A polarization splitter is one of the key componentsin an optical communication system and has manyapplications in, e.g., polarization diversity systems[1–3], polarization-independent wavelength filters[4,5], and polarization stabilizers [6]. According tothe operation principle, polarization splitters canbe divided into two classes. One is based on the modeinterference [7], where the two polarization statescan be separated due to the difference in their cou-pling lengths. This kind of splitter can be designedmore flexibly. The other class is based on the mode-sorting effect [8,9], which can operate over a broadwavelength range and has more relaxed fabricationtolerances. A variety of polarization splitters havebeen reported in the literature [10–15]. Recently,with the development of photonic crystal fibers(PCFs) [16], polarization splitters [12–14,17] basedon PCFs have attracted more attention. Althoughsuch splitters possess special and excellent proper-ties, their splicing with conventional single-modefibers remains nerve wracking. To overcome this ob-
stacle, one solution has been proposed through intro-ducing intermediate fibers [18].
Most PCFs or microstructure fibers are made of asingle material with multiple air holes periodicallyarranged around the core. The single-material PCFshave been widely investigated due to their uniqueproperties, such as high degree of freedom in design,endless single-mode guidance [19], extremely largeeffective-core area in the single-mode region [20],high birefringence [21–23], abnormal dispersion[24,25], and high nonlinear effect [26]. However, itis too difficult to avoid structural deformations andhole collapse during fiber drawing, especially for fu-sion splicing [27,28] between a conventional fiberand a PCF. In 2003, the first all-solid holey fibers(SOHO) [29] made of two types of multicomponentglass were drawn. The structure of the all-solid PCFremained unchanged during fiber drawing. There-fore, the all-solid PCF is useful to avoid structuraldeformations.
In this paper, a new kind of polarization splitter inall-solid PCF is presented. The characteristics of thesplitter are optimized by adjusting the parameters ofthe circular inclusions surrounding the cores. Afull-vector finite-element method (FEM) is used todesign the splitter. In addition, a semi-vector
three-dimensional beam propagation method (BPM)is employed to analyze the propagation properties ofthis splitter.
2. Configuration and Principle
A cross section of the polarization splitter in an all-solid PCF is shown in Fig. 1; it is a triangular-arrayed twin-core PCF formed by removing four cir-cular inclusions. The lattice constant Λ (the pitch) isequal to 2 μm. The diameter d of the cladding circu-lar inclusions is 0:92 μm. The diameters di (i ¼ 1–5)of circular inclusions surrounding the cores are illu-strated in Fig. 1. The borosilicate glass doped withPbO (B1) and the borosilicate glass doped with KF(H1) are selected as the background material andthe microrod material, respectively. As is shown in[29], the two glasses are thermally matched. The re-fractive indices of B1 glass and H1 glass are 1.764and 1.529 at 1:55 μm, respectively.
The coupler is based on the interference effect be-tween two supermodes. If the individual isolated core
of the splitter is single mode, the splitter only sup-ports the two lowest guided supermodes (the evenmode and the odd mode). Figure 2 shows the evenmode and odd mode of Ex. The coupling length LC,which denotes the length of a complete power trans-fer from one core to the other core, is defined as
LC ¼ λ2ðneven − noddÞ
; ð1Þ
where neven and nodd are the effective indices of theeven mode and the odd mode, respectively.
Because of the broken sixfold rotation symmetry,couplers are birefringent and their transmissionsare polarization dependent. Therefore, the couplinglength of the x-polarized mode (denoted Lx
C) is differ-ent from that of the y-polarized mode (denoted Ly
C).Their expressions are given by
LxC ¼ λ
2ðnxeven − nx
oddÞ; Ly
C ¼ λ2ðny
even − nyoddÞ
; ð2Þ
where nx;yeven and nx;y
odd are the effective indices of thesupermodes for the even mode and the odd mode,respectively. In this paper, nx;y
even and nx;yodd are calcu-
lated through a full-vector FEM. For one given wave-length,
LyCðλ0Þ∶Lx
Cðλ0Þ ¼ðnx
even − nxoddÞ
ðnyeven − ny
oddÞ¼ m∶n: ð3Þ
If m∶n ¼ even∶odd or odd∶even, polarization split-ting will be achieved at the transmission distanceL ¼ mLx
C ¼ nLyC. The condition of Ly
Cðλ0Þ∶LxCðλ0Þ ¼
m∶n ¼ 5∶4 is obtained by adjusting the structureparameters of circular inclusions surrounding the
Fig. 1. (Color online) Cross section of the proposed polarizationsplitter in all-solid PCFs.
Fig. 2. (Color online) Electric field component of x-polarized mode: (a) even mode; (b) odd mode.
Table 1. Related Parameters of the Polarization Splitter
cores. The numerical values of d1–d5 are presented inTable 1. It can be seen from the Table 1 that the split-ting length is 6:8 mm.
3. Numerical Analysis
To numerically analyze the polarization splittingproperties in detail, a semi-vector three-dimensionalBPM is employed. The x-polarized and y-polarizedlight at λ0 ¼ 1:55 μm are launched into core A simul-taneously. Figure 3 gives the normalized power ver-sus the transmission distance of the splitter in core Aand core B. According to Fig. 3, we can see that the x-polarized mode in core B and the y-polarized mode incore A reach their peaks at the same propagation dis-tance, which is approximately equal to 6:8 mm. Like-wise, the x-polarized mode in core A and the y-polarized mode in core B reach the bottom at a pro-pagation distance of 6:8 mm. Therefore, it can be con-cluded that polarization splitting is realized at atransmission length of 6:8 mm.
Figures 4(a) and 4(b) present the field distribu-tions of the x-polarized and the y-polarized modes ob-served at the output (L ¼ 6:8 mm), respectively. The
lights are launched into core A. It is apparent fromthe figure that the x-polarized and the y-polarizedmodes are equally separated into core B and coreA, respectively.
Polarization extinction ratio and polarizationcrosstalk are two key technical parameters for thepolarization splitter. The polarization extinction ra-tio is defined as the power of a particular polarizationin the expected output core compared to the power ofthe other polarization in the same core. In this case,the extinction ratio measured in core A, ERA, andcore B, ERB, can be expressed as
ERA ¼ 10log10ðPAy=PAxÞ;ERB ¼ 10log10ðPBx=PByÞ; ð4Þ
where PAxðBxÞ and PAyðByÞ are the power of the x-polarized and y-polarized modes in core A and coreB, respectively.
The ratio of the power of a certain polarizationfrom the nonexposed core to the power from the ex-posed core is defined as polarization crosstalk. Thecrosstalk of x polarization and y polarization (de-noted as CTx and CTy) are expressed as
In Fig. 5, the output extinction ratio [Fig. 5(a)] andcrosstalk [Fig. 5(b)] are plotted as a function of thewavelength where the splitter length is 6:8 mm.The material dispersion of the PCF is taken into ac-count. According to the figures, an extinction ratio ofmore than 20 dB and a crosstalk of less than −20 dBare obtained over a wavelength range of 1:541–1:556 μm. The peaks of the extinction ratios, whichare 28.9 and 29:9 dB, corresponding to x and y polar-ization, respectively, are obtained at 1:55 μm. Thecrosstalk bottoms at 1:55 μm wavelength, whichare −29:0 and −29:8 dB for x and y polarization, re-spectively, are also shown in Fig. 5.
Fig. 3. (Color online) Normalized power versus the transmissiondistance of the splitter in core A and core B.
Fig. 4. (Color online) (a) x-polarized and (b) y-polarized mode field distributions at L ¼ 6:8 mm.
In this paper, we propose a new kind of polarizationsplitter based on the mode interference effects in all-solid PCFs. A full-vector FEM and a semi-vectorthree-dimensional BPM are employed to investigatethe splitter. Numerical simulation results show thatthe splitting length is equal to 6:8 mm. An extinctionratio of more than 20 dB and a crosstalk of less than−20 dB are achieved within the wavelength range of1:541–1:556 μm. Through adjusting the structureparameters of circular inclusions surrounding thecores, different m∶n can be obtained. As a result, ahigher extinction ratio and shorter splitting lengthcan be realized.
This work was supported by the NationalNatural Science Foundation of China (NSFC) undergrant 60877046, in part by the Special Foundationfor Harbin Young Scientists under grant2008RFQXG031, and by the Special Foundationfor Basic Scientific Research of Harbin EngineeringUniversity under grant HEUCF20101102.
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