Horizontal slot waveguides for polarization branching control Nai-Chia Cheng,1 Yao-Feng Ma,2 Po-Han Fu,1 Chun-Chieh Chin,3 and Ding-Wei Huang1,* 1
Institute of Photonics and Optoelectronics, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Taipei 10617, Taiwan 2
Quanta Computer Inc., No. 211, Wenhua 2nd Rd., Tao Yuan 33377 Taiwan 3
Genesis Photonics Inc., No. 5, Dali 3rd Rd., Tainan 74144, Taiwan *Corresponding author:
[email protected]
Received 13 October 2014; revised 21 November 2014; accepted 9 December 2014; posted 10 December 2014 (Doc. ID 224081); published 14 January 2015
The capability of polarization branching control of silicon-on-insulator horizontal slot waveguidebased directional couplers (DCs) was investigated, and a highly efficient polarization beam splitter (PBS) and a polarization-independent DC (PIDC) were proposed by tailoring the ratio of the coupling lengths for quasi-TE and quasi-TM modes. Due to structural birefringence, the coupling effects of the quasi-TE and quasi-TM modes in the DC may vary with the waveguide geometry. Numerical simulations were conducted to obtain the optimal design parameters for high efficiency and compact device size by varying the aspect ratios and waveguide spacing. The coupling lengths of the designed PBS and PIDC are 65.87 μm and 6.93 μm, respectively. They deliver good performance with extinction ratios of ∼20 dB for PBS and 15 dB for PIDC. The PBS and PIDC are also broadband with a 1 dB bandwidth larger than 30 nm and 100 nm, respectively. The fabrication-error tolerance of the practical device is also discussed. © 2015 Optical Society of America OCIS codes: (060.1810) Buffers, couplers, routers, switches, and multiplexers; (130.3120) Integrated optics devices; (130.5440) Polarization-selective devices. http://dx.doi.org/10.1364/AO.54.000436
1. Introduction
Silicon nanowires on the silcon-on-insulator (SOI) platform have great potential for ultrasmall photonic circuits [1–4] because of their compatibility with mature complementary metal-oxide-semiconductor (CMOS) technologies [5], excellent processing control, cost-effectiveness, and mass production. These advantages facilitate the making of highly compact photonic integrated devices using electronics fabrication facilities. Moreover, their ultrahigh refractiveindex contrasts allow for bending the radii of silicon nanowires down to a few micrometers with negligible 1559-128X/15/030436-08$15.00/0 © 2015 Optical Society of America 436
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bending loss. Therefore, silicon nanowires are promising candidates for integrated optics and optoelectronic integration in the future. The directional coupler (DC) is a fundamental component in integrated optics because it performs the functions of splitting and combining. Because of the DC’s simplicity and easy design, it has been employed in various applications including optical polarization splitters [6–10]. It is well known that a silicon nanowire waveguide coupler exhibits highly intrinsic polarization dependence due to a large refractive-index contrast, which is suitable for realizing a compact polarization-splitting devices. On the other hand, although DCs with broadband lowpolarization dependence have been proposed and implemented with an integrated Mach–Zehnder
interferometer configuration [11], the design requires a relatively large device size. Other types of polarization-independent (PI) DCs have been presented in various previous studies [12–14]. However, these devices must be implemented carefully by a complicated three-dimensional process, and their total lengths are still on the several-hundred micrometers scale. Slot waveguides, which allow light to be guided and strongly confined inside a nanometer-scale region of low refractive index, were recently proposed for use in many applications such as biosensors, chemical sensors, and DCs [15,16]. Since slot waveguide structures provide an additional degree of freedom for waveguide geometry design, the mode properties for both polarizations in slot waveguides were found to be controllable [17–21]. Due to the sandwiched structures, the structural birefringence of slot waveguides is further enhanced compared with conventional strip waveguides. Therefore, DCs with slot waveguide structures are useful in applications where strong polarization dependence is required. By combining horizontal slot waveguides and DC-based polarization splitters, it is probable that an effective polarization splitting or PI coupling can be accomplished. A previous simulation work has been proposed to realize a polarization splitter consisting of two horizontal slot waveguides and achieve an extinction ratio of more than 20 dB [22]. Experimental results of such a device were implemented by another group [23]. Although the device achieved a high extinction ratio for both ports, the relatively wide waveguide width may lead to higher-order modes propagating along the waveguide. In this paper, a compact polarization beam splitter (PBS) and a PIDC formed by horizontal slot waveguides on the SOI platform are investigated and presented through a different design philosophy. Compared with our previous report [24], the DC formed by horizontal slot waveguides would provide lower propagation loss because of the smoother interfaces between the high-index-contrast materials. In practicality, the devices based on horizontal slot waveguides would be more suitable for mass production than the devices based on vertical slot waveguides since the slot and strip thickness of horizontal slot waveguides are defined by the thinfilm deposition technique or thermal oxidation, which provides better control of the layers’ dimensions. In order to pursue better simulation accuracy, we also adopted the finite-element-method-based commercial simulation software (COMSOL Multiphysics) as our simulation tool rather than the beam propagation method used previously. However, by varying the dimensions of the waveguide structure, it is also possible to control the structural birefringence of the SOI horizontal slot waveguides and the coupling lengths of the quasi-TE and quasi-TM modes. Thus, either excellent polarization splitting or a PI coupling behavior can be obtained by properly choosing the design parameters. Because the light
confinement mechanism is total internal reflection (TIR) in the slot waveguide, the wavelength dependence is not as strong as for other structures (e.g., photonic crystal waveguides), in which light confinement is based on interference and string dispersion cannot be avoided. Bandwidth and device size as a function of the cross-sectional geometry will also be discussed. 2. Design of the Horizontal Slot Waveguide
Figures 1(a) and 1(b) show the transverse mode profile for quasi-TE and quasi-TM modes in a single horizontal slot waveguide with the slot layer (silica, ns 1.444) sandwiched by silicon layers (nr 3.478). The guided mode polarized to one of the major axes (y-axis, quasi-TM modes) is strongly confined in the slot region [25,26] because of the electric-field discontinuity between the high- and low-refractiveindex regions. Light can be strongly confined in the slot region due to the TIR, as can be seen in Fig. 1(b). A schematic of a DC using two horizontal slot waveguides is shown in Fig. 1(c). The device is patterned on the SOI substrate with air (nc 1) as the upper cladding and silica (ns 1.444) as the lower cladding for guiding the optical signal at the wavelength of λ0 1.55 μm. The labels h, hs , and w refer to the height of a single silicon layer, the height of the slot layer and the width of the waveguide, respectively. The spacing between the two waveguides is denoted by g. The coupling length of the DC is denoted by Lc. 3. Supermode Theory
When light propagates in such a dual-channel DC, the guiding behavior of the total device can be viewed as the summation of waves propagating in even and odd modes with effective indices ne and no . Transverse field distributions of even and odd modes of TE-(ne;TE and no;TE ) and TM-(ne;TM and no;TM ) polarized waves are shown in Figs. 2(a)–2(d). The differences in the field continuity at the boundaries between the core and the cladding of quasi-TE and quasi-TM modes are obvious, and these properties can be used to distinguish the modes with different polarizations. The evolution of the effective index of each corresponding waveguide mode as a function
Fig. 1. Transverse field distributions of the quasi-TE and quasiTM modes in a single horizontal slot waveguide: (a) the quasi-TE mode, (b) the quasi-TM mode. (c) Schematic of the directional coupler formed by a horizontal slot waveguide. 20 January 2015 / Vol. 54, No. 3 / APPLIED OPTICS
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Fig. 2. Transverse field distributions of the even and odd quasiTE and quasi-TM modes in a dual-channel directional coupler: (a) the even quasi-TE mode, (b) the odd quasi-TE mode, (c) the even quasi-TM mode, and (d) the odd quasi-TM mode. (e) Effective indices of even and odd quasi-TE modes (ne;TE , no;TE ) and quasi-TM modes (ne;TM , no;TM ) in a dual-channel coupler as a function of the waveguide spacing g.
of the waveguide spacing g is shown in Fig. 2(e). Apparently, the difference between the effective indices of even and odd modes increases as the waveguide spacing decreases due to the apparent coupling that occurs between the optical signals propagating in both horizontal slot waveguides. On the other hand, when the spacing g between the two adjacent horizontal slot waveguides is sufficiently large, the effective indices of even and odd modes converge to the values of individual horizontal slot waveguides’ effective indices. In this case, the DCs act like two independent horizontal slot waveguides. According to the supermode solution method [27,28], the length Lc required for a complete power transfer between the two adjacent waveguides in a dual-channel DC is related to the difference between the effective indices of the even and odd modes, i.e., Lc
π π ; k0 ne − no k0 Δn
(1)
where k0 2π∕λ0 is the propagation constant in free space at the operating wavelength λ0 and Δn ne − no is the difference between the effective indices of the even and odd modes. Because the width of the horizontal slot waveguide is slightly smaller than its height (w < 2 h hs ), the quasi-TE modes have longer field tails in the cladding region (waveguide spacing region) than the quasi-TM modes. Moreover, the quasi-TM mode has a strong field confined in the slot region, but the quasi-TE mode does not. Thus, the effective indices ne and no of the quasi-TE modes may converge more significantly than those of the quasi-TM modes as the waveguide spacing g increases as observed in Fig. 2(e). Based on the difference mentioned above, we can tune the ratio of the coupling lengths of the quasi-TE and quasi-TM modes (LTE ∕LTM ) with an extra degree of freedom with different aspect ratios of the horizontal slot waveguides (w∕h). To simplify the design process, hs is fixed to 80 nm, and the reason will be explained below. Single silicon layers with different h and w are used to manipulate the structural 438
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birefringence and the coupling effect between the two adjacent horizontal slot waveguides. Silicon layers with heights of h 210, 230, 250, and 270 nm and widths of w 270 nm and w 280 nm were considered. These parameters satisfied the singlemode propagation condition. The evolution of LTE ∕LTM as a function of the waveguide spacing g was obtained for each aspect ratio value w∕h (see Fig. 3). The effect of slot thickness hs on the performance of the dual-channel DC is also analyzed. On actual SOI wafers, the thickness of the buried oxide (BOX) layer used as the lower cladding is finite. Thus, the leakage behavior of the evanescent field in the silicon substrate below the BOX layer needs to be investigated. In general, the thicker the slot layer, the weaker the confinement of the optical mode, and therefore the more power extends into the silicon substrate. Consider a single horizontal slot waveguide with the structural dimensions chosen as follows: w 270 nm, h 250 nm, and BOX layer thickness hBOX 2 μm. We calculated the ratio of the power in the silicon substrate and the total mode power as a function of hs [see Fig. 4(a)]. As predicted, the leaky power ratio increases with hs . On the other hand, considering that a dual-channel DC consists of two such horizontal slot waveguides with waveguide spacing g 400 nm, the coupling length decreases as hs increases due to the weaker confinement of the mode, which is shown in Fig. 4(b). Figure 4(b) also shows the effective index difference (Δneff nTE − nTM ) of the horizontal slot waveguide as a function of hs. It is observed that Δneff increases with the slot thickness, meaning that the confinement of the quasi-TE and quasi-TM modes are approaching each other as hs increases, and therefore LTE and LTM also approach the same value [Fig. 4(b)]. Briefly speaking, a more compact device size can be achieved by increasing the slot thickness hs . Therefore, there is a trade-off between the propagation loss and the total device size when selecting a proper hs value. Here, a
Fig. 3. Evolution of the coupling-length ratio LTE ∕LTM of quasiTE and quasi-TM modes for each aspect ratio (w∕h) as a function of waveguide spacing g.
Fig. 4. (a) The ratio of optical mode power leaked into the silicon substrate as a function of the slot thickness. (b) Coupling lengths LTE and LTM of the dual-channel directional coupler and the effective index difference of a single horizontal slot waveguide neff are examined as functions of the slot thickness hs
thickness of 80 nm is chosen for our design to take the mode confinement, optimal coupling length, and ease of fabrication into account. 4. Design of the Polarization Beam Splitter
Based on Fig. 3, when w 270 nm and h 210 nm, it can be deduced that the difference between the effective indices of the even and odd quasi-TE modes is larger than that of the quasi-TM modes when the waveguide spacing larger than ∼0.25 μm. According to Eq. (1), the coupling length for quasi-TE modes LTE is shorter than that for quasi-TM modes LTM . This provides the opportunity to use the dualchannel direction coupler for efficient polarization splitting by appropriately adjusting the waveguide spacing g. When the difference between ne and no for quasi-TE modes (ΔnTE ne;TE − no;TE ) is exactly twice that for quasi-TM modes (ΔnTM ne;TM − no;TM ), i.e., ΔnTE 2ΔnTM , the coupling length for quasi-TE modes LTE will be exactly half of that for quasi-TM modes LTM (i.e., LTE ∕LTM 0.5) according to Eq. (1). Under such a condition, the incident light can be efficiently split into two orthogonally polarized modes propagating in separate output ports if the length of the device is appropriately chosen so that Lc LTM 2LTE . Thus, an efficient polarization-splitting performance can be obtained. According to Fig. 3, the condition ΔnTE 2ΔnTM is satisfied when g 0.72 μm is chosen, and efficient polarization splitting of the optical signals at λ0 1.55 μm can be achieved. The resultant length of the coupling section is Lc 65.87 μm. The propagation of the optical signals along the coupling section for both quasi-TE and quasi-TM modes were conducted using a full-wave analysis tool based on the finite-element method (from COMSOL). For one polarization, the input of the optical signal was implemented by exciting both the even and odd modes simultaneously at the boundary with the same power. Since the propagation constants of the two supermodes are different, there will be a beating between these two waves. The results in Fig. 5 show that the quasi-TM mode is completely
transferred to the cross-port, and the quasi-TE mode is first coupled out and then brought back completely to the bar port. Thus, efficient polarization splitting is achieved. The wavelength dependence of bar port and cross ports for both quasi-TE and quasi-TM modes are shown in Fig. 6(a). At the operation wavelength of λ0 1.55 μm, it is observed that the polarization extinction ratio is ∼21 dB and 26 dB for quasi-TE and quasi-TM modes, respectively. The 1 dB bandwidth for quasi-TM modes is nearly 100 nm, which is more than three times larger than that for quasi-TE modes because there is one more instance of complete energy transfer between adjacent photonic wires for quasi-TE modes than for quasi-TM modes. Consequently, the operation tolerance of quasi-TE modes becomes tighter than that for quasi-TM modes. The tolerances to the coupling length Lc and the width of the waveguide w are shown in Figs. 6(b) and 6(c), respectively. It can be seen that the tolerance of the quasi-TM mode is not so critical compared with that of the quasi-TM mode. This is due to the extra energy transfer of the quasi-TE mode as discussed above. Moreover, the tolerance to w is not as strong as that to Lc because, for SOI horizontal
Fig. 5. COMSOL simulation results of the evolutions of the mode fields for (a) quasi-TE and (b) quasi-TM modes between the adjacent waveguides along the coupling section of the PBS. 20 January 2015 / Vol. 54, No. 3 / APPLIED OPTICS
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and quasi-TM modes, and satisfying the PI condition LTE LTM Lc . Based on this design, the incident light of the quasi-TE and quasi-TM modes can be coupled from the bar port to the cross port simultaneously. Therefore, an efficient PI coupling can be achieved. In this work, the silicon layer height h 210 nm, the waveguide width w 280 nm, and the waveguide spacing g 0.31 μm are chosen to ensure that ΔnTE ΔnTM at λ0 1.55 μm. Consequently, LTE LTM Lc 6.93 μm can be set to accomplish a successful PI coupling as in the simulation result shown in Fig. 7. The transmission spectra of bar ports and cross ports for both quasi-TE and quasi-TM modes are shown in Fig. 8(a). It is observed that the polarization extinction ratios are ∼15 dB and 18 dB for quasi-TE and quasi-TM modes at the operation wavelength of λ0 1.55 μm, respectively. In this device, the complete energy transfer occurs once for both quasi-TE and quasi-TM modes, leading to a similar 1 dB bandwidth for both modes. The polarization extinction ratio of the designed PIDC is not as high as the proposed PBS. This is due to the much more compact device size of the PIDC. The tolerances to the coupling length Lc and the width of the waveguide w are shown in Figs. 8(b) and 8(c), respectively. We can observe that in Fig. 8(c) the deviation to the initial chosen waveguide width w has hardly any influence on the polarization extinction ratio of the quasi-TM mode. This reflects the fact that ΔnTM is relatively tolerant to the variation of w. The similar phenomenon can also be observed in Fig. 6(c). 6. Discussion and Summary
Note that in the case of designing a PBS, the corresponding waveguide spacing g required for satisfying the criterion for complete polarization splitting (i.e., LTE ∕LTM 0.5) becomes smaller when the aspect ratio w∕h decreases. Consequently, the device size is reduced. Furthermore, the evolution of the coupling length ratio LTE ∕LTM is smoother for a larger aspect ratio at the selected waveguide spacing g. This is because the quasi-TM mode tails are strongly Fig. 6. (a) Transmission spectra of both modes in the device and the transmittance as a function of (b) Lc and (c) Δw of PBS.
slot waveguides, the transverse geometry is crucial to mode-field distribution and thus the effective indices. On the other hand, this implies that a dramatic change of propagation characteristics can be obtained by external effects like the thermo-optic and nonlinear optical effect, making it possible to realize ultrasmall functional devices with a low operating power. 5. Design of the Polarization-Independent Directional Coupler
We also propose an alternative design based on horizontal slot waveguides, as observed in Fig. 3, by carefully setting the aspect ratio to manipulate ΔnTE and ΔnTM , tuning the coupling lengths of the quasi-TE 440
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Fig. 7. COMSOL simulation results of the evolutions of the mode fields for (a) quasi-TE and (b) quasi-TM modes between the adjacent waveguides along the coupling section of the PIDC.
splitting is 517.34 μm, which is ∼7 times longer than that of the case when w 270 nm (Lc 70.61 μm). However, in the case of w 280 nm, the fabrication tolerance and the operation bandwidth are much more than that of the case of w 270 nm, which is more compact. Hence, while designing such a device, we should choose an appropriate w∕h that allows a compact size, an acceptable operation bandwidth, and a coupling performance required for practical applications. Also note that when the waveguide width w 280 nm, there was a point where different LTE ∕LTM evolution curves with different aspect ratios intersected almost at LTE ∕LTM 1. This was highlighted with a circular arrow in Fig. 3. This operation point implies large tolerance to fabrication error of the height of the silicon layer. However, for different waveguide widths, an intersection at LTE ∕LTM 1 does not necessarily exist for curves corresponding to different aspect ratios w∕h. To achieve this design point, the following conditions must be satisfied: dLTE dLTM ; dh dh
(2)
LTE LTM :
(3)
Using ΔnTE ΔnTM at λ0 1.55 μm [from Eq. (3)] and combining the relations between Lc and Δn according to Eq. (1), we can reduce Eq. (2) to dΔnTE dΔnTM : dh dh
Fig. 8. (a) Transmission spectra of both modes in the device and the transmittance as a function of (b) Lc and (c) w of PIDC.
suppressed due to the “narrowed” cross-sectional geometry in the adjacent waveguide, whereas the quasi-TE polarized ones are not. Thus, the coupling length ratio LTE ∕LTM increases as the aspect ratio w∕h increases, as shown in Fig. 3. Because sharper evolution leads to less fabrication tolerance, the trade-off between the device size and the fabrication-error tolerance should be considered. Generally speaking, more fabrication-error tolerance also leads to more wavelength-deviation tolerance. For example, when h 250 nm and w 280 nm, the corresponding waveguide spacing is ∼0.91 μm, which is 1.4 times larger than that of the case when w 270 nm (g 0.63 μm). Meanwhile, the corresponding coupling length for complete polarization
(4)
However, in practicality, it is difficult to find such an operation point directly. It would be feasible to first sketch the evolution of LTE ∕LTM as a function of the waveguide spacing g for a specific set of w and h to find the waveguide spacing g at LTE LTM . This would be followed with the calculation of ΔnTE and ΔnTM as functions of h for different w values with small variations to the original value. The conditions described by Eqs. (2) and (3) will be satisfied when the two curves of ΔnTE and ΔnTM almost overlap with the same slope. It is worthwhile to note that in our design, due to the unaffordable simulation effort with the calculation resources at hand, the input/output section of the entire branching device is not considered in the simulation. For practical application, mode-size converters may be introduced to connect the strip waveguide to the horizontal slot waveguide so as to reduce potential loss arising from large field mismatch [29]. As the waveguide spacing g gets smaller, the separated fields near the converter section may further couple to each other, altering the power-coupling ratio and thus reducing the polarization extinction ratio. In order to minimize this unwanted excess coupling effect, the converter section should be 20 January 2015 / Vol. 54, No. 3 / APPLIED OPTICS
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considered as part of the coupling region. Thus, the coupling section in real devices should be slightly shorter than Lc obtained in the simulation results. However, in this paper, we provide a general guideline for designing efficient PBS and PIDC by making use of the additional degree of freedom on the slot waveguide geometry, and this method would be helpful for evaluating entire device performance before fabricating actual devices. In summary, the structural birefringence in the dual-channel DCs formed by horizontal slot waveguides on an SOI platform can be precisely controlled with appropriate selections of the waveguide geometry. Such a feature can be used for designing compact PBSs and compact PIDCs with good performance. We investigated the effect of the aspect ratio of the slot waveguide and discussed the trade-off between device size and performance. Moreover, based on the simulation results, we also propose a procedure for designing PIDCs with large fabrication tolerance. In this work, the coupling length of the PBS is 65.87 μm with the spacing g 0.72 μm between the two adjacent slot waveguides. The polarization extinction ratios are 21 dB and 26 dB for quasi-TE and quasi-TM modes, respectively. On the other hand, the coupling length of the PIDC is 6.93 μm with the spacing g 0.31 μm between the two adjacent slot waveguides. The polarization extinction ratios are 15 dB and 18 dB for quasi-TE and quasi-TM modes, respectively. The 1 dB bandwidth for the quasi-TM modes is nearly 100 nm, which is three times larger than that of the quasi-TE modes in the PBS. The 1 dB bandwidths for the PIDC are both larger than 100 nm. Compared with other designs of polarization splitters based on DCs and PIDCs, our design based on horizontal slot waveguides has the advantages of more compact size, higher polarization extinction ratios, and wider operation bandwidths. The authors are thankful for the financial support from the Aim for Top University Project from the Ministry of Education, Taiwan, and those from the Ministry of Science Technology, Taiwan, under grant nos. MOST 103-2221-E-002-060 and MOST 102-2221-E-002-175. References 1. P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. Van Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. Van Thourhout, and R. Baets, “Low-loss SOI photonic wires and ring resonators fabricated with deep UV lithography,” IEEE Photon. Technol. Lett. 16, 1328–1330 (2004). 2. H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Si photonic wire waveguide devices,” IEEE J. Sel. Top. Quantum Electron. 12, 1371–1379 (2006). 3. T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, “Microphotonics devices based on silicon microfabrication technology,” IEEE J. Sel. Top. Quantum Electron. 11, 232–240 (2005). 4. K. K. Lee, D. R. Lim, H.-C. Luan, A. Agarwal, J. Foresi, and L. C. Kimerling, “Effect of size and roughness on light 442
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