single-pass configuration. 99 ； Chapter 4 Firstly, the single-pass NRZ-to-RZ modulation format conversion is performed with the experimental configuration shown in Fig. 4.26. The nonlinear medium is either the 3.2 km DSF or 64 m PCF, with the parameters listed in Table 3.1. In both cases, a synchronized 10 GHz pulse train is used as the control for XPM. This pulse source is prepared by gain-switching a DFB-LD with a 500 m DCF for chirp compensation. The FWHM pulsewidth of the compressed pulse is 17.5 ps. It is then amplified with an EDFA to provide 0.1 W of peak power for DSF, or 1 W for PCF (after amplification) to achieve sufficient XPM-induced spectral broadening to the signal. A PC is used to maximize the XPM efficiency. The NRZ signal is encoded with a 2^-1 bits PRBS at 10 Gb/s through a MZ-IM with a PC at its input to align the SOP of the cw beam from a DFB-LD with the transmission axis of the MZ-IM. In the following experiments, the synchronization is done by adjusting the delay of the electrical signal with an electrical delay line (not shown in the figure). This synchronization can also be achieved by replacing it with an optical delay line. Two beams are combined with a 3-dB coupler and launched into the nonlinear fiber (DSF or PCF). A tunable bandpass filter and a fiber Bragg grating (FBG), with 3-dB bandwidth of 1 nm and 0.4 nm respectively, are used to select the red-chirped components as the converted RZ signal output and remove the control pulse train, the blue-chirped and the un-chirped parts of the XPM spectral broadened output. 100 ； Chapter 4 ‘ 1 I Control pulse peak power = 0.1 WI • j l.'^jj^j^.. • - -I - - r -j-i - - Conversion efficiency = -18 dB -”"一 i ， ^ —I — _�1^ - -——;——. ……丁 ……, • — m^ L 1 1 1 i 1 1 i i B . I 1... -ilKrSl Time (20ps/div) 「 . . • ！ I j j I ^ 今 I , , Control pulse peak power = 1W | ^ 1 - - r - - Conversion efficiency = -18.3 dB 1一“― Jt —•"， • — —1 — — f- ^^^ —一— — ™—.. (Q • ~ H — — h^Hft —— 一―—卜一 一一 —I 一一 I — • . I — ！ i 丄丄T H “ —「腿 “ I - -J -_�-�-_J —-[ . 1ft" 'j I I 「丨门，丨,,,“ 1 1 i 1 1 1 1 i 1 r, • '"'•X^jrr -"V^n Time (20ps/div) ' : Fig. 4.27 Simulation (left) and experimentally (right) measured output eye diagrams of the converted signal using (upper) DSF and (lower) PCF for the single-pass configuration with fixed input SOP. Time base: 20 ps/div. The single-pass format conversion is polarization-sensitive due to the polarization-dependent XPM efficiency. In the case of constant input SOP of the NRZ signal, a PC is used to align the SOP of the control pulse train and maximize the XPM efficiency. Simulation results (details of the simulation are provided in Appendix C) and the corresponding experimental results of the single-pass NRZ-to-RZ modulation format conversion are shown in Fig. 4.27. The conversion efficiencies (defined as the average power ratio between the converted RZ signal and the input NRZ signal) are -18.5 dB for DSF and -19.1 dB for PCF. Widely-open eye diagrams are obtained with 2 minutes acquisition time (the same acquisition time will be used for the following eye diagram measurements) for both fibers. There is a good agreement between simulation and experimental results in terms of the conversion efficiency and the output waveform. 101 ； Chapter 4 _ I ！ ^ I j j ....j j : , \ Control pulse peak power = 0.1 W ; i ； ^^ i .了—「:——厂 T -. 1 醒.r-r-：霧-丨 7 -r-r|--r-r-r-:i:-T- -工縫-厂-+ 鐘-一 立• 卜^^^ 1 Jjy • 1- Jlj^^^BK II^^H « in-t" «-I t I - -t-i-n- I-- - L__i__L --iHR--I—— | J^^^k； —i—i—I—I—I—I—1—i—i— r 11 " —."“ mnj Time (20ps/div) | . , ： . ______ , 1 , ijfc. ！ 1 ~一 T3 i I I I I Control pulse peak power = 1W 墓—…—_ , 屬 —I—r *p—1 — 1 i-ttT — — • '^B J ^^k q • —--？蠢-十十-：董十. —...鍾..--I .- ^ —I- - l^H[-一 -�- _L —�—— Time (20ps/div) | ： | Fig. 4.28 Simulation (left) and experimentally (right) measured output eye diagrams of the converted signal using (upper) DSF and (lower) PCF for the single-pass configuration with scrambled input SOP. Time base: 20 ps/div. To study the polarization-sensitivity of the single-pass scheme, the input SOP of the NRZ signal is scrambled by an electrical polarization-scrambler. In both DSF and PCF, highly fluctuating output amplitude is observed with a PDL measured to be around -3 dB which is agreed with the value predicted by the XPM coefficient in a random birefringence fiber. The simulation and experimental results are shown in Fig. 4.28. 2 minutes acquisition time for the eye diagram measurement ensures that all possible input SOPs of the NRZ signal are being tested in a given scanning rate of the polarization-scrambler (the scanning rate of the scrambler is set to 360°/sec). 102 ； Chapter 4 10 GHz ^ > PPG SOO^CF 231-1 bits PRBS i (() tv. PC DFB-LD * ED^QQQ ^ 1549.255 nm PC ]/ DFB-LD ^"XY) ^ __j Pol. Scrambler \ ^ 1551.065 nm 1 PBS .•二 • 3 J 3.2 km DSF ~llllllll— BPF ^ or 64 m PCF Format converted RZ Centered at ‘細 signal at PC Vonpy Fig. 4.29 Experimental setup of the NRZ-to-RZ modulation format conversion by spectral filtering with polarization-diversity loop configurations. The polarization-diversity loop is then applied for NRZ-to-RZ modulation format conversion to minimize the polarization-sensitivity. The experimental setup is shown in Fig. 4.29. Control pulse train and NRZ signal are prepared in a similar way as the single-pass scheme. The peak power of the amplified pulse train is 0.27 W for DSF and 3 W for PCF, and is roughly 3 times larger than the case of single-pass to reach the same XPM effect for orthogonally-polarized interaction. In this scheme, the SOP of the control pulse source is aligned to be 45° with respect to the principle axis of the 4-port PBS to equally divide the power into two orthogonal components, while the NRZ signal is launched into the polarization-diversity loop from the other input port through an optical circulator. Inside the polarization-diversity loop, a PC is used to adjust the SOP for a round trip polarization rotation of 90° or its odd multiple to reflect the lights at both input ports as mentioned previously. The nonlinear medium used is either DSF or PCF. After propagating the polarization-diversity loop, the reflected control pulse train is blocked by the isolator inside the EDFA and the spectral broadened NRZ signal is switched through the circulator for chirp filtering same as the single-pass scheme. 103 Chapter 4 I i \ \Control pulse peak power = 0.27 W I^S^ '--t - - r ^-i - Conversion efficiency = -20.8 dB - - -tj^jj^: - -, -y^H^ — 丨一丨，- •冊——一卜 一— 一 — — — — I—I^B -t — —)— — • • • ••.-‘― •一一 .. —一 丨::栽:::::：-fB '1- :_.+ I I 1 1 I I I i i •丨I III . “ ^^—TtH^. jpi • I—'I ‘ Hfc^ • Time (20ps/div) 「| 丨 ； |： , , i i [ '丨 Control pulse peak power = 3 W ;產 ： 基丨 1 - - r -1-1 - - 1 Conversion efficiency = -21 dB —...- ...... — i ―… 十—墨 ：一 I…|膽i—— I — r T 二— n -r • —一卜——… __II_I_1__i__1_i_i_i_ p' I — i“ V一1~N^- Time (20ps/div) _； . ‘ "t j , j ； Fig. 4.30 Simulation (left) and experimentally (right) measured output eye diagrams of the converted signal using (upper) DSF and (lower) PCF for the polarization-diversity loop configuration with fixed input SOP. Time base: 20 ps/div. i i ！Control pulse peak power = 0.27 W I 1 - - r -i-i- Conversion efficiency = -20.8 dB [ .J^lk.- j ‘yDLLjQLj —I—I—i—i—i—i—i—I—I_I — —敏-..‘遽 Time (20ps/div) ^^： ^^ \ \ \ ； Control pulse peak power = 3 W ‘.重. | ---1--1- -U-I- - 1 Conversion efficiency = -21 dB —iJI^ + - -...... -.^h -•-i -__!_“•;_:；；；風 I 卜 —.麗 [mk ： i 二表i r li r -十壓+-「薩i Mi ^^^ JM ^^^ •. I *‘•..•�t^^^^H^^^ t-l-*b" t-I- t . ‘ I-1-1 1 1 i i 1 1 1——I 1 Time (20ps/div) | ' _ : 丨 ： Fig. 4.31 Simulation (left) and experimentally (right) measured output eye diagrams of the converted signal using (upper) DSF and (lower) PCF for the polarization-diversity loop configuration with scrambled input SOP. Time base: 20 ps/div. 104 ； Chapter 4 The converted outputs are shown in Fig. 4.30 in which the SOP of the NRZ signal is fixed. For a scrambled input SOP of the NRZ signal, similar output eye diagrams are obtained as shown in Fig. 4.31 with the input SOP of the control pulse train being optimized (45° aligned to the principle axis of the PBS) to have the minimum polarization-sensitivity for the converted signal. In both cases, the measured conversion efficiencies are around -21 dB for both fibers (in the polarization-scrambled case, the converted average power is a mean of a fluctuating output power due to a finite PDL). A smaller conversion efficiency of the polarization-diversity loop is due to the insertion loss of the PBS of-1.2 dB in each pass. The RZ eye opening factors of the converted output for the polarization scrambled input NRZ signal, defined in (4.2, below), measured with a high speed oscilloscope are 0.742 for DSF and 0.827 for PCF compared with 0.753 for DSF and 0.861 for PCF in the case of nonpolarization—scrambled input NRZ signal. Only a slightly amplitude fluctuation is introduced when the input SOP is highly scrambled. Eye opening factor = ([ + 色+�� ) (4.2) P^-PO where p. and a^ (/ = 0, 1) are the average power and the standard deviation for the noise contribution of level-0 or level-1 respectively. 40 20 _ Amplified pulse train |jijj|L m Q Jn I Input NRZ signal 一 -60 - 丨1||^^ \ Format converted JllllllliFl \RZ signal output _3Q ‘ ““..•‘.. -.-i .. >•• (Ii I yi Iiillllllllnlr" Li lHlHiiiliiii..i...it.iiil 1545 1547 1549 1551 1553 1555 Wavelength (nm) Fig. 4.32 Measured optical spectra of the input NRZ signal at 1551.065 nm, the control pulse train at 1549.255 nm , the PCF output after XPM, and the converted signal at 1551.5 nm after the chirp filtering. Spectral resolution: 0.01 nm. 105 ； Chapter 4 Fig. 4.32 shows an example of the measured optical spectra at different stages. The control pulse train at 1549.255 nm and the input NRZ signal at 1551.065 nm are combined and launched into the PCF. Both the control pulse train and the NRZ signal are broadened in their spectrum at the output of the PCF due to the SPM and XPM respectively. By applying the FBG and the tunable bandpass filter, the red-chirped components at the longer wavelength side of the carrier wavelength of the input NRZ signal is extracted as the converted output. 2 1 1 1 1 1 m H. ^ vXXXXXx乂 vxXXXXxx eg 0 ！- -- 7-x-x^^- -- - o 0 • o.o��... 1 -2 • \�Z. ^ • O-D-O-d'O "to E -4 • u. X Polarization diversified loop 2 • o Single pass -6 ‘ ' ‘ ‘ ‘ 0 30 60 90 120 150 180 Angle of rotation (degree) Fig. 4.33 Normalized peak power variation of the converted signal versus the angle between two linearly polarized lights for (o) single-pass and (x) polarization—diversity loop configurations using PCF. PDL of the two configurations is characterized by applying an electrically-driven PC to rotate the input SOP of the NRZ signal. Fig. 4.33 shows the normalized output peak power of the converted signal versus the angle between two linearly polarized lights. In the single-pass configuration, the nonlinear index change of two orthogonally-polarized lights induced by XPM is 1/2 of that induced in co-polarized lights in the case of random birefringence fiber. Thus, the peak power of the converted signal in the case of Orthogonally-polarized lights is expected to be around 50% of the co-polarized case, which is consistent with the measurements. 106 ； Chapter 4 In the polarization-diversity scheme, power variation of the output is found to be less than 0.8 dB in PCF as the input signal polarization is rotated through 180°. The PDL is reduced from � 3dB to less than 0.8 dB in both fibers. This shows a significant minimization of the polarization-sensitivity of the XPM-based nonlinear signal processing schemes. The nonzero PDL of the polarization-diversity scheme is believed to be contributed by un-optimized input SOP of the control that gives a period oscillation of the PDL in every 45° and the intrinsic PDL of the fibers and the PBS as the control pulse train and the NRZ signal are orthogonal to each other when they propagate. It is worth noting that, in all cases, the converted RZ signal with DSF suffered severely from amplitude fluctuation and timing jitter, which is not observed in the simulation results with the above model. Long fiber length, where the uniformity of the fiber and its parameters are not guaranteed, is believed to be a possible cause of this signal degradation. as 10 ^W \\ “ Input NRZ signal ^ ^^ A "1 . DSF (Pol. scrambled) (5 7 \ \ \ »DSFO=ixedpd.) Q^ 1。 \\ A \ : PCF (pS.'®sCTambled) %、、 ‘ PCF (Fixed pol.) w8 . ^ \ » PCF single pass • p 10 W H \ . RZ signal baseline (~17.5ps) 妻；w 丨 u -40 -35 -30 -25 Receiver Optical Power (dBm) Fig. 4.34 Plot of the measured BER performance of different input and converted signals. BER measurements are performed with single-pass and polarization-diversity loop to evaluate the influence of the input SOP fluctuation of the proposed noninterferometric modulation format conversion scheme based on XPM effect. Fig. 4.34 plots the BER of different signals against the received optical power. The plot shows the results of nonpolarization—scrambled case in single-pass configuration, and both nonpolarization-scrambled and polarization-scrambled cases in polarization-diversity loop configuration. The BERs of the nonpolarization-scrambled input SOP are similar for single-pass and polarization-diversity 107 ； Chapter 4 loop configurations with a power penalty of 2.1 dB for DSF and 1 dB for PCF at 10—9 BER level compared with the back-to-back RZ signal with similar pulsewidth, while the polarization-scrambled case in polarization-diversity loop configuration has a power penalty of 2.8 dB for DSF and 2 dB for PCF at the same BER level. BER measurement is not performed in the case of single-pass configuration with polarization-scrambled input SOP because of the highly fluctuating output amplitude of the converted signal that limits the receiver sensitivity. All-optical modulation format conversion by spectral filtering for pulsed data output is based on chirp filtering of a XPM-broadened spectrum corresponding to the (rising or falling) edges of the control pulse train with the temporal intensity value following the NRZ signal. With this scheme it is possible, although not demonstrated, to convert simultaneously several NRZ channels with the same bit-rate based on the characteristic of XPM [133] while the converted wavelengths remain nearly the same as their original inputs. 108 ； Chapter 4 Summary Two applications developed in this dissertation are the all-optical wavelength conversion and the all-optical modulation format conversion from NRZ signal to RZ signal. NOLM-based and XPolM-based approaches are proposed to realize the wide band operation of the all-optical wavelength conversion. In the modulation format conversion, a modified NOLM is proposed to achieve a simultaneous conversion of multiple signals, and a polarization insensitive technique is also developed with spectral filtering technique. Properties of all these proposed schemes are listed in Table 4.1 for comparison. XPM-based XPM-based Application wavelength conversion modulation format conversion Approach NOLM-based XPolM-based NOLM-based Spectral filtering Format 10 Gb/s RZ signal 10 Gb/s NRZ signal 10 Gb/s NRZ signal to RZ signal Features Simultaneous Wide band operation Wideband operation Polarization conversion of up to 4 60 nm conversion >120 nm conversion insensitive operation channels Advantages - Simple structure - Simple structure - Simple structure - Potential for -High conversion - High conversion - High conversion multi-channel efficiency efficiency efficiency operation -High output - Multi-channel extinction ratio operation Disadvantage - Low output ER - Fixed input SOP - Fixed input SOP - Asymmetric of the NRZ of the NRZ output pulse signal signals shape Table 4.1 List of the properties for the proposed all-optical nonlinear signal processing approaches. 109 ； Chapter 4 4.3 Proposed System Application WDM Channels • • o r, • “ / NRZ-to-RZ format I — Time interleaver — � : :� conversion • (single channel) ‘� • I Recovered clock Wavelength Clock recovery —' I conversion OTDM channel [ mi^ Fig. 4.35 Schematic illustration of the intermediate node for the WDM-to-OTDM networks using all-optical nonlinear signal processing techniques proposed in this dissertation. The ultimate goal of the work proposed in this dissertation is to realize an all-optical intermediate node for interconnecting between WDM and OTDM networks as shown in Fig. 4.35. In such an intermediate node, technique proposed for multi-channel NRZ-to-RZ modulation format conversion can be used to simultaneously convert multiple incoming NRZ signals from a WDM network into RZ signals. These converted RZ signals are then time interleaved to the respective time slots. The time aligned RZ signals are combined through wavelength conversion. In order to maintain the output signal quality of the time multiplexed output over different time slots/channels, the wavelength conversion must be transparent to the input wavelength of the RZ signals. Such wavelength transparent operation can be achieved with the wide band wavelength conversion techniques proposed in the previous section. 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Desurvire, "All-Optical Fiber Signal Processing and Regeneration for Soliton Communications," IEEE J. Select. Topics Quantum Electron., vol. 3, no. 5, pp. 1208-1223, 1997. [129] J. W. Lou, J. K. Andersen, J. C. Stocker, M. N. Islam, and D. A. Nolan, "Polarization insensitive demultiplexing of 100-Gb/s words using a twisted fiber nonlinear optical loop mirror," IEEE Photon. Technol Lett., vol. 11, no. 12, pp. 1602-1604, 1999. [130] J. W. Lou, K. S. Jepsen, D. A. Nolan, S. H. Tarcza, W. J. Bouton, A. F. Evans, and M. N. Islam, "80 Gb/s to 10 Gb/s polarization-insensitive demultiplexing with circularly polarized spun fiber in a two-wavelength nonlinear optical loop mirror," IEEE Photon. Technol. Lett., vol. 12, no. 12, pp. 1701-1703,2000. [131] T. Tanemura, J. Suzuki, K. Katoh, and K. Kikuchi, "Polarization-insensitive all-optical wavelength conversion using cross-phase modulation in twisted fiber and optical filtering," IEEE Photon. Technol. Lett., vol. 17’ no. 5’ pp. 1052-1054，2005. [132] C.-J. Chen, P. K. A. Wai, and C. R. Menyuk, "Soliton switch using birefringent optical fibers," Opt. Lett., vol. 15，no. 9, pp. All-419, 1990. [133] J. H. Lee, Z. Yusoff, W. Belardi, M. Ibsen, T. M. Monro, and D. J. Richardson, "A Tunable WDM Wavelength Converter Based on Cross-Phase Modulation Effects in Normal Dispersion Holey Fiber," IEEE Photon. Technol. Lett., vol. 15, no. 3，pp. 437-439,2003. 113 ； Chapter 4 Chapter 5 Conclusion and Future Work 5.1 Comparisons between Proposed and Existing Approaches Major properties of an all-optical wavelength converter are conversion efficiency, conversion range, output extinction ratio, and bit-rate it can support. Regarding these properties, the approaches proposed in this dissertation have generally higher conversion efficiency and larger conversion range when compared with the fiber-based FWM (four-wave-mixing) schemes. The bit-rate or pattern dependence usually encountered in the SOA (semiconductor optical amplifier)-based schemes is normally insignificant in the fiber-based approaches owing to the fast response time of the nonlinear effects in fibers. Comparing between the NOLM (nonlinear optical loop mirror) and the cross-polarization switch, the later approach can achieve a very high output extinction ratio for the converted signal by using the crystal-based polarizer. This high output extinction ratio improves the overall signal quality and transmission performance of the converted output. In NRZ (nonretum-to-zero)-to-RZ (return-to-zero) modulation format conversion, major features and contributions of the approaches proposed in this dissertation are the multi-channel capability and the polarization insensitive operation, when compared with the previously demonstrated schemes. With these newly proposed techniques, a generic multi-channel NRZ-to-RZ modulation format converter with low polarization sensitivity can be developed to minimize the overall system complexity and cost. 114 ； Chapter 4 5.2 Conclusion of the Dissertation This dissertation described the all-optical devices and subsystems that may be needed for next generation all-optical networks. The aim of the research on these all-optical techniques and applications is to reduce system cost, complexity and improve functionality. Applications developed in this dissertation are based on the XPM (cross-phase modulation) phenomenon in silica-based single-mode fibers. Several major properties of fibers are studied to optimize the nonlinear interaction for a better signal quality in the processed output. All-optical nonlinear signal processing techniques based on XPM are described in this dissertation and reviews of several important applications are also given. Among these applications, improvements or new approaches are proposed for all-optical wavelength conversion and modulation format conversion applications as they are identified as important elements that would enable a flexible wavelength routed network and an interconnection of different types of optical networks, which employ the data formats that are best suited for the respective network's coverage. As the core element in the proposed all-optical nonlinear signal processing devices, fibers play the crucial role in the ultimate performance of the processed signals. Properties, which can affect the performance in the nonlinear XPM interaction, are explored in this dissertation. These properties include the fiber dispersion and its variation in the longitudinal direction, the nonlinear refractive index, and the electrostrictive resonance contribution to the refractive index change. Theories of the importance of these parameters are explained in Chapter 2，and the parameters of three types of fiber used in developing the all-optical nonlinear signal processing devices are measured and summarized in Chapter 3. Devices with wide band, low input control power, or multi-wavelength operation can be specifically designed with an appropriate choice of the nonlinear fiber and the structure of these devices. 115 ； Chapter 4 Chapter 4 surveyed different approaches for the all-optical wavelength conversion and modulation format conversion applications. In the all-optical wavelength conversion, both RZ (retum-to-zero) and NRZ (nonreturn-to-zero) modulation formats are investigated, and remarkable conversion ranges are reported for both modulation formats with the use of a dispersion-flattened PCF (photonic crystal fiber). Comparing between the NOLM (nonlinear optical loop mirror) and the cross-polarization switch, the former scheme suffers from an ER (extinction ratio) degradation due to a finite constant phase shift seen by the counter-propagating beam in the NOLM, while the cross-polarization switch can achieve a high output ER which is only limited by the polarization ER of the crystal-based fiber polarizer. Therefore, it can be concluded that the cross-polarization switch provides a better overall device performance when compared with the NOLM in the all-optical wavelength conversion application. To address the issue of high input control power for NRZ signal in the XPM—based nonlinear signal processing devices, an enhanced cross-polarization switch is proposed to apply the Raman amplification which acts as a distributed amplifier to lengthen the effective nonlinear interaction length. With this Raman amplifier, the effective fiber nonlinear coefficient can be doubled in a 1 km HNL-DSF (highly nonlinear dispersion-shifted fiber) for a small Raman pump power of around 350 mW. In other words, the required input control power to achieve a full swing switching can be reduced by half. The ability of multi-wavelength operation for the developed all-optical nonlinear signal processing device is reported in the NRZ-to-RZ modulation formation conversion. Under the high power regime, FWM (four-wave-mixing) components are usually generated during the nonlinear interaction. When the XPM is utilized for the all-optical nonlinear signal processing, such FWM effects are considered to be destructive to the overall system performance. Unlike the single-channel operation, in which the FWM generated idlers at new wavelengths can be removed by a wavelength selective element, the in-band FWM components generated in the multi-wavelength operation can not be removed after the nonlinear interaction. A major breakthrough is made in this dissertation to overcome this in-band cross-talk issue. By utilizing the 116 ； Chapter 4 different characteristics between the XPM and the FWM in the co-polarized and orthogonally-polarized operations, the in—band cross-talk caused by the FWM generated idlers can be significantly reduced. A simultaneous multi-channel all-optical modulation format conversion from NRZ signal to RZ signal is demonstrated with minimal signal distortion in each converted signal. In additional to the multi-wavelength capability, the polarization issue is also addressed in this dissertation by applying the noninterferometric spectral filtering technique in a modified polarization-diversity loop. With this proposed configuration, polarization-sensitivity of the input signal to the converted one is significantly minimized. As the proposed modified polarization-diversity loop applies the orthogonal-XPM technique, it has potential to support multi-channel operation as demonstrated in the NOLM structure. 5.3 Prospects and Directions of Future Work Research into all-optical nonlinear signal processing will continue to prove fruitful from both the fundamental physics and the system applications viewpoints. The nonlinear optical properties of fibers should find applications in many different aspects for optical signal processing, particularly in optical communications. This section describes various areas which can be explored as possible extensions of the work proposed in this dissertation. Due to the constraints on time or resource, such possible extensions are not included in this dissertation and are worth to be explored in the future. Enhanced Approach for Clock Recovery with Nonlinear Self-Phase Modulation In the NRZ (nonretum-to-zero)-to-RZ (retum-to-zero) modulation format conversion, an electrical clock signal at a frequency same as the signal bit-rate is needed to be extracted from the incoming NRZ signals. Traditional electrical clock recovery scheme for NRZ signals requires a sensitive photodetector to extract the rf component for clock recovery in a phase-locked loop. In contrast, RZ signal has proven to have a stronger clock component that is suitable for clock recovery purpose. Therefore, it is a trivial extension to 117 ； Chapter 4 firstly convert a NRZ signal to a RZ-like output before the clock recovery. All-optical NRZ-to-pseudo-RZ (PRZ) conversion can be applied in this situation. The conversion from a NRZ signal to a PRZ one can be achieved by spectral filtering of a SPM (self-phase modulation)-broadened NRZ signal spectrum, so that either the rising or the falling edge of the NRZ signal can be extracted as a RZ-like output. The strengthened clock component from this PRZ output can significantly relax the optical power and electrical phase noise margins in the clock recovery process. All-Optical RZr-to-NRZ Modulation Format Conversion All-optical RZ-to-NRZ modulation format conversion can be achieved by spectral filtering of either a SPM- or a XPM (cross-phase modulation)-broadened signal spectrum for signal propagating in the normal group velocity dispersion region. The normal dispersion in fiber broadens the RZ pulsewidth for SPM approach or temporally reallocates the intensity of a cw beam for XPM approach. Instead of extracting the chirped parts as the converted output in NRZ-to-RZ modulation format conversion demonstrated in this dissertation, the extraction of the unchirped part of the nonlinear phase modulation broadened spectrum gives a NRZ-like waveform as the converted signal output. Suggested Approaches for Signal Time Interleaving Time interleaving of the RZ converted outputs can be realized by either using a pair of AWGs (arrayed waveguide gratings) with suitable time delays for each channel to align a particular RZ signal to the prescribed time slot, or simply using a piece of DCF (dispersion-compensating fiber) to time spread the signals at different wavelengths through fiber dispersion. The first approach can provide wavelength flexibility if different nonadjacent channels are considered, while the later approach is obviously simpler and at reasonability low cost for signals with constant wavelength separation. 118 -- • , I :4. • . 乂 rr- ‘-. :-- 1. •. it / i• . n ... 1., . 1 - • * - •• ..... J ‘ - • - r • • » . ^ •• X • - .:.. ...tv ‘ / ’“ i wv 二 t - .. ‘ - ... .. • • - M: V - V • • >•• . .. , ...... ^ • . - ', ‘.. . • - • - . . . ; ,•、- . ,• .. 〕 :、‘‘ , 、— . •“ ； 二 V . ： ： • .... v. . • • , . ... .. „ • • , • I- • . , •, . ... . . r; ‘ • . -- - r . -•- V:. ^ - Appendix A Appdenix A Numerical Model for Dispersion Calculation Total dispersion of the modeled fiber is approximated by summing the material dispersion and the waveguide dispersion. In calculating the material-induced dispersion, a plane wave is considered to propagate in an infinitely extended dielectric medium which has a refractive index n{X), equal to that of the fiber core. The propagation constant p, is given as, J 一 � (A.l) P ；I The material dispersion induced group delay T咖,after propagating at a distance L，is, L( . dn^ (A.2) — 、八…乂 mat =— n-A, I c \ dA J and the material dispersion D細⑷，is, therefore, D U)=丄i = (A.3) ) L dX cdX^ where c is the speed of light in vacuum. The wavelength dependent refractive index n{X), of a material is calculated using the Sellmeier fitting with the coefficients list in Table 2.1. For the waveguide dispersion, the group delay r^^，of a fiber with length 乙，and a step-like refractive index profile can be approximated as, ~ L\ a/1 _ 2人Y| (A.4) ^Wg 然 一 ^cladding + ncladding ' } 7W7\ where c is the speed of light in vacuum; �is the cladding refractive index which is approximated as a constant for any wavelength; b^ifilk- n^orc)hciadd,ns is normalized propagation constant; I Appendix A = {im^^jXf - ； and a is the core radius. In calculating the overall fiber dispersion as shown in Fig. 2.4, either the refractive index difference A = (p贈-’ or the core radius a, is varied from its original value by 士 5%. II Appendix A Appdenix B Simulation Model of Wide Band Cross—Polarization Switch Commercial system simulation software, OptiSystem, is used in simulating the performance of the wide band operation of the proposed PCF—based cross-polarization switch for all-optical wavelength conversion. Fig. B.l shows the schematic of the configuration used in the simulation, with the major simulation parameters listed in Table B.l. About the Simulation This simulation is used to verify the capability of wide band operation for the XPolM—based wavelength converter using PCF in a simplified structure. It models the conversion of a NRZ signal under the XPolM nonlinear interaction. In the simulation, effects of timing jitter, fiber birefringence, and electrical noise which may degrade the output signal performance are neglected to simplify the simulation process and isolate the cause of signal degradation. The simplified structure, therefore, helps to characteristics the process of XPolM under wide band operation without losing the accuracy. Parameters Value / Model Unit Laser Linewidth 10 MHz Noise threshold -100 dB Noise dynamic 3 dB Modulator (MZ-IM) Extinction ratio 26 dB NRZ signal Pulse shape 3-rd order super-Gaussian pulse Rise and fall time 5 ps III Appendix A EDFA Mode Saturation mode Gain 40 dB Saturated power 27 dBm Optical BPF Shape Gaussian Order 1 3-dB bandwidth 2 or 0.65 nm Data pattern Pattern length 128 bits Pattern style DBBS � Electrical lowpass filter Shape Bessel Order 4 Cutoff frequency 30 or 7.5 GHz Fiber (PCF) Model Nonlinear Schrodinger equation Propagator type Exponential Step size Adaptive Max. nonlinear phase error 3 m rad Dispersion From measurement in Chapter 3 Length 0.064 km Core area 6.125 ^m^ Nonlinear refractive index, n: 2.75x1m^/W OptiSystem: Version 4.0.1.268 � A de Bruijn bit sequence (DBBS) of length 2L is a pseudo-random bit sequence (PRBS) of length 2L-1 with an additional zero bit added to the longest run of zeros in the PRBS. Table B. 1 List of the major parameters and simulation models used in the wide band XPolM simulation. IV Appendix B I =：：：：：=：：：= J^； ^： ^ Alk： BER An«4yzM Eye Oia^am Antriyzer Input sign- OSA OSA ^" ^ J DID.. O-i-^ IflU LowP«sB«i»$^FiHw I I Cutoff frequ^cy = 0.75' Bit rate Hz PRBS NRZ (3rd Super Gaussian) ^ 工： i ^ H^ ^^^ 2 L^^^ J Laser MZ-M PCI EDFA i\PGi BPf (Gaussian) l^ow j^ss B»ssel Filter 1 Fre __ L^^��幻 丨 —— tzIT ^^^^ 二二 丨二二。„c:=— cw Laser Polarizef (Lhear> Bandwidth® 0.65 nm Fr6ajencv= 1S60 nm Device angle = 0 deg Power = 10 dBm 办 Ground Fig. B.l Schematic of the configuration used in the XPolM simulation. V Appendix A Appdenix C Simulation Model of Spectral Filtering under XPM Performance of the spectral filtering of a XPM-broadened NRZ signal for RZ output format is evaluated with commercial system simulation software, OptiSystem. Fig. C.l shows the schematic of the configuration used in the simulation, with the major simulation parameters listed in Table C.l. About the Simulation Due to the limited degree of freedom for the simulation models and components in the simulation software, the structure used in evaluating the proposed nonlinear signal processing scheme is revised. The polarization-diversity loop used in the experiment is modified as a Mach-Zehnder-like structure with a polarization beam splitter and combiner at each end to individually calculate the nonlinear effects for the two orthogonal polarizations. This single-pass structure can efficiently model the co-propagating nonlinear interactions within the polarization-diversity loop with the nonlinear effects from the counter-propagating beams being neglected. As the backward-XPM introduces an averaged time irrelevant nonzero phase shift which does not contributes to the spectral broadening, such simplified single-pass structure can efficiently model the spectral broadening effect. Besides the modification of the polarization-diversity loop in the simulation, effects of timing jitter, fiber birefringence, and electrical noise are also neglected to simplify the simulation. Polarization fluctuation of the input NRZ signal is simulated by changing the polarization angle of the signal to study the polarization dependent effect in the modulation format conversion. Parameters Value / Model Unit Laser Wavelength 1551.04 nm Linewidth 10 MHz Noise threshold -100 dB Noise dynamic 3 dB VI Appendix A RZ signal Wavelength 1549.26 nm Pulse width (FWHM) 20 ps Pulse shape Hyperbolic-secant EDFA Mode Saturation mode Gain 40 dB Saturated power 36 dBm Optical BPF Shape Gaussian Order 1 3-dB bandwidth 2 or 0.65 nm Center wavelength 1549.26 or 1551 nm Fiber Bragg grating Center wavelength 1551.04 nm 3-dB bandwidth 0.25 nm Reflectivity 0.9999 (40dB) Data pattern Pattern length 128 bits Pattern style DBBS ("") Electrical lowpass filter Shape Bessel Order 4 Cutoff frequency 30 GHz Fiber (PCF) Model Nonlinear SchrOdinger equation Propagator type Exponential Step size Adaptive Max. nonlinear phase error 3 m rad Dispersion From measurement in Chapter 3 Length 0.064 km Core area 6.125 iW Nonlinear refractive index, n) 2.75x1m^AV OptiSystem: Version 4.0.1.268 � A de Bruijn bit sequence (DBBS) of length 2L is a pseudo-random bit sequence (PRBS) of length 2L-1 with an additional zero bit added to the longest run of zeros in the PRBS. Table C.l List of the major parameters and simulation models used in the polarization insensitive spectral filtering simulation. VII Appendix B …邏 画 …遲 [-^.1 OSA OSA OSA ……-jl/i/l'l I no： Opticat TtiM Doman \Asuaiz«c • •jl^M JttftttL J~m=iJ OutpaSgMl .� DID.. s-r—dr^M ^ Oolical P»Js«(S«ch) PC PRBS Folk (1x2) FreouMKV 1549.26 nrfiottfion an 9l«<=45 d«g : Power >=17 d^ " — i EDFA <\PG) BPF (Gaussian) jo ⑨ t>_ i Sfl*ifationDO\wd=B 36 dBrpraou^ncBancfwvkth«v = 21549.2 nm6 nm 64 m PCF I J � I Length«0.064 km�[——I I_！_I I 1 Power Combiner 2)(13BS 64m PCF PBC ^ 1 IM M • CW Las^r ： PC Length«0.064 km l^f Braoa Graina BPF «Gaus$m> EDfA ！R««iv«r <1 IN) Fr«ou#ncv* 1551.04 rrni RotaBon angle - 0 deg 沪 , Ff»ou#ocv«1551.04 nm Fr«ou«ncv ‘ 1551 nm Om\'2S dB Pow*r = 10 :dBm Ban(*Aridrh = 0.25 nm Bandwidth «= 0.65 nm Nois« figur"4d B 办 I Ground I I III Eye Diagram Analyzer NRZ Ptis® Gensrator LPF (B«ss»n __ Cutoff frequency = 30 GHz Fig. C. 1 Schematic of the configuration used in the polarization insensitive spectral filtering simulation. VIII List of Publications List of Publications Journal Publications [P-l] C. W. Chow, C. H. Kwok, H. K. Tsang and Chinlon Lin, "Optical label switching of DRZ/DPSK orthogonal signal generated by photonic crystal fiber," Opt. Lett., vol. 31，no. 17, pp. 2535-2537, 2006. [P-2] C. H. Kwok and Chinlon Lin, "Polarization Insensitive All-optical NRZ-to-RZ Format Conversion by Spectral Filtering of a Cross Phase Modulation Broadened Signal Spectrum," IEEE J. Sel. Topic Quantum Electron., vol. 12, no. 2, pp. 451^58, 2006 [P-3] C. H. Kwok, C. W. Chow, H. K. Tsang, Chinlon Lin and A. Bjarklev, "Nonlinear polarization rotation in a dispersion-flattened photonic-crystal fiber for ultrawide band (> 100 nm) all-optical wavelength conversion of 10 Gbit/s nonreturn—to~zero signals," Opt. Lett., vol. 31，no. 12, pp. 1782-1784,2006. [P-4] C. W. Chow, C. H. Kwok, H. K. Tsang and Chinlon Lin, "3-bit/symbol optical data format based on simultaneous DRZ, DPSK and PolSK orthogonal modulations," Opt. Express, vol. 14，no. 5, pp. 1720-1725,2006. [P-5] C. H. Kwok, S. H. Lee, K. K. Chow, C. Shu and Chinlon Lin, "Widely Tunable Wavelength Conversion with Extinction Ratio Enhancement using PCF Based NOLM," IEEE Photon. TechnoL Lett., vol. 17’ no. 12, pp. 2655-2657, 2005. [P-6] C. H. Kwok, S. H. Lee, K. K. Chow and Chinlon Lin, "Photonic Crystal Fiber Based All-Optical Modulation Format Conversions between NRZ and RZ with Hybrid Clock Recovery from a PRZ signal," lEE Proc. Optoelectron., (to be published), 2006. Conference Publications [P-7] Y. Liu, C. H. Kwok, C. W. Chow, P. S. Chan, H. K. Tsang and Chinlon Lin, "Multiple-wavelength Dynamic Gain Transient Compensation Based on Silicon Platform," in Proc. of the 19 th IEEE Lasers & Electro-Optics Society (LEOS) Annual Meeting, Montreal, QC, Canada, WU 3，2006. [P-8] C. H. Kwok, C. W. Chow, H. K. Tsang and Chinlon Lin, "Simultaneous Four Channels Modulation Format Conversion in a Nonlinear Optical Loop Mirror with Suppressed Four-Wave-Mixing Crosstalk," in Proc. European Conf. on Optical Communications (ECOC 2006), Cannes, France, Paper We3.P.l 1,2006. IX List of Publications [P-9] Rebecca W. L. Fung, Henry K. Y. Cheung, P. P. Kuo, C. H. Kwok and Kenneth K.Y. Wong, "Wavelength Exchange Using Two Pumps in Anomalous Regime," in Proc. European Conf. on Optical Communications (ECOC2006), Cannes, France, Paper Thl.3.2, 2006. [P-10] C. H. Kwok, Chinlon Lin, Rebecca W. L. Fung, Henry K. Y. Cheung, P. P. Kuo and Kenneth K.Y. Wong, "First Demonstration of Pulsed Pumping Wavelength Exchange," in Proc. OptoElectronics and Communications Conf. (OECC 2006), Kaohsiung, Taiwan, Postdeadline Paper PDP2, 2006. [P-11] C. H. Kwok and Chinlon Lin, "Multi-Wavelength Nonlinear Optical Loop Mirror with Suppressed Four-Wave Mixing Components," in Proc. OptoElectronics and Communications Conf. (OECC 2006), Kaohsiung, Taiwan, Paper 4D2-1, 2006. [P-12] Y. Liu, C. H. Kwok, C. W. Chow, P. S. Chan, H. K. Tsang and Chinlon Lin, "High Speed Gain Transient Compensation," in Proc. OptoElectronics and Communications Conf. (OECC 2006), Kaohsiung, Taiwan, Paper 6B1-4,2006. [P-13] Rebecca W. L. Fung, C. H. Kwok and Kenneth K.Y. Wong, "Raman Effect on Parallel and Orthogonal Wavelength Exchange," in Proc. OptoElectronics and Communications Conf. (OECC 2006), Kaohsiung, Taiwan, Paper 4D2-7,2006. [P-14] C. H. Kwok S. H. Lee, K. K. Chow, C. Shu and Chinlon Lin, "Polarization-Insensitive All-Optical Wavelength Multicasting by Self-Phase-Modulation in a Photonic-Crystal Fiber," in Proc. IEEE Conf. Lasers and Electro-Optics/Quantum Electron, and Lasers Sci. Conf. (CLEO/QELS 2006), Long Beach, California, Paper CTuD4, 2006 [P-15] C. H. Kwok and Chinlon Lin, "Raman Enhanced Wavelength Conversion by Cross-Polarization Modulation in a Highly Nonlinear Dispersion-Shifted Fiber," in Proc. IEEE Conf. Lasers and Electro-Optics/Quantum Electron, and Lasers Sci. Conf. (CLEO/QELS 2006), Long Beach, California, Paper JThC60, 2006. [P-16] C. W. Chow, C. H. Kwok, Y. Liu, H. K. Tsang and Chinlon Lin, "High Extinction-Ratio Orthogonal Label Switching of DRZ/DPSK Generated by Photonic Crystal Fiber," in Proc. IEEE Conf. Lasers and Electro-Optics/Quantum Electron, and Lasers Sci. Conf. (CLEO/QELS 2006), Long Beach, California, Paper CMNN6, 2006. [P-17] C. W. Chow, C. H. Kwok, Y. Liu, H. K. Tsang and Chinlon Lin, "3-Bit/Symbol Optical Modulation-Demodulation Simultaneously Using DRZ, DPSK and PolSK," in Proc. IEEE Conf. Lasers and Electro-Optics/Quantum Electron, and Lasers Sci. Conf, (CLEO/QELS 2006), Long Beach, California, Paper CFH2, 2006. X List of Publications [P-18] C. H. Kwok, C. W. Chow, H. K. Tsang, Chinlon Lin and A. Bjarklev, "S/C/L-Band Wavelength Conversion by Cross-Polarization Modulation in a Dispersion-Flattened Nonlinear Photonic-Crystal Fiber," in Proc. Optical Fiber Conf. and National Fiber Optic Eng. Conf., (OFC/NFOEC 2006), Anaheim, CA, Paper 0ThA4, 2006. [P-19] C. H. Kwok, C. W. Chow, H. K. Tsang and Chinlon Lin, "All-Optical ASK Header and DPSK Payload Separator," in Proc. Optical Fiber Conf. and National Fiber Optic Eng. Conf., (OFC/NFOEC 2006)’ Anaheim, CA, Paper OWI83, 2006. [P-20] C. H. Kwok and Chinlon Lin, "Polarization insensitive all-optical NRZ-to-RZ format conversion by spectral filtering of a cross phase modulation broadened signal spectrum," in Proc. 6-th IEEE Hong Kong LEOS Postgraduate Conf., Hong Kong, Paper PSP12, 2005. [P-21] C. H. Kwok, S. H. Lee, K. K. Chow, C. Shu and Chinlon Lin, "Widely Tunable Wavelength Conversion with Extinction Ratio Enhancement Using PCF Based NOLM," in Proc. European Conf. on Optical Communications (ECOC 2005), Glasgow, Scotland, Paper Tu4.4.6, 2005. [P-22] C. H. Kwok, K. K. Chow, C. Shu and Chinlon Lin, "All-Optical Sampling System using Nonlinear Optical Loop Mirror with Soliton Self-Frequency Shifted Control Pulses," in Proc. International Quantum Electron. Conf. and the lEEE/OSA Pacific Rim Conf. Lasers and Electro-Optics (IQEC/CLEO-PR 2005), Tokyo, Japan, Paper CTuC3-P6, 2005. [P-23] C. H. Kwok, K. K. Chow, C. Shu and Chinlon Lin, "All-Optical sampling using an injection-locked Fabry-Perot laser diode," in Proc. 5-th IEEE Hong Kong LEOS Postgraduate Conf., Hong Kong, Paper PSP2, 2005. Publications Related to Wavelength Conversion [P-3，P-5，P-10, P-17, P-20] Publications Related to Modulation Format Conversion [P-2, P-^, P-7, P-14, P-19] XI • .‘ . • , . . ‘ • • • ••‘ ...‘ • • ’ ，. . 1-. , . . , • • ’，._•:,..,.,...、.• ... ； .. . 、 • . • 、 ‘ . • , ... ‘ ••,.、.... . • , ...... -•,‘..•• ...::、 CUHK Libraries 004359251