1. Introduction

Silicon wire waveguides have great potential as a platform for ultra-small photonic circuits [1–3]. Their bending radius with negligible loss is as small as a few microns because of their large refractive index contrast. Several kinds of functional devices based on Si wire have been demonstrated [4–6]. However, polarization mode dispersion (PMD), polarization-dependent loss (PDL), and polarization-dependentwavelength characteristics (PDλ) caused by large structural birefringence are not negligible. These drawbacks narrowly limit their application range.

There are several approaches to making a polarization-independent photonic circuit. The simplest way is to use a square core. However, for high-index-contrast waveguides, such as Si wire, fabrication errors of just a couple of nanometers are critical and result in birefringence. For instance, for waveguide length of 5 cm, the differential group delay between cores with a 300±5-nm width and 300-nm height reaches 6.6 ps, which degrades high-speed signals with the data rates of 40 Gbps. Furthermore, it is hard to remove the stress-induced birefringence which also causes the PDL, PMD and PDλ. In addition, the fluctuation of core width varies the group index and results in PDλ in wavelength filters. The difference in the resonant wavelength between transverse electric (TE) and transverse magnetic (TM) modes is larger than 100 GHz for a 10-µm-radius ring resonator with 300±1-nm-wide core. Therefore, accuracy of under a nanometer is required for devices used in polarization-independent dense wavelength division multiplexing systems. This is a big obstacle to mass production.

Another solution is the use of a polarization diversity system consisting of polarization splitters and rotators. If TE and TM components are separated by the splitter, and the TM component is rotated 90 degrees by the rotator, we need to fabricate functional devices (e.g., filter) for the TE mode only, not for both modes. Several key components for the polarization diversity have been presented [7–11, 13]. D. Tailaert et al. developed a two-dimensional grating coupler, which couples orthogonal modes from a fiber into identical modes of two waveguides [7]. This device is efficient for polarization splitting, although the coupling efficiency is as small as approximately -7 dB. M. R. Watts et al. demonstrated a polarization splitter and rotator with an asymmetric core cross section for SiN waveguides [8, 9]. However, the fabrication of such three-dimensional structures is difficult and would still be more demanding for Si wire because its core is smaller than that of the SiN waveguides.

In this paper, we first describe the principle of a polarization diversity system. Next, we show experimental results for a polarization splitter based on a directional coupler (DC) consisting of Si photonic wires and those for a polarization rotator based on an off-axis double-core structure consisting of a short Si photonic wire and an SiO_xN_y waveguide. Our polarization splitter and rotator have low insertion losses and are easy to fabricate because there is no need for complex processes for the fabrication of three-dimensional structures. In addition, we show experimental results for a polarization-independent wavelength filter with the polarization diversity system.

 

Fig. 1. Schematic diagram of a photonic circuit with polarization diversity consisting of polatization splitters and rotators.

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Fig. 2. Two-route configuration for the polarization diversity circuit.

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2. Principle and design

2.1. Polarization diversity circuit

A schematic diagram of the polarization diversity system is shown in Fig. 1. There are two optical paths as shown in Fig. 2. The splitter (PS1) separates the TE and TM components of the input light and feeds them into route 1 and route 2, respectively. Next, the rotator (PR1), which is inserted in route 1, rotates the TM component 90 degrees. After the functional processing, such as wavelength adding and dropping, the component of route 2 is rotated 90 degrees by the rotator (PR2), and compensation is made for the propagation distance for both routes. Finally, the two components are combined by the combiner (PS2) and coupled into the output fiber.

In such geometry, there is no PDλ because functional devices work only on the TE mode. Therefore, changing the polarization of the input light does not degrade the performance of functional devices. Since sharp bends allow propagation of TE light and eliminate TM one, there is no influence of the fraction of light, which is not efficiently splitted/rotated.

The symmetry of the circuit reduces the PDL and the PMD. When the propagation lengths of the TE and TM modes for route 1 are the same as those for route 2, respectively, the PDL and PMD are canceled out even if the Si wire waveguides have large polarization dependence. In additon, although the polarization splitting ratios of the splitters and the polarization rotation angles of the rotators are insufficient, the polarization dependence of output light can be reduced. The efficiencies of route 1 (η ₁) and route 2 (η ₂) are calculated by

where η ^TE _PS1, η ^TM _PS1, η ^TE _PS2, η ^TM _PS2 are the transmittances of the splitters for the TE and the TM modes, respectively, and η _PR1 and η _PR2 are the fractions of the polarization rotation by the rotators. The values of η ^TE _PS1, η ^TM _PS1 and η _PR1 are close to those of η ^TE _PS2, η ^TM _PS2 and η _PR2 respectively, because the splitters and the rotators are fabricated close to each other the same chip. Thus, the difference between η ₁ and η ₂ can be quite small. Eventually, the fabrication errors for these devices lead to only insertion loss, which is not dependent on the polarization of the input light.

2.2. Polarization splitter

Our polarization splitter is based on a DC [13]. A Si wire with an oblong core produces large PMD due to structural birefringence. There is large difference between propagation constants for the TE and TM modes. In a DC fabricated using such Si wire waveguides, the coupling length for the TM mode is much shorter than for the TE mode. Thus, just a simple DC works as a polarization splitter. From the results of propagation simulations, the DC consisting of Si wires with a 200-nm height and 400-nm width and a 480-nm gap between the wires separates two orthogonal polarizations with only 10-µm long propagation.

For a practical design, we have to pay attention to the bending radius around the DC. In the case of a rectangular core 200-nm high and 400-nm wide, the bending radius without bending loss for light with TE polarization and for that with TM polarization is quite different: the former can propagate through a sharp bend but the latter can not. Although light with either polarization mode can propagate through slight bends without loss, sharp bends are better for high-density integration. Therefore, we designed one waveguide (for TE) to bend sharply and the other (for TM) to be straight along the DC.

2.3. Polarization rotator

Our rotator has an off-axis double-core structure. The Si core confines light weakly, and the second core controls the polarization of the light. A Si wire whose square core is smaller than a regular core is embedded in a second waveguide. The left and bottom edges of the Si wire overlap the corresponding edges of the second waveguide. The schematic diagram of the cross-section of our rotator is shown in Fig. 3. The eigen axes of such a double-core structure are tilted towards the substrate. Thus, propagation through the waveguide produces a rotation of the polarization plane when the polarization of the incident light is parallel (TE) or orthogonal (TM) to the substrate.

 

Fig. 3. Schematic diagram of the polarization rotator.

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The design parameters are the material of the second core and the sizes of the Si core and second core. The second core with a large refractive index provides a large difference in the effective indices between two orthogonal eigenmodes. We assumed that the material of the second core was SiO_xN_y with a refractive index of 1.60. The cross-section of the Si core has to be just square to split the optical power into the two eigenmodes equally and ought to be a little smaller than that of a normal Si wire waveguide for single-mode propagation. It was set to 200-nm square because the input and output waveguides are normal Si wires with a 200-nm height and 400-nm width. The size of the second core also determines the rotator length. A shorter rotator is prefered because it has a wider wavelength range. From the calculation of the effective indices of the orthogonal eigenmodes as a function of the size of the second core, we found that the difference in the effective index is larger for a bigger second core. However, for the core size of over 850 nm, the difference again becomes smaller. Therefore, we set the cross-section of the second core to be 840-nm square.

The effective indices of the two orthogonal eigenmodes calculated from the conditions just mentioned are 1.542 and 1.525. Under these conditions, a device only 45-µm long provides a polarization rotation of 90 degrees.

3. Experiments

3.1. Sample preparation

Devices were fabricated on a SOI wafer with a 200-nm-thick Si layer and a 3-µm-thick SiO₂ buried layer. The Si wire waveguides for the input and output are 400-nm wide. For efficient coupling between the Si wire and external fiber, we made spot-size converters (SSCs) at the ends of the Si wires [12]. The Si wires and SSCs were fabricated by electron beam lithography and electron cyclotron resonance plasma etching. The propagation loss was measured by the cutback method and found to be 2.2 dB/cm for the TE mode and 1.7 dB/cm for the TM mode.

3.2. Polarization splitter

An SEM image of the fabricated polarization splitter is shown in Fig. 4(a). The length of the DC is 10 µm, the gap between the two waveguides is 480 nm, and the bending radius is 3 µm. Measured transmission spectra of the bar and cross ports for input light with TE and TM modes are shown in Fig. 4(b) and (c). The transmittance is defined as the output power ratio between the splitter and a simple Si wire with the same length as the splitter. The measured polarization extinction ratios (PERs) of the cross and bar ports in the C-band are 10 and 13 dB, respectively. The excess loss for the pass light is less than 0.5 dB for each port. The PER for the cross port can be improved by using a two-stage configuration. The measured values agree with the simulated ones. Details are discussed and demonstrated in Ref. [13].

 

Fig. 4. (a) SEM image of a fabricated splitter. (b, c) Measured transmittion spectra for the splitter.

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Fig. 5. (a) Schematic diagram of the polarization rotator. (b) Transmission spectra of the polarization rotator with a 35-µm length. (c) Polarizatin rotation angle estimated by the measured Poincaré map and polarization extinction ratio calculated from the measured polarization rotation angle.

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3.3. Polarization rotator

A schematic diagram of a fabricated rotator is shown in Fig. 5(a). The Si wires for the input and output are 200-nm high and 400-nm wide. These cores are adiabatically connected to the 200-nm-square Si core by 10-µm-long tapers. The polarization of the input light is TM. The transmission spectra filtered for the TE and TM components are shown in Fig. 5(b). When the length of the rotator is 35 µm, the TM component is greatly suppressed, and the TE component is transmitted with an excess loss of about 1 dB. The spectral ripples are caused by the polarization rotation of the ordinary Si wire waveguides used for input and output, and they complicate the estimation of the actual extinction ratio.

To obtain the actual extinction ratio, we measured the state of polarization with a Poincaré sphere. Figure 5(c) show the rotation angle estimated from the Poincaré map along with the extinction ratio calculated from the rotation angle as a function of rotator length. The maximum rotation angle is 72 degrees and the maximum extinction ratio is about 11 dB when the rotator length is 35 µm.

Insufficient rotation may be caused by half-round shape of second core. For 90-degree rotation, the amplitudes of two eigenmodes of the rotator must be just equal. Thus the eigen axes of two eigenmodes have to be tilted 45 degrees toward the substrate. We deposited silicon oxinitride film on fabricated Si wires as a second core. Therefore surface of the SiO_xN_y film is uneven, and the cross-section of the second core is partially half-round, not square.

 

Fig. 6. Photograph and schematic diagram of the polarization diversity circuit.

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Fig. 7. Transmission spectra of wavelength filters with and without polarization diversity.

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3.4. Polarization diversity circuit

We also fabricated a polarization-independent wavelength filter as a practical application of our polarization diversity system. A photograph and a schematic diagram of the fabricated polarization diversity circuit are shown in Fig. 6. The circuit consists of polarization splitters, rotators, and a ring resonator. The splitters and the rotators are the same as those mentioned in Sec. 3.2 and 3.3, respectively. The radius of the ring resonator is 10 µm and the gap toward the bus-line is 300 nm. The filter is designed for TE polarization. Therefore, for the light with TM polariation, the ring works as only directional coupler with low coupling efficiency.

Transmission spectra for wavelength filters with and without the polarization diversity configuration are shown in Fig. 7. Without the diversity, the transmittance is about 10 dB smaller for TM than for TE input. In other words, the PDL is 10 dB. On the other hand, with polarization diversity, the PDL is only 1.2 dB. This means that these elements do actually constitute a polarization-independent circuit.

We measured the high-speed signal response of the filter. The experimental setup is shown in Fig. 8(a). Light (λ: 1561.0 nm) from a tunable laser diode was modulated by a lithiumniobate intensity modulator with the data rate of 10 Gbps (NRZ, PRBS 231-1, Mark ratio 0.5). It was then coupled into a polarization scrambler, which scrambled the polarization of the incident light randomly. The light from the polarization scrambler was launched into the input waveguide of the filter. The output waveform from the filter was measured with an O/E-converter and a sampling oscilloscope. Measured eye-diagrams with and without the polarization diversity configuration are shown in Fig. 8(b) and (c), respectively. Without diversity configuration, the eyes are collapsed because of large PDL. On the other hand, with diversity configuration, the eyes are clear and open. This means that our polarization diversity circuits are already good enough for practical use in high-speed data transmission.

 

Fig. 8. 10-Gbps data transmission for the polarization-independent wavelength filter. (a) Experimental setup. (b, c) Measured eyediagram with and without polarization diversity.

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4. Discussion

For a practical device, it is important to estimate the fabrication tolerance. The most critical parameter for fabrication is the offset between the Si core and the second core in the rotator (Fig. 9)(a). An offset that is too large results in an insufficient polarization rotation in the rotator and thereby produces excess loss for the diversity system.

We fabricated rotators with various offsets and measured the polarization rotation angle by using the Poincaré sphere. From the results, we found that the rotators with offsets of around 30 nm maintain the rotation angles over 65 degrees, which correspond the insertion loss under 1 dB for the diversity circuit. Details are discussed and demonstrated in Ref. [14].

We also fabricated wavelength filters with polarization diversity consisting of rotators with various offsets. Figure 9(b, c) show the eyediagrams of the filters for 10-Gbps data streams. The eyes are open, even when the offset is around 30 nm. Therefore, we can conclude that the fabrication tolerance of our devices is around 30 nm. This value is practical for current fabrication technology.

 

Fig. 9. (a) Definition of offset. (b) Eyediagram for the filter with 0-nm offset. (c) Eyediagram for the filter with 30-nm offset.

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5. Conclusion

We have presented a polarization diversity system based on Si wire waveguides.We developed a DC-type polarization splitter and a polarization rotator with an off-axis double-core structure. Both devices can be made by planar fabrication technology and require no complex processes for the fabrication of three-dimentional structures.We demonstrated a polarization-independent wavelength filter as one application of polarization diversity. The filter consists of the polarization splitters, the rotators and a ring resonator. The PDL of the filter is reduced from 10 dB to 1 dB by using the polarization diversity.We obtained clear eye openings for 10-Gbps data streams with scrambled polarization. In addition, we found that our polarization diversity system allows a fabrication error of 30 nm.