Design of single-polarization wavelength splitterbased on photonic crystal fiber
Shanshan Zhang, Weigang Zhang,* Pengcheng Geng, Xiaolan Li, and Juan RuanKey Laboratory of Optical Information Science and Technology, Ministry of Education,
Institute of Modern Optics, Nankai University, Tianjin 300071, China
In recent years, due to their unique photonic con-trolled advantages, photonic crystal fibers (PCFs) [1],also known as microstructured optical fibers (MOFs)have attracted considerable research interest. PCFsare composed of a single material (generally silica)with multiple air-holes periodically arranged aroundthe core. PCFs could be divided into two categories:the index guided PCF [2,3], where light is guidedby modified total internal reflection and the band-gap guided PCF [4], where light propagation in thephotonic bandgap (PBG) region is prohibited. ThePCFs possess several distinguished properties suchas wide single-mode wavelength tunability, anoma-lous dispersion from visible to near-infrared range,easily controlled effective mode area and nonlinear-ity, flexible design, and high birefringence. The diam-eter and position of the air holes can be flexiblychosen to allow the construction of complex dual-core[5,6] or multicore structures [7].
Single-polarization single-mode (SPSM) PCFshave been extensively reported in recent years[8,9]. These fibers guide only one polarization funda-mental mode, while its orthogonal polarization-mode is suppressed. The SPSM guiding eliminatesthe polarization-mode coupling as well as thepolarization-mode dispersion. This feature is veryuseful to improve the stability of optical devicesand signal-noise ratio of transmission system, mak-ing SPSM fibers good candidates for various applica-tions, such as polarizing elements in fiber opticgyroscopes, high-power fiber lasers, and many otherpolarization-sensitive occasions. F. Zhang et al. [10]have proposed a rectangular-lattice PCFwith a wide-band SPSM range and confinement loss less than0.1 dB∕km for a wavelength range of 1.20 μm to1.66 μm. An SPSM PCF coupler based on the SPSMPCF was proposed and analyzed by Yue et al. in [11]for the first time.Other SPSMPCFcoupler structureshave been designed and investigated since then[12,13]. Polarization splitters can split one light intotwo orthogonal polarization states. Polarization split-ters based onPCFswith various structures have beenreported [14,15] and can achieve ideal extinction
ratios with short length in contrast to conventionaldual-core fiber- or wave-guide-based polarizationsplitters.
A key component in reconfigurable optical commu-nication systems is a wavelength division multiplex-er (WDM), since the 1.3 μm and 1.55 μm wavelengthbands can be used for carrying data/voice and video,respectively. A PCF structure with polarization-independent propagation characteristics operat-ing at these two different wavelength regimes hasbeen proposed in [16], which is very importantfor construction of passive optical networks (PON).However, this structure can only realize the wave-length splitting, the two polarizations are in thesame cores and cannot be split. The task to designa single-polarization wavelength splitter based onPCF has not been done so far. In this paper, we havetheoretically designed a new different type of single-polarization wavelength splitter through a full-vector finite-element method (FEM). The structureis constructed by introducing two cores in the SPSMPCF [10] and designing different parameters of theair holes around the cores, which can guaranteesingle-polarization guiding and wavelength splittingsimultaneously. Through designing the diameters ofthe large and small air holes to obtain the proper cou-pling length ratio, we realize the splitting of the twocommunication wavelengths of 1.3 μm and 1.55 μmand keep each core single-polarization guiding. Thisstructure acts as a combination of the functions ofWDM and polarizer which will have great applica-tions in high-power fiber lasers, mode-locked lasers,and future optical communication systems.
2. Structure Design and Principle
Figure 1 shows the schematic cross section of theproposed PCF-based wavelength splitter. It consistsof two lines of five enlarged air holes and two puresilica cores which are formed by removing two airholes. There are three different diameters of air holesaround each core which are indicated as d1, d2, andd4. The diameter of cladding air holes is indicated as
d3. The air holes are arrayed in a rectangular-lattice.The hole pitches along the x- and y-direction are Λxand Λy, respectively. The background refractiveindex is calculated according to the Sellmeier equa-tion [17] and the refractive index of air holes is 1.In our simulation, the pitch constant is selected tobe Λx � 2.6 μm, Λy � 1.8 μm with four layers in thecladding. The diameters of the largest air holes andthe cladding air holes are d1 � 2.2 μm and d3 �1.26 μm. A full-vector FEM is applied to analyze thedispersion properties of the PCF. Because of the sym-metric nature of the splitter, only a quarter of thecross section is used during the simulation and aperfect electric or perfect magnetic conductor (PECor PMC) is applied along the symmetric plane Γ1and Γ2. PEC or PMC makes the electric field perpen-dicular or parallel to the boundaries, respectively.
The splitter is based on the interference effect be-tween two supermodes. If the individual isolated coreof 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 oddmode and even mode of Ex. The directions of the elec-tric field in cores A and B are identical for even modewhile contrast for odd mode. When light is incidentupon one core, the fundamental mode of that core isexcited. An evanescent or exponentially decayingportion of that field will be present in the claddingand inevitably enter the other core due to the smalldistance between two cores. Then this energy may betrapped in the other core and becomes a source for apropagating mode. Then the propagating modes intwo cores will couple each other. Therefore, the fun-damental mode in the dual-core structure consists offour polarized components, which are denoted as fol-lows: Eeven
x , Eoddx , Eeven
y , Eoddy , where subscripts x and y
represent the x and y polarizations and superscriptseven and odd represent the even and odd modes. Asshown in Fig. 1, the structure of this dual-core PCF iseven along z-direction; thus the x and y componentsof the electric field along z-direction can be describedby the overlap of even and odd modes for x- andy-polarizations and given by
→ Ex�x; y; z� � a�→ Eevenx �x; y�eineven
x kz
� a−→ Eoddx �x; y�einodd
x kz; (1)
Fig. 1. Cross section of the proposed single-polarization wave-length splitter.
Fig. 2. (Color online) Electric field component of x-polarizedmode: (a) odd mode; (b) even mode.
where a� and a− represent the excited coefficients ofeven and odd modes, respectively. They have to satis-fy 0 < a�, a− < 1, a2� � a2
− � 1. k is the wave number.noddx;y , and neven
x;y denote the effective indexes of the oddand even modes for x- and y-polarizations, respec-tively. In general, the propagation constants of oddand even modes for each polarization state are differ-ent. The phase difference between odd and evenmodes for two orthogonal polarization states canbe given by
δx;y � kz�nevenx;y − nodd
x;y �. (3)
It can be seen from Eq. (3) that δx;y will varywith the propagation distance. When the variationvalue of the phase difference is π, the correspondingpropagation distance is defined as the couplingwavelength. The smaller the value of the couplinglength is, the stronger the coupling strength is be-tween two cores. The coupling length for x- and y-polarizations can be derived from Eq. (3) and givenby [18]
Lci �
πβeveni − βoddi
� λ2�neven
i − noddi � ; (4)
where i � x, y, βoddi , and βeveni denote the propagatingconstants of the odd and even modes for x- and y-polarization modes, respectively. If the two cores areidentical, the energy from one core mode will becoupled into the other core mode after propagatinga coupling length. Assuming that the light is incidentupon core A, the periodic powers at the output side ofcores A and B can be calculated by [16]
Pout;A � Pin cos2�π2
zLci
�; (5)
Pout;B � Pin sin2
�π2
zLci
�; (6)
where Pin is the input light power, z is the propaga-tion length, Lc
i is the coupling length for two ortho-gonal polarization modes. For the wavelengthsplitter operating at two distinct wavelengths ofλ1 and λ2 with λ1 < λ2, the total physical length Lshould satisfy:
L � mLxc�λ1� � nLx
c�λ2�; (7)
where m∶n � even∶odd or odd∶even. This relationensures that after propagating a length of L, thetwo different wavelengths will exit via differentout ports. The coupling length ratios are relatedto the effective indices of the PCF by the followingformula:
Lxc�λ1�
Lxc�λ2�
� λ1λ2
•nevenx �λ2� − nodd
x �λ2�nevenx �λ1� − nodd
x �λ1�. (8)
We can conclude that by an accurate modal analysisof the proposed PCF wavelength splitter for variousvalues of the design parameters, we can finallyobtain the optimized geometrical characteristics ofthe PCF-splitter.
3. Numerical Analysis
Figure 3 shows the effective indices of the slow axis(x-polarization), the fast axis (y-polarization), andthe fundamental space mode (FSM), nclad, whichis evaluated by applying FEM for the cladding airhole arrays of the splitter as a function of wavelengthwith Λx � 2.6 μm, Λy � 1.8 μm, d1 � 2.2 μm, d2 �1.8 μm, d3 � 1.26 μm, and d4 � 1 μm. Two eigen-modes (even mode and odd mode) appear insidethe core region for each polarization orientation.Both the even and odd modes should be located inthe guiding region above the cladding line to ensureeffective coupling. Thus, the guiding wavelengthshould be less than cutoff wavelength. As discussedin [10], the airholes in the cladding region arearranged in a rectangular-lattice and the FSMsare no longer degenerate to achieve wideband single-polarization operation. As we all know, when ns ishigher than nFSMx or nf is higher than nFSMy, themode is guided, otherwise the mode cuts off. FromFig. 3 we can see the dispersion curves of odd modesand even modes almost overlap for the same polari-zation state; we only need to estimate a rough rangeof the single-polarization guiding. So it is unneces-sary to calculate exactly the intersection points ofthe effective index curves of odd and even modesand that of the cladding index curves, respectively.From Fig. 3 the cutoff wavelengths of y- and x-polarization modes are estimated to be less than1 μm and higher than 1.7 μm, respectively. Thisultrawide single-polarization range covers the
1.0 1.2 1.4 1.6 1.8 2.01.34
1.36
1.38
1.40
1.42
1.44
y-polarization
FSM(x-polarized)
FSM(y-polarized)
x-polarization
effe
ctiv
e in
dex
wavelength (µm)
odd modes
even modes
Fig. 3. Effective indices of two orthogonal polarization modesand cladding index as a function of wavelength for the dual-coreSPSM PCF. The hole pitch Λx � 2.6 μm, Λy � 1.8 μm, d1 �2.2 μm, d2 � 1.8 μm, d3 � 1.26 μm, and d4 � 1 μm.
communication windows at 1.3 μm and 1.55 μmwhich provide us an appropriate condition to designthe single-polarization wavelength splitter.
Figure 4 shows the coupling length ratios for the x-polarization at λ1 � 1.3 μm and λ2 � 1.55 μm as afunction of the parameter d2, for different d4.Through calculation we can obtain two best ratiochoices which are 1.71 (≈12∕7) and 1.87 (≈15∕8)and the corresponding parameters should bed2 � 1.55 μm, d4 � 1 μm and d2 � 1.77 μm, d4 �1 μm as designated by arrows in the figure.Thus the total physical length L1 � 7Lx
c�1.3� �12Lx
c�1.55�; L2 � 8Lxc�1.3� � 15Lx
c�1.55�.We plot the simulated dispersion curves for the
first case d2 � 1.55 μm, d4 � 1 μm in Fig. 5. The cut-off wavelengths of y- and x-polarization modes areestimated to be 1.0 μm and higher than 1.8 μm,respectively, which means that the PCF allows forsingle-polarization guiding (x-polarization) at 1.3 μmand 1.55 μm. According to Eq. (4), the coupling
lengths are calculated to be Lxc�1.3� � 1.53 mm,
Lxc�1.55� � 0.89 mm. Therefore, the total length
should be L � 7Lxc�1.3� � 12Lx
c�1.55� ≈ 10.7 mm,which is acceptable for most practical applications.Thus if two-wavelength signal is launched into coreA, after a propagation distance of 10.7 mm, the1.55 μm signal will still propagate in core A, whilethe 1.3 μm signal will be coupled to core B. Hencethis PCF structure exhibits single-polarization wave-length splitting characteristics and therefore isappropriate for WDM operation at two distinct wave-length bands around λ1 � 1.3 μm and λ2 � 1.55 μm.
Then we simulate the effective index for the secondcase d2 � 1.77 μmand d4 � 1 μm, as shown in Fig. 6.The cutoff wavelengths of y- and x-polarizationmodes are estimated to be less than one μmand high-er than 1.7 μm. The single-polarization wavelengthrange also covers the wavelength bands around λ1 �1.3 μm and λ2 � 1.55 μm. The coupling lengths arecalculated to be Lx
c�1.3� � 2.38 mm, Lxc�1.55� �
1.27 mm. The total length should be L � 8Lxc�1.3� �
15Lxc�1.55� ≈ 19 mm, which is a little longer than the
first case, but still acceptable for most practical ap-plications. After a propagation distance of 19 mm,the 1.3 μm signal will still propagate in core A, whilethe 1.55 μm signal will be coupled to core B, which isin contrast to the situation in the first case. However,it also realizes the function of wavelength splittingand single-polarization guiding.
The confinement losses of the two orthogonal po-larization modes for the aforementioned two casesas a function of wavelength is also shown in Fig. 7.The loss difference between the odd modes and theeven modes are so small that we only consider theodd modes for simplicity. As can be seen in the figure,the confinement loss of y-polarized modes is about103 larger than the loss of x-polarized modes in awide wavelength range which further confirms thesingle-polarization guiding property. We list the ex-act loss value at wavelength of 1.3 μm and 1.55 μm
1.4 1.5 1.6 1.7 1.8 1.9 2.01.2
1.4
1.6
1.8
2.0
2.2
2.4L(
1.3)
/L(1
.55)
d4=0.6 µm
d4=0.8 µm
d4=1 µm
d4=1.2 µm
d2 (µm)
1.71
1.87
1.55 1.77
Fig. 4. Coupling length ratio for x-polarization modes at 1.3 μmand 1.55 μm as a function of the parameter d2 for various values ofthe small hole diameter d4.
1.0 1.2 1.4 1.6 1.8 2.01.36
1.38
1.40
1.42
1.44
y-polarization
x-polarization
FSM(x-polarized)FSM(y-polarized)
effe
ctiv
e in
dex
wavelength (µm)
odd modes
even modes
Fig. 5. Effective indices of two orthogonal polarization modesand cladding index as a function of wavelength for the PCF-splitter. The hole pitch Λx � 2.6 μm, Λy � 1.8 μm, d1 � 2.2 μm,d2 � 1.55 μm, d3 � 1.26 μm, and d4 � 1 μm.
1.0 1.2 1.4 1.6 1.8 2.01.34
1.36
1.38
1.40
1.42
1.44
FSM(x-polarized)
FSM(y-polarized)
y-polarization
x-polarization
effe
ctiv
e in
dex
wavelength (µm)
odd modes
even modes
Fig. 6. Effective indices of two orthogonal polarization modesand cladding index as the functions of wavelength for the PCF-splitter. The hole pitch Λx � 2.6 μm, Λy � 1.8 μm, d1 � 2.2 μm,d2 � 1.77 μm, d3 � 1.26 μm, and d4 � 1 μm.
after a propagation of the physical length in Table 1.The y-polarized modes will be nearly totally leakyas their loss value reaches to 30 ∼ 70 dB, while thex-polarized modes experience a very low loss whichare less than 0.05 dB.
As the physical length of the first case is shorterthan the second case and is more appropriate forpractical applications, wemainly investigate the firstcase below to illustrate the function of wavelengthsplitting. To verify the exact coupling length, in Fig. 8we plot the normalized power propagation versus thetransmission distance of the splitter in core A andcore B using an accurate BPM analysis [19]. Fromthe figure we can see that the 1.3 μm light in coreB and 1.55 μm light in core A reach their peaks afterpropagating for the same distance, approximatelyequal to 10.7 mm as designated by pink straight linein the figure. The 1.3 μm light in core A and 1.55 μmlight in core B reach the minimum intensity afterpropagating for a distance of 10.7 mm. The 1.3 μmlight experiences seven coupling lengths while the1.55 μm light experiences twelve coupling lengths.Therefore, it can be concluded that wavelength split-ting is achieved for a propagation length of 10.7 mm,which is in accordance with aforementioned calcula-tion results.
To visualize the wavelength splitting mechanismof the proposed PCF, in Fig. 9 we plot the electric fielddistribution by using the beam propagation analysis.
At z � 0, we could see the input field in core A andafter propagating for 5mm, different wavelengthsare coupled between the two cores. The 1.3 μm lightis perfectly coupled between the two cores for threetimes and then a fraction of the light is recoupledback into core A, as shown in Fig. 9(b). The 1.55 μmlight is perfectly coupled between core A and B forfive times and, after that, most of the light is coupledfrom core B into core A, as shown in Fig. 9(e). After apropagating for 10.7 mm, the 1.3 μm light is fullycoupled between the two cores for seven times andfinally exists in core B. The 1.55 μm light is fullycoupled between the two cores for twelve timesand still exists in core A. In this way, the two dif-ferent wavelengths exist in different cores, thusrealizing the splitting of different communicationwavelengths.
4. Cross Talk Analysis
Crosstalk between the two cores is a key parameterfor this kind of single-polarization wavelength split-ter, which will determine the influence of unwantedwavelengths in a particular output-core and thus cancharacterize the transmission performances. Accord-ing to [16], crosstalk should be defined as
Crosstalk � 10 log10
�P�λu�P�λd�
��dB�; (9)
where P�λu� is the signal power for an unwantedwavelength λu, P�λd� is the signal power for the de-sired wavelength λd.
Figure 10 shows the crosstalk of our designed PCF-splitter as a function of the unwanted wavelengthλu for the desired wavelengths of λd1 � 1.3 μm and
1.0 1.2 1.4 1.6 1.8 2.010-2
10-1
100
101
102
103
104
105
y-polarization
x-polarization
Con
finem
ent l
oss
(dB
/m)
Wavelength (µm)
d2=1.55µm
d2=1.77µm
Fig. 7. Confinement losses of the two orthogonal polarizationmodes (odd modes) as a function of wavelength for the PCF-splitter. The parameters are Λx � 2.6 μm, Λy � 1.8 μm,d1 � 2.2 μm, d2 � 1.55 μm (solid line), d2 � 1.77 μm (dash line),d3 � 1.26 μm, and d4 � 1 μm.
Table 1. Confinement Loss of the Two Orthogonal Polarization Modes for the PCF-Splitter at Wavelength of 1.3 μm and 1.55 μm after aPropagation of the Physical Length
First case (L1 � 10.7 mm) Second case (L2 � 19 mm)
λd2 � 1.55 μm. Here we consider the available opticalbandwidth (BW) defined as the wavelength rangewithin which the crosstalk is lower than −20 dB.We can see that the proposed PCF wavelengthsplitter has a reasonable BW [(a) BW � 5.3 nmaround λu � 1.55 μm and (b) BW � 8.5 nm aroundλu � 1.3 μm]for practical applications.
5. Conclusion
In this paper, for the first time to the best ofour knowledge, two cores are introduced into theSPSM PCF to achieve a single-polarization PCF
wavelength splitter. This splitter can realize thesplitting of two communication windows at 1.3 μmand 1.55 μm as well as keep the light maintain-ingsingle-polarization. A full-vector FEM and asemi-vector BPM are applied to investigate thesingle-polarization guiding characteristics and thewavelengt splitting properties. By tuning the struc-tural parameters of air holes, we can obtain differentm∶n. Numerical simulation results indicate that twocases are appropriate, of which the splitting lengthare equal to 10.7 mm and 19 mm, respectively. Lowcrosstalk over reasonable BW is also achieved. This
Fig. 9. (Color online) Electric field distribution of the single-polarization PCF wavelength splitter for (a) λ � 1.3 μm and z � 0 mm,(b) λ � 1.3 μm and z � 5 mm, (c) λ � 1.3 μm and z � 10.7 mm, (d) λ � 1.55 μm and z � 0 mm, (e) λ � 1.55 μm and z � 5 mm,(f) λ � 1.55 μm and z � 10.7 mm.
paper provides a new idea for the design of the PCF-based single-polarization wavelength splitter. We be-lieve this new type of splitter will be useful in futureoptical communication systems and other relatedoptical applications.
This work is jointly supported by the NationalNatural Science Foundation of China under GrantNo. 10974100, 10 674 075, 60 577 018 and NaturalScience Foundation of Tianjin under Grant No.10JCZDJC24300.
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1.53 1.54 1.55 1.56 1.57-30
-25
-20
-15
-10
-5
0
Wavelength (µm)
Cro
ssta
lk (
dB)
BW=5.3nm
1.28 1.29 1.3 1.31 1.32-40
-35
-30
-25
-20
-15
-10
-5
0
Wavelength (µm)
Cro
ssta
lk (
dB)
BW=8.5nm
Fig. 10. (Color online) Crosstalk between the two cores of thePCF-splitter and the available bandwidth for (a) λd1 � 1.3 μmand (b) λd2 � 1.55 μm.
