Robust polarization-insensitive strip-slot waveguide mode converter based on symmetric multimode interference

Strip-slot waveguide mode converters for TE0 have been widely investigated. Here we demonstrate a polarization-insensitive converter numerically and experimentally. The polarization-insensitive performance is achieved by matching the optical field distribution of the 2-fold image of the Multimode Interference (MMI) and the TE0 (TM0) mode of a slot waveguide. The working principle for this MMI-based mode converter is thoroughly analyzed with the quantitatively evaluated optical field overlap ratio that is theoretically derived from the orthonormal relation of eigenmodes. Based on the analysis, the MMI-based polarization-insensitive converters are then simulated and fabricated. The simulation and measurement results indicate that the proposed scheme is a robust design since it is not only polarization-insensitive but also wavelength-insensitive and fabrication-tolerant. Moreover, the mode converter is as small as 1.22 μm × 4 μm while the measured conversion efficiencies are 95.9% for TE0 and 96.6% for TM0. All these excellent properties make the proposed mode converter an ideal solution for coupling light between strip and slot waveguides when both TE and TM polarizations are considered. ©2016 Optical Society of America OCIS codes: (130.0130) Integrated optics; (130.3120) Integrated optics devices; (130.2790) Guided waves. References and links 1. V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004). 2. Q. Xu, V. R. Almeida, R. R. Panepucci, and M. Lipson, “Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material,” Opt. Lett. 29(14), 1626–1628 (2004). 3. C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. 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Introduction
Slot waveguides have the unique property of enhancing and confining light in a low-index material that is embedded between two high-index regions [1,2].Such uniqueness has attracted considerable attention for constructing various functional devices based on slot waveguide, such as all-optical high-speed signal processors [3], optical tweezers for nanoparticles and biomolecules [4], athermal microring resonators [5], polarization beam splitters [6], on-chip optical sensors [7], and energy-efficient electro-optic modulators [8].Nevertheless, slot waveguides only appear in these functional regions while strip waveguides act as basic component for guiding light in integrated optical systems since strip waveguides have relatively lower loss [9][10][11].Therefore, coupling between slot waveguide and strip waveguide is unavoidable in any integrated optical system when slot waveguides are used, but the optical mode mismatch between slot (non-Gaussian-like mode) and strip (Gaussianlike mode) waveguides makes the coupling efficiency of direct strip-slot butt-joints very low [12].Various strip-slot waveguide mode converters have been proposed for efficient coupling [12][13][14][15][16][17].These approaches do have enhanced the coupling efficiency but fabrication is a problem since extremely sharp tips are introduced, which must be well shaped or significant degradation in efficiency will occur [13].Recently, we have proposed a fabrication-friendly strip-slot waveguide mode converter, which is compact, wavelength-insensitive, and efficient, based on symmetric multimode interference (MMI) [9].However, all these converters are demonstrated for TE-polarized light, while many integrated photonics applications, for example polarization multiplexing, require polarization insensitive mode converters.
In this paper, the working principle of MMI-based strip-slot mode converters are thoroughly explained.Then, a robust polarization-insensitive strip-slot waveguide mode converter is built according to this working principle.We have presented the proposed polarization-insensitive converter with some preliminary simulated results in Conference on Lasers and Electro-Optics 2015 [18], while the complete simulation results with experimental verifications are analyzed here.

Working principle of MMI-based strip-slot mode converter
Figure 1 illustrates the schematic of a MMI-based strip-slot mode converter which consists of a symmetric 1 × 2 MMI region and a slot-taper.The MMI region is used to convert mode profiles between the strip waveguide and the 2-fold image of the MMI while the slot-taper transforms the 2-fold image to a guided mode of the slot waveguide and vice versa.Such a converter is efficient for coupling between the TE-polarized fundamental mode (TE 0 ) of the strip and slot waveguides as the optical field evolution indicates in Fig. 1.Actually, it also works very well for TM-polarized fundamental mode (TM 0 ) conversion.To fully understand the reason of high-efficiency coupling, both the MMI region and the slot-taper will be investigated in the following.Fig. 1.Schematic of MMI-based strip-slot mode converter.All results presented in this paper are based on a material platform of silicon-on-insulator (SOI) with SiO 2 cladding, and the thickness of top silicon is H = 250 nm; All simulations in this paper are performed with 3D full vector finite element method (FEM) while the refractive index of Si and SiO 2 are set to 3.48 and 1.45 respectively; The optical wavelength is 1550 nm if not specified; W ST and W SL are widths of strip and slot waveguides while W slot denotes the width of the slot which is located at the center of the slot waveguide and slot-taper; W mmi (L mmi ) is the width (length) of the multimode region while L represents the total length of the mode converter; The Cartesian coordinate system used in this paper: z-direction, the propagation direction of waveguides, ydirection, the normal direction of top silicon/ buried oxide (BOX) interface; Embedded color plot, half of the simulated optical field (Ex) 3D-profile, cut across the central plane of waveguides, for TE 0 mode conversion.
According to self-imaging principles [19], the incident optical energy in a symmetric 1 × 2 MMI waveguide, TE 0 or TM 0 mode, is rebuilt into a 2-fold image periodically along the propagation direction as the top-view plots in Fig. 2 show.The first 2-fold image [A-A' (B-B') cut in Fig. 2 for TE 0 (TM 0 ) incidence] is selected as the output of the MMI region to minimize the converter length.The corresponding optical field distributions of these 2-fold images are also plotted in Fig. 2 which are quite similar with the fundamental eigenmode of a slot waveguide with the same waveguide width and mode polarization.To quantitatively analyze this similarity, a mode overlap between the first 2-fold image in the MMI region and the fundamental eigenmodes in the slot waveguide should be performed.
where [ ] z represents the component of a vector in z-direction, and , ν μ δ is Kronecker delta function.Moreover, all eigenmodes in this waveguide constitute a system of complete orthogonal functions, which means any optical field { , } t t Ε H propagating in the waveguide can be expressed as the superposition of the eigenmodes: exp( ) exp( ) The mode expansion coefficient ( a ν ) can be expressed as follows based on Eq. ( 1): Mode overlap ratios ( ν Γ ), calculated from Eq. ( 4), between the first 2-fold image in the MMI region and the fundamental eigenmode in slot waveguide are plotted in Fig. 3.The results indicate that ν Γ can be very high (TE 0 : >98%, TM 0 : >97%) for any slot width in the analyzed span (W slot = 50~200 nm), which covers the range for commonly used slot waveguides, when a proper MMI width (W mmi ) is chosen.Such high similarity of optical field distributions makes efficient mode-conversion between strip and slot waveguides possible.However, a slot-taper is also essential to achieve efficient mode-conversion for slot waveguides with arbitrary width since this similarity is only optimized at some specific waveguide widths.The mode conversion efficiencies of slot-tapers are analyzed in Fig. 4. As the inset of Fig. 4(a) shows, a wide-width slot waveguide with incident optical power (P in ) in TE 0 (TM 0 ) mode is converted to a narrow-width slot waveguide through a slot-taper, and then converted to a wide-width waveguide again with the same slot-taper.The mode conversion efficiency per slot-taper is calculated as = in out P P η where P out is the output optical power from the second wide-width slot waveguide in the same mode as the incident light.The mode conversion efficiency is higher than 99% when cot 8 θ ≥ , that is 7 θ ≤  .The mode profile evolutions for cot 8 θ = are plotted in Fig. 4(b) which confirm that the slot-taper can convert the fundamental mode from a wide-width slot waveguide to a narrow-width slot waveguide and vice versa with negligible losses for both TE and TM polarizations.
Benefiting from the two points demonstrated above: i) the high similarity in optical field distributions between the first 2-fold image of the symmetric 1 × 2 MMI and the fundamental eigenmodes in the slot waveguide, and ii) the efficient mode conversion between slot waveguides with different width through a slot-taper, the MMI-based strip-slot mode converter, constructed as Fig. 1, is capable of converting a TE 0 (TM 0 ) mode between strip and slot waveguides with negligible losses.

Robust polarization-insensitive strip-slot mode converter
The working principle of MMI-based strip-slot mode converters, which works well for both TE 0 and TM 0 , have been analyzed in Section 2, while polarization-insensitive mode converters, designed for strip and slot waveguides with W ST = 400 nm, W SL = 620 nm and W slot = 100 nm as an example, will be demonstrated here following this working principle.
The key to the polarization-insensitive performance of MMI-based strip-slot mode converters is to match the optical field distribution between the output in the MMI region and the fundamental eigenmode in the slot waveguide for both TE and TM polarizations under the same dimensions of the MMI region, W mmi and L mmi .When W mmi is chosen around 1.2 μm, mode overlap ratios ( ν Γ ) in Fig. 3  The polarization-insensitive performance can be achieved with a set of (W mmi , L mmi ), the converter in Fig. 5(b) is one possible solution, W mmi = 1.22 μm and L mmi = 1.46 μm, with a conversion efficiency of 96%.Furthermore, η ΤΕ0 − η ΤΜ0 is kept in the range of ± 1% even if W mmi or L mmi has deviated ± 15 nm from the critical polarization-insensitive dimensions as indicated in Fig. 6(c).Therefore, the proposed polarization-insensitive converter is a robust design in terms of the tolerance for fabrication errors of W mmi and L mmi .Prototype converters with different length (L) have been fabricated on a SOI wafer with 250-nm-thick top silicon and 2-μm-thick BOX by electron-beam lithography, followed by inductively coupled plasma etching.Then, plasma enhanced chemical vapor deposition was used to form a 1-μm-thick SiO 2 upper-cladding.The top-view scanning electron microscope (SEM) picture [Inset of Fig. 7(a)], captured before the SiO 2 cladding is deposited, shows one pair of the fabricated converters with L = 4 μm.Based on the SEM pictures, dimensions of the fabricated devices are measured to be W SL = 620 nm, W ST = 400 nm, W slot = 90 nm, W mmi = 1.21 μm and L mmi = 1.41 μm with a measurement uncertainty of ± 10 nm.Five pairs of such identical converters, ten converters in total, are cascaded in each device to reduce the influence of measurement error [9].To characterize these devices, a tunable CW laser (AQ 2200-136TLS, YOKOGAWA) coupled with a polarization controller (DPC5500, THORLABS) is used to provide light input with desired polarization.Light is then butt-coupled into the chip and then butt-coupled out to an optical spectrum analyzer (AQ 6370C, YOKOGAWA) through tapered lens single mode fibers.Figure 7(a) shows the measured mode conversion efficiencies which are extracted by normalizing the measured spectra with respect to that of a single mode strip waveguide to exclude the loss of butt-coupling.These results proved the proposed converters are not only polarization-insensitive but also wavelength-insensitive for the communication band around 1550 nm at least since the efficiency differences are less than 4.5% in a wavelength range of 125 nm (1475 nm to 1600 nm).However, the signal-to-noise ratio is degraded by Fabry-Perot resonances formed by the reflection on both end facets.Therefore, trend lines [black solid lines in Fig. 7(a)] are extracted with robust locally weighted regression to suppress noise [21,22].To make sure the experiment results are reliable, 3 identical testing devices are fabricated for each converter length (L) and the mean values of their measured response are used for the final results.As shown in Fig. 7(b), the measurements agree well with the simulations.Both, measurements and simulations, indicate that the proposed converter is capable of achieving strip-slot mode conversion with an efficiency of >95% for both TE and TM polarizations simultaneously if the converter is not shorter than 4 μm.The measured efficiencies are 95.9% for TE 0 and 96.6% for TM 0 while the converter length is only 4 μm.These results indicate that the proposed polarization-insensitive converter is a robust design also in terms of the wavelength dependence or the tolerance for fabrication errors of L.
It is worthwhile to mention that even though all the results presented in this paper are analyzed in the communication window of 1550 nm, the proposed scheme is also applicable for the optical communication window of 1310 nm since the working principles, symmetric 1 × 2 MMI and slot-taper based mode conversion, are still suitable.Re-optimizing the device parameters according to the designing procedure presented in this paper, a polarizationinsensitive strip-slot mode converter for 1310 nm window can be achieved.

Conclusion
In summary, a polarization-insensitive strip-slot mode converter has been numerically and experimentally demonstrated in this paper.The working principle is based on the similarities in optical field distribution for both TE and TM polarizations between the first 2-fold image of a symmetric 1 × 2 MMI and the fundamental eigenmodes of the slot waveguide, while slottapers are also introduced to transform the slot-waveguide width adiabatically.The proposed MMI-based strip-slot mode converter is a robust design since it has the characteristics of i) polarization-insensitivity: the measured mode conversion efficiencies are 95.9% for TE 0 and 96.6% for TM 0 ; ii) wavelength-insensitivity: the measured mode conversion efficiencies maintain >92% for both TE 0 and TM 0 in a wavelength range of 1475 ~1600 nm; and iii) fabrication-tolerance: the variation of mode conversion efficiency is kept in a range of ± 1% even if W mmi or L mmi deviate ± 15 nm from the optimized size.Moreover, it is compact with typical dimensions of 1.22 μm × 4 μm.All these excellent properties make the proposed mode converter an ideal solution for coupling light between strip and slot waveguides when both TE and TM polarizations are considered simultaneously.

Fig. 2 .
Fig. 2. Comparison of optical field distribution between the first 2-fold image in MMI region and the eigenmodes in slot waveguide with W SL = W mmi = 1.22 μm and W slot = 100 nm: (a) TE 0 and (b) TM 0 incidence.P, optical power flow density, E, electric field, H, magnetic field while the subscript indicates the component in a certain direction; L 2 , the first 2-fold image distance.Assuming { , } tμ tμ Ε H and { , } tν tν Ε H are normalized transverse optical fields of two eigenmodes in a waveguide propagating along + z direction with propagation constant μ β power flow in eigenmode { , }

Fig. 3 .
Fig. 3. Mode overlap ratio ( ν Γ ) between the first 2-fold image in the MMI region and the fundamental eigenmode in the slot waveguide with W SL = W mmi : (a) TE 0 and (b) TM 0 incidence.

.Figures 6
Figures 6(a) and 6(b) display the mode conversion efficiencies which show high efficiency for both TE 0 and TM 0 mode conversion.The polarization-insensitive performance can be achieved with a set of (W mmi , L mmi ), the converter in Fig.5(b) is one possible solution, W mmi = 1.22 μm and L mmi = 1.46 μm, with a conversion efficiency of 96%.Furthermore, η ΤΕ0 − η ΤΜ0 is kept in the range of ± 1% even if W mmi or L mmi has deviated ± 15 nm from the critical polarization-insensitive dimensions as indicated in Fig.6(c).Therefore, the proposed polarization-insensitive converter is a robust design in terms of the tolerance for fabrication errors of W mmi and L mmi .Prototype converters with different length (L) have been fabricated on a SOI wafer with 250-nm-thick top silicon and 2-μm-thick BOX by electron-beam lithography, followed by inductively coupled plasma etching.Then, plasma enhanced chemical vapor deposition was used to form a 1-μm-thick SiO 2 upper-cladding.The top-view scanning electron microscope (SEM) picture [Inset of Fig.7(a)], captured before the SiO 2 cladding is deposited, shows one pair of the fabricated converters with L = 4 μm.Based on the SEM pictures, dimensions of the fabricated devices are measured to be W SL = 620 nm, W ST = 400 nm, W slot = 90 nm, W mmi =

Fig. 5 .
Fig. 5. (a) The first 2-fold image distance (L 2 ) versus the width of the MMI region (W mmi ); (b) Optical field evolution between strip and slot waveguides (W mmi = 1.22 μm, L mmi = 1.46 μm, L = 4 μm).P in and P out , the input and output optical power in the same mode, TE 0 or TM 0 .

Fig. 7 .
Fig. 7. (a) Measured wavelength dependence of mode conversion efficiency with L = 4 μm; the bottom inset shows the corresponding top-view SEM picture of the fabricated converters; the black solid lines are trend lines extracted with robust locally weighted regression.(b) Simulated (squares) and measured (dots) mode conversion efficiencies with different converter lengths at 1550 nm (wavelength in free space); The error bars show the standard deviation of the measured results.