Design of an Ultrahigh Birefringence Photonic Crystal Fiber with Large Nonlinearity Using All Circular Air Holes for a Fiber-Optic Transmission System

hv photonics

Article Design of an Ultrahigh Birefringence Photonic Crystal Fiber with Large Nonlinearity Using All Circular Air Holes for a Fiber-Optic Transmission System

Shovasis Kumar Biswas 1,* ID , S. M. Rakibul Islam 1, Md. Rubayet Islam 1, Mohammad Mahmudul Alam Mia 2, Summit Sayem 1 and Feroz Ahmed 1 ID

1 Department of Electrical and Electronic Engineering, Independent University Bangladesh, Dhaka 1229, Bangladesh; [email protected] (S.M.R.I.); [email protected] (M.R.I.); [email protected] (S.S.); [email protected] (F.A.) 2 Department of Electronics & Communication Engineering, Sylhet International University, Sylhet 3100, Bangladesh; [email protected] * Correspondence: [email protected]; Tel.: +880-1717-827-665

Received: 11 August 2018; Accepted: 29 August 2018; Published: 5 September 2018

Abstract: This paper proposes a hexagonal photonic crystal fiber (H-PCF) structure with all circular air holes in order to simultaneously achieve ultrahigh birefringence and high nonlinearity. The H-PCF design consists of an asymmetric core region, where one air hole is a reduced diameter and the air hole in its opposite vertex is omitted. The light-guiding properties of the proposed H-PCF structure were studied using the full-vector finite element method (FEM) with a circular perfectly matched layer (PML). The simulation results showed that the proposed H-PCF exhibits an ultrahigh birefringence of 3.87 × 10−2, a negative dispersion coefficient of −753.2 ps/(nm km), and a nonlinear coefficient of 96.51 W−1 km−1 at an excitation wavelength of 1550 nm. The major advantage of our H-PCF design is that it provides these desirable modal properties without using any non-circular air holes in the core and cladding region, thus making the fiber fabrication process much easier. The ultrahigh birefringence, large negative dispersion, and high nonlinearity of our designed H-PCF make it a very suitable candidate for optical backpropagation applications, which is a scheme for the simultaneous dispersion and nonlinearity compensation of optical-fiber transmission links.

Keywords: photonic crystal ﬁber; dispersion compensating ﬁber; birefringence; nonlinearity

1. Introduction Photonic crystal fibers (PCF) recently drew significant attention, as they exhibit extraordinary optical characteristics such as high birefringence, large effective mode area, high nonlinearity, and very low confinement loss as compared to other conventional optical fibers [1–3]. A typical PCF microstructure is composed of a lattice of air holes surrounded by a silica background. The waveguiding takes place at the fiber core, which may be solid or hollow. PCFs with high-index cores were shown to exhibit similar features to conventional optical fibers, where the light-guiding properties are largely based on a physical mechanism called total internal reflection (TIR). However, in order to achieve TIR in conventional fibers, a higher refractive index of the core compared to the surrounding media is required. In recent years, photonic bandgap (PBG) materials were realized for localizing and controlling light in cavities and waveguides. Periodically structured materials such as PCFs exhibit the PBG property, since certain photonic bandgaps may be forbidden by selectively choosing the lattice structure and dimensions within the crystal [4].

Photonics 2018, 5, 26; doi:10.3390/photonics5030026 www.mdpi.com/journal/photonics Photonics 2018, 5, 26 2 of 11

In high-bit-rate fiber-optic transmission systems, the major impairment for optical pulses is group velocity dispersion. Dispersion causes pulse broadening and must be compensated for when transmitting data over long distances. One of the effective methods of compensating for dispersion is simply using a highly negative dispersion fiber. Recently, photonic crystal fibers drew the attention of researchers due to some striking properties such as ultrahigh negative dispersion characteristics, high birefringence, and high nonlinearity compared to classical fibers. These modal properties make them a more suitable candidate for various application areas including telecommunications, sensors, spectroscopy, medicine, etc. [5,6]. Multicore PCFs are also finding some special applications due to their optical waveguide and photonic design possibilities, such as the development of optical splitters with larger splitting ratios and optical couplers with lower coupling lengths [7,8]. Diode-pumped alkali lasers (DPALs) are another special field of application, where embedding the alkali gas in hollow-core PCFs was shown to be an effective method of overcoming high-power limitations [9]. The PCF structure can be modified with different types of air-hole shapes and arrangements to alter the guiding properties, such as in the case of achieving ultrahigh birefringence characteristics [10,11]. For example, Wang et al. proposed a novel PCF using rectangular air holes in the core region to achieve birefringence of 1.83 × 10−2 at 1.55 µm [11]. Zhang et al. enlarged two of the central air holes of the fiber and reported a birefringence property on a scale of 10−3 at 1550 nm [12]. Xu et al. also achieved birefringence of 10−3 by proposing a PCF consisting of a hexagonal cladding with a pentagonal core [13]. Rashid et al. designed a dodecagonal-shaped PCF and reported a birefringence of 2.05 × 10−2, nonlinearity of 39.02 W−1 km−1, and a negative dispersion of −396.9 ps/(nm km) [14]. Golden spiral PCF designs were recently developed to obtain high birefringence values such as 1.16 × 10−2 [15]. For instance, Agrawal et al. proposed arranging elliptical air holes in a spiral pattern to achieve a golden spiral PCF with a high birefringence of 2.2 × 10−2 at 1.55 µm [16]. Revathi et al. also designed a spiral PCF with elliptical air holes which had a large birefringence of 2.56 × 10−2 [17], as well as a soft glass photonic crystal fiber with a large modal birefringence of 2.96 × 10−2 [18]. However, spiral PCFs consisting of elliptical or rectangular air holes have poor light confinement in the core region. Moreover, it is challenging to implement non-circular air holes in practice using current fabrication methods. Different types of PCF structures were suggested in order to overcome the weak confinement of light in the fiber core. For example, Shawkat et al. proposed a PCF with a defected core and hybrid cladding to get a birefringence of 4.39 × 10−2 [19]. Chen et al. reported high birefringence of 1.5 × 10−2 by arranging a core of elliptical air holes and a cladding of circular air holes in a hexagonal lattice [10]. Although these hybrid PCFs offer high birefringence and large nonlinearity, the challenge of fabricating elliptical air holes with perfect accuracy still remains. For practical applications, it is not only crucial to design a PCF structure with high birefringence, large nonlinearity, and low confinement losses, but it is also easier to manufacture. Hence, if the PCF design is limited to using only circular air-hole shapes, the fiber can be easily fabricated using the drilling method or the conventional stack-and-draw technique. Several such PCFs that attain the abovementioned properties using all circular air holes were the subject of many studies. For example, Chau et al. designed a simple PCF structure using only circular air holes and obtained birefringence of about 5.501 × 10−3 at 1550 nm [20]. Yang et al. proposed a novel PCF with all circular air holes, with two enlarged air holes in the first ring of the cladding and three shrunken air holes in the core region. This study reported a high birefringence of 2.22 × 10−2, a large nonlinearity of 68 W−1 km−1, and confinement losses on the order of 10−4 dB/m [21]. In this paper, we propose a highly nonlinear hexagonal-structure-based photonic crystal fiber for the application of supercontinuum generation, as well as broadband dispersion compensation. In order to analyze the various waveguiding properties of the proposed structure, the finite element method (FEM) with a perfectly matched layer (PML) was used. The hexagonal PCF (H-PCF) design consists of an asymmetric core region, where one air hole was omitted. From the simulation results, we achieved ultrahigh birefringence of 3.87 × 10−2, a nonlinearity of 96.51 W−1 km−1, and an approximate negative dispersion of −753.2 ps/(nm km) at 1.55 µm. However, to the best of our knowledge, our reported Photonics 2018, 5, 26 3 of 11 ultrahigh birefringence is the highest achievable birefringence when using all circular air holes in the fiberPhotonics core 2018 and, 5, x cladding FOR PEER region. REVIEW 3 of 11

2. Design Methodology of the Proposed H-PCFH-PCF Figure 11 conveys conveys thethe transversetransverse sectional sectional mensuration mensuration of of the the proposed proposed H-PCF H-PCF with with proper proper distribution of air holes. We avoided introducing any non-circularnon-circular air holes, such as rectangular-rectangular- or elliptical-shapedelliptical-shaped holes, in intoto the H-PCFH-PCF structure to make the fabricationfabrication process simple. The lattice structure comprised fivefive air-holeair-hole rings,rings, wherewhere allall ofof the air holes werewere circular in shape and the chosen backgroundbackground material waswas fused silica. The proposed H H-PCF-PCF is composed of an isosceles triangular ◦ lattice with a vertex angle of 60° 60 forfor producing producing hexagonal hexagonal symmetry. symmetry. The The fir first,st, seco second,nd, thi third,rd, four fourth,th, and fif fifthth rings rings contain contain 5, 5, 12, 12, 18, 18, 24 24,, and and 30 30air airholes, holes, respectively. respectively. Hence, Hence, a total a totalof 89 ofcircular 89 circular air holes air holeswith two with different two different diameter diameter values values (d1 and (d d12)and were d2 incorporated) were incorporated into the into design the to design obtain to the obtain desired the desiredultrahigh ultrahigh birefringence birefringence and large and nonlinearity. large nonlinearity. The diameter The of diameter one of the of air one holes of the in airthe holes core regi in theon corewas changed region was to d changed2, while the to dre2,mainder while the of remainderthe air holes of in the the air lattice holes ha ind thethe latticediameter had d the1. Ideally, diameter the dmaximum1. Ideally, value the maximum of d1 was valuechosen of, since d1 was a larger chosen, value since will a result larger in value the overlapping will result in of the air overlappingholes within ofthe air same holes ring. within The minimum the same ring.separation The minimum between two separation air holes between in the cladding two air region holes wa in thes about cladding 0.015 regionμm in wasorder about to avoid 0.015 theµm crosstalk in order to effect. avoid The the crosstalkdistance effect.between The two distance consecutive between air two holes, consecutive i.e., the airpitch, holes, is denoted i.e., the by pitch, Λ in is Figure denoted 1. byTheΛ upperin Figure and1 .lower The uppertwo air and holes lower in the two core air holesregion in we there core also regionrelatively were much also larger relatively than much the air larger hole thanwith thediameter air hole d2 with. This diameter irregularity d2. Thisreduce irregularityd the area reduced of pure thesilica area and of enhance pure silicad the and H enhanced-PCF’s nonlinearity the H-PCF’s and nonlinearity modal birefringence. and modal Subsequen birefringence.tly, our Subsequently, proposed ourH-PCF proposed design H-PCF had a designtotal of had three a total degrees of three of freedom degrees (d of1, freedom d2, and (dΛ)1 , which d2, and is Λfewer) which than is fewer other thancontemporary other contemporary PCF designs PCF such designs as that such proposed as that in proposed Reference in [21], Reference where [ 21there], where were therefive degrees were five of degreesfreedom. of The freedom. variations The in variations the optical in thechara opticalcteristics characteristics of the H-PCF of thedue H-PCF to deviations due to deviationsin the geometric in the geometricparameters parameters (d1, d2, and (d 1Λ, d) 2wer, ande Λalso) were thoroughly also thoroughly investigated investigated to account to account for the for precision the precision of the of thefabrication fabrication processes. processes.

Figure 1. CrossCross-section-section of proposed photonic crystal fiber ﬁber ( (PCF)PCF) design methodology.

3. Numerical Method The ﬁnitefinite element method (FEM) was employed as a numerical simulation tool to realize the different light-guidinglight-guiding properties of the proposed H-PCFH-PCF structure.structure. This includes modal properties such as birefringence, chromaticchromatic dispersion, conﬁnementconfinement loss, and nonlinearity. In order to simulate the wavelength wavelength dependence dependence characteristics characteristics of the of H-PCF, the H- thePCF, perfectly the perfectly matched matched layer (PML) layer technique (PML) wastechnique utilized wa withs utilized a thickness with a of thickness 10% of the of 10% cladding of the radius cladding [22]. radius The commercially [22]. The commercia availablelly full-vector available FEMfull-vector software, FEM COMSOL software, Multiphysics, COMSOL Multiphysics, was employed was for employed handling thefor handling simulation the tasks simulation for the modal tasks analysisfor the modal of the analysis proposed of H-PCFthe proposed structure. H-PCF Maxwell’s structure. vector Maxwell’s equation vector was solvedequation using was the solved FEM using with the FEM with circular PML for evaluating the effective refractive index (neff). The modal birefringence (B), chromatic dispersion (D(λ)), and propagation loss (αloss) could be calculated using the following equations [11,23]:

2 2 Chromatic Dispersion, 퐷(휆) = −휆/푐(푑 푅푒[푛푒푓푓]/푑휆 ), (1)

3 Propagation Loss, 훼푙표푠푠 = 8.686 × 푘0퐼푚[푛푒푓푓] × 10 dB/km, (2)

Photonics 2018, 5, 26 4 of 11

circular PML for evaluating the effective refractive index (neff). The modal birefringence (B), chromatic dispersion (D(λ)), and propagation loss (αloss) could be calculated using the following equations [11,23]:

2 h i 2 Chromatic Dispersion, D(λ) = −λ/c d Re ne f f /dλ , (1)

h i 3 Propagation Loss, αloss = 8.686 × k0 Im ne f f × 10 dB/km, (2)

Modal birefringence, B = nx − ny , (3) Photonics 2018, 5, x FOR PEER REVIEW 4 of 11 where nx and ny refer to the effective refractive index of the x-polarization and y-polarization fundamental modes, respectively.ModalRe[n birefringenceeff] and Im[n, eff퐵 ]= are|푛푥 the− 푛푦 real|, and imaginary parts of(3n) eff, respectively. K0 is the free-space number, defined as K0 = 2π/λ, where λ is the wavelength and where nx and ny refer to the effective refractive index of the x-polarization and y-polarization c is the velocity of light in a vacuum. The effective mode area is a crucial term for studying the fundamental modes, respectively. Re[neff] and Im[neff] are the real and imaginary parts of neff, nonlinear properties of microcavities [24], optical fibers, and PCFs. The effective area (A ) of a respectively. K0 is the free-space number, defined as K0 = 2π/λ, where λ is the wavelength and ceff is the 2 photonicvelocity crystal of light fiber in a in vacuum.µm , given The effective the amplitude mode area of the is a electric crucial fieldterm infor thestudying medium the (nonlinearE), can be calculated as properties of microcavities [24], optical fibers, and PCFs. The2 effective area (Aeff) of a photonic crystal RR 2 fiber in µm2, given the amplitude of the electric field|E| indxdy the medium (E), can be calculated as Ae f f = . (4) RR(∫ ∫||E퐸||42dxdy푑푥푑푦)2 퐴 = . (4) 푒푓푓 ∫ ∫|퐸|4푑푥푑푦 Nonlinearity (γ) is inversely proportional to the effective area (Aeff), and can be written as Nonlinearity (γ) is inversely proportional to the effective area (Aeff), and can be written as 2π n2 γ = 2휋× 푛2 . (5) 훾 =λ ×Ae f f . (5) 휆 퐴푒푓푓 TheThe nonlinearity nonlinearity can can be be enhanced enhanced using using doped doped materials materials inin thethe core region region,, since since nonlinearity nonlinearity highlyhighly depends depends on on the the Kerr Kerr constant constant (n (2n)2 of) of the the material. material.

4. Simulation4. Simulation Results Results and and Discussion Discussion FigureFigure2a shows2a shows the the modal modal birefringence birefringence characteristics characteristics of the the proposed proposed H H-PCF-PCF as asa function a function of of wavelengthwavelength ((λλ)) whenwhen thethe pitchpitch was 0.76 µm.µm. From the the figure, ﬁgure, it it can can be be observed observed that that the the H H-PCF-PCF structurestructure shows shows an an ultrahigh ultrahigh birefringence birefringence of of about about 3.873.87 ×× 1010−−2 at2 at1.55 1.55 µmµ.m. A ±1% A ± 1%varia variationtion in the in air the air hole-to-holehole-to-hole spacing is generally considered considered in in the the simulation simulation process process to to account account for for the the practical practical accuracyaccuracy of the of PCFthe PCF fabrication fabrication technique. technique. Considering Considering this this fabrication fabrication issue, issue, the pitchthe pitch was wa varieds varied from ±1 tofrom±2%, ±1 to and ±2% its, and impact its impact on the on birefringence the birefringence and dispersion and dispersion results results was was studied. studied The. The effect effect of thisof pitchthis variation pitch variation on birefringence on birefringence is demonstrated is demonstrated in Figure 2 inb, whereFigure it 2b, is evident where it that is evidentthe birefringence that the increasesbirefringence as the pitchincreases decreases. as the pitch This decreases. is due to This the is increasing due to the asymmetryincreasing asymmetry in the core in andthe co claddingre and regioncladding with decreasing region with pitch, decreasing which leads pitch, to whicha larger leads contrast to ain larger refractive contrast index. in Consequently, refractive index. light Consequently, light confinement and birefringence also increase as pitch decreases. conﬁnement and birefringence also increase as pitch decreases.

(a) (b)

Figure 2. Birefringence as a function of wavelength for (a) optimal design parameters: pitch (Λ) = 0.76, Figure 2. Birefringence as a function of wavelength for (a) optimal design parameters: pitch (Λ) = 0.76, d1/Λ = 0.95, and d2/Λ = 0.8; and (b) by varying the value of pitch (Λ) = 0.76 from ±1% to ±2%. d1/Λ = 0.95, and d2/Λ = 0.8; and (b) by varying the value of pitch (Λ) = 0.76 from ±1 to ±2%.

Figure 3a shows the effect of changing d1/Λ on the birefringence characteristics, while the pitch (Λ) = 0.76 and d2/Λ = 0.80 parameters were kept fixed. According to the variation in d1/Λ to 0.93, 0.95, and 0.97, the calculated birefringence values were 3.51 × 10−2, 3.87 × 10−2, and 4.25 × 10−2, respectively, at λ = 1.55 µm. It is clearly shown that changing the d1/Λ parameter results in drastic changes to the birefringence characteristics of the fiber, as the effective refractive index of both x- and y-polarized modes decreases with diameter d1. However, nx,eff decreases at a faster rate compared to ny,eff because nx,eff is more sensitive to changes in d1. As a result, birefringence increases almost linearly with d1, as the structure exhibits larger index differences between the two polarization modes. Next, d2/Λ was changed while the pitch (Λ) = 0.76 and d1/Λ = 0.95 parameters were kept fixed. The variations in d2/Λ

Photonics 2018, 5, 26 5 of 11

Figure3a shows the effect of changing d 1/Λ on the birefringence characteristics, while the pitch (Λ) = 0.76 and d2/Λ = 0.80 parameters were kept fixed. According to the variation in d1/Λ to 0.93, 0.95, and 0.97, the calculated birefringence values were 3.51 × 10−2, 3.87 × 10−2, and 4.25 × 10−2, respectively, at λ = 1.55 µm. It is clearly shown that changing the d1/Λ parameter results in drastic changes to the birefringence characteristics of the fiber, as the effective refractive index of both x- and y-polarized modes decreases with diameter d1. However, nx,eff decreases at a faster rate compared to ny,eff because nx,eff is more sensitive to changes in d1. As a result, birefringence increases almost linearly with d1, as the structure exhibits larger index differences between the two polarization modes. Photonics 2018, 5, x FOR PEER REVIEW 5 of 11 Next, d2/Λ was changed while the pitch (Λ) = 0.76 and d1/Λ = 0.95 parameters were kept fixed. The −2 −2 variationsto 0.75, in 0.80 d2, /andΛ to 0.85 0.75, resulted 0.80, and in 0.85birefringence resulted invalues birefringence of 3.80 × values10−2, 3.87 of 3.80× 10×−2, 10 and , 3.94 3.87 ×× 1010−2, , −2 andrespectively 3.94 × 10 , at, respectively,the wavelength at of the 1550 wavelength nm. From of Figure 1550 3 nm.b, it Fromcan be Figure clearly3 b,seen it canthat be changing clearly the seen thatd2 changing/Λ parameter the d results2/Λ parameter in very slight results changes in very to slight the birefringence changes to the characteristics birefringence as comparedcharacteristics to as comparedchanges in tothe changes d1/Λ parameter. in the d1 Essentially,/Λ parameter. the proposed Essentially, H-PCF the proposedoffers an ultrahigh H-PCF offers birefringence an ultrahigh of birefringenceabout 3.87 × of 10 about−2, which 3.87 is× approximately10−2, which is77 approximately times larger than 77 the times current larger ordinary than the PM current fibers ordinarywith a PMmodal fibers birefringence with a modal of about birefringence 5 × 10−4. This of about means 5 that× 10 our−4 .H This-PCF meanscan act thatas a good our H-PCF substitute can for act PM as a goodfibers substitute in fiber forsensors, PM fibers lasers, in and fiber filters sensors, [25]. lasers, It is worth and filtersmentioning [25]. It that is worth the birefringence mentioning of that the the birefringenceproposed H of-PCF the can proposed be further H-PCF increased can be if further a background increased material if a background with a higher material refractive with aindex, higher refractivei.e., AsSe index,2 glass, i.e., is used AsSe instead2 glass, of is silica. used instead of silica.

(a) (b)

Figure 3. Effect of changing (a) d1/Λ on the birefringence characteristics, when the remaining Figure 3. Effect of changing (a) d1/Λ on the birefringence characteristics, when the remaining parameters (Λ = 0.76 and d2/Λ = 0.80) were kept constant; and (b) d2/Λ on the birefringence parameters (Λ = 0.76 and d2/Λ = 0.80) were kept constant; and (b) d2/Λ on the birefringence characteristics, when the remaining parameters (Λ = 0.76 and d1/Λ = 0.95) were kept constant. characteristics, when the remaining parameters (Λ = 0.76 and d1/Λ = 0.95) were kept constant. Figure 4a demonstrates the dispersion characteristics for both x- and y-polarizations, using the optimFigureal pitch4a demonstrates (Λ) = 0.76, d1 the/Λ = dispersion 0.95, and d characteristics2/Λ = 0.80. According for both to thex- and figure,y-polarizations, the proposed usingH-PCF the optimaldemonstrates pitch (Λ a) =large 0.76, negative d1/Λ = dispersion 0.95, and coefficient d2/Λ = 0.80. of about According −753.2 to ps the/(nm figure, km) along the proposed the y- H-PCFpolarization demonstrates at an operating a large wavelength negative dispersion of 1550 nm. coefficient Figure 4b ofaccordingly about −753.2 shows ps/(nm the effect km) of varying along the y-polarizationpitch from ±1 at toan ±2% operating on the wavelength chromatic dispersion, of 1550 nm. when Figure the4 bremaining accordingly parameters shows thewere effect kept of varyingconstant. pitch It can from be± observed1 to ±2% from on the the chromaticfigure that dispersion, the value of when dispersion the remaining becomes more parameters and more were keptnegative constant. with Itdecreasing can be observed values of frompitch. theFor figurethe pitch that variation the value of −1 of%, dispersion the dispersion becomes was calculated more and moreas − negative620.3 ps/( withnm km decreasing), −799.8 ps values/(nm km of),pitch. and −8 For50.8 theps/( pitchnm km variation) at wavelength of −1%,s of the 1.4dispersion µm, 1.55 µm was, calculatedand 1.61 asµm−, 620.3respectively ps/(nm, w km),hereas− 799.8the dispersion ps/(nm for km), the and optim−850.8al value ps/(nm of pitch km) wa ats wavelengths−753.2 ps/(nm of km) at an excitation wavelength of 1.55 µm. 1.4 µm, 1.55 µm, and 1.61 µm, respectively, whereas the dispersion for the optimal value of pitch was −753.2 ps/(nm km) at an excitation wavelength of 1.55 µm. Figure5a shows the results of the dispersion characteristics when only the d 1/Λ parameter was changed, while the pitch (Λ) = 0.76 and d2/Λ = 0.80 parameters were kept constant. When d1/Λ was changed to 0.93, 0.95, and 0.97, the calculated dispersion coefficients were −722.6 ps/(nm km), −753.2 ps/(nm km), and −786.5 ps/(nm km), respectively, at λ = 1.55 µm. It can also be seen in Figure5a that changing the d 1/Λ parameter led to slight variations in the dispersion coefficient. On the other hand, Figure5b shows the effect of changing d 2/Λ on the dispersion results, while the pitch (Λ) = 0.76 and d1/Λ = 0.95 parameters were kept fixed. Upon changing d2/Λ to 0.75, 0.80, and 0.85,

(a) (b)

Figure 4. (a) Wavelength dependence dispersion curve for the slow axis and fast axis; (b) effect on dispersion upon varying the value of pitch (Λ) from ±1 to ±2%.

Figure 5a shows the results of the dispersion characteristics when only the d1/Λ parameter was changed, while the pitch (Λ) = 0.76 and d2/Λ = 0.80 parameters were kept constant. When d1/Λ was changed to 0.93, 0.95, and 0.97, the calculated dispersion coefficients were −722.6 ps/(nm km), −753.2 ps/(nm km), and −786.5 ps/(nm km), respectively, at λ = 1.55 µm. It can also be seen in Figure 5a that

Photonics 2018, 5, x FOR PEER REVIEW 5 of 11

to 0.75, 0.80, and 0.85 resulted in birefringence values of 3.80 × 10−2, 3.87 × 10−2, and 3.94 × 10−2, respectively, at the wavelength of 1550 nm. From Figure 3b, it can be clearly seen that changing the d2/Λ parameter results in very slight changes to the birefringence characteristics as compared to changes in the d1/Λ parameter. Essentially, the proposed H-PCF offers an ultrahigh birefringence of about 3.87 × 10−2, which is approximately 77 times larger than the current ordinary PM fibers with a modal birefringence of about 5 × 10−4. This means that our H-PCF can act as a good substitute for PM fibers in fiber sensors, lasers, and filters [25]. It is worth mentioning that the birefringence of the proposed H-PCF can be further increased if a background material with a higher refractive index, i.e., AsSe2 glass, is used instead of silica.

(a) (b)

Figure 3. Effect of changing (a) d1/Λ on the birefringence characteristics, when the remaining

parameters (Λ = 0.76 and d2/Λ = 0.80) were kept constant; and (b) d2/Λ on the birefringence

characteristics, when the remaining parameters (Λ = 0.76 and d1/Λ = 0.95) were kept constant. Photonics 2018, 5, 26 6 of 11 Figure 4a demonstrates the dispersion characteristics for both x- and y-polarizations, using the theoptim calculatedal pitch dispersion(Λ) = 0.76, coefficientsd1/Λ = 0.95, wereand d calculated2/Λ = 0.80. asAccording−752.5 ps/(nm to the figure, km), − the753.2 proposed ps/(nm H km),-PCF anddemonstrates−753.7 ps/(nm a large km), negative respectively, dispersion at λ = coefficient 1.55 µm. of These about results −753.2 indicate ps/(nm that km) changing along the the y- polarization at an operating wavelength of 1550 nm. Figure 4b accordingly shows the effect of varying d2/Λ parameter led to even smaller variations in the dispersion coefficient compared to changing pitch from ±1 to ±2% on the chromatic dispersion, when the remaining parameters were kept the d1/Λ parameter. Nonetheless, our optimal value for the negative dispersion coefficient was aboutconstant.−753.2 It can ps/(nm be observed km) at fromλ = 1.55 the µfigurem. This that fairly the value large of negative dispersion dispersion becomes makes more ourand fibermore suitablenegative for with broadband decreasing dispersion values of compensationpitch. For the pitch in high-speed variation of optical −1%, the transmission dispersion wa systemss calculated and alsoas − in620.3 polarization-maintaining ps/(nm km), −799.8 ps/( applications.nm km), and Moreover, −850.8 ps/( thenm large km) negativeat wavelength dispersions of 1.4 of µm our, 1.55 H-PCF, µm, combinedand 1.61 withµm, respectively its ultrahigh, birefringence,whereas the dispersion makes it particularly for the optim suitableal value for of dispersion pitch was compensation −753.2 ps/(nm andkm sensing) at an excitation applications wavelength [26]. of 1.55 µm.

Photonics 2018, 5, x FOR PEER REVIEW 6 of 11

changing the d1/Λ parameter led to slight variations in the dispersion coefficient. On the other hand, Figure 5b shows the effect of changing d2/Λ on the dispersion results, while the pitch (Λ) = 0.76 and d1/Λ = 0.95 parameters were kept fixed. Upon changing d2/Λ to 0.75, 0.80, and 0.85, the calculated dispersion coefficients were calculated as −752.5 ps/(nm km), −753.2 ps/(nm km), and −753.7 ps/(nm km), respectively, at λ = 1. 55 µm. These results indicate that changing the d2/Λ parameter led to even smaller variations in the dispersion coefficient compared to changing the d1/Λ parameter. Nonetheless, our optimal value for the negative dispersion coefficient was about −753.2 ps/(nm km) (a) (b) at λ = 1.55 µm. This fairly large negative dispersion makes our fiber suitable for broadband dispersion compensationFigure 4. (a) Wavelength in high-speed dependence optical dispersion transmission curve systems for the slow and axis also and in fast polarization axis; (b) effect-maintaining on Figure 4. (a) Wavelength dependence dispersion curve for the slow axis and fast axis; (b) effect on dispersion upon varying the value of pitch (Λ) from ±1 to ±2%. applications.dispersion upon Moreover, varying the value large of negative pitch (Λ) dispersionfrom ±1 to ± of2%. our H-PCF, combined with its ultrahigh birefringence, makes it particularly suitable for dispersion compensation and sensing applications [26]. Figure 5a shows the results of the dispersion characteristics when only the d1/Λ parameter was changed, while the pitch (Λ) = 0.76 and d2/Λ = 0.80 parameters were kept constant. When d1/Λ was changed to 0.93, 0.95, and 0.97, the calculated dispersion coefficients were −722.6 ps/(nm km), −753.2 ps/(nm km), and −786.5 ps/(nm km), respectively, at λ = 1.55 µm. It can also be seen in Figure 5a that

(a) (b)

Figure 5. Effect of changing (a) d1/Λ on the dispersion characteristics, when the remaining parameters Figure 5. Effect of changing (a) d1/Λ on the dispersion characteristics, when the remaining parameters (Λ = 0.76 and d2/Λ = 0.80) were kept constant; and (b) d2/Λ on the dispersion characteristics, when the (Λ = 0.76 and d2/Λ = 0.80) were kept constant; and (b) d2/Λ on the dispersion characteristics, when remaining parameters (Λ = 0.76 and d1/Λ = 0.95) were kept constant. the remaining parameters (Λ = 0.76 and d1/Λ = 0.95) were kept constant. Figure 6 demonstrates the effect of pitch deviation on nonlinearity in the 1.35–1.6-µm Figure6 demonstrates the effect of pitch deviation on nonlinearity in the 1.35–1.6- µm wavelength wavelength range. Since the effective area is inversely proportional to nonlinearity, the proposed range. Since the effective area is inversely proportional to nonlinearity, the proposed structure structure achieved very large nonlinearity of 96.51 W−1 km−1 at 1550-nm wavelength, which also achieved very large nonlinearity of 96.51 W−1 km−1 at 1550-nm wavelength, which also increased increased with decreasing pitch. The results of independently varying d1/Λ and d2/Λ on nonlinearity with decreasing pitch. The results of independently varying d1/Λ and d2/Λ on nonlinearity were were also investigated, and the results are shown in Figure 7a,b respectively. As d1 increased, the also investigated, and the results are shown in Figure7a,b respectively. As d 1 increased, the effective effective refractive indices of both the x-polarized mode (nx,eff) and y-polarized mode (ny,eff) decreased refractive indices of both the x-polarized mode (nx,eff ) and y-polarized mode (ny,eff ) decreased while while their corresponding nonlinear coefficients increased. This is due to the fact that a larger d1 their corresponding nonlinear coefficients increased. This is due to the fact that a larger d corresponds corresponds to a greater filling fraction of the air holes, which, in turn, results in 1a lower average to a greater filling fraction of the air holes, which, in turn, results in a lower average refractive index refractive index of the cladding. Furthermore, the increase in d1 in the cladding region nibbles the of the cladding. Furthermore, the increase in d in the cladding region nibbles the area of the core, area of the core, resulting in a higher concentration1 of light. As a consequence, decreasing effective resulting in a higher concentration of light. As a consequence, decreasing effective refractive indices refractive indices and increasing nonlinear coefficients were observed for both the x- and y-polarized and increasing nonlinear coefficients were observed for both the x- and y-polarized modes. From the modes. From the figures, it can also be observed that higher values of d1/Λ and d2/Λ resulted in higher nonlinear coefficients. Nevertheless, the obtained value of nonlinearity was convincingly large enough for supercontinuum generation application, provided that the negative dispersion properties of our H-PCF are sufficiently compensated [27].

Photonics 2018, 5, 26 7 of 11

figures, it can also be observed that higher values of d1/Λ and d2/Λ resulted in higher nonlinear coefficients. Nevertheless, the obtained value of nonlinearity was convincingly large enough for supercontinuum generation application, provided that the negative dispersion properties of our H-PCFPhotonics are2018 sufficiently, 5, x FOR PEER compensated REVIEW [27]. 7 of 11 Photonics 2018, 5, x FOR PEER REVIEW 7 of 11

Figure 6. Effect of pitch deviation on nonlinearity. FigureFigure 6. 6.Effect Effect of of pitch pitch deviation deviation on on nonlinearity. nonlinearity.

(a) (b) (a) (b) Figure 7. Effect of changing (a) d1/Λ on nonlinearity, when the remaining parameters (Λ = 0.76 and Figure 7. Effect of changing (a) d1/Λ on nonlinearity, when the remaining parameters (Λ = 0.76 and Figured2/Λ = 0.80 7. Effect) were of kept changing constant (a;) and d1/ Λ(b)on d2/Λ nonlinearity, on nonlinearity, when when the remaining the remaining parameters parameters (Λ = ( 0.76Λ = d2/Λ = 0.80) were kept constant; and (b) d2/Λ on nonlinearity, when the remaining parameters (Λ = and0.76 dand2/Λ d1=/Λ 0.80) = 0.95 were) we keptre kept constant; constant. and (b) d2/Λ on nonlinearity, when the remaining parameters 0.76 and d1/Λ = 0.95) were kept constant. (Λ = 0.76 and d1/Λ = 0.95) were kept constant. Figure 8 shows the wavelength dependence properties of propagation loss with the optimal parameterFigure of 8 the shows pitch the (0.76 wavelength μm). The dependence propagation properties loss was of small propagation, on the order loss with of 10 the−4, for optim theal parameterFigure8 ofshows the pitch the wavelength (0.76 μm). dependence The propagation properties loss wa ofs propagation small, on the loss order with of the 10 optimal−4, for the parameterproposed structure. of the pitch This (0.76 is becauseµm). The light propagation was strongly loss confined was small, to theon the core order region. of 10 Moreover,−4, for the a smallerproposed value structure. of pitch Thiswill also is because lead to strong light was light strongly confinement. confined It can to be the observed core region. that, Moreover,at 1550-nm a proposed structure. This is because light was strongly confined to the core region. Moreover, a smaller wavelength,smaller value the of optimpitch alwill value also oflead propagation to strong light loss confinement.was 0.0001156 It can dB/cm. be observed Since propagation that, at 1550 loss-nm value of pitch will also lead to strong light confinement. It can be observed that, at 1550-nm wavelength, stronglywavelength, depends the on optim the alcladding value of region, propagation one can loss easily wa improves 0.0001156 the dB/cm.propagation Since loss propagation by adding loss a the optimal value of propagation loss was 0.0001156 dB/cm. Since propagation loss strongly depends numberstrongly of depends air-hole ringson the in cladding the cladding region, region. one can easily improve the propagation loss by adding a onnumber the cladding of air-hole region, rings one in can the easilycladding improve region. the propagation loss by adding a number of air-hole rings in the cladding region. Figure9 shows the electric-field distribution of our proposed H-PCF structure using a pitch of 0.76 µm for both x- and y-polarization modes, at λ = 1.55 µm. From Figure9, it can be confirmed that both the x- and y-polarization modes were strongly confined within the core region. This is because the core region of our proposed H-PCF structure was effectively enclosed by introducing two circular air holes in the first ring, thus leading to stronger confinement of light in the core region. Moreover, smaller values of the pitch will also lead to greater light confinement.

Figure 8. Propagation loss curve of the proposed hexagonal photonic crystal fiber (H-PCF) for optimal Figure 8. Propagation loss curve of the proposed hexagonal photonic crystal fiber (H-PCF) for optimal design parameters (Λ = 0.76, d1/Λ = 0.95, and d2/Λ = 0.80). design parameters (Λ = 0.76, d1/Λ = 0.95, and d2/Λ = 0.80).

Photonics 2018, 5, x FOR PEER REVIEW 7 of 11

Figure 6. Effect of pitch deviation on nonlinearity.

(a) (b)

Figure 7. Effect of changing (a) d1/Λ on nonlinearity, when the remaining parameters (Λ = 0.76 and d2/Λ = 0.80) were kept constant; and (b) d2/Λ on nonlinearity, when the remaining parameters (Λ =

0.76 and d1/Λ = 0.95) were kept constant.

Figure 8 shows the wavelength dependence properties of propagation loss with the optimal parameter of the pitch (0.76 μm). The propagation loss was small, on the order of 10−4, for the proposed structure. This is because light was strongly confined to the core region. Moreover, a smaller value of pitch will also lead to strong light confinement. It can be observed that, at 1550-nm wavelength, the optimal value of propagation loss was 0.0001156 dB/cm. Since propagation loss Photonicsstrongly2018 depends, 5, 26 on the cladding region, one can easily improve the propagation loss by adding8 of 11 a number of air-hole rings in the cladding region.

Photonics 2018, 5, x FOR PEER REVIEW 8 of 11

Figure 9 shows the electric-field distribution of our proposed H-PCF structure using a pitch of 0.76 µm for both x- and y-polarization modes, at λ = 1.55 µm. From Figure 9, it can be confirmed that both the x- and y-polarization modes were strongly confined within the core region. This is because Figure 8. Propagation loss curve of the proposed hexagonal photonic crystal fiber (H-PCF) for optimal the coreFigure region 8. Propagation of our proposed loss curve H-PCF of the structure proposed was hexagonal effectively photonic enclosed crystal by ﬁber introducing (H-PCF) for two optimal circular design parameters (Λ = 0.76, d1/Λ = 0.95, and d2/Λ = 0.80). air holesdesign in the parameters first ring, (Λ thus= 0.76, leading d1/Λ = to 0.95, stronger and d2 /confinementΛ = 0.80). of light in the core region. Moreover, smaller values of the pitch will also lead to greater light confinement.

(a) (b)

Figure 9. The optical-field distributions of fundamental modes at 1550 nm for (a) x-polarization, and Figure 9. The optical-ﬁeld distributions of fundamental modes at 1550 nm for (a) x-polarization, and (b) y-polarization. (b) y-polarization.

Finally, in Table 1, we compared the modal properties of our designed H-PCF structure with other Finally,contemporary in Table PCF1, we designs compared from therelated modal works. properties In the oftable, our we designed presented H-PCF the comparison structure with in termsother of contemporary dispersion, bir PCFefringence, designs fromeffective related mode works. area, and In the nonlinearity table, we presented at the effective the comparison wavelength in ofterms 1.55 ofµm dispersion,. The shape birefringence, of the air holes effective used to mode design area, each and structure nonlinearity was also at the taken effective into account wavelength, since of µ the1.55 feasibilitym. The of shape fabricating of the airthe holes actual used fiber to is design also an each issue. structure From the was table, also the taken proposed into account, H-PCF sincehad athe comparable feasibility dispersion of fabricating value the to actual Reference fiber is[28 also], which an issue. also From used thecircular table, air the holes. proposed In contrast, H-PCF Refhaderence a comparable [29] used dispersiona square PCF value lattice to Referencewith circular [28 ],and which elliptical also usedair-hole circular shapes air to holes. get a Invery contrast, large negativeReference dispersion [29] used compared a square PCF to our lattice results. with However, circular and considering elliptical air-hole the objectives shapes of to getthis astudy, very large the proposednegative dispersionH-PCF achieved compared the highest to our results.birefringence However, value considering compared the to objectivesall the other of thisPCF study,designs. the Oproposedther works H-PCF reported achieved in the highest table were birefringence also aimed value at compared achieving to ultrahigh all the other birefringence PCF designs. values Other; however,works reported the proposed in the H table-PCF were design also surpasses aimed at them achieving all using ultrahigh only circular birefringence air holes, values; which however,was one ofthe the proposed goals of its H-PCF design. design The proposed surpasses fiber them ha alld the using lowest only e circularffective area air holes, overall, which and wasit also one had of the the highestgoals of nonlinearity. its design. The Only proposed Reference fiber [ had29] thehad lowest nonlinearity effective which area overall,was comparable and it also tohad our the results highest; however,nonlinearity. considering Only Reference the manufacturing [29] had nonlinearity complexity whichof elliptical was comparableair holes, the to proposed our results; fiber however, has an advantage.considering The the p manufacturingroposed PCF achieved complexity the ofhighest elliptical birefringence, air holes, the lowest proposed effective fiber area has, an and advantage. highest nonlinearityThe proposed in PCFcomparison achieved to the all highestthe other birefringence, PCF designs lowestwith both effective circular area, and and elliptical highest air nonlinearity holes. in comparison to all the other PCF designs with both circular and elliptical air holes. Table 1. Modal properties of the proposed photonic crystal fiber (PCF) in comparison with other PCFs at 1.55 µm.

Reference D(λ) (ps/(nm km)) B = |nx − ny| (×10−2) γ (W−1 km−1) Air-Hole Nature [21] --- 2.200 68.00 Circular [26] −578.50 2.640 53.10 Circular [30] −544.70 2.20 52.7 Circular and elliptical [28] −650.00 2.10 45.50 Circular [29] −1694.80 --- 92.83 Circular and elliptical Proposed PCF −753.20 3.87 96.51 Circular

Photonics 2018, 5, 26 9 of 11

Table 1. Modal properties of the proposed photonic crystal ﬁber (PCF) in comparison with other PCFs at 1.55 µm.

−2 −1 −1 Reference D(λ) (ps/(nm km)) B = |nx − ny| (×10 ) γ (W km ) Air-Hole Nature [21] --- 2.200 68.00 Circular [26] −578.50 2.640 53.10 Circular [30] −544.70 2.20 52.7 Circular and elliptical [28] −650.00 2.10 45.50 Circular [29] −1694.80 --- 92.83 Circular and elliptical Proposed PCF −753.20 3.87 96.51 Circular

A key challenge when designing any PCF structure is ensuring the maximum feasibility of the fabrication process. The drilling method is generally used for fabricating PCFs with a small number of air holes, but it is restricted to circular air-hole shapes only. Non-circular air holes are difficult to implement using the widely used stack-and-draw method, since the holes can undergo re-circularization or other deformations due to the consequences of heating, surface tension, viscous stresses, and pressure changes during the preform stage [31]. Hence, more complex techniques recently emerged for fabricating elliptical- or spiral-shaped PCFs, such as the sol–gel method [32]. Apart from the standard drilling and stack-and-draw methods, a newer fabrication method called the capillary-stacking technique was proposed by Argyros et al. [33] for fabricating PCFs with circular air holes. The proposed H-PCF can be easily fabricated using these relatively simple methods, since the design uses only circular air-hole shapes in both the core and cladding region. It should also be pointed out that the proposed H-PCF gives additional design flexibility, using only two different air-hole diameters. One of the major applications of the proposed H-PCF can be for ideal optical backpropagation purposes. An ideal optical backpropagation scheme simultaneously compensates for both dispersion and nonlinear effects introduced in optical transmission fibers. Typically, such schemes consist of optical phase conjugators, high-dispersion-compensating fibers, and also highly nonlinear fibers [34]. However, an optical backpropagation scheme involving dispersion-compensating and highly nonlinear fibers was recently studied [35]. Hence, the proposed H-PCF provides an added advantage for optical backpropagation applications, due to its coexisting large negative dispersion and high nonlinearity. Moreover, the ultrahigh birefringence and large nonlinearity of the proposed H-PCF means that comparatively shorter lengths of fiber will be required during practical applications.

5. Conclusions In conclusion, we proposed a hexagonal PCF with all circular air holes to obtain both ultrahigh birefringence and high nonlinearity. From the simulation results, the proposed H-PCF design showed an ultrahigh modal birefringence of 3.87 × 10−2 and a large nonlinear coefficient of 96.51 W−1 km−1 at the operating wavelength of 1550 nm. The advantage of our H-PCF design over contemporary PCF designs is that it achieves the highest birefringence and nonlinearity results using only circular air holes in the core and cladding region, thus making the fiber feasible to manufacture using current existing fabrication techniques. A negative dispersion coefficient ranging from −482.6 ps/(nm km) to −830.8 ps/(nm km) was obtained in the wavelength range of 1.34 µm to 1.64 µm. The large negative dispersion and high nonlinearity indicate that the proposed H-PCF is a potential candidate for optical backpropagation schemes, while the large negative dispersion and ultrahigh birefringence make it useful for dispersion compensation purposes.

Author Contributions: S.K.B. and M.M.A.M. designed the model and performed the numerical simulations. M.R.I. and S.M.R.I. performed the calculations and Matlab simulations. S.K.B. and S.S. wrote the manuscript with input from all authors. F.A. and S.K.B. proposed the core idea, and were in change of overall direction and planning when performing the numerical simulations. All authors discussed the results and contributed to the ﬁnal manuscript. Funding: The author acknowledges ﬁnancial support from the Independent University, Bangladesh. Photonics 2018, 5, 26 10 of 11

Acknowledgments: The authors would like to thank Shiva Kumar (McMaster University, Department of Electrical and Computer Engineering, Canada) for giving valuable suggestions and comments to improve the manuscript. Conﬂicts of Interest: The authors declare that there are no conﬂicts of interest regarding the publication of this paper.

References

1. Sonne, A.; Ouchar, A. Improving of high birefringence photonic crystal fiber with low confinement loss using small elliptical air holes in the core region. J. Mod. Opt. 2015, 62, 588–592. [CrossRef] 2. Sonne, A.; Ouchar, A.; Sonne, K. Improving of high birefringence with negative dispersion using double octagonal lattice photonic crystal fiber. Int. J. Light Electron Opt. 2016, 127, 8–10. [CrossRef] 3. Hao, R.; Li, Z.; Sun, G.; Niu, L.; Sun, Y. Analysis on photonic crystal fibers with circular air holes in elliptical configuration. Opt. Fiber Technol. 2013, 19, 363–368. [CrossRef] 4. Broeng, J.; Mogilevstev, D.; Barkou, S.E.; Bjarklev, A. Photonic crystal fibers: A new class of optical waveguides. Opt. Fiber Technol. 1999, 5, 305–330. [CrossRef] 5. Malka, D.; Peled, A. Power splitting of 1× 16 in multicore photonic crystal fibers. Appl. Surf. Sci. 2017, 417, 34–39. [CrossRef] 6. Malka, D.; Cohen, E.; Zalevsky, Z. Design of 4× 1 power beam combiner based on multiCore photonic crystal fiber. Appl. Sci. 2017, 7, 695. [CrossRef] 7. Malka, D.; Zalevsky, Z. Multicore photonic crystal fiber based 1× 8 two-dimensional intensity splitters/couplers. Electromagnetics 2013, 33, 413–420. [CrossRef] 8. Malka, D.; Sintov, Y.; Zalevsky, Z. Fiber-laser monolithic coherent beam combiner based on multicore photonic crystal fiber. Opt. Eng. 2013, 54, 011007. [CrossRef] 9. Sintov, Y.; Malka, D.; Zalevsky, Z. Prospects for diode-pumped alkali-atom-based hollow-core photonic-crystal fiber lasers. Opt. Lett. 2014, 39, 4655–4658. [CrossRef][PubMed] 10. Chen, D.; Shen, L. Ultrahigh birefringent photonic crystal fiber with ultralow confinement loss. IEEE Photonics Technol. Lett. 2007, 19, 185–187. [CrossRef] 11. Wang, W.; Yang, B.; Song, H.; Fan, Y. Investigation of high birefringence and negative dispersion photonic crystal fiber with hybrid crystal lattice. Int. J. Light Electron Opt. 2013, 124, 2901–2903. [CrossRef] 12. Zhang, M.Y.; Li, S.G.; Yao, Y.Y.; Zhang, L.; Fu, B.; Yin, G.B. Influence of microstructured core on characteristics of photonic crystal fibers. Acta Phys. Sin. 2010, 59, 3278–3284. 13. Xu, D.; Song, H.; Wang, W.; Fan, Y.; Yang, B. Numerical analysis of a novel high birefringence photonic crystal fiber. Int. J. Light Electron Opt. 2013, 124, 1290–1293. [CrossRef] 14. Rashid, M.M.; Anower, M.S.; Hasan, M.R.; Tabassum, N. Hexagonal shaped core dodecagonal PCF with high birefringence and nonlinear coefficient. In Proceedings of the International Conference on Electrical, Computer and Communication Engineering (ECCE), Cox’s Bazar, Bangladesh, 16–18 February 2017; pp. 447–450. 15. Agrawal, A.; Kejalakshmy, N.; Chen, J.; Rahman, B.M.A.; Grattan, K.T.V. Golden spiral photonic crystal fiber: Polarization and dispersion properties. Opt. Lett. 2008, 33, 2716–2718. [CrossRef][PubMed] 16. Agrawal, A.; Kejalakshmy, N.; Rahman, B.M.A.; Grattan, K.T.V. Polarization and dispersion properties of elliptical hole golden spiral photonic crystal fiber. Appl. Phys. B 2010, 99, 717–726. [CrossRef] 17. Revathi, S.; Inbathini, S.R.; Saifudeen, R.A. Highly nonlinear and birefringent spiral photonic crystal fiber. Adv. OptoElectron. 2014, 2014, 464391. [CrossRef] 18. Revathi, S.; Inabathini, S.; Sandeep, R. Soft glass spiral photonic crystal fiber for large nonlinearity and high birefringence. Opt. Appl. 2015, 45, 15–24. 19. Shawkat, M.T.B.; Razzak, S.M.A.; Kabir, S. Defected core hybrid cladding photonic crystal fiber with high birefringence & highly negative dispersion properties. In Proceedings of the 2015 IEEE International WIE Conference on Electrical and Computer Engineering (WIECON-ECE), Dhaka, Bangladesh, 19–20 December 2015; pp. 507–510. 20. Chou Chau, Y.F.; Lim, C.M.; Yoong, V.N.; Syafi’ie Idris, M.N. A simple structure of all circular-air-holes photonic crystal fiber for achieving high birefringence and low confinement loss. J. Appl. Phys. 2015, 118, 243102. [CrossRef] Photonics 2018, 5, 26 11 of 11

21. Yang, T.; Wang, E.; Jiang, H.; Hu, Z.; Xie, K. High birefringence photonic crystal fiber with high nonlinearity and low confinement loss. Opt. Express 2015, 23, 8329–8337. [CrossRef][PubMed] 22. Islam, M.T.; Moctader, M.G.; Ahmed, K.; Chowdhury, S. Benzene Shape Photonic Crystal Fiber Based Plasma Sensor: Design and Analysis. Photonic Sens. 2018, 8, 263–269. [CrossRef] 23. Wang, F.; Sun, Z.; Liu, C.; Sun, T.; Chu, P.K. A highly sensitive dual-core photonic crystal fiber based on a surface plasmon resonance biosensor with silver-graphene layer. Plasmonics 2017, 12, 1847–1853. [CrossRef] 24. Kumar, S.; Biswas, S.K. Impact of Kerr nonlinearity and stimulated Raman scattering on the whispering gallery modes of an optical microsphere. JOSA B 2016, 33, 1677–1687. [CrossRef] 25. Hasan, M.R.; Anower, M.S.; Hasan, M.I. Polarization maintaining highly nonlinear photonic crystal fiber with closely lying two zero dispersion wavelengths. Opt. Eng. 2016, 55, 056107. [CrossRef] 26. Hasan, M.R.; Islam, M.A.; Rifat, A.A.; Hasan, M.I. A single-mode highly birefringent dispersion-compensating photonic crystal fiber using hybrid cladding. J. Mod. Opt. 2017, 64, 218–225. [CrossRef] 27. Lee, J.H.; Teh, P.C.; Yusoff, Z.; Ibsen, M.; Belardi, W.; Monro, T.M.; Richardson, D.J. A holey fiber-based nonlinear thresholding device for optical CDMA receiver performance enhancement. IEEE Photonics Technol. Lett. 2002, 14, 876–878. [CrossRef] 28. Haque, M.M.; Rahman, M.S.; Habib, M.S.; Habib, M.S. A single mode hybrid cladding circular photonic crystal fiber dispersion compensation and sensing applications. Photonics Nanostruct. Fundam. Appl. 2015, 14, 63–70. [CrossRef] 29. Islam, M.I.; Khatun, M.; Ahmed, K. Ultra-high negative dispersion compensating square lattice based single mode photonic crystal fiber with high nonlinearity. Opt. Rev. 2017, 24, 147–155. [CrossRef] 30. Hasan, M.I.; Habib, M.S.; Razzak, S.M.A. An elliptical-shaped core residual dispersion compensating octagonal photonic crystal fiber. IEEE Photonics Technol. Lett. 2014, 26, 2047–2050. [CrossRef] 31. Issa, N.A.; van Eijkelenborg, M.A.; Fellew, M.; Cox, F.; Henry, G.; Large, M.C. Fabrication and study of microstructured optical fibers with elliptical holes. Opt. Lett. 2004, 29, 1336–1338. [CrossRef][PubMed] 32. Bise, R.T.; Trevor, D. Solgel-derived microstructured fibers: Fabrication and characterization. In Proceedings of the Optical Fiber Communication Conference (OWL6), Anaheim, CA, USA, 6 March 2005. 33. Argyros, A.; Bassett, I.M.; Van Eijkelenborg, M.A.; Large, M.C.; Zagari, J.; Nicorovici, N.A.; McPhedran, R.C.; de Sterke, C.M. Ring structures in microstructured polymer optical fibres. Opt. Express 2001, 9, 813–820. [CrossRef][PubMed] 34. Shao, J.; Kumar, S. Optical backpropagation for fiber-optic communications using optical phase conjugation at the receiver. Opt. Lett. 2012, 37, 3012–3014. [CrossRef][PubMed] 35. Kumar, S.; Yang, D. Optical backpropagation for fiber-optic communications using highly nonlinear fibers. Opt. Lett. 2011, 36, 1038–1040. [CrossRef][PubMed]

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).