Bimodal grating coupler design on SOI technology for mode division multiplexing at 1550 nm

In this paper, we evaluate by means of simulation and experimentally the simultaneous coupling of the LP01x-LP11ax fiber modes and the TE0-TE1 nanophotonic SOI waveguide modes using a grating coupler for a two-mode fiber at 1550 nm. Both the grating width (ranging from 10 μm to 15 μm) and the grating vertical profile have been considered in the design procedure. The optimum design (14 μm width and 609 nm grating period) has been selected in terms of coupling efficiency (both LP01x-TE0 and LP11ax-TE1), compactness and tolerance to lateral misalignments between fiber and coupler. The LP01x-TE0 and LP11axTE1 modes achieved coupling efficiencies of 49% and 45%, respectively. © 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement OCIS codes: (050.2770) Gratings; (060.1810) Buffers, couplers, routers, switches, and multiplexers; (060.4230) Multiplexing; (130.3120) Integrated optics devices; (230.7400) Waveguides, slab. References and links 1. D. J. 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Introduction
In the last decade, the data traffic demand has been continuously increasing due to new internet based-services, particularly video streaming and machine-to-machine communications, driving optical-communication systems based on single-mode fibers to their capacity limit [1].Spatial-division multiplexing (SDM) or mode-division multiplexing (MDM) are promising techniques to overcome the capacity limit of the optical fiber [1].In its simplest implementation, MDM permits to propagate the LP 01 and LP 11 modes in a two-mode fiber (TMF) [2].
An important aspect in the different integrated devices for MDM is the coupling to the optical fiber.Depending on the employed technology, a vertical or horizontal coupling is required.On one hand, PLC favors the use of the horizontal coupling due to the similar dimensions between the waveguide and the fiber core.This technology offers low loss and mass productivity due to their mature manufacturing technology.However, the main drawback are the higher sizes and higher bending radius (above 5 cm [15]).On the other hand, SOI technology offers lower size, better repeatability and higher robustness than the PLC based devices but the coupling to the fiber is more demanding.
When a few mode fiber (FMF) is under consideration the coupling of the different modes to/from the SOI waveguides must be solved.SOI with horizontal coupling are traditional based on spot size converter which were limited to the fiber fundamental mode [13].Recently some modifications have been proposed in order to combine several inverse taper spot size converters by means of Y-junction or trident waveguides to couple to fiber higher modes [13,14].The inverse tapers provide highly efficient, polarization insensitive, and broad bandwidth optical coupling but they require a high alignment precision, a complex design and long lengths [13,16].Besides, a single horizontal coupler is required for each fiber mode to couple.
On the other hand, vertical coupling in SOI technology is based on the use of grating couplers.Grating couplers have been successfully used to couple the TE 0 mode of the SOI waveguide to the LP 01 mode of the standard single mode fiber (SSMF), and vice versa [17][18][19].Although grating couplers are easy to fabricate and provide on chip test measurements with small footprints, the main drawbacks are the limited bandwidth and their polarization sensitivity.
One first approach to vertically couple light from the SOI waveguide to the LP 01 /LP 11 modes in a FMF was based on the use of one 2D grating coupler excited from two 90 degrees apart waveguides propagating the TE 0 and TE 1 modes [20].Other proposed SOI devices are based on the use of 2D gratings simultaneously excited from several waveguides propagating the TE 0 modes but with a fixed phase relation between the waveguide modes [21][22][23].These devices offer the generation of up to six fiber modes (all LP 01 and LP 11 degenerated modes) but a more complex feeder circuit is required with a higher footprint and thermal tuning to adjust the phase shift at the different waveguides [21][22][23].A strictly vertical coupling to the fiber is also required on these devices with the corresponding issues of second order reflection at the waveguide fiber interface [20][21][22][23].
Thus, using a single grating coupler that couples simultaneously the TE 0 and TE 1 modes from a single SOI waveguide to the LP 01 and LP 11 modes in the FMF would be a key component for low cost and low size integrated devices in the MDM systems.
In this letter, a grating coupler for the simultaneous coupling of the TE 0 and TE 1 modes into one single polarization of the LP 01 mode and one single polarization and azimuthal orientation of the LP 11 mode of the TMF is designed.Both the nominal performance of the grating coupler at the design wavelength and the sensibility of the coupling efficiency to lateral misalignment of the fiber are considered.The best grating design is selected in terms of both TE 0 -LP 01 and TE 1 -LP 11 coupling.The selected device has been fabricated and measured.

Grating coupler design
The general concept of the MDM link is depicted in Fig. 1.It consists of two lasers emitting at 1550 nm propagating the LP 01 mode in a standard single-mode fiber (SSMF).Both LP 01 modes pass through a polarization controller to impinge the standard LP 01 -TE 0 grating coupler with the s-polarization.The TE 0 mode from the upper branch is converted into the TE 1 mode and it is multiplexed with the optical signal coming from the lower branch, propagating both modes, TE 0 and TE 1 , to the common output.The TE 1 mode is excited and coupled to the TMF propagating the LP 11a mode with s-polarization.Finally, both modes are coupled to the two mode fiber (TMF) using a specific grating coupler, corresponding now to the fiber LP 01 and LP 11a modes.At the receiver, the same device is used in order to demultiplex each mode to the corresponding photodiode.As in any other mode demultiplexer based on vertical grating couplers, the polarization of the fiber modes must be properly aligned to the s-polarization at the fiber waveguide interface.Depending on the mode coupling induced by the TMF link a multiple input multiple output (MIMO) digital processing stage could be required at the receiver to properly split both data streams.

Grating theory
The periodic structures are defined by the Bragg condition that describes the relation between the wave-vectors of the incident and diffracted waves.In the case of waveguide grating couplers, the incident wave is replaced by the guided mode of the waveguide, which is characterized by its propagation constant β.The equation can be defined as [24] cov m 2 2 2 sin( ) where λ is the design wavelength, n cover is the refractive index of the cover substrate, θ m is the tilt angle, n eff the effective index of the optical mode in the grating waveguide, Λ is the grating period and the integer m is the diffraction order.Considering the grating as an output coupler, the coupling to the optical fiber is done for the first diffraction order (m = −1) with a specific tilted angle (θ), as depicted in Fig. 2. In the case of simultaneous TE 0 and TE 1 modes coupling, Eq. ( 1) must be fulfilled in both cases, therefore, the effective indexes for both modes need to be approximately equal.If the waveguide widths are sufficiently large, the TE 0 and TE 1 modes are expected to have similar effective indexes.
The coupling efficiency from fiber to waveguide is the same as from waveguide to fiber due to reciprocity theorem.When the electromagnetic fields at the position of the fiber facet are known, the coupling efficiency to fiber becomes [25] where E is the normalized electrical field of the diffracted wave from the grating, and H fib is the normalized magnetic fields of the optical mode in the fiber and S is the fiber facet.Equation ( 2) is a good approximation, even if the grating is covered by air instead of silica [26].
When the optical mode of the waveguide is launched from the grating, some light is refracted upwards and the rest is refracted downwards (across the substrate), due to the vertical grating symmetry.Thus, for this design the efficiency will not be higher than 50% unless reflective elements are used [17,24].
The complete coupler problem is a 3D problem but can be approximated by two 2D problem due to the highly different dimensions between the waveguide width and height where the width is much larger than the height.In Fig. 3, the fundamental mode (TE 0 ) and the first higher order mode (TE 1 ) for a 12 µm SOI waveguide width are shown.

Grating design
As previously commented, the complete coupler design problem can be divided into two 2D problems.Firstly we will assess the width of the grating coupler by taking into account the overlap between the mode field distributions in the transverse planes of both the SOI waveguide and the FMF.The most common grating coupler design based on SOI technology (SiO 2 layer height = 220 nm) for the TE 0 -LP 01 coupling to SMF-28 fiber has a waveguide width (w g ) of 12 µm [17].If we take a TMF at 1550 nm such as SM2000 fiber from Thorlabs (11 μm core diameter with a SiO 2 cladding, n core = 1.4495 at 1550 nm), the LP 01 mode profile is slightly wider than the LP 01 mode profile for the SMF-28 (11 μm in SM2000 vs. 10.4 μm in SMF-28).Besides, the TE 1 mode needs to be coupled to the LP 11 mode and, as shown in Fig. 4, the LP 11 mode profile in the SM2000 fiber is much wider than the TE 1 mode profile in the 12 µm waveguide.If the peak of the modes are taken as a reference, the LP 11 mode is 1.64 μm wider than the TE 1 mode.Therefore, the optimum waveguide width is expected to be 1 μm to 2 μm greater than 12 µm.The grating coupler is composed by a Si core (t core ), a SiO 2 cladding (t cladding ) and a Si substrate (t substrate ), as can be seen in Fig. 5.We use SOI wafers of 220 nm/2 μm Si/SiO 2 layers thicknesses, corresponding to t core and t cladding .The upper cladding layer of the grating is supposed to be air.The main parameters in the grating coupler design are the filling factor or duty cycle (ff = w/Λ), the grating period (Λ) and the etching depth (e d ).Some typical values for the TE 0 -LP 01 coupling using SMF-28 are: ff = 0.5, e d = 70 nm and Λ = 630 nm, to maximize coupling efficiency at 1550 nm [26].The incident angle (ϴ) is around 10 degrees in order to optimize the coupling efficiency and avoid reflections.Figure 6 shows the simulation results of the coupling efficiency for the LP 01 -TE 0 and LP 11 -TE 1 modes with respect to the grating period and the filling factor.The results shown in this figure have been obtained according to the simulation approach described in section 3 for a 12 μm waveguide width.Figure 6(a) results show a maximum efficiency region corresponding to an almost vertical line with optimum grating periods ranging from 607 nm to 611 nm when the filling factor varies from 0.48 to 0.52, respectively.From all these possible design parameters the optimum grating period, Λ = 609 nm, for a filling factor of ff = 0.5 was selected.A similar performance is shown in Fig. 6(b) for the TE 1 -LP 11 coupling.Figure 6 was also simulated for different grating widths (w g = 10 to 15 μm) with no influence on the results shown for w g = 12 μm.Once the filling factor and the grating period were fixed the sensitivity to variations of the etching depth was found to be of less magnitude than the tolerance of the fabrication process in the vertical dimension so the typical 70 nm etching depth was not modified.
Finally, it can be stated that both couplings (TE 0 -LP 01 , TE 1 -LP 11 ) obtained the maximum efficiency for the same design parameters of the grating coupler and, therefore, it is possible to couple them simultaneously.Once the vertical dimensions of the grating coupler are fixed (t core = 220 nm, e d = 70 nm, ff = 0.5) the SOI mode indexes in the grating can be estimated as the average value between the effective indexes of the unperturbed (t core = 220 nm) and perturbed (t core -e d = 150 nm) waveguides.For a w g = 12 µm grating width quite similar effective indexes (n effTE0 = 2.6920 vs n effTE1 = 2.6897) are obtained.As aforementioned in the grating theory subsection, both modes effective indexes are quite similar so Eq. ( 1) is fulfilled simultaneously and the small index difference would translate to a negligible 0.13 degrees difference in the incident angle.Thus, the grating coupler can be used for simultaneous coupling.

Simulation
Simulations of fiber-grating coupling has been performed using 3D Finite Difference Time Domain method (3D-FDTD).Eigenmodes' effective indices in waveguides and optical fibers are obtained by means of three-dimensional (3D) finite element method (3D-FEM) and threedimensional beam (3D) propagation method (3D-BPM), respectively.
FDTD method is appropriate to simulate reduced regions with fast speed and low memory requirements.Therefore, we optimize the fiber height above the grating (h = 1 μm) to reduce our simulation region.Complete grating coupler has been simulated at 1550 nm for different waveguide widths (10 µm, 11 µm, 12 µm, 13 µm, 14 µm and 15 µm).The refractive indexes of Si and SiO2 are taken as n Si = 3.4758 and n SiO2 = 1.4442, respectively.LP 01 and LP 11 modes are excited from the optical fiber and coupled to the waveguide.In order to assess the sensitivity to eventual fiber to coupler misalignments, the center of the fiber can be displaced along the width of the grating from −4 µm to 4 µm with respect to the center of the grating coupler.Results of the coupling efficiency are depicted in Fig. 7.
Figure 7(a) displays the coupling efficiency (CE) from LP 01 to TE 0 and the undesired coupling efficiency from LP 01 to TE 1 , or leakage, as a function of displacement.All coupling efficiencies are symmetric and slow-varying with respect to the center of the grating coupler, remaining practically constant for minor variations (up to ± 1 μm).However, depending on the selected width, the coupling efficiency from LP 01 to TE 0 increases from 26.4% (for a shift of 4 µm) to as high as 45.9% (no misplacement) for the 10 µm width or, from 29.3% to as high as 49.7%, respectively, for the 15 µm width.For the maximum coupling, the difference between both grating widths is 3.8%.If a 1 dB penalty in the coupling efficiency due to lateral misplacement is considered a ± 2.4 µm (10 µm coupler) to ± 2.6 µm (15 µm coupler) alignment range are obtained.Besides that, the LP 01 to TE 1 leakage is null for all widths when the fiber and the grating are perfectly aligned, but it ranges from 8.4% (w g = 15 µm) to 13.3% (w g = 10 µm) for the maximum misplacement considered.The best performance in terms of LP 01 to TE 0 coupling efficiency is obtained for w g = 15 μm with a 49.7% efficiency, value that would decrease for wider widths (49.6% and 49.1% for w g = 16 μm and w g = 17 μm).With this result in mind, widths wider than 15 μm were not taken into consideration in the simulation.
The simulation results for the coupling efficiency from LP 11 to TE 1 and the undesired LP 11 to TE 0 leakage are shown in Fig. 7(b).In this case, the different responses are also symmetric with respect to the center of the grating coupler, but the sensitivity to lateral misalignment is quite higher than in the LP 01 -TE 0 case.From LP 11 to TE 1 , the coupling efficiency increases approximately from 0.2% (for a lateral displacement of 4 µm) to 34.8% (no misplacement) for the 10 µm width or, from 3.5% to as high as 46.35%, respectively, for the 15 µm width.In this case, the maximum difference between both cases is 11.5%, 3 times higher than for the LP 01 -TE 0 coupling.The alignment range for the same 1 dB coupling efficiency penalty is reduced to ± 1.25 µm (10 µm coupler) to ± 1.35 µm (15 µm coupler) in this case.In terms of LP 11 to TE 0 leakage, the efficiency at the maximum misplacement ranges from 42.3% to 21.8% for the 10 µm and 15 µm widths, respectively.It can be stated that LP 11 shows a remarkable dependence with the waveguide width and the lateral displacement.
Even though the coupling efficiency simulation results imply that the w g = 15 µm, Λ = 609 nm, ff = 0.5, e d = 70 nm grating coupler would be the best option in terms of coupling efficiency a w g = 14 µm width has been selected to be fabricated as the best compromise when the integrated device size is also considered.The improvement in coupling efficiency with the wider coupler (0.1% and 1.2% difference for LP 01 -TE 0 and LP 11 -TE 1 coupling, respectively) is incremental and the increase of 1 μm in width (9.3% increase) would translate to a quite longer adiabatic taper, increasing the device footprint by the same 9.3% factor.It is important to point out that the final design is 2 µm wider than the optimum design for the LP 01 -TE 0 and SMF-28 fiber, according to the SOI state-of-art.In this conventional LP 01 -TE 0 grating coupler design for SMF-28 fiber the selected width (w g = 12 μm) is also slightly narrower than the optimal theoretical width.Figure 8 shows the optical intensity profiles at the grating coupler output (at a Δz = 15 μm distance from the end of the grating coupler) when the coupler is excited from a TMF fiber with just one mode with the proper polarization and azimuthal orientation.These plots are presented for the most sensitive design and the selected width from Fig. 7, that is, w g = 10 μm (a-d) and w g = 14 μm (e-h) waveguide widths.Two positions for the fiber are shown in the figure, centered (x = 0 µm) and with a 4 µm lateral misalignment.The field intensity is represented by color scale, being brown the most intense area and blue the least one.TE 0 is symmetric at x = 0 μm and non-symmetric at x = 4 μm respect to x-y axes for both w g = 10 μm (a-b) and w g = 14 μm (e-f) waveguides.Without displacement, mode profiles exhibit a unique Gaussian profile whereas for a 4 μm displacement, a fraction of the TE 0 power is converted into TE 1 mode.That trend is more pronounced as we increase the waveguide width.Apart from that, for w g = 14 μm, the mode profile is more confined than for the other width at x = 0 μm and less confined at x = 4 μm, which is consistent with the coupling efficiency results.TE 1 is symmetric at x = 0 μm and breaks the symmetry at x = 4 μm respect to x-y axes for both 10 μm (c-d) and 14 μm (g-h) waveguides.Undesired mode conversion is evidenced for a 4 μm displacement by the conversion of TE 1 mode into TE 0 .This effect is enhanced for the w g = 10 μm waveguide in which case most of the power has been transformed into TE 0 mode (Fig. 8(d)).LP 11 is coupled to the TE 1 mode for both waveguide widths, nonetheless, the original mode profile is better preserved for the w g = 14 μm waveguide.

Experimental results
The grating couplers with 12 µm and 14 μm waveguide widths have been fabricated on samples from 6" SOI wafers.The wafers were purchased from SOITEC and have a 220 nm thin silicon top layer and a 2 µm thick buried oxide layer.The total wafer thickness is approximately 750 µm, taking into account the silicon bulk.The NTC laboratory employed the SOI CMOS-compatible process based on an electron beam direct writing lithography on HSQ resist, followed by dry etching of 220 nm SOI wafers, a typical process to be found in fabrication foundries.Figure 9 shows the experimental configuration based on two schemes, one for the TE 0 -LP 01 mode coupling and the other for the TE 1 -LP 11 .In both cases, light is launched to a standard LP 01 -TE 0 grating (w g = 12 μm) by means of a standard single mode fiber (SSMF).Previously, a polarization controller is employed to adjust and maximize the coupling to the grating coupler.When the first scheme is considered, the configuration does not need an ADC as only TE 0 mode is propagated and coupled to the LP 01 mode in the TMF.The second scheme uses a mode converter based on an asymmetrical directional coupler (ADC) in order to transform the TE 0 into TE 1 [6].Next, the TE 1 mode reaches the output grating coupler and it is finally coupled to the TMF.The optical modes are propagated in the TMF pigtail with a length of 2 meters.Additionally, to avoid any undesirable reflection, the ADC waveguides were tapered.
In order to characterize the performance of the grating couplers (w g = 12 µm and w g = 14 μm wide) the insertion losses and the modal purity of the LP 01 and LP 11 modes in the TMF output were measured for all four cases.The modal purity has been determined by means of the normalized mode overlap integral of the measured mode with the theoretical pure LP 01 or LP 11 mode for the SM2000 fiber.Figure 10 depicts the intensity pattern and modal profile of the LP 01 and LP 11 modes when the grating coupler is driven by the TE 0 or the TE 1 modes to be coupled to the SM2000 TMF.A CCD camera Beam Profiler (Thorlabs BP209-IR) is placed at the output of the TMF verifying the correct coupling of both modes for the 12 µm and 14 µm widths.Both LP 01 modes achieved a perfect Gaussian profile (modal purity of 100%) and the two LP 11 modes obtained a modal purity of 89% for the w g = 12 µm width and 92% for the w g = 14 µm width, respectively.The insertion losses (IL) for the LP 01 mode were 9 dB and 8.2 dB, respectively.In the case of the LP 11 mode, the IL obtained were 18 dB and 16 dB, respectively.It can be stated that the LP 01 mode achieved a better power coupling than LP 11 mode due to the extra losses added by the mode integrated mode converter needed to obtain the TE 1 mode in the experimental setup.These insertion losses values correspond to the losses from the laser output to the TMF output including all fiber pigtails, connectors and polarization controller needed for the experiment.Finally, both modes obtained an excellent modal purity and the insertion losses are lower than the state-of-the-art result for TE 1 -LP 11 vertical grating couplers in SOI technology which show insertion losses higher than 20 dB [21][22][23].In order to check the sensitivity of both designs to the fiber to grating coupler misalignment, the fiber was slightly laterally misplaced when the TE 1 to LP 11 was under measurement and the results are shown in Fig. 11.The pictures were captured moving the positioner (NEWPORT M-562 XYZ with DM-13 micrometers) around 3 µm respect to the waveguide center.Thus, the LP 11 mode profile at the SM2000 fiber output for the w g = 14 µm coupler obtains a higher purity (86%) than the LP 11 mode for the w g = 12 µm coupler (77%), as shown in Fig. 11.The experimental results confirm the greater tolerance to fiber-coupler lateral misalignments for the w g = 14 µm design.

Fig. 2 .
Fig. 2. Schematic waveguide grating coupler diagram for coupling light to/from an optical fiber.

Fig. 4 .
Fig. 4. Comparison between the normalized horizontal field profile of the LP 01 and LP 11 modes from SM2000 fiber and the TE 0 and TE 1 modes for a SOI waveguide (height = 220 nm and waveguide width = 12 µm).

Fig. 5 .
Fig. 5. Grating coupler scheme based on SOI technology with an input fiber.

Fig. 6 .
Fig. 6.Coupling efficiency as a function of the grating period and filling factor for: (a) LP 01 -TE 0 modes and (b) LP 11 -TE1 modes coupling.

Fig. 7 .
Fig. 7. (a) Coupling efficiency from LP 01 to TE 0 (solid line) and from LP 01 to TE 1 (dashed line) and (b) Coupling efficiency from LP 11 to TE 1 (solid line) and from LP 11 to TE 0 (dashed line).

Fig. 9 .
Fig. 9. 3D-sketch of the experimental configuration in order to achieve the LP 01 and LP 11 modes in the TMF.

Fig. 10 .
Fig. 10.Experimental intensity pattern and modal profile at the TMF from 12 µm (solid blue line) and 14 µm (dashed red line) waveguide widths for: (a) LP 01 mode and (b) LP 11 mode.

Fig. 11 .
Fig. 11.Captured image of the intensity pattern and modal profile of the LP 11 modes when a little misalignment in the coupling from fiber to grating coupler is produced for: (a) 12 µm width and (b) 14 µm width.