1.
Introduction

In recent years, photonic integrated circuits (PICs) have attracted wide attention due to their low power consumption, high data transmission rate and small chip size. Silicon-on-insulator (SOI), compatible with complementary metal oxide semiconductor (CMOS) processes, is the most commonly used platform for integrated photonics. However, the high refractive index contrast, which improves optical confinement and reduces chip dimensions, leads to a large birefringence of different polarization. Polarization independent devices have been investigated to address this problem. A straightforward approach to minimize the birefringence is to optimize the device size^{[1, 2]}. Therefore, the difference in the effective index for the TM and TE mode can be reduced and single-mode conditions can be achieved. This method is more applicable to large SOI ridge waveguides. Other practical operations are required for silicon nanowires due to its compact size and manufacturing difficulty. Ultrasmall polarization beam splitters (PBSs), polarization rotators (PRs) and polarization rotator-splitters (PRSs) are desired for PICs. There are several different types of PBSs based on directional coupler (DC)^[3–5], multimode interference (MMI)^{[6, 7]} and Mach–Zehnder interferometer (MZI)^{[8, 9]}. Compared with PBSs, it is difficult to realize polarization rotation using SOI nanowires because of the good polarization maintenance of a planar waveguide. PRs based on asymmetric structures such as periodically loaded waveguides and ridge waveguides with slanted sidewalls are proposed in Refs. [10, 11]. PRSs, which can realize polarization splitting and rotation simultaneously, are far more widespread. In Ref. [12], the PRS based on an asymmetrical directional coupler (ADC) is shown. However, the top cladding of this device is air. The integration with other SOI-based devices and stability is limited. Hence, it is of great significance to find PRSs with SiO₂ top cladding. Ref. [17] presents a PRS covered by SiO₂. This device is based on sub-wavelength grating and the design and fabrication are relatively complex. In Ref. [18], another type of PRS based on slot structure is proposed. Despite its compact size, the complicated structure restricts the use for chip integration. Table 1 summarizes several reported results of the silicon PRSs.

Structure	Cladding	Device size (μm)	Loss (dB)	Extinction ratio (dB)	Bandwidth (nm)	Tolerance (nm)
Tapered DC [12]	Air	140	< 1	?20		14
Taper-etched DC*[13]	SiO2	> 80	< 0.5	< ?30	160	50
Double-etched DC[14]	SiO2	27	< 0.5	< ?20	30	< 10
ADC with a MMI filter[15]	Air	70	< 1.5	< ?20	50
Bent DC[16]	Air	> 8.77	< 1	< ?18	40	20
ADC with sub-wavelength gratings[17]	SiO2	35	< 1	?10	50	6
Tapered DC with slot*[18]	SiO2	19.6	< 0.6	?20	50	20
ADC with a MMI rotator and a bent DC filter[19]	SiO2	47.5	< 0.57	< ?20	85
*Simulation results.

Table1.
Comparison of various silicon PRSs.



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Structure	Cladding	Device size (μm)	Loss (dB)	Extinction ratio (dB)	Bandwidth (nm)	Tolerance (nm)
Tapered DC [12]	Air	140	< 1	?20		14
Taper-etched DC*[13]	SiO2	> 80	< 0.5	< ?30	160	50
Double-etched DC[14]	SiO2	27	< 0.5	< ?20	30	< 10
ADC with a MMI filter[15]	Air	70	< 1.5	< ?20	50
Bent DC[16]	Air	> 8.77	< 1	< ?18	40	20
ADC with sub-wavelength gratings[17]	SiO2	35	< 1	?10	50	6
Tapered DC with slot*[18]	SiO2	19.6	< 0.6	?20	50	20
ADC with a MMI rotator and a bent DC filter[19]	SiO2	47.5	< 0.57	< ?20	85
*Simulation results.

2.
Device design and simulation

As is illustrated in Fig. 1, the device is designed on an SOI platform and the upper cladding is SiO₂. The gray region represents the SiO₂ cladding layer. The dark blue region represents the rib Si waveguides of 0.22 μm thickness and the light blue region represents a slab layer of 0.07 μm thickness. The mode-evolution structure is designed in a bi-level taper. Through the bi-level taper, the TM₀ mode can be converted into TE₁ mode and the TE₀ mode propagates without mode conversion. An asymmetric directional coupler is utilized to split the TE₁, TE₀ mode into two waveguides, while the TE₁ mode is coupled into the TE₀ mode at the cross branch simultaneously.






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Figure1.
(Color online) Schematic conifiguration of the prosposed PRS.




The rest of this section is composed of three parts: in Section 2.1, we introduce the mode evolution theory and propose the bi-level taper structure; in Section 2.2, we design and simulate the ADC in detail. Finally, in Section 2.3, we provide a complete demonstration of the PRS.

2.1
Bi-level taper principle and design

Due to the asymmetric characteristic of waveguides, mode evolution occurs when the structure is specifically designed. An asymmetrical Y-junction^{[20, 21]} and asymmetrical Mach-Zehnder interferometers (MZIs)^[22] are used as mode converters between TM₀ mode and TE₁ mode. However, the asymmetric Y-junction is difficult to manufacture for its high precision, and the asymmetric MZIs have a large footprint and high design complexity. In Ref. [23], a bi-level taper is indicated. This structure breaks the vertical symmetry to realize mode hybridization when light propagates along the waveguide. The fundamental TM mode is converted into high-order TE modes consequently.



To calculate the mode field profiles and determine the bi-level structure, we use a commercial 3D finite-difference time domain (3D-FDTD) software (Lumerical) as the simulation tool. In this paper, we choose a SOI wafer of 0.22 μm height and the refractive indices of Si and SiO₂ are n_Si = 3.455, and $n_{{text {SiO}}_2}$= 1.445, the rib width varies from 0.45 to 0.55 μm while the slab width varies from 0.45 to 2.4 μm simultaneously. The effective indices of modes supported in the waveguide are presented in Fig. 2. The TM₀ mode develops in mode 2 as the layers’ width widens. It evolves into a hybridized mode of TM₀ and TE₁ modes at first and then TE₁ mode finally. The mode features of TE₀ mode remain unchanged.






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Figure2.
(Color online) The calculated effective indices for the eigen modes of composite waveguide.




A schematic of the bi-level taper is demonstrated in Fig. 3. The input waveguide width W₁ is determined by the ADC coupler. The bi-level taper widths W₂, W₃ and W_t, chosen from the simulation results above, are 0.55, 0.45, and 2.4 μm respectively. We chose the taper widths L₁ = 20 μm and L_t = 150 μm.






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Figure3.
(Color online) Schematic configuration of the prosposed bi-level taper.




We simulate the mode propagation and calculate the mode conversion efficiency. The results are shown below. In Fig. 4, we can observe the TE₀ mode stays the same and mode evolution occurs from TE₁ mode to TM₀ mode when inputting the TE₁ mode. The conversion efficiency is higher than 99% for both TE₀ and TE₁ modes, as is indicated in Fig. 5(a).






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Figure4.
(Color online) Light propagation for (a) TE₀ mode and (b)TE₁ mode at 1550 nm.






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Figure5.
(Color online) (a) The mode conversion efficiency for input TE₀ and TE₁ modes as a function of the wavelength. (b) The dependence of conversion efficiency on the variation of the slab height.




Fig. 5(b) illustrates the dependence of conversion efficiency on the variation of the slab height. The fabrication tolerance is within 10 nm while the conversion efficiency is more than 99%.

2.2
ADC structure and simulation

Multimode interference (MMI) couplers^[24], Y-junctions^[21] and ADCs^[25] are applied as the universal solution to mode multiplexers. Among them, ADCs are increasingly concerned for the compact size and low design difficulty.



The basic principle of ADCs is based on mode selective coupling. The maximum power coupling efficiency is given by

$F = frac{1}{{1 + {{(delta /kappa )}^2}}},$

(1)

where $kappa $ is the coupling coefficient, $delta = ({beta _1} - {beta _2})/2$ (in which ${beta _1}$, ${beta _2}$ are the propagation constants of the ADCs). When $delta = 0;({beta _1} = {beta _2})$, the 100% power coupling efficiency can be achieved. In contrast, the mode-mismatching occurs when $delta ne 0$, and the F can be fairly low. To realize the mode-selective phase matching, the effective index of SOI waveguides is calculated precisely and the results are shown below in Fig. 6. For the fundamental TE₀ mode and higher order TE₁, TE₂, TE₃ modes, the effective index is quite different at the same width. Therefore, in an ADC, we can choose two waveguides of matched widths to satisfy the mode-selective phase matching condition.






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Figure6.
(Color online) Simulated effective index of the optical modes in waveguides of different widths at 1550 nm.




The structure of the ADC is demonstrated schematically in Fig. 7. It has a narrow input waveguide and a wide coupling waveguide. As the cross section of the ADC shows, we choose the width of narrow input waveguide W₀ = 0.4 μm, the coupling gap Gap = 0.4 μm, the ridge height H = 0.22 μm and the slab height H_slab = 0.07 μm. The width of wide coupling waveguide W₁ can be obtained from Fig. 6. When W₀ = 0.4 μm, the effective index of TE₀ mode n₀ = 2.682. To realize the full coupling between the input TE₀ mode and the TE₁ mode, W₁ is chosen as 0.906 μm as the n_eff of TE₁ mode is nearest to 2.682.






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Figure7.
(Color online) Schematic configuration of the ADC.




To optimize the ADC structure and evaluate its performance, we use 3D-FDTD as simulation tools. When W₁ = 0.906 μm, the transmission at the cross and through ports is shown in the red solid and dashed line in Fig.8. The extinction ratio (ER) at the wavelength 1550 nm is lower than ?20 dB while the EL is almost zero (less than 0.1 dB). The coupling length L_c is 38 μm. We simulate the transmission at W₁ = 0.886, 0.896, 0.901, 0.911, 0.916, 0.926 μm to find the optimized width and measure the fabrication tolerance. As is shown in Fig.8, the fabrication tolerance is within 10 nm while the ER is lower than ?18 dB and at 1550 nm. The light propagation is shown in Fig. 9 for W₁ = 0.906 μm at the wavelength of 1550 nm.






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Figure8.
(Color online) Simulated transmission at the through and cross ports as a function of the wavelength.






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Figure9.
(Color online) Light propagation for the ADC when W₁ = 0.906 μm at 1550 nm.

2.3
Overview of the PRS

The full illustration of the mode propagation in our PRS is displayed in Fig. 10. For input TM polarization, the mode evolves into TE₁ mode through the mode-evolution structure and is coupled into the TE₀ mode in the cross waveguide. The input TE polarization propagates directly and is output from the through waveguide. The mode profiles of input TE/TM mode and output TE mode are also shown in Fig. 10.






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Figure10.
(Color online) Light propagation for the proposed PRS when input (a) TM₀ mode and (b) TE₀ mode.




The transmission dependence of the PRS on the wavelength has been studied and the simulation results are demonstrated in Fig. 11.






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Figure11.
(Color online) Simulated transmission at the through and cross ports as a function of the wavelength for the (a)input TE₀ mod and (b) input TM₀ mode.




When TE₀ mode is injected into the device, the light almost fully passes the through waveguide and the ER is extremely low, less than ?35 dB. The EL is also lower than0.5 dB. As for input TM₀ mode, the transmission is largely related to the coupling efficiency of the ADC. The simulated ER reaches the lowest value at 1562 nm, which is about ?23.7 dB. There is an increasing tendency for ER when the input wavelength changes from 1562 to 1570 nm, as well as changing from 1562 to 1530 nm. At the whole C-band, the ER is less than ?15 dB and the EL is less than 0.5 dB.

3.
Experiment and measurement

Fig. 12 shows the scanning electron microscope (SEM) images for the PRS. The device is fabricated on a SOI wafer with 0.22 μm thick silicon on a 3 μm thick buried oxide layer using electron-beam lithography. Then a SiO₂ of 1.5 μm thickness is deposited on the waveguides through the method of plasma-enhanced chemical vapor deposition.






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Figure12.
(Color online) Microscope and SEM image of the fabricated device.




The measuring procedures are described as follows.



We select a tunable laser to generate input light at the wavelength from 1527.5 to 1567.5 nm. After the laser, orthogonal linear polarizations (TE and TM) are acquired through the manually-adjustable polarization controller. Then the light is coupled to the chip using a silicon inverse taper covered by the air-bridge silicon dioxide intermediate transition waveguide. The power of the TE modes at the through and cross ports is measured by an optical power meter. We set a single straight waveguide as a reference and measure the output power in the same way as above. Thus, the output spectra of the PRS can be normalized by those of the reference waveguide. The coupling loss between one waveguide and one single-mode fiber is about 3 dB.



In Fig. 13, the transmissions at the through and cross ports for input TE₀ and TM₀ modes are shown respectively. For input TE₀ mode, the EL is less than 1 dB and ER is less than ?30 dB at the wavelength from 1530 to 1565 nm. Due to the mode conversion and coupling existing, the input TM₀ mode has a decrease in ER, less than ?10 dB at the wavelength from 1530 to 1565 nm while EL is less than 1.5 dB. The scattering loss due to the side-wall roughness of the waveguide and the fabrication inaccuracy of the ADC width should also be concerned intensively.






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Figure13.
(Color online) Measured transmission at the through and cross port at different wavelengths for the (a) input TE₀ mode and (b) input TM₀ mode.




There are several prospective methods to improve the device performance. Since the TE₁ mode is not fully coupled to the cross waveguide and part of the TM₀ mode remains, filters used for modes cleanup can be added to the cross branch. As is shown in Refs. [4, 15], polarization filters are employed to ensure only one polarization using MMIs. Ref. [26] demonstrates a sub-wavelength-grating polarizer to filter out the weak cross-coupling for TE polarization. Similar operations can be adopted for the undesired TM₀ mode left. Thus, the influence of the remaining TM₀ and TE1 modes can be removed. Moreover, the bi-level taper of the mode evolution structure is supposed to be optimized in the future.

4.
Conclusion

In conclusion, we propose a CMOS-compatible PRS using a mode-evolution structure and an ADC. The input TM₀ mode satisfies the mode evolution condition and develops into TE₁ mode. The optimized width is selected therefore the TE₁ mode is coupled into TE₀ mode in the cross waveguide. The TE₀ polarization propagates along the through waveguide without mode conversion. The PRS is designed on a SOI platform with the device length of ~250 μm. From the experimental results, the ER of ?30(?10) dB and EL of 1(1.5) dB for input TE(TM) mode are achieved at the whole C-band.