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Title:
SUBWAVELENGTH GRATING COUPLER FOR MID-INFRARED SILICON PHOTONICS INTEGRATION
Document Type and Number:
WIPO Patent Application WO/2019/212414
Kind Code:
A1
Abstract:
In example embodiments, designs for a SOI-based mid-infrared SWGC, for example, operating in the 3.7 µm wavelength range, are provided that achieve high coupling efficiency and optical bandwidth, while also being suitable for low-cost mass production. The designs may include to uniform or apodized subwavelength gratings. The designs may be constructed using standard CMOS processes. The subwavelength grating may be formed, for example using only a single full etch.

Inventors:
CHEN, Nan (Faculty of Engineering Department of Electrical and Computer Engineering,21 Lower Kent Ridge Road, Singapore 7, 11907, SG)
DONG, Bowei (Faculty of Engineering Department of Electrical and Computer Engineering,21 Lower Kent Ridge Road, Singapore 7, 11907, SG)
LEE, Chengkuo (Faculty of Engineering Department of Electrical and Computer Engineering,21 Lower Kent Ridge Road, Singapore 7, 11907, SG)
Application Number:
SG2019/050243
Publication Date:
November 07, 2019
Filing Date:
May 02, 2019
Export Citation:
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Assignee:
NATIONAL UNIVERSITY OF SINGAPORE (21 Lower Kent Ridge Road, Singapore 7, 119077, SG)
International Classes:
G02B6/34; G02B5/18
Attorney, Agent or Firm:
KALANI, Ameen (Henry Goh Pte Ltd, 2 Venture Drive #15-21 Vision Exchange, Singapore 6, 608526, SG)
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Claims:
CLAIMS

1. A silicon-on-insulator (SOI)-based mid-infrared subwavelength grating coupler (SWGC), comprising:

a substrate;

a buried oxide (BOX) layer disposed over the substrate;

a silicon (Si) device layer disposed over the BOX layer and having a fully etched subwavelength grating, taper and waveguide, the subwavelength grating defined by a plurality of unit cells repeated at a first periodicity in a first dimension and a second periodicity in a second dimension, a length of a subwavelength hole of each unit cell defined by the product of the periodicity in the first dimension and a filling factor in the first dimension, and a width of the subwavelength hole of each unit cell defined by the product of the periodicity in the second dimension and a filling factor in the second dimension; and

a cladding disposed over the device layer.

2. The SOI-based mid-infrared SWGC of claim 1, wherein the subwavelength grating is configured to operate at substantially a 3.7 pm optical mode.

3. The SOI-based mid-infrared SWGC of claim 1, wherein the subwavelength grating includes uniform subwavelength holes.

4. The SOI-based mid-infrared SWGC of claim 3, wherein the periodicity in the first direction is between 2 and 2.1 pm and the filling factor in the first direction is between 0.5 and 0.58, and the periodicity in the second dimension is substantially 0.8 pm and the filling factor in the second dimension is substantially 0.3.

5. The SOI-based mid-infrared SWGC of claim 3, wherein the periodicity in the first direction is substantially 2.1 mih and the filling factor in the first direction is substantially 0.58, and the periodicity in the second dimension is substantially 0.8 pm and the filling factor in the second direction is substantially 0.3.

6. The SOI-based mid-infrared SWGC of claim 1, wherein the subwavelength grating includes apodized subwavelength holes.

7. The SOI-based mid-infrared SWGC of claim 6, wherein the periodicity in the first direction is substantially 2 pm and the filling factor is either substantially 0.5 or apodized as 0.25 +0.03/7, where n is a number of the unit cells in the first direction, and the periodicity in the second dimension is between 0.8 pm and 1 pm and the filling factor in the second dimension is either substantially 0.3 or apodized in the second dimension as .275 + x*n, where x is between 0.01 and 0.03.

8. The SOI-based mid-infrared SWGC of claim 6, wherein the periodicity in the first direction is substantially 2 pm and the filling factor is either substantially 0.5, and the periodicity in the second dimension is substantially 0.8 pm and the filling factor in the second dimension is apodized in the second dimension as .275 + 0.03/7, where n is a number of the unit cells in the first direction.

9. The SOI-based mid-infrared SWGC of claim 1, wherein a width of the subwavelength grating is a product of a number of unit cells in the first dimension and the first periodicity, and a length of the subwavelength grating is a product of a number of unit cells in the second dimension and the second periodicity

10. The SOI-based mid-infrared SWGC of claim 9, wherein the width of the

subwavelength grating is substantially 10 pm and the length of the subwavelength grating is substantially 50 pm.

11. The SOI-based mid-infrared SWGC of claim 1, wherein the taper has a length of substantially 20 pm and the waveguide has a width of substantially 1.2 pm.

12. A chemical identification or detection instrument, comprising:

a light source configured to supply 3.7 pm light;

an input optical fiber configured to receive light from the light source;

a silicon-on-insulator (SOI)-based mid-infrared subwavelength grating coupler (SWGC) having a fully etched silicon (Si) subwavelength grating, taper and waveguide, the subwavelength grating defined by a plurality of unit cells repeated at a first periodicity in a first dimension and a second periodicity in a second dimension and configured to receive 3.7 pm light from the input optical fiber, the taper configured to connect the subwavelength grating to the waveguide, and the waveguide configured to supply an output of the SWGC.

12. A chemical identification and/or detection instrument of claim 12, wherein the subwavelength grating includes uniform subwavelength holes.

13. The chemical identification and/or detection instrument of claim 12, wherein the subwavelength grating includes apodized subwavelength holes.

14. The chemical identification and/or detection instrument of claim 12, wherein a width of the subwavelength grating is substantially 10 pm, a length of the subwavelength grating is substantially 50 pm, a length of the taper is substantially 20 pm, and a width of the waveguide is substantially 1.2 pm.

15. A method for producing a silicon-on-insulator (SOI)-based mid-infrared

subwavelength grating coupler (SWGC), comprising: 3 applying a buried oxide (BOX) layer to a substrate;

4 applying a silicon (Si) device layer over the BOX layer;

5 etching a subwavelength grating, taper and waveguide into the device layer, the

6 subwavelength grating defined by a plurality of unit cells repeated at a first periodicity in

7 a first dimension and a second periodicity in a second dimension, a length of the

8 subwavelength hole of each unit cell defined by the product of the periodicity in the first

9 dimension and a filling factor in the first dimension, and a width of the subwavelength

10 hole of each unit cell defined by the product of the periodicity in the second dimension n and a filling factor in the second dimension; and

12 applying a cladding over the device layer.

1 16. The method of claim 15, where the etching etches the subwavelength to operate at

2 substantially a 3.7 pm optical mode.

1 17. The method of claim 15, wherein etching etches uniform subwavelength holes in the

2 subwavelength grating.

1 18. The method of claim 17, wherein the periodicity in the first direction is between 2 and

2 2.1 pm and the filling factor in the first direction is between 0.5 and 0.58, and the

3 periodicity in the second dimension is substantially 0.8 pm and the filling factor in the

4 second dimension is substantially 0.3.

1 19. The method of claim 15, wherein the etching etches apodized subwavelength holes in

2 the subwavelength grating.

20. The method of claim 15, wherein the periodicity in the first direction is substantially 2 pm and the filling factor is either substantially 0.5 or apodized as 0.25 +0.03/7, where n is a number of the unit cells in the first direction, and the periodicity in the second dimension is between 0.8 pm and 1 pm and the filling factor in the second dimension is either substantially 0.3 or apodized in the second dimension as .275 + x*n, where x is between 0.01 and 0.03.

Description:
SUBWAVELENGTH GRATING COUPLER FOR MID-INFRARED SILICON PHOTONICS INTEGRATION

BACKGROUND Technical Field

The present application relates generally to grating couplers, and more specifically to mid-infrared subwavelength grating couplers (SWGCs), for example, operating in the 3.7 pm wavelength range.

Background

The mid-infrared region of the spectrum includes vibration fingerprints of many kinds of chemical bonds, useful in chemical (e.g., gas) identification and detection. While a variety of technologies may be used to sense the mid-infrared region, silicon photonics has proved promising. A typical silicon photonics chemical (e.g., gas) sensor includes an external light source (laser in most cases) that supplies light via a single-mode optical fiber to an in-plane waveguide that leads to photonic integrated circuits. A grating coupler is commonly used to couple the optical fiber to the waveguide. Often such grating coupler is structured as a SWGC, where the grating period is much smaller than the wavelength of the light. Due to the subwavelength dimensions of holes in the grating, the SWGC behaves like a homogeneous medium. A SWGC may provide a number of advantages over other designs, including greater ability to engineer effective index contrast to alleviate backside reflection, increased optical bandwidth, enhanced field overlap with the fiber mode, etc.

It is desirable to produce a SWGC that has high coupling efficiency and optical bandwidth, but that also is simple to construct, and is thereby suitable for low-cost mass production. However, this goal has eluded prior efforts. Some prior attempts at achieving high efficiency have involved exotic manufacturing techniques, such as a bottom metal mirror and multilayer Bragg reflectors for producing constructive interference, and an overlay on the grating region to intrinsically diminish downward radiation. However, with the increase in efficiency has also come an increase in manufacturing complexity, requiring additional bonding efforts or complementary metal-oxide-semiconductor (CMOS) non-compatible processes. Other prior attempts have involved expensive materials, including arrangements such as germanium-on-silicon-on-insulator (Ge-on- SOI), germanium-on-silicon (Ge-on-Si) and silicon-on-sapphire (SOS), etc. Although arrangements involving germanium and sapphire may provide a wide transparent window and high refractive index, they can be expensive and are not well established in commercial manufacturing. Still further prior attempts have involved design and optimization methods that have yielded a considerable gap between simulation and actual results, such that the coupling efficiency actually achieved is far short of the theoretical maximum coupling efficiency of the design.

Accordingly, there is a need for an improved mid-infrared SWGC that may be, for example, used in silicon photonics chemical (e.g., gas) sensors, that addresses some or all of the above described shortcomings of prior attempts.

SUMMARY

In example embodiments, designs for a silicon-on-insulator (SOI)-based mid infrared SWGCs, for example, operating in the 3.7 pm wavelength range, are provided that achieve high coupling efficiency and optical bandwidth, while also being suitable for low-cost mass production. The designs may include uniform or apodized subwavelength gratings. The designs may be constructed using standard CMOS processes. The subwavelength grating may be formed, for example, using only a single full etch, simplifying manufacture. Design and optimization methods may be used to achieve results that are closer to the theoretical maximum coupling efficiency.

In one specific embodiment, a SOI-based mid-infrared SWGC is provided that includes a substrate, a buried oxide (BOX) layer disposed over the substrate, a silicon (Si) device layer disposed over the BOX layer having a fully etched subwavelength grating, taper and waveguide, and a cladding dispose over the device layer. The subwavelength grating is optimized to operate at substantially a 3.7 pm optical mode. The

subwavelength grating is defined by a plurality of unit cells repeated at a first periodicity in a first dimension and a second periodicity in a second dimension. A length of the subwavelength hole of each unit cell defined by the product of the periodicity in the first dimension and a filling factor in the first dimension, and a width of the subwavelength hole of each unit cell defined by the product of the periodicity in the second dimension and a filling factor in the second dimension. The filing factor may be adjusted to provide uniform or apodized configurations.

It should be understood that a variety of additional features and alternative embodiments may be implemented other than those discussed in this Summary. This

Summary is intended simply as a brief introduction to the reader, and does not indicate or imply that the examples mentioned herein cover all aspects of the disclosure, or are necessary or essential aspects of the disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

The description below refers to the accompanying drawings of example embodiments, of which:

Fig. 1A is a top-down view of an example SOI-based mid-infrared SWGC (disposed in a x-y plane) having a waveguide output, taper, subwavelength grating and an end portion, with a zoomed in insert showing details of the wavelength grating; Fig. 1B is a perspective view of the example SOI-based mid-infrared SWGC of

Fig. 1A, illustrating a single-mode input fiber that supplies light to the SWGC from an external light source (e.g., a 3.7 pm laser);

Fig. 1C is a pair of tables showing various example values of parameters (e.g., P x , /x, N x , P y ,f y and N y ) defining uniform (e.g., labeled A1-A3, Bl-B-3) and apodized (e.g., labeled C1-C4, D1-D2) SWGC designs;

Fig. 1D is a scanning electron microscope (SEM) image of SWGC design Al from Fig. 1C;

Fig. 1E is a SEM image of a portion of the uniform subwavelength grating of SWGC design Al from Fig. 1C;

Fig. 1F is a SEM image of a portion of a y-direction apodized subwavelength grating of SWGC design C2 from Fig. 1C; Fig. 1 G is a SEM image of a portion of an x-direction apodized subwavelength grating of SWGC design Dl from Fig. 1C;

Fig. 2A is a graph showing correlation of the effective index with the width of the high index region by curve fitting;

Fig. 2B is a graph showing simulated directionality spectra of SWGC device Al of Fig. 1C with different device layer thicknesses ranging from 300 nm to 500 nm, when the BOX layer is 3 pm thick;

Fig. 2C is a graph showing simulated dependence of directionality on BOX layer thickness when the device layer is 400nm thick for SWGC device Al of Fig. 1C;

Fig. 2D is a graph showing simulated dependence of directionality on device layer thickness when the BOX layer is 3 pm thick for SWGC device Al of Fig. 1C;

Fig. 3A is a graph of simulated spectra for uniform SWGC designs Al, A2 and A3 of Fig. 1C;

Fig. 3B is a graph of measured spectra from physical testing for uniform SWGC designs Al, A2 and A3 of Fig. 1C, with an example of 3dB and ldB bandwidth extraction of device A3 through parabolic fit;

Fig. 3C is a graph of simulated spectra for uniform SWGC designs Bl, B2 and B3 of Fig. 1C;

Fig. 3D is a graph of measured spectra from physical testing for uniform designs Bl, B2 and B3 of Fig. 1C;

Fig. 4 A is a graph of simulated spectra for apodized SWGC designs Cl, C2 and C3 of Fig. 1C;

Fig. 4B is a graph of measured spectra from physical testing for apodized SWGC designs Cl, C2 and C3 of Fig. 1C;

Fig. 4C is a graph of simulated spectra for apodized SWGC designs C2 and C4 of

Fig. 1C, with an insert showing a single row grating with apodized f y ;

Fig. 4D is a graph of measured spectra from physical testing for apodized SWGC designs C2 and C4 of Fig. 1C; Fig. 4E is a graph of simulated spectra for apodized SWGC designs Dl and D2 of Fig. 1C, with an insert showing a single row grating with apodized f x ;

Fig. 4F is a graph of measured spectra from physical testing for apodized SWGC designs Dl and D2 of Fig. 1C;

Fig. 5A is an illustration of simulated electric field disruption of SWGC design

Al of Fig. 1C;

Fig. 5B is an illustration of simulated index of mode profile in SWGC design Al of Fig. 1C;

Fig. 5C is an illustration of simulated electric field disruption of SWGC design C3 of Fig. 1C;

Fig. 5D is an illustration of simulated index of mode profile in SWGC design Cl of Fig. 1C;

Fig. 5E is a graph of simulated index of mode profile and electric field profile along the x-axis of SWGC design Al of Fig. 1C;

Fig. 5F is a graph of simulated index of mode profile and electric field profile along the x-axis of SWGC design Cl of Fig. 1C;

Fig. 5G is a graph of diffracted modes from uniform SWGC designs Al and B 1 of Fig. 1C verse the Gaussian profile of the input fiber mode;

Fig. 5H is a graph of diffracted modes from apodized SWGC designs C3 and Dl of Fig. 1C verse the Gaussian profile of the input fiber mode;

Fig. 6 is a multipart graph showing in a first portion simulated and measured maximum coupling efficiency of the SWGC designs of Fig. 1C, with the best data marked, in a second portion simulated and measured peak wavelength of the SWGC designs of Fig. 1C, in a third portion simulated and measured 1 dB bandwidth of the SWGC designs of Fig. 1C, with the best data marked, and in a fourth portion simulated and measured 3dB bandwidth of the SWGC designs of Fig. 1C, with the best data marked; Fig. 7A is a graph of measured coupling efficiency spectra of SWGC designs B3 and C3 of Fig. 1C with a shaded region being the Area, and the calculation formula inserted; and

Fig. 7B is a graph of simulated and measure Area for all the SWGC designs of Fig. 1C.

DETAILED DESCRIPTION

Definitions

As used herein, the term“substrate” should be interpreted broadly to refer to a structure to which one or more materials, or one or more layers of material, may be deposited.

As used herein, the term“layer” should be interpreted broadly to refer to a level or thickness in a plane parallel to a substrate that is distinguishable from another level or thickness. A layer is not limited to a single material, but may comprise one or more sub layers or intermediate layers of one or more materials.

As used herein, the term“and/or” (e.g., as in“X and/or Y”) should be interpreted to mean either“and” or“or” (e.g., as in“X and Y” or“X or Y”).

Further, as used herein, the term“substantially” should be understood to include, exactly or completely, and also to include within a reasonable variation, defined as a variation of no more than +/- 5% when used in reference to a value. Example Embodiments

1. Device Structures

Fig. 1A is a top-down view of an example SOI-based mid-infrared SWGC 100 (disposed in a x-y plane) having a waveguide output 110, taper 120, subwavelength grating 130 and an end portion 135, with a zoomed in insert showing details of the wavelength grating 130. The SWGC 100 is configured to operate, for example, in the 3.7 pm wavelength range. Fig. 1B is a perspective view of the example SOI-based mid- infrared SWGC 100 of Fig. 1A, illustrating a single-mode input fiber 140 that supplies light to the SWGC 100 from an external light source (e.g., a 3.7 pm laser) (not shown). The SWGC 100 includes a substrate (e.g., a Si layer) 150, a BOX layer (e.g., a 3 pm S1O2 layer) 160, a device layer (e.g., 400 nm Si layer) 170 and a top cladding (e.g., a 2 pm Si0 2 layer) (not shown). The SWGC 100 may be fabricated by standard CMOS processes. In one implementation, the SWGC 100 may start as a commercially available SOI wafer (e.g., with a 220nm thick device layer and 3 pm BOX) layer) and an additional device layer thickness (e.g., of l80nm) may be epitaxially grown to yield the full device layer.

The subwavelength grating 130 may be defined by a number of unit cells N x repeated at a periodicity P x in the x-dimension, and a number of unit cells N y repeated at a periodicity P y in the y-dimension, as shown in the insert in Fig. 1A. Each unit cell includes a subwavelength hole which may be substantially rectangular when viewed from above. The size of each subwavelength hole may be defined by products of the periodicities and filling factors. For instance, a length of each subwavelength hole may be defined by P x * / x , and the width of each subwavelength hole may be defined by P y * / y, where / x and/ y are filling factors in the respective dimensions. The subwavelength holes may be uniform in size (e.g., where both/ x and/ y are a constant value) or may be apodized (e.g., where at least one of/ x and/ y are a function of hole location), yielding uniform or apodized configurations.

The subwavelength grating 130 may have a width that is defined as a product of the number of unit cells N y and the periodicity P y in the y-dimension. The width may be matched with the core diameter of the single-mode input fiber 140. In one

implementation, the width is substantially 10 pm. The subwavelength grating 130 may have a length that is defined as a product of the number of unit cells N x and the periodicity P x in the x-dimension. In one implementation of a uniform grating 130, the length is substantially 50 pm. The length may be shorter for an apodized design, limited by the feature size in microfabrication. In one implementation, the end portion width is substantially 5 pm long. Further, in one implementation, the taper 120 is substantially 20 pm long, to provide high transmission.

The subwavelength grating 130 may be formed by a full etch to reduce complexity of fabrication. In one implementation, a hard mask of silicon oxide may be applied and deep ultra-violet (DUV) photolithography used to define a pattern.

Subsequently, the pattern may be transferred to device layer 170 by performing silicon reactive ion etching (RIE) which creates the holes of the subwavelength grating 130.

The single-mode input fiber 140 that supplies light to the SWGC 100 may be tilted at an angle Q (e.g., 13.5°) with respect to the z-axis. The tilted angle Q may encourage mode match and suppress second-order Bragg reflection loss.

Fig. 1C is a pair of tables showing various example values of parameters (e.g., P x , /x, N x , P y ,f y and N y ) defining uniform (e.g., labeled A1-A3, Bl-B-3) and apodized (e.g., labeled C1-C4, D1-D2) SWGC designs. Such designs may be illustrated by SEM images Fig. 1D is a SEM image of SWGC design C2 from Fig. 1C. Fig. 1E is a SEM image of a portion of the uniform subwavelength grating of SWGC design Al from Fig. 1C. Fig. 1F is a SEM image of a portion of a y-direction apodized subwavelength grating of SWGC design C2 from Fig. 1C. Fig. 1G is a SEM image of a portion of an x-direction apodized subwavelength grating of SWGC design Dl from Fig. 1C.

2. Design Methods

The above discussed example SOI-based mid-infrared SWGC 100 may be designed based on a phase match condition (PMC)

/p if only the first diffraction order is considered, where is the effective index of the grating region, Q is 13.5°, n c is the refractive index of the cladding (e.g., silicon oxide) and P x is the periodicity in the x-direction. The ultimate goal is to find the desired subwavelength grating dimensions: the periodicities P x and P y of the subwavelength holes in both the x- and y-directions and the filling factors / x and/ y subwavelength holes in both the x- and y- directions, which are able to fulfill the requirement of PMC for the specific wavelength. However, there is no direct solution to these dimensions without being linked to the effective index. Therefore, the effective medium theory (EMT) that correlates the effective index with the dimensional parameters may be deployed. Applying the zeroth- order TE mode EMT as shown in Eq. (l)-(2) below, and simultaneously assuming P y < p — l ./

Bragg /max( i7 e ) to frustrate other disturbing diffractions, a two-dimensional subwavelength grating can be approximated to a one-dimensional grating model through projecting the y-axis periodic subwavelength grating component onto the x-axis:

Veff — fx LX 4 (1 fx) HX (¾ where h ίg and h Hg are the low and high refractive index in terms of the alternating subwavelength hole and grating in the y-direction. The values of h ίg and h Hg may be 1.5 (for oxide cladding) and 3.45, respectively. h ίc is the low effective index of the one dimensional region on the x-axis, equivalently converted from the aforementioned alternating hole and grating along the y-axis by the EMT method. h Hc is the high effective index along the x-axis, associated with the width w Hx of the grating. In order to improve design accuracy (e.g., aiming the maximum coupling efficiency at 3.7 pm) h Hc may be simulated and fitted with respect to the grating width before launching the numerical calculation. The correlation between h Hc and w Hx can be expressed as the cubic curve h Hc = 0.2 + 2.807 w Hx + 1.192 w Hx 2 + 0.173 w Hx 3 , which is valid for a uniform subwavelength grating with oxide cladding. Fig. 2A is a graph showing correlation of the effective index with the width of the high index region by curve fitting.

3. Designs and Optimization

Using the above discussed design method, it may be observed that more than one sets of parameters can meet the requirements. From the possible designs shown in Fig. 1C produced by the above discussed design method, two designs (Al and Bl) may be selected that have optimum coupling efficiency (e.g., of -4.3 dB) at a wavelength of 3.7 pm.

Directionality for optical fiber-to-chip coupling can be defined as the ratio of the transmitted optical power to the fraction of total diffracted optical power. The thickness of the device layer 170 and BOX layer 160 can strongly affect directionality due to the formation of constructive and destructive interference within the layers. Fig. 2B is a graph showing simulated directionality spectra of SWGC device Al of Fig. 1C with different device layer thicknesses ranging from 300 nm to 500 nm, when the BOX layer is 3 mih thick. By extracting the directionality for each thickness at 3.7 mih, the thickness of 400nm is found to be able to achieve the optimum directionality (e.g., of 50.89%). Fig. 2C is a graph showing simulated dependence of directionality on BOX layer thickness when the device layer is 400nm thick for SWGC device Al of Fig. 1C. Fig. 2D is a graph showing simulated dependence of directionality on device layer thickness when the BOX layer is 3 pm thick for SWGC device Al of Fig. 1C.

4. Characterization and Testing Results

The above discussed designs may be simulated and physical tested to verify performance. FDTD simulation may be used. Fig. 3A is a graph of simulated spectra for uniform SWGC designs Al, A2 and A3 of Fig. 1C. Fig. 3B is a graph of measured spectra from physical testing for uniform SWGC designs Al, A2 and A3 of Fig. 1C, with an example of 3dB and ldB bandwidth extraction of device A3 through parabolic fit. Fig. 3C is a graph of simulated spectra for uniform SWGC designs B l, B2 and B3 of Fig. 1C. Fig. 3D is a graph of measured spectra from physical testing for uniform designs Bl, B2 and B3 of Fig. 1C. From the simulated results in Figs. 3A and 3C it may be observed that designs Al and Bl successfully produce transmission peak (greatest coupling efficiency) at 3.7 pm. Peak wavelength experiences red shift while P x is lengthened which complies with the Bragg condition. From the physical testing results in Figs. 3B and 3D it may be noted that the measured spectra are exceedingly congruous with the simulated results in terms of peak shift, coupling efficiency change and spectrum profile, although the measured peak wavelength is slightly red-shifted by at most 50 nm and the measured coupling efficiency is decreased by 3 dB. In order to precisely attain 1 dB and 3 dB bandwidth, the measured spectra (in dB) are fit by a parabola function resulting from the logarithm transformation from Gaussian profile in percentage, as described by the example of device A3 in Fig. 3B. Generally, the measured bandwidth in testing is narrower than the ideal case.

Apodized subwavelength grating designs may circumvent the limitation of mode mismatch between the input fiber and the coupled light. To compare uniform and apodized designs, consider designs C1-C4 and D1-D2 of Fig. 1C. Fig. 4A is a graph of simulated spectra for apodized SWGC designs Cl, C2 and C3 of Fig. 1C. Fig. 4B is a graph of measured spectra from physical testing for apodized SWGC designs Cl, C2 and C3 of Fig. 1C. Fig. 4C is a graph of simulated spectra for apodized SWGC designs C2 and C4 of Fig. 1C, with an insert showing a single row grating illustrating apodized f y . Fig. 4D is a graph of measured spectra from physical testing for apodized SWGC designs C2 and C4 of Fig. 1C. Fig. 4E is a graph of simulated spectra for apodized SWGC designs Dl and D2 of Fig. 1C, with an insert showing a single row grating illustrating apodized f x . Fig. 4F is a graph of measured spectra from physical testing for apodized SWGC designs Dl and D2 of Fig. 1C. As may be observed in Figs. 4A and 4B, the increased df y causes the transmission peak to be blue-shifted. This is because the larger subwavelength hole size lowers the effective index, causing interference at a smaller wavelength. The measured spectra of devices Cl, C2 and C3 in Fig. 4B share the same pattern but with lower coupling efficiency and more significant wavelength shift and intensity drop. Meanwhile, the impact of P y is shown between C2 and C4, and Dl and D2, in Figs. 4C-4F, indicating that smaller P y could contribute higher peak coupling efficiency. More specifically, for C2 and C4 apodized in f y , the varying P y leads to peak wavelength shift because the apodization of the effective index along the y-axis will be partially modulated, thus the accumulated change drives wavelength shift. However, for Dl and D2 with the apodized f X the change of P y does not impose much on the effective index along the x-axis, hardly causing a noticeable wavelength shift.

In order to illustrate the difference between uniform and apodized subwavelength gratings, simulated electric field, index distribution of mode profile and the radiated grating mode of designs may be plotted at peak wavelengths. Fig. 5A is an illustration of simulated electric field disruption of SWGC design Al of Fig. 1C. Fig. 5B is an illustration of simulated index of mode profile in SWGC design Al of Fig. 1C. Fig. 5C is an illustration of simulated electric field disruption of SWGC design C3 of Fig. 1C. Fig. 5D is an illustration of simulated index of mode profile in SWGC design Cl of Fig. 1C. Fig. 5E is a graph of simulated index of mode profile and electric field profile along the x-axis of SWGC design Al of Fig. 1C. Fig. 5F is a graph of simulated index of mode profile and electric field profile along the x-axis of SWGC design Cl of Fig. 1C. Fig. 5G is a graph of diffracted modes from uniform SWGC designs Al and Bl of Fig. 1C verse the Gaussian profile of the input fiber mode. Fig. 5H is a graph of diffracted modes from apodized SWGC designs C3 and Dl of Fig. 1C verse the Gaussian profile of the input fiber mode.

As can be seen from Fig. 5A and Fig 5C, the electric field distribution mainly differs around the taper center region and the very first subwavelength gratings close to the taper. The distinguishing dissimilarities of the index distribution of mode profile are spotted within the subwavelength grating region in Fig. 5B and 5D. Design Al has a uniformly gradual index change with lower mode index at the edge and higher index in the center. On the contrary, the mode index of design C3 is arrow-like, distributed along the light propagating direction. Figs. 5E and 5F show the mode profile index of design Al along y = 0.4 pm (to ensure probing swept across one entire row of subwavelength holes with fixed hole width) and design C3 along y = 0.6 pm (to ensure probing swept across one entire row of subwavelength holes with varied hole width). The evenly alternating high-low mode profile index of the uniform subwavelength grating zone has a weaker electric field of the waveguide mode than the gradually changing high-low index of the apodized subwavelength grating zone. The mild and less intense index contrast modulated by the first few holes next to the taper in the apodized SWGC structure is able to diminish the severe impedance discontinuity or suppress Fresnel reflection in the interface between the high and low index region. In contrast, the sudden index change within the taper-uniform subwavelength grating transition region has difficulty in facilitating the initiate grating Bloch mode. Lastly, the diffracted beam modes of uniform and apodized subwavelength gratings are compared, with the referenced Gaussian profile of fiber input in Fig. 5G and 5H. It can be seen by the normalized electric field profile that mode mismatch is substantially mitigated via the approach of grating apodization. The apodized SWGC can better assist and support mode overlap than the uniform SWGC.

The simulated and physical testing results may be summarized. Fig. 6 is multipart graph showing in a first portion 610 simulated and measured maximum coupling efficiency of the SWGC designs of Fig. 1C, with the best data marked, in a second portion 620 simulated and measured peak wavelength of the SWGC designs of Fig. 1C, in a third portion 630 simulated and measured 1 dB bandwidth of the SWGC designs of Fig. 1C, with the best data marked, and in a fourth portion 640 simulated and measured 3dB bandwidth of the SWGC designs of Fig. 1C, with the best data marked. As can be seen, the maximum simulated and measured coupling efficiencies are -3.872 dB and -6.477 dB respectively, contributed by the apodized design C3. The largest 1 dB and 3dB bandwidths are offered by the uniform designs: 193.2 nm (for simulated design B3) and 152 (for measured design B3) for ldB bandwidth, and 399.45 nm (for simulated design

Bl) and 263 nm (for measured design B3) for 3dB bandwidth, respectively.

In order to assess SWGC performance, a new figure of merit Area may be calculated taking into account both coupling efficiency and bandwidth. The area under the Gaussian profile of coupling efficiency is given as:

in which FWHM is in the unit of nm, and the maximum intensity of coupling efficiency is in unit one, thus the unit of the Area is nm.

Fig. 7A is a graph of measured coupling efficiency spectra of SWGC designs B3 and C3 of Fig. 1C with the shaded region being the Area, and the calculation formula inserted. As can be observed, the Area of device B3 is 0.0489 nm and the Area of device C3 is 0.0401 nm. Fig. 7B is a graph of simulated and measure Area for all the SWGC designs of Fig. 1C. As can be observed, device B3 beats the rest owing to its broad 3 dB bandwidth. While device C3 has the best coupling efficiency, its lacking of large bandwidth makes it less competitive when it comes to the integral transmission.

In conclusion, designs for SOI-based mid-infrared SWGCs are provided that are configured to, for example, operate in the 3.7 pm wavelength range. The designs may achieve high coupling efficiency and optical bandwidth, while being suitable for low-cost mass production. The designs may include uniform or apodized subwavelength gratings. The designs may be constructed using standard CMOS processes. The subwavelength grating may be formed, for example using a single full etch.

It should be understood that various adaptations and modifications may be made to the above-discussed designs. Various elements described above may be made from differing materials, implemented in different combinations or otherwise formed or used differently without departing from the intended scope of the disclosure. Example embodiments are not necessarily mutually exclusive as some may be combined with one or more others to form new example embodiments. Figures are not drawn to scale and relative relationships in size may be exaggerated for clarity in presentation. The example embodiments are, therefore, to be considered in all respects to be illustrative and not restrictive. What is claimed is: