Optical coupling and splitting with two parallel waveguide tapers

A coupling and splitting device comprising a width taper and a spatial-modulated subwavelength grating waveguide (SSGW) is proposed. The width taper is a waveguide with increasing width and the SSGW is a waveguide grating whose width and thickness are constant but the filling factor increases along the light propagation. Thus, the effective index of the subwavelength grating increases according to the effective medium theory. Light of orthogonal polarizations from a single-mode fiber can be coupled efficiently with the two parallel tapers. Furthermore, the coupled lights of orthogonal polarizations in the two tapers can be further split with connecting bent waveguides. Fabrication of the device is fully compatible with current complementary metal oxide semiconductor technology. ©2011 Optical Society of America OCIS codes: (060.1810) Fiber optics and optical communications: buffers, couplers, routers, switches, and multiplexers; (230.5440) Optical devices: polarization-selective devices; (230.7380) Optical devices: waveguides, channeled. References and links 1. D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002). 2. Z. Lu, and D. W. Prather, “Total internal reflection-evanescent coupler for fiber-to-waveguide integration of planar optoelectric devices,” Opt. Lett. 29(15), 1748–1750 (2004). 3. H. Li, Z. Cao, H. Lu, and Q. 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Introduction
In recent years photonic-integrated-circuits (PICs) have received increasing interests owing to the promising applications for the next-generation telecommunication, computation, and sensing.Normally, PICs comprise many passive and active photonic devices such as couplers, waveguides, bends, splitters, resonators, switches, modulators, photo-detectors, and so on.Photonic devices based on silicon-on-insulator (SOI) material system can be fabricated with current complementary metal oxide semiconductor (CMOS) fabrication technology and are the building blocks of PICs.However, due to indirect bandgap of silicon material and limitations of current micro-and nano-fabrication technology, silicon-based lasers are very inefficient and lasers made from other material systems cannot be monolithically integrated on silicon-based PICs.Therefore, external laser sources have to be employed to provide lights for SOI photonic devices.A single-mode fiber (SMF) is usually used to transfer light from an external laser source to a sub-micron waveguide.However, due to mode mismatch caused by the great index and size differences between the SMF and sub-micron waveguide, coupling efficiency of a direct coupling between them can be as low as 20 dB.Furthermore, polarization orientation of guided light in an SMF is unstable and changes along the propagation, thus it is important for fiber-waveguide couplers to couple lights of both orthogonal polarizations.
To improve coupling efficiency researchers have proposed many methods, which can be categorized as out-of-plane coupling and in-plane coupling.The out-of-plane coupling usually involves components such as gratings, prisms or coated metal layers, which couple light from a vertical or slanted fiber to a horizontal waveguide [1][2][3].For the gratings, the bandwidths are narrow and coupling efficiencies are not high.As for the prisms and coating metal layers, the device sizes are too large for a single-mode silicon channel waveguide and the fabrication is complicated.Among the in-plane couplings, tapering and/or index-varying waveguides are commonly used [4][5][6][7][8][9], but the index-varying waveguides are difficult to fabricate due to various materials and multi-layers involved.Three-dimensional (3D) tapers were also proposed, but the fabrication is challenging.Therefore, two-dimensional (2D) tapers with varying width and constant thickness are widely used for coupling light between an SMF and a high-index-contrast (HIC) waveguide.The achieved experimental coupling efficiency for a width taper with tip width of 60 nm can be as high as 0.8 dB [4].Researchers also demonstrated a double-tip coupler to couple light efficiently between an SMF and a single-mode silicon nitride waveguide [10].A waveguide grating coupler based on gradual modification of the waveguide mode effective index by the subwavelength grating effect was also proposed to efficiently couple light [11].However, the above mentioned couplers cannot efficiently couple lights of both orthogonal polarizations.When light of one polarization orientation in an SMF is favorably coupled, light of other polarizations will not be coupled efficiently.On the other hand, polarization splitter is important for PICs as HIC wire waveguide devices in PICs are polarization dependent owing to structural birefringence.Polarization mode dispersion and polarization dependent loss in HIC waveguides are not negligible.A solution to the problem is the use of polarization diversity system consisting of polarization rotators and splitters [12,13].Many novel polarization splitters have been reported.Taillaert et al. used 2D grating to out-of-plane couple lights of orthogonal polarizations although the bandwidth is narrow [14].Fukuda et al. demonstrated an ultra small polarization splitter based on a directional coupler structure consisting of silicon wire waveguides [15].The polarization extinction ratio reaches 23 dB and the extra loss is only 0.5 dB; however, much computation and fabrication calibration are required to obtain the structural parameters of high performance.Hong et al. proposed a compact polarization splitter based on a multimode interference coupler.Although lights of orthogonal polarizations can be split effectively, the splitter is sensitive to wavelength [16].
For efficient coupling of light of any polarization orientations from an SMF to a submicron waveguide, in this letter we propose a device that comprises a width taper and a spatial-modulated subwavelength grating waveguide (SSGW).Both the tapers are parallel and utilized for mode converters and couplers.Based on mode conversion and coupling theory, the width taper with increasing waveguide width will couple transverse electric (TE) mode efficiently while the SSGW with increasing effective waveguide thickness will couple transverse magnetic (TM) mode efficiently.Both the width taper and the SSGW are not sensitive to wavelength.Furthermore, since the width taper and the SSGW are parallel and separated from each other, the coupled lights in the tapers can be further split with connecting bent waveguides.Thus, the device can also be used as polarization splitter in polarization diversity systems.

Design of the device
The proposed device is schematically shown in Fig. 1.The coupling and splitting device consists of two parallel tapers, Taper 1 and Taper 2. In the bottom an SMF inputs or outputs light to or from the tapers.Taper 1 is designed as a width taper, whose width is linearly increased while the thickness is constant.The width taper is employed to efficiently couple TE light.Taper 2 is an SSGW, whose width and thickness are constant while the filling factor is varying.It is worth mentioning that the positions of Taper 1 and Taper 2 are exchangeable.Based on the effective medium theory [17], effective index of a subwavelength grating is a function of the filling factor.The filling factors of the SSGW are chosen in a way such that the effective indices of the grating increase along the light propagation.Thus, the SSGW with increasing effective index is theoretically analogous to a thickness taper, whose index and width are constant but the thickness is increasing.The SSGW can efficiently couple TM light.As the width taper and the SSGW are separate from each other, the guided lights in the other ends of the tapers can be further separated with bent waveguides.Therefore, the device with two parallel tapers can act as orthogonal polarization coupler and splitter.

Simulation results
We use 3D finite-difference time-domain (FDTD) method to verify light coupling effect of the proposed device.The device is constructed on SOI.Thickness of the buried silicon dioxide layer is set as 2 μm.Thickness of the silicon layer is 300 nm.Width and thickness of the normal waveguide are both 300 nm, so both TE and TM fundamental modes can be guided.A top cladding box of 2 μm thick and 4 μm wide is used.It is worth mentioning that the tapers are clad with uniformly deposited silicon dioxide film.Wavelength is chosen as 1.55 μm.Width and thickness of the SSGW are also 300 nm, but the filling factor of the grating increases along the grating.The effective index of the SSGW is determined by the following parameters, period and filling factor of the grating, refractive indices of the waveguide material and the material filling the grating trench.The filling factor ƒ is defined as d/Λ, where d is the width of the ridge of the grating and Λ is the period of the grating.The period is shorter than λ/n, where λ is the wavelength in the vacuum and n the refractive index of the waveguide material.Due to limited computing power we have to choose a more compact structure even though the performance of the device is strongly affected.Both the width taper and the SSGW are set as only 15 μm long.The gap between two parallel tapers is 3.4 μm.Width of the width taper is linearly increased from 100 nm to 300 nm.For the SSGW, the period is 300 nm and the filling factor increases from 0.1 to 0.6 by a step of 0.01.In practice, for the consideration of fabrication capability, a longer SSGW can be realized by increasing the filling factors segment by segment, i.e., the SSGW consists of many segments with the same number of grating periods and in each segment the filling factor is constant.The calculated effective index of the grating for the TM mode increases from 1.56 to 2.10.On the basis of the effective medium theory, the effective index of the subwavelength grating is nearly independent with wavelength, thus the SSGW is not sensitive to wavelength and is applicable to broadband light sources.A lensed single-mode fiber is used, and diameter of the focus spot of the fiber is set as 3 μm.Note that the lensed fiber is not required to be close enough to the coupling facets of the tapers for efficient coupling as the emitted light of the lensed fiber is focused a distance from the end of the fiber.Cross-section of the coupling interface of the device is schematically shown in Fig. 2, where the enclosed small rectangle in the left represents the tip of the width taper and the rectangle in the right is the SSGW.The final cross-section of the coupler has the similar structure to that in Fig. 2, except that the width of the width taper in the left has increased to the normal.As two tapers are parallel to each other, directional coupling could occur and affect coupling efficiency of the device.Thus, the coupling gap between two tapers needs to be optimized for high coupling efficiency.Simulations for light coupling and propagation are shown in Fig. 3. Figure 3(a) shows light coupling and propagation with TE light incident, and Fig. 3(b) shows light coupling and propagation with TM light incident.It can be observed from Fig. 3 that the width taper couples TE light more efficiently whereas the SSGW couples TM light more efficiently.Therefore, when an SMF emits light with changing polarization orientation, the width taper and the SSGW will couple the lights of different polarizations efficiently.However, it can be observed from Fig. 3 that the crosstalks in the two tapers are rather high.To increase coupling efficiencies and decrease crosstalks of the two tapers, we need greatly increase lengths of the tapers and optimize the gap between two tapers.In [4] it was found that length of the 2D width taper should be in the range of 200-300 μm.However, 3D FDTD simulations for a greater structure would consume tremendous computing power and thus cannot be implemented in our available computers.
As mentioned earlier, the subwavelength grating with increasing filling factors is analogous to a thickness taper whose thickness increases but other structural parameters are constant.We can simulate a greater-size structure with 3D beam propagation method (BPM), which is much faster and consumes less computer memory.Thus, in the simulations we use a thickness taper with normal width and linearly increased thickness to replace the SSGW.Both the width taper and the thickness taper are 200 μm long.Thickness of the thickness taper is increased from 100 nm to 300 nm and the width remains 300 nm; width of the width taper is increased from 100 nm to 300 nm and the thickness remains 300 nm.The top cladding box is increased to 5 μm wide, so the gap between the two tapers can vary in a greater range.Other structural parameters of the device are maintained.We can adjust the gap between the two parallel tapers and compute the corresponding coupling efficiencies.Coupling efficiency is defined as the ratio between optical powers of the coupled light in a taper and the light from the fiber.The gap is increased from 600 nm to 4.6 μm by a step of 200 nm.The simulated coupling efficiencies as a function of the gap with TE light incident are shown in Fig. 4(a), where the upper curve represents coupling efficiency of the width taper and the lower one represents that of the thickness taper.It can be seen from Fig. 4(a) that coupling efficiency of the width taper is much higher than that of the thickness taper.Coupling efficiency of the width taper reaches the highest at the gap of 4.2 μm.Coupling efficiency ratio (CER) of the width taper and the thickness taper exceeds 42 dB at the gap of 4.2 μm.CER is defined as the logarithm ratio between optical powers of lights of the same polarization coupled in the two tapers.Implementation of the alignment between an SMF and the double tapers is similar to that between an SMF and a single-tip taper.It is found in simulations that at the gap of 4.4 µm, vertical misalignment of  0.5 µm causes both the coupling losses of the double tapers to increase about 0.45 dB, and horizontal misalignment of  0.5 µm would result in higher coupling loss for one taper and lower coupling loss for the other one.For instance, when the laser source is 0.5 µm closer to the SSGW horizontally, the coupling losses for the width taper and the SSGW are about 0.7 dB and 1.76 dB, respectively.With current precision stages, less than  0.5 µm misalignment can be easily achieved.Thus, coupling loss fluctuation resultant from misalignment can be controlled as less than 1 dB.Both the width taper and the SSGW can be fabricated with current CMOS technology as they have uniform thickness.As mentioned previously, the device with the two coupling tapers can also be used as splitter.When the coupled lights in the width taper and the SSGW are guided with bent waveguides to diverse circuits, the device is functioned as polarization splitter.

Conclusion
In summary, we have proposed an optical coupling and splitting device, which comprises a width taper and an SSGW.The width taper and the SSGW are used to efficiently couple TE and TM modes, respectively.Thus, the device can be used to couple lights of both orthogonal polarizations.The device can also function as polarization splitter when the coupled lights in the width taper and the SSGW are separated with bent waveguides.High coupling efficiency and coupling efficiency ratio for lights of orthogonal polarizations can be achieved.The fabrication is fully compatible with current CMOS technology and the device will find potential applications in photonic devices and PICs.

Fig. 1 .
Fig. 1.Schematic layout for the optical coupling and splitting device comprising two parallel tapers, Taper 1 and Taper 2, which are designed to efficiently couple TE and TM lights, respectively.

Fig. 2 .
Fig. 2. Cross-section of the proposed device.The enclosed small rectangle in the left is the tip of the width taper and the one in the right is the tip of the SSGW.

Fig. 3 .
Fig. 3. 3D FDTD simulations for light couplings and propagations of the width taper located in the left of the device and the SSGW located in the right of the device with (a) TE light incident, and (b) TM light incident.
Figure 4(b) shows light coupling and propagation in the width taper positioned in the left and the thickness taper positioned in the right of the device at the gap of 4.4 μm.Clearly, the width taper couples TE light with high efficiency.

Figure 5 (
a) shows coupling efficiencies as a function of the gap for TM light incident.The upper curve represents coupling efficiency of the thickness taper and the lower one represents that of the width taper.Coupling efficiency of the thickness taper reaches the highest at the gap of 4.6 μm.The CER exceeds 40 dB at the gap of 4.2 μm and even 47 dB at the gap of 4.6 μm. Figure 5(b) presents light coupling and propagation in both the tapers.Clearly, the thickness taper couples TM light with high efficiency.It can be observed from both Figs. 4 and 5 that the width taper and the thickness taper can achieve approximately the same high coupling efficiency and the lowest coupling loss about 1 dB.Thus, the double tapers can efficiently couple both TE and TM polarization lights.Furthermore, as the CERs of the two tapers are high, the coupled light in each taper is nearly pure TE or TM light.Hence, incident lights of orthogonal polarizations can be coupled and split with the two tapers and connecting waveguide bends.

Fig. 4 .
Fig. 4. TE light input for the device, (a) coupling efficiencies of the width taper (upper curve) and the thickness taper (lower curve) as a function of the gap, (b) light coupling and propagation in the width taper (located in the left) and the thickness taper (located in the right) at the gap of 4.4 μm.

Fig. 5 .
Fig. 5. TM light input for the device, (a) coupling efficiencies of the thickness taper (upper curve) and the width taper (lower curve) as a function of the gap, (b) light coupling and propagation in the width taper (located in the left) and the thickness taper (located in the right) at the gap of 4.4 μm.