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A wavelength splitter and a polarization splitter with high compactness and extremely simple structures are designed for optical communication wavelengths. Operation principle of the devices is based on directional coupling in two parallel periodic dielectric waveguides. The device performances have been evaluated by the finite-difference time-domain simulations. The wavelength splitter with a coupling region length of 5 µm can route 1.31 and 1.55 µm wavelengths to corresponding outputs with a transmittance of more than 93%, while the polarization splitter with a coupling region length of 4.6 µm can divide lightwaves in TM and TE polarizations with a degree of polarization higher than 90% at 1.55 µm.
©2008 Optical Society of America
1. Introduction
Wavelength splitters (also called demultiplexers) and polarization splitters are essential components for optical signal redistributing in photonic integrated circuits (PICs). In the past several years, wavelength and polarization splitters based on photonic crystals (PCs) have been designed and demonstrated with different structures [1–11]. However, PC-based devices have an intrinsic disadvantage that the device structures must follow the PC lattice orientation. This becomes an obstacle for flexible control of lightwaves. Furthermore, PC-based devices require a wide PC background (at least several lattice constants) and usually occupy much space in transverse dimension. These may cause inconvenience for highly integrated PICs. As a good candidate for building ultracompact devices, periodic dielectric waveguide (PDWG) has the ability to provide high transmission in arbitrary shaped device with very little space [12]. Therefore, we propose wavelength and polarization splitters using PDWGs with principle of directional coupling. Analyses are given for the two structures and the coupling region lengths are determined for optical communication wavelengths, which offer functions of splitting wavelengths of 1.31 and 1.55 µm, and splitting TM and TE polarizations at 1.55 µm, respectively.
2. Wavelength splitter
PDWGs can be formed by dielectric cylinder array in air or air-hole array in dielectric [13]. Here the considered single-row PDWG is a dielectric cylinder array with a dielectric constant of ε=11.9. The radius of the cylinders is set to be r=0.4a, where a is the center-to-center spacing between two adjacent cylinders, as shown in Fig. 1(a). Figure 1(b) shows the TM band structure of the single-row PDWG which is calculated by the plane wave expansion (PWE) method for an a×9a supercell shown by the dashed frame in Fig. 1(a) [14]. The shaded region (light line region) represents the extended modes. It can be seen that the band curve is below the light line region, which indicates that the mode is a guided mode in the PDWG. For operating at optical communication wavelengths, a is specified as a=157 nm. Two normalized frequencies of 0.120(a/λ) and 0.101(a/λ) can be obtained for the wavelengths of λ=1.31 and 1.55 µm, respectively. The inset in Fig. 1(b) is the guided single mode pattern.
Fig. 1. (a) A single-row PDWG model. The dashed frame shows the supercell for the PWE calculation. (b) Band structure of the model. The shaded region represents the extended modes (light line region) and the inset shows the single mode pattern.
To perform a function of wavelength splitter, a directional coupling model is formed by arranging two parallel single-row PDWGs with a distance d, as shown in Fig. 2(a). By the PWE calculation, d=2.55a is chosen for the directional coupling model. Figure 2(b) shows the band structure for the a×12.55a supercell shown by the dashed frame in Fig. 2(a). It can be seen from Fig. 2(b) that there are two modes with different wave vectors and mode patterns. For such a directional coupling model, when a guided mode from a single-row PDWG is injected into the directional coupling region, the injected mode will be excited into two modes. k 1 and k 2 represent the wave vectors for the excited first and second band modes, respectively. Then the two modes interfere with each other via establishing phase difference along the propagation direction. Energy will be transferred from one PDWG to the other after a coupling length L c, which is defined as [15]:
If the two coupling lengths L c1 (for λ1) and L c2 (for λ2) satisfy (2N-1)×L c1=2N×L c2, where N is a natural number, we can route λ1 and λ2 to different output waveguides.
Fig. 2. (a) Directional coupling model. The dashed frame shows the supercell for the PWE calculation. (b) Band structure of the model. The insets show the mode patterns of the first and second band mode.
For 1.31 and 1.55 µm, the respective coupling lengths L c1=31.3a and L c2=16.1a can be calculated by taking k 1 and k 2 from Fig. 2(b) and substituting them into Eq. (1). The results satisfy L c1≈2L c2. Therefore, if the coupling region length L is set to be L=32a, 1.31 µm can be totally coupled from one PDWG to the other while 1.55 µm will be totally coupled back into the original PDWG after twice coupling. To confirm the validity, two-dimensional (2D) finite-difference time-domain (FDTD) simulations with perfectly matched layer (PML) boundary conditions are run in the directional coupling region with L=32a. Figure 3 shows the steady-state field distributions, which agree well with the calculations.
Fig. 3. Steady-state field distributions in the directional coupling region with a length of L=32a for lightwaves at (a) 1.31 µm and (b) 1.55 µm.
Based on the above models, a wavelength splitter is formed by adding an additional straight input PDWG to the left of the directional coupling model with L=32a (5 µm) and two symmetrical S-shaped output PDWGs to the right of the model, as shown in Fig. 4. The distance between two adjacent cylinders in the PDWG bends keeps a to provide the same transmission condition. To achieve low bending loss, we choose a bending angle of 60° for each bend where the radius of curvature is R=0.5a/(sin5°)=5.74a. For performance evaluation, the FDTD simulations are run for 1.31 and 1.55 µm. Figure 5 shows the steady-state field distributions, in which the two wavelengths are routed to the corresponding outputs. By taking FDTD simulations with wavelengths from 1.25 to 1.60 µm at the two outputs, the normalized intensity spectrum is obtained (Fig. 6). It can be seen that the peak intensities of the two outputs are at 1.30 and 1.54 µm. A shift of 10 nm in wavelength is mainly caused by the additional coupling at the connection part of the two parallel PDWGs with the two S-shape bends. We rerun the FDTD simulations for the wavelength splitter with L less than 32a. The results indicate that by reducing L to 30a, the peak intensities (above 93%) at the two outputs can be shifted to 1.31 and 1.55 µm, as shown by the dashed curves in Fig. 6.
Fig. 6. Normalized intensity spectrum from 1.25 to 1.60 µm for the wavelength splitter. The solid curves are for the coupling region with L=32a, while the dashed curves for L=30a.
3. Polarization splitter
In this section, we use the concept of directional coupling in PDWGs in TM/TE polarization splitter. To guide lightwaves in both TM and TE polarizations, a single-row PDWG model without gaps between two adjacent cylinders is considered, as shown in Fig. 7(a). The center-to-center spacing between the two adjacent cylinders is a and the radius of the cylinders is r=0.56a, which leads to part overlapping of cylinders. Although no gaps exist between cylinders, it can still be considered as a PDWG due to the periodic nature of dielectric constant distributing along the propagating direction. The supercell for band structure calculation is a×9a, as shown by the dashed frame in Fig. 7(a). Figure 7(b) shows the calculated band structure. It can be seen that the band curves of both TM and TE polarizations are below the light line region, which indicates that the modes in both polarizations are guided modes. For 1.55 µm operation, a is specified as a=230 nm. Single-mode guiding can be achieved for 1.55 µm at a frequency of 0.148(a/λ) and the insets show the corresponding mode patterns.
Fig. 7. (a) A single-row PDWG model. The dashed frame shows the supercell for the PWE calculation. (b) Band structure of the model. The insets show the single mode patterns.
The directional coupling model is also formed by arranging two parallel PDWGs with a distance of d, as shown in Fig. 8(a). The PWE calculations show that as d increases, the first and second band curves tend to become closer. Moreover, the TM band curves are much closer than TE ones at the frequency of 0.148(a/λ). This means it is much more difficult for the TM modes to change field patterns and to transfer energy from one PDWG to the other in the coupling region. Therefore, with a proper d, the directional coupling model can ensure the TM band curves superposed while the TE band curves are still separated. This results in a finite L c for TE polarization and a nearly infinite L c for TM polarization. Thus directional coupling only occurs for the lightwave in TE polarization in the coupling region. According to the PWE calculations, d=2.91a is chosen and the band structure is obtained (Fig. 8b) for the a×12.91a supercell shown by the dashed frame in Fig. 8(a). In Fig. 8(b), the first and second band curves for TM polarization superpose at 1.55 µm while the curves for TE polarization are still separated. Concerning the mode patterns shown by the insets, the first and second band modes are different for the TE polarization, while the two mode patterns are nearly the same for the TM polarization. These indicate that only the TE modes can be coupled from one PDWG to the other in the coupling region. Therefore, a polarization splitter for 1.55 µm can be obtained.
Fig. 8. (a) Directional coupling model. The dashed frame shows the supercell for the PWE calculation. (b) Band structure of the model. The insets show the first and second band mode patterns in TM and TE polarizations.
By taking the corresponding wave vectors for the TE modes from Fig. 8(b) and substituting them into Eq. (1), a coupling length of Lc=22.2a is obtained for 1.55 µm. The polarization splitter is then formed by adding a straight input PDWG to the left of the directional coupling model, and a straight and an S-shape bending output PDWGs to the right of the model (Fig. 9). We choose 20a (4.6 µm) a bit less than 22.2a to compensate the coupling in branching section cascaded at the end of the coupling region. Different from the PDWG-based wavelength splitter, the S-shape bending output PDWG here is designed only for the TM signal output since the TE signal suffers rather high bending loss through the bends. The centre-to-centre spacing between two adjacent cylinders in the bends is still a, the bending angle is 90°, and the radius of curvature is R=0.5a/(sin5°)=5.74a. The loss for TM polarization through the bends is less than 10% for wavelengths from 1.52 to 1.58 µm.
Fig. 10. Steady-state field distributions in the polarization splitter for 1.55 µm in different polarizations.
To evaluate performance of the polarization splitter, FDTD simulations are run for 1.55 µm in both TM and TE polarizations (with the same input intensity). The results of steady-state field distributions are shown in Fig. 10. By taking the FDTD simulations from 1.52 to 1.58 µm and calculating the intensities at the two outputs, the intensity spectrum for the two outputs with different polarizations is obtained and shown in Fig. 11. The maximum normalized intensity for TM polarization in output 1 and TE polarization in output 2 reaches 92.7% and 90.3%, respectively. Furthermore, the degree of polarization P in each output is calculated by the definition of P
where I TE and I TM are the intensities in the TE and TM polarizations at the outputs, respectively. Figure 12 shows the calculated curves for degree of polarization versus wavelengths from 1.52 to 1.58 µm. It can be seen that the degree of polarization in output 2 is above 90% over the wavelength range from 1.52 to 1.58 µm, while in output 1 there is a peak of 94.5% at 1.55 µm with a high-polarization (above 90%) bandwidth of 19 nm.
Fig. 11. Normalized intensity of the polarization splitter in a wavelength region of 1.52 to 1.58 µm.
Fig. 12. Degree of polarization of the polarization splitter in a wavelength region of 1.52 to 1.58 µm at the two outputs.
4. Discussion
As a comparison, the coupling region length (5 µm) of the wavelength splitter based on PDWGs in this work is much shorter than those reported in Ref [1] (24 µm) and Ref. [2] (15 µm) based on PC waveguides. The coupling region lengths of all these demultiplexers (including the proposed one) can be further reduced by varying the normalized input frequencies. However, for the PC waveguide-based wavelength splitters, the distance between the two parallel waveguides is limited to integral times of lattice constant. By contrast, the distance between the two parallel waveguides in the PDWG-based wavelength splitter can be changed arbitrarily. This flexibility may lead to further tuning of the coupling length and the wavelength finesse of demultiplexer. Wavelength splitters based on other principles have also been achieved in PCs such as by introducing different defects in a T-junction [3], utilizing intersecting dispersion curves in triangular PCs [4], and using high Q coupling cavities [5]. These wavelength splitters apply different propagation properties in PCs and thus they have relatively complex structures. Compared with those reported in PCs, the structure of the PDWG-based wavelength splitter is much simpler due to the operation principle of directional coupling. Moreover, the device can be easily tuned for different wavelengths by changing the coupling region length. For polarization splitter, several prominent methods have been reported to achieve polarization splitting in PCs utilizing different photonic band gaps [6,10], polarization anisotropies [7,9], resonances in coupled PC microcavity arrays [8], negative/positive refraction [11] and so on. Compared with the these PC-based polarization splitters, the PDWG-based polarization splitter proposed in this work has a much simpler structure, while satisfactory performances in transmittance (90.3% for 1.55 µm) and degree of polarization (over 90%) can still be maintained. Finally, both PDWG-based devices occupy much less space in the transverse dimension because they do not require a wide PC background, which will provide high compactness for PICs.
It is notable that the changes of the coupling region length L will affect the performances of the proposed devices because the values of L are obtained for specific wavelengths. This means there may be certain impact on the transmissions due to the fabrication errors for the fabricated devices in practice. However, as the distance d between the two parallel PDWGs in the two devices can be changed arbitrarily, the band structure of the directional coupling region can be tuned and the coupling length L c can be changed for the applied wavelengths accordingly. Therefore, the impact of the fabrication errors can be diminished by changing d to compensate the errors in L. It should also be pointed out that the discussed structures and performed simulations in this work are all 2D, i.e., the dielectric cylinders in all the models are considered as infinite on the vertical direction in simulations. As revealed by Fan et al. in Ref. [13], 2D PDWG systems are more constructive to computation than their three-dimensional (3D) counterparts, and their steady-state fields are much easier to visualize in simulations. Furthermore, in 3D PDWG systems, guided modes may still be approximately characterized as TE-like or TM-like according to their dominant polarization directions. Therefore, it is hoped that the results gained from the 2D models can be readily applied to more realistic 3D systems. Of course, if a third dimension is added, unavoidable out-of-plane losses will be caused. However, according to our calculations, if a minimum height of 2λ (λ is the wavelength of interest) is chosen for the dielectric cylinders, it can be ensured that the cylinders are regarded as infinite on the vertical direction in simulations while the out-of-plane losses will be lower than 20% due to the very short length of the devices. Since the caused losses by adding the third dimension is not due to the 2D models, the main result of this work should also be valid for a 3D structure.
5. Conclusion
Wavelength and polarization splitters have been proposed based on directional coupling in two parallel PDWGs for optical communication wavelengths. The two devices offer functions of splitting 1.31/1.55 µm wavelengths with a transmittance more than 93% and splitting TE/TM polarizations at 1.55 µm with degree of polarization higher than 90%, respectively. Compared with those reported in PC waveguides, the devices have higher compactness, much simpler and more flexible structures, which would be benefit for highly integrated PICs.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant Nos. 60625404 and 60577001).
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