Electrically Controlled Optical Polarization Rotation on a Silicon Chip Using Berry's Phase THESIS

Electrically Controlled Optical Polarization Rotation on a Silicon Chip Using Berry’s Phase

THESIS

Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University

Qiang Xu, B. Sc.

Graduate Program in Electrical and Computer Science

The Ohio State University

2015

Master's Examination Committee:

Prof. Ronald M. Reano, Advisor

Prof. Fernando L. Teixeira

Qiang Xu

2015

Abstract

Since the introduction of thin film integrated optics in 1969, the dominant light guiding paradigm has been based on planar optical waveguides. The continued convergence of electronics and photonics on the chip scale can benefit from the voltage control of optical polarization for applications in communications, signal processing, and sensing. It is challenging, however, to electrically manipulate the polarization state of light in planar optical waveguides. Here, we exploit all three physical dimensions by realizing optical waveguides that guide light out-of-plane. Three-dimensional photonic integrated circuits allow access to Berry's phase, a quantum mechanical phenomenon of purely topological origin, enabling electrically tunable optical polarization rotation on the chip-scale for the first time. Devices fabricated in the high-confinement silicon-on-insulator material platform are no longer limited to a single static polarization state. Rather, they can exhibit dynamic tuning of optical polarization between transverse electric and transverse magnetic fundamental modes at infrared wavelengths. Electrical tuning of optical polarization over a 19 dB range of polarization extinction ratio is demonstrated with less than 1 dB of conversion loss. Compact polarization diverse system architectures involving dynamic control of optical polarization in photonic integrated circuits are envisioned.

Dedication

To my family.

iii

Acknowledgments

I would like to express my sincere gratitude to my advisor, Professor Ronald M. Reano, for this continuous support and guidance in the past three years. I would also like to thank

Professor Fernando L. Teixeira for your valuable time serving on my committee.

I would like to thank my team members in the research group: Dr. Li Chen, Dr. Peng Sun,

Justin Burr, Michael Wood, for their helpful advices and discussions. I would also thank staff members at the Nanotech West Laboratory of the Ohio State University, in particular,

Aimee Price, Paul Steffen and Derek Ditmer, for their help during the fabrication.

Above all, I am grateful for my parents for their love and encouragement in every stage of my life.

Vita

2008...... B.S. Electrical Engineering, Shanghai Jiao

Tong University, China

2012 to present ...... Graduate Research Associate, The Ohio

State University, Columbus, OH

Publications

Qiang Xu, Li Chen, Michael G. Wood, Peng Sun, and Ronald M. Reano, “Electrically tunable optical polarization rotation from Berry’s phase on a silicon chip,” Nat. Commun.

5 (2014).

Li Chen, Qiang Xu, Michael G. Wood, and Ronald M. Reano, “Hybrid silicon and lithium niobate electro-optical ring modulator,” Optica 1 (2014).

Fields of Study

Major Field: Electrical and Computer Engineering

Table of Contents

Abstract ...... ii

Dedication ...... iii

Acknowledgments...... iv

Vita ...... v

List of Figures ...... viii

Chapter 1: Introduction ...... 1

1.1 Background ...... 1

1.2 Conventional polarization conversion methods ...... 2

1.3 Berry’s phase ...... 3

Chapter 2: Berry’s phase on a silicon chip: accessing and simulation ...... 6

2.1 Accessing Berry’s phase ...... 6

2.2 Numerical Simulation ...... 8

2.2.1 Mode decomposition for extraction of polarization rotation angle ...... 8

2.2.2 Simulation results ...... 9

2.2.3 Considering sidewall angle ...... 11

Chapter 3: Device design and operation theoretical analysis ...... 14

3.1 Device design ...... 14

3.2 Device operation coupled mode theory description ...... 16

Chapter 4: Measurement results and analysis ...... 20

4.1 Measurement setup ...... 20

4.2 Experimental observation of polarization rotation due to Berry’s phase ...... 20

4.3 Comparison with calculation ...... 24

Chapter 5: Summary ...... 26

Bibliography ...... 27

Appendix A: Fabrication processes ...... 32

A.1 Waveguide patterning...... 32

A.2 ICP and PECVD ...... 33

A.3 Titanium micro-heater ...... 34

A.4 Aluminum electrode pad ...... 34

A.5 Releasing process ...... 35

vii

List of Figures

Figure 1. Off-axis double core structure diagram of the polarization rotator ...... 2

Figure 2. Cut corner triangle core structure diagram of the polarization rotator ...... 3

Figure 3. Momentum-space representation of Berry’s phase. In optics, Berry’s phase manifests as optical polarization rotation. (a) For planar paths, no significant optical polarization rotation is observed. (b) A two-dimensional momentum-space with non-zero

(Gaussian) curvature...... 4

Figure 4. Berry’s phase observation where it is manifested as optical polarization rotation in optical fiber, (a) Helical optical fiber experiment, (b) Fiber helix in a ring experiment. 4

Figure 5. Concept to realize Berry’s phase in silicon photonic integrated circuits. (a)

Physical space: Waveguide layout involving out-of-plane waveguides. (b) Momentum space: Non-zero solid angle subtended by the shaded surface corresponds to the Berry’s phase which manifests as polarization rotation. The numbers in parentheses correspond to paths in physical-space in (a)...... 7

Figure 6. FDTD modeling of optical polarization rotation from Berry’s phase. (a)

Rotation angle versus deflection angle with bend radius as parameter for TE polarized input light at 1,550 nm wavelength. Inset: Schematic of out-of-plane waveguide in computational domain. (b) Rotation angle versus wavelength with deflection angle as viii parameter for TM polarized input light. (c) Waveguide mode at 1,550 nm wavelength for deflection angle equal to 0, 15, 30, and 45 in sequence. The silicon waveguide core cross-section is 300 nm square. The core is clad in silicon dioxide on all sides...... 10

Figure 7. FDTD modeling of polarization rotation from Berry’s phase with angled sidewalls. The waveguide cross-section full-width-half-height is designed to be equal to the waveguide height. The sidewall angle is denoted w. The out-of-plane computational domain is the same as the inset of Figure 6(a)...... 12

Figure 8. Electrically tunable polarization rotation. (a) Schematic of device, (b) Top- down optical micrograph of fabricated device, (c) Optical interferometric surface profilometer measurements of out-of-plane waveguide. The silicon waveguide core bottom width is 310 nm and the height is 300 nm. The sidewall angle is 86...... 15

Figure 9. Schematic of bus waveguide to ring system. (a) Bus waveguide to ring coupling without external feedback. The optical wave amplitude into and out of the coupling region are a1, a2, b1, and b2, (b) Bus waveguide to ring coupling with external feedback.

The optical wave amplitudes into and out of the Mach-Zehnder coupling region are a1, a2, d1, and d2. Parameters L1 and L2 are the lengths of the waveguide inside the ring between the two coupling regions. Parameter L3 is the length of the waveguide in the feedback arm...... 17

Figure 10. Optical transmission measurements. The input optical polarization is TE.

Green-colored windows indicate a full FSR of identical resonance order. Electrical power

P dynamically converts the optical polarization from TE to TM. Blue curve indicates TE polarization. Red curve indicates TM polarization...... 21

Figure 11. Measurements of polarization extinction ratio. (a) Maximum and minimum polarization extinction ratio versus wavelength for a specific electrical power. (b) PER versus electrical power with wavelength as parameter. Continuous tuning between TE and TM optical polarization is observed. Wavelengths are selected from green shaded region in Figure 11(a)...... 23

Figure 12. Calculated optical transmission. (a) TE and (b) TM mode output. The input is

TE optical polarization. Only identical order resonances are shown for clarity. Black arrows mark the phase matched resonance points where βL1 + βL3 + δφ = 2πm and m is an integer...... 24

Chapter 1: Introduction

1.1 Background

Silicon photonics is a promising candidate for chip-scale integrated optics due to its compatibility with CMOS technology and potential for monolithic integration with electronic devices [1]. In microelectronic integrated circuits, charged carriers utilize metal interconnects, whereas in photonic integrated circuits, photons are guided in optical waveguides. Guided optical waves exhibit inherent properties including amplitude, phase, frequency, wavelength, and polarization. Chip scale silicon strip waveguides are strongly polarization dependent at infrared wavelengths because of the high refractive index contrast to silicon dioxide and the sub-micrometer light confinement [2]. A challenge for high confinement silicon photonic integrated circuits is to achieve polarization independence. Large polarization mode dispersion (PMD), polarization dependent loss

(PDL), and polarization dependent wavelength characteristics are caused by structural birefringence in silicon strip waveguides. While operation in a single polarization state has been demonstrated to be effective for communications, signal processing, and sensing [3-

5], the lack of dynamic polarization control is a significant lacuna in the technology.

Electrical control of optical polarization would create new avenues, including routes to

1 advances in modulation [6-9], coherent communications [10], quantum computing [11-12], and polarization diversity [13-14].

1.2 Conventional polarization conversion methods

To effectively achieve polarization independent photonic integrated circuits, devices and architectures that attempt to rotate and control optical polarization are being pursued.

These devices and architectures are referred to as systems with polarization diversity or polarization transparency. It is challenging, however, to achieve on-chip polarization control. Approaches include asymmetric gratings, dual core waveguides with asymmetric axes (Figure 1), waveguides with asymmetric slanted sidewalls (Figure 2), waveguides with asymmetric trenches, triple waveguide couplers, and bi-layer slots [15-20].

Figure 1. Off-axis double core structure diagram of the polarization rotator

Figure 2. Cut corner triangle core structure diagram of the polarization rotator

These current methods to realize polarization rotation in silicon suffer from several drawbacks. First, they are static, in the sense that they rotate the polarization by only a fixed amount. Second, they rely on asymmetric geometries with impedance mismatches resulting in degradation of insertion loss. And third, they exhibit wavelength dependent loss because they rely on periodic structures or mode coupling.

1.3 Berry’s phase

To overcome these challenges, we propose and demonstrate chip-scale polarization rotation utilizing Berry’s phase [21]. Berry’s phase is a quantum-mechanical phenomenon that may be observed at the macroscopic optical level through the use of an enormous number of photons in a single coherent state [22]. A direct macroscopic measurement of

Berry's phase may be obtained through an observation of the polarization rotation of plane- polarized light when it is transported along a closed path in momentum space [23] (Figure

3).

Few experiments on the manifestations of Berry’s phase for photons have been reported, and those that have been can be divided into those that use optical fibers [23-25], shown in

Figure 4,

Figure 4. Berry’s phase observation where it is manifested as optical polarization rotation in optical fiber, (a) Helical optical fiber experiment, (b) Fiber helix in a ring experiment.

4 and those that use discrete optical components [26-27]. The angle of rotation of the polarized light does not come from a local elasto-optic effect caused by torsional stress and the effect is independent of detailed material properties. The rotation angle arises only from the overall geometry of the path taken by the light. It is a global topological effect

[23]. In the special case of planar (non-helical) paths, such as the paths typically taken by planar optical waveguides, no significant optical rotation is observed independent of the complexity of the path [23]. The key to manifest Berry's phase in photonic integrated circuits is to introduce out-of-plane three-dimensional waveguides to create a two- dimensional momentum-space with non-zero (Gaussian) curvature.

Chapter 2: Berry’s phase on a silicon chip: accessing and simulation

2.1 Accessing Berry’s phase

Berry’s phase is accessed by an out-of-plane 3D waveguide structure. We introduce the physical waveguide layout shown in Figure 5(a) and its momentum space in Figure 5(b).

Monochromatic light at wavelength  carries a momentum which is given by the equation

 p  xˆpx  yˆpy  zˆpz  k , where k is the propagation vector with magnitude 2/ and is Planck's constant divided by 2. In physical space, the layout consists of three main portions. The first portion, shown in red in Figure 5(a), consists of an ascending out-of- plane 180 waveguide bend. The second portion, shown in green, consists of an out-of- plane waveguide that descends to the chip surface. Finally, the third portion consists of an in-plane 180 bend. In momentum-space, the corresponding paths for each waveguide portion are shown in Figure 5(b). Light propagation along the three-dimensional path in physical space results in a non-zero subtended solid angle in momentum-space, shown as the shaded area in Figure 5(b). Therefore, the waveguide geometry will exhibit Berry's phase. A change in wavelength results in a change of the radius of the sphere in momentum-space but not the solid angle. Therefore, the effect is intrinsically broadband.

If the deflection angle of waveguide portion 1 in the physical space shown in Figure 5(a) is θ, then the output light will appear with polarization rotation equal to 2θ due to Berry's 6 phase because the magnitude of the solid angle extended by the gray area in momentum space, shown in Figure 5(b), is 2θ.

Figure 5. Concept to realize Berry’s phase in silicon photonic integrated circuits. (a) Physical space: Waveguide layout involving out-of-plane waveguides. (b) Momentum space: Non-zero solid angle subtended by the shaded surface corresponds to the Berry’s phase which manifests as polarization rotation. The numbers in parentheses correspond to paths in physical-space in (a).

2.2 Numerical Simulation

A commercial-grade simulator [28] based on the finite-difference time-domain method

[29-31] was used to perform the calculations. Polarization analysis is done by mode decomposition for extraction of polarization rotation angle.

2.2.1 Mode decomposition for extraction of polarization rotation angle

The polarization rotation angle is determined by mode decomposition. In our structure, the bend radius is large. Therefore, we approximate the bent waveguide modes with straight waveguide modes. We assume monochromatic light at frequency . The complex amplitude for the transverse electric-field components of the fundamental transverse electric (TE) and transverse magnetic (TM) modes are written

 jx ETE  yˆETE ,y  zˆETE ,z e (1) and

 jx ETM  yˆETM ,y  zˆETM ,z e (2)

where ETE,y and ETM,z are the major field components for the fundamental TE and TM modes, respectively, and ETE,z and ETM,y are the minor field components for the fundamental TE and TM modes, respectively. The mode propagation constant, denoted

8 with β, is assumed to be the same for the fundamental TE and TM modes in the nominally square waveguide cross-section. Propagation is in the x-direction.

Rotated polarization states are described in terms of the fundamental modes as

E  axETE  bxETM (3)

where amplitudes a(x) and b(x) are functions of propagation distance. For TE polarized input, the polarization rotation angle 2 is computed as

tan2   b / a (4)

For TM polarized input, the right hand side of Eq. (4) is inverted. Inserting Eq. (1) and (2) into Eq. (3) yields

ˆ E  yaxETE ,y  bxETM ,y  zˆaxETE ,z  bxETM ,z  (5)

2.2.2 Simulation results

We introduce the concept model into numerical simulation environment. Figure 6 shows the results of numerical simulation of polarization rotation due to the out-of-plane 180 degree silicon waveguide bend using FDTD computations at 1,550 nm wavelength. The geometry for the simulation domain is shown in the inset of Figure 6(a). Figure 6(a) shows

9 the polarization rotation of transverse electric (TE) polarized input light versus vertical deflection angle θ for bend radii R equal to 5 µm and 10 µm.

Figure 6. FDTD modeling of optical polarization rotation from Berry’s phase. (a) Rotation angle versus deflection angle with bend radius as parameter for TE polarized input light at 1,550 nm wavelength. Inset: Schematic of out-of-plane waveguide in computational domain. (b) Rotation angle versus wavelength with deflection angle as parameter for TM polarized input light. (c) Waveguide mode at 1,550 nm wavelength for deflection angle equal to 0, 15, 30, and 45 in sequence. The silicon waveguide core cross-section is 300 nm square. The core is clad in silicon dioxide on all sides.

The simulated polarization rotation angle is in good agreement with 2θ. The polarization rotation angle does not change with radius because the solid angle 2θ is constant with radius. Figure 6(b) shows the polarization rotation angle of transverse magnetic (TM) polarized input light versus wavelength for θ equal to 15 and 30 degrees. The polarization rotation is weakly dependent of wavelength, with less than 0.2° variation from 1,460 nm to 1,580 nm. For TE input polarization at 1,550 nm wavelength, Figure 6(c) shows the output electrical fields of the waveguide mode horizontal component, Ey, and vertical component, Ez, for θ equal to 0, 15, 30, and 45. The corresponding polarization rotation angles are 2θ.

2.2.3 Considering sidewall angle

Fabricated silicon waveguides with nominally square cross-section can exhibit sidewall angles less than 90. Here, we use finite difference time domain (FDTD) modeling to determine the effect of sidewall angle on polarization rotation from Berry's phase at 1550 nm optical wavelength.

The simulated cross-section, shown in the inset to Figure 7, consists of a silicon waveguide core surrounded on all sides by a silicon dioxide cladding. The waveguide core height is

300 nm and the full-width-half-height (FWHH) is 300 nm. The sidewall angle is denoted

w.

Modeling results for single pass polarization rotation versus deflection angle  for sidewall angles from 80 to 90 are shown in Figure 7. The polarization rotation is in good agreement with 2 for deflection angles  from 0 to 25. For  equal to 45, sidewall angles greater than 82 produce polarization rotation within 90% of the ideal 90 sidewall angle.

In our fabricated devices, the sidewall angle is measured to be 86 and the deflection angle is 1.5.

Chapter 3: Device design and operation theoretical analysis

3.1 Device design

In fabricated devices, deflection angles larger than a few degrees are challenging to achieve. Therefore, for a first proof-of-concept experiment, a compact microring cavity with small deflection angle is utilized to accumulate polarization rotation over multiple round trips [25][32]. The narrow band spectral features of the ring resonator superimpose on the broadband polarization rotation from Berry's phase. A schematic of the out-of-plane ring cavity is shown in Figure 8(a).

The out-of-plane portion of the ring consists of a waveguide bend and an inclined straight section. The out-of-plane deflection is produced by thin film stress in the silicon dioxide bilayer. Light is coupled to the ring by a Mach-Zehnder coupling region with a Ti micro- heater for thermo-optic control of waveguide-coupled feedback [33-35]. Electrical tuning enables dynamic control of the polarization rotation. Figure 8(b) shows a top-down optical micrograph of the fabricated device. The out-of-plane ring radius is 20 m and the straight sections are 40 m in length. The vertical out-of-plane deflection is 1 µm, measured by optical interferometric surface profilometry and shown in Figure 8(c).

Figure 8. Electrically tunable polarization rotation. (a) Schematic of device, (b) Top-down optical micrograph of fabricated device, (c) Optical interferometric surface profilometer measurements of out-of-plane waveguide. The silicon waveguide core bottom width is 310 nm and the height is 300 nm. The sidewall angle is 86.

The deflection is currently guaranteed from passive bilayer thin film stress difference. It could have minor modification by Rapid Thermal Annealing which would change oxide stress distribution. The ring-to-bus coupling gaps are 100 nm to enable strong coupling

[33], so that the outer 343.4 µm optical path dominates the optical resonance characteristics.

Devices were fabricated on a silicon on insulator (SOI) wafer with a 300 nm thick silicon device layer and 1 µm of buried oxide (BOX). Silicon waveguides were patterned by electron-beam lithography (EBL) using an HSQ mask and etched by Cl2/O2 reactive ion etching [36]. A top cladding of silicon oxide was deposited using plasma enhanced chemical vapor deposition to a thickness of 1 µm. The microheater consists of 150 nm

15 thick titanium and 250 nm thick aluminum electrical pads, deposited by electron beam evaporation and sequentially patterned using a lift-off process. Pad-to-pad metal resistance was measured to be 2.8 kΩ. A 300 nm thick PECVD oxide was then deposited to passivate the metal. A 200 nm Cr film was then evaporated and 300 nm PECVD oxide was deposited for EBL writing to form a Cr mask for SF6 RIE release of the out-of-plane portion of the ring and the cantilever couplers [37, 38]. The Cr mask was etched by wet chemistry prior to device characterization. More fabrication details can be seen in Appendix A.

3.2 Device operation coupled mode theory description

In this section, the tunable polarization rotation from Berry’s phase in the ring resonator with waveguide-coupled feedback is described using coupled mode theory. A waveguide coupled ring resonator without feedback is shown in Figure 9(a) and with feedback in

Figure 9(b). In the case of no feedback, optical waveguide amplitudes a1, a2, b1, and b2 are related through coupling matrix C as

b1  a1   t  j    C , C    b2  a2   j t  (6)

where t is the transmission coefficient and κ is coupling coefficient. For lossless waveguide

2 2 coupling, t and κ are real numbers that satisfy t + κ = 1. In the ring, amplitude a2 and b2

L  jL are related by a2  b2e e where β is the waveguide mode propagation constant, α is the amplitude loss coefficient, and L is the ring circumference. 16

Parameters L1 and L2 are the lengths of the waveguide inside the ring between the two coupling regions. Parameter L3 is the length of the waveguide in the feedback arm.

In the case of waveguide-coupled feedback, as implemented in our experiments, optical

wave amplitudes a1, a2, d1, and d2 are related through coupling matrix C e as

d1  a1  Ce11 Ce12 a1     C e       d2  a2  Ce21 Ce22 a2  (7)

where parameters Ce11, Ce12, Ce21, Ce22 are the matrix elements of C e , where

L  jL    t  je 3 e 3 0  t  j C e    L  jL    j t  0 e 2 e 2  j t  (8)

Parameters δϕ is an additional phase shift which is implemented by the voltage controlled thermos-optic phase shifter in our experiments. In the ring, amplitudes a2 and d2 are related

L1  jL1 by a2  d2e e . The waveguide-coupled feedback enables voltage controlled bus waveguide to ring coupling coefficients [33].

To access Berry’s phase, a section of the waveguide of length L1 is released from the substrate by angle θ, implementing a single pass polarization rotation of 2θ. The coupled mode equations in (7) are extended into TE and TM optical polarization components as

d1,TE  a1,TE  d1,TM  a1,TM     C e   ,    Ce   d2,TE  a2,TE  d2,TM  a2,TM  (9)

For simplicity, we assume C e and δϕ are the same for TE and TM polarizations. Including polarization dependence in and δϕ does not change the major qualitative trends observed in the modeling results. The polarization components of a2 are related to the

polarization components of d2 by rotation matrix R as

a2,TE  d2,TE  L  jL cos 2  sin 2     R  e 1 e 1 , R    a2,TM  d2,TM  sin 2 cos 2  (10)

Using (9) – (10) together with the input polarization condition a1,TE = 1 and a1,TM = 0 for

TE polarized input, the output bus waveguide polarization components, d1,TE and d1,TM, are calculated as

2 L1  jL1 2 L1  jL1 Ce11  Ce12Ce21  2Ce11Ce22 e e cos 2  Ce11Ce22  Ce12Ce21Ce22 e e  d1,TE  2 L1  jL1 L1  jL1 1 2Ce22e e cos 2  Ce22e e 

(11)

L1  jL1 Ce12Ce21e e sin 2 d1,TM  2 L1  jL1 L1  jL1 1 2Ce22e e cos2  Ce22e e  (12)

Power transmission is given by the module square of d1,TE and d1,TM. Equations (11) and

(12) provide a complete coupled mode theory description of tunable polarization rotation from Berry's phase in the ring resonator with waveguide-coupled feedback.

Chapter 4: Measurement results and analysis

4.1 Measurement setup

To characterize the polarization rotation, the output bus waveguide is connected to an on- chip TE-TM polarization splitter with 10 dB polarization extinction ratio in the optical C band [39]. DC electrical power is applied to the thermo-optic heater from 0 mW to 76 mW in increments of 4 mW.

To experimentally characterize on-chip polarization rotation, light from an off-chip tunable infrared continuous-wave laser is connected to a fiber polarization controller that produces linearly polarized TE light with a cross polarization extinction ratio of 16 dB. Tapered fibers are used for fiber-to-chip coupling using cantilever couplers [37, 38]. Output light from the on-chip polarization splitter is collected to a photodetector and measured with a power meter. The optical transmission measurements are normalized by the off-resonance

TE power.

4.2 Experimental observation of polarization rotation due to Berry’s phase

The optical transmission spectra for TE input light as a function of wavelength and applied electrical power P to the thermo-optic heater are shown in Figure 10. Due to the phase

20 tuning of the feedback arm, the polarization state and the resonance wavelength are tuned simultaneously. Coupling between TE and TM modes produce optical transmission lineshapes that evolve from a single notch, to two separate notches, and then back to a single notch over the range of electrical powers shown.

Figure 10. Optical transmission measurements. The input optical polarization is TE. Green- colored windows indicate a full FSR of identical resonance order. Electrical power P dynamically converts the optical polarization from TE to TM. Blue curve indicates TE polarization. Red curve indicates TM polarization.

The polarization conversion efficiency is highest at the resonance wavelengths. In Figure

10, a green-colored window is used to track a full free-spectral range (FSR) of identical resonance order for each value of electrical power as the resonance wavelength is tuned at a rate of 0.04 nm/mW. Comparing Figures 10(a) and 10(f), we observe that the FSR window for the same resonance order exhibits a similar spectrum, indicating that the electrical power required to achieve a 2 optical phase shift in the feedback arm is approximately 72 mW. In Figure 10(b), the local minimum at 1,556.2 nm corresponds to a TE resonance with 9 dB transmission extinction ratio. We observe nearly complete conversion from TE input polarization to TM output polarization. Comparing Figures

10(b) and 10(d), the TM-to-TE polarization extinction ratio (PER = PTM/PTE), dynamically changes from +9 dB at 1,556.2 nm in Figure 10(b) to –10 dB at 1,557.48 nm in Figure

10(d), with less than 1 dB conversion loss. The loss is attributed primarily to propagation loss.

Figure 11(a) presents maximum PER, denoted PERMAX, and minimum PER, denoted

PERMIN, versus wavelength for a specific electrical power in the range from 0 to 76 mW.

The maximum to minimum PER can be as large as 21.4 dB. The PER versus electrical power at four specific wavelengths is shown in Figure 11(b). For each wavelength, the

PER is observed to be continuously tunable between TM and TE polarizations.

4.3 Comparison with calculation

Calculated optical transmission is shown in Figure 12. For definiteness, we consider waveguide lengths implemented in the experiment, namely L1 = 174.2 µm, L2 = 31.4 µm and L3 = 169.2 µm. TE polarization mode propagation constant  and coupling parameter t = 0.32 extracted from 3D FDTD are used for characterization. The waveguide loss is set to 3 dB/cm based on loss measurements using the cut-back method. The deflection angle

θ = 1.5 as obtained from optical surface profilometry. The on-chip TE-TM polarization splitter with 10 dB polarization extinction ratio is also implemented in the modeling.

Figure 12. Calculated optical transmission. (a) TE and (b) TM mode output. The input is TE optical polarization. Only identical order resonances are shown for clarity. Black arrows mark the phase matched resonance points where βL1 + βL3 + δφ = 2πm and m is an integer.

The calculated optical transmission captures the major trends observed in the experiments.

First, tunable polarization rotation is observed on resonance as a function of , due to the

24 thermo-optic phase shift in the section of waveguide of length L3. Second, the resonance wavelength shifts with . The wavelength shift is due to strong coupling (t2 << κ2) resulting in a dominant resonance path consisting of L1 and L3 [33]. Since the thermo- optic heater is patterned above waveguide L3, the ring resonance wavelength is tuned along with the polarization rotation. The resonance wavelength shift can be controlled independently of the polarization rotation by introducing a second thermo-optic heater

2 2 above L1. Furthermore, weak coupling (t >> κ ) can be used to change the dominant resonance path to L1 and L2.

Third, resonances are observed to evolve from a single notch, to a double notch, and then back to a single notch. The center of double notches occur at phase matched resonances

(βL1 + βL3 + δφ = 2πm, m integer), labelled using black arrows in Figure 12, where the polarization ratio is the greatest. The notches occur when the polarization rotation is greater than 90 degrees (TM polarization) because TM polarization returns to towards TE polarization.

Finally, double notches are observed to appear for TE and TM polarization when  is

1.16. In this case, |Ce11| is close to 1, switching off the microring resonator (L1 and L2).

Since the TE to TM polarization rotation is very low, the observed double notch in the TM output is due to optical power leakage from the on-chip polarization splitter with 10 dB polarization extinction ratio. This case appears in the experiment in Figure 10(d). We note that the measured transmission resonance linewidth and resonance asymmetry are larger in the experiment than in the calculation. We attribute the difference primarily to birefringence (βTE ≠ βTM) in the fabricated waveguides [32][40, 41]. 25

Chapter 5: Summary

Our first demonstration of electrically controllable optical polarization rotation utilizing

Berry's phase in silicon photonics establishes new horizons for the dynamic control of optical polarization on the chip-scale. In addition to polarization rotators, dynamic control of optical polarization rotation can be utilized to realize a new class of components in integrated photonics including polarization mode modulators, multiplexers, filters, and switches for advanced optical signal processing, coherent communications, and sensing.

Furthermore, a cascade of out-of-plane waveguides can be designed to yield broadband polarization rotation without the bandwidth constraints of a resonant ring structure.

Dynamic control of optical polarization can then be achieved by tuning the deflection angle of the out-of-plane waveguides by mechanisms such as the electrostatic [42] or piezoelectric effects [43].

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Appendix A: Fabrication processes

This appendix describes the detailed fabrication processes that are involved in this thesis.

The fabrication was conducted at the Nanotech West Laboratory at the Ohio State

University.

A.1 Waveguide patterning

1. Cleave SOI wafer and a bare Si wafer into proper sizes. The bare Si wafer is used as a companion wafer for characterization purpose only.

2. Wet etch the SOI substrate and the companion Si substrate in 10 : 1 buffered hydrofluoric acid (BHF) dip for 4 min 30 sec, which is to remove the silicon dioxide on the substrates.

3. Rinse the substrates in de-ionized (DI) water for 10 min.

4. Blow dry the substrates with nitrogen gun.

5. Dehydrate the substrates on a 200 °C hotplate for 10 min.

6. Let the substrates cool down to room temperature.

7. Apply Dow Corning XR-1541 (4% hydrogen silsesquioxane (HSQ) in Methyl Isobutyl

Ketone (MIBK)) with filters.

8. Spin coat HSQ on the substrates using a three-step recipe: 750 rpm, 300 rpm/s, 2s; 1850 rpm, 500 rpm/s, 3s; 3000 rpm/s, 2000 rpm/s, 45s.

9. Prebake the substrates in a 50 °C oven for 40 min.

10. Electron-beam lithography (EBL) in a Leica EBPG-5000 tool at high voltage = 100 kV, aperture = 200 µm, beam current = 3 nA, Beam Step Size (BSS) = 5 nm, resolution =

5nm, dose = 1250 µC/cm2 each pass, 4 passes (quad-pass writing strategy to reduce sidewall roughness).

11. Develop the unexposed HSQ resist in 25% TMAH for 1 min on a 25 °C hotplate.

External probe is required. Stir is required.

12. Rinse the substrates in DI water for 1 min.

13. Nitrogen gun blow dry.

14. Check the developed pattern under microscope.

15. Post bake: (1) place the substrates on a 150 °C hotplate for 2 min, (2) Rapid Thermal

Annealing (RTA) 1 min in O2 ambient and 1000 °C.

A.2 ICP and PECVD

ICP stands for Inductively-Coupled Plasma and PECVD stands for Plasma-Enhanced

Chemical Vapor Deposition (PECVD).

16. ICP chamber clean (Ar and oxygen): Ar 50 sccm/ O2 20 sccm/ 10 mT/ RF1 = 100 W/

RF2 = 500 W/ He 5 sccm/ 5 min.

17. ICP chamber season: Cl2 49 sccm/ O2 1.5 sccm/ 8 mT/ RF1 = 175 W, RF2 = 385 W/

He 5 sccm/ 5 min.

18. ICP etching on substrates: Cl2 49 sccm/ O2 1.5 sccm/ 8 mT/ RF1 = 175 W, RF2 = 385

W/ He 5 sccm/ 110 sec.

19. PECVD 1 µm. Recipe: 900 mTorr, 100 sccm SiH4, 300 sccm N2O, 250 °C.

A.3 Titanium micro-heater

20. Surface organic clean: Acetone bath 1 min, IPA bath 2 min.

21. Nitrogen gun blow dry.

22. Dehydrate on a 200 °C hotplate for 10 min.

23. Spin coat PMMA EL11, 2000 rpm, 500 rpm/s, 90s.

24. Bake: 200 °C hotplate for 5 min.

25. Spin coat PMMA A4, 1500 rpm, 500 rpm/s, 90s.

26. Bake: 200 °C hotplate for 5 min.

27. EBL exposure at 50 kV, beam current 3 nA, aperture = 200, BSS = 10 nm, resolution

= 10 nm, dose = 1000 uC/cm2, single pass.

28. Develop the pattern: (1) Stir in 3:1 IPA:MIBK for 3 min, (2) IPA bath for 30 sec, (3)

IPA spray for 30 sec.

29. Nitrogen gun blow dry.

30. Check developed pattern under microscope.

31. Ashing for 1 min.

32. Evaporate 150 nm thickness Ti using E-Gun evaporator in Bay 4.

33. Lift-off: NMP on 125 °C hotplate, can be combined with assisted NMP spray, until lift- off is clean.

34. Check lift-off effect under microscope. If lift-off is not finished, return to step 32.

A.4 Aluminum electrode pad

35. Surface organic clean: Acetone bath 1 min, IPA bath 2 min.

36. Nitrogen gun blow dry.

37. Dehydrate on a 200 °C hotplate for 10 min.

38. Spin coat PMMA EL11, 2000 rpm, 500 rpm/s, 90s.

39. Bake: 200 °C hotplate for 5 min.

40. Spin coat PMMA A4, 1500 rpm, 500 rpm/s, 90s.

41. Bake: 200 °C hotplate for 5 min.

42. EBL exposure at 50 kV, beam current = 70 nA, aperture = 200, BSS = 50 nm, resolution

= 10 nm, dose = 850 uC/cm2, single pass.

43. Develop the pattern: (1) Stir in 3:1 IPA:MIBK for 3 min, (2) IPA bath for 30 sec, (3)

IPA spray for 30 sec.

44. Nitrogen gun blow dry.

45. Check developed pattern under microscope.

46. Ashing for 2 min.

47. Evaporate 250 nm thickness Al using E-Gun evaporator in Bay 4.

48. Lift-off: NMP on 125 °C hotplate, can be combined with assisted NMP spray, until lift- off is clean.

49. Check lift-off effect under microscope. If lift-off is not finished, return to step 48.

A.5 Releasing process

50. Deposit high pressure (1.9 Torr) PECVD 300 nm as protection layer (when surface has no metal connections, this step is not required).

51. Evaporate 200 nm Cr using E-Gun evaporator in Bay 4.

52. SEM to check coverage.

53. Deposit high pressure (1.9 Torr) PECVD 300 nm.

54. Spin coat PMMA EL11, 2000 rpm, 500 rpm/s, 90s.

55. Bake: 200 °C hotplate for 5 min.

56. EBL exposure at 50 kV, resolution = 10 nm, BSS = 50 nm, aperture = 200, single pass, beam current = 10 nA, dose = 300 uC/cm2.

57. Develop the pattern: (1) Stir in 3:1 IPA:MIBK for 3 min, (2) IPA bath for 30 sec, (3)

IPA spray for 30 sec.

58. ICP oxide:

(a) Clean chamber: Ar 50 sccm/ O2 20 sccm/ 10 mT/ RF1 = 100 W/ RF2 = 500 W/

He 5 sccm/ 5 min.

(b) Season chamber: CHF3 30 sccm/ 35 mT/ DC = 400 V/ RF2 = 300 W/ He = 5

sccm/ 5 min.

59. NMP 125 °C : At this step, removing MMA is a little hard. It usually takes > 10 min, better around 15 min. If there are still residues, ashing will help remove them and become clean. Take out and cool down for some seconds, IPA spray 30 sec.

60. Ashing 3 min.

61. ICP Cr

(a) Clean chamber: Ar 50 sccm/ O2 20 sccm/ 10 mT/ RF1 = 100 W/ RF2 = 500 W/

He 5 sccm/ 5 min

(b) Season chamber: Cl2 20 sccm/ O2 5 sccm/ 5 mT/ RF1 = 150 W/ RF2 = 500 W/

He = 5 sccm/ 5 min

62. ICP Oxide

(a) Clean chamber: Ar 50 sccm/ O2 20 sccm/ 10 mT/ RF1 = 100 W/ RF2 = 500 W/

He 5 sccm/ 5 min

(b) Season chamber: CHF3 30 sccm/ 35 mT/ DC = 400 V/ RF2 = 300 W/ He = 5

sccm/ 5 min.

63. LAM Etch: 16.5 min for ~15 µm etched depth in silicon substrate updated to 02/2015

(rate varies so pre etching rate test is required at this step).

64. SEM now can measure dimensions and do some angled view figures.

65. ICP Ar milling

(a) Clean chamber: Ar 50 sccm/ O2 20 sccm/ 10 mT/ RF1 = 100 W/ RF2 = 500 W/

He 5 sccm/ 5 min

(b) Season chamber: Ar 50 sccm/ 10 mT/ RF1 = 100 W/ RF2 = 150 W/ He 5 sccm/

5 min

66. CR-7S wet etch Cr 15 min.

67. DI rinse 5 min.

68. Nitrogen gun blow dry.

69. Nanospec surface oxide fit check.