CN103901563B - A kind of adjustable grating coupler of refractive index and preparation method thereof - Google Patents
A kind of adjustable grating coupler of refractive index and preparation method thereof Download PDFInfo
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Abstract
The present invention relates to photonic device technical field, the specifically manufacture method of the adjustable grating coupler of a kind of refractive index, it is characterized in that: grating groove is the sub-wavelength structure of different horizontal dutycycle, and grating is have different transverse directions and y direction dutycycle f at the x position that longitudinal direction and x direction are differentyGrating；Grating is at longitudinal dutycycle fxValue is a definite value between (0,1)；Constitute the sub-wavelength structure of longitudinally upper different x position grating groove, its horizontal dutycycle fyValue by export required for Gaussian field distribution G (x) leakage factor distribution α (x) determine.The grating coupler of this structure can effectively reduce coupling loss when optical fiber and waveguide coupling.
Description
Technical field
The present invention relates to optic communication and light network field, particularly relate to design and the preparation of the adjustable optical wave guide coupling structure of a kind of refractive index.The grating coupler of this structure can effectively reduce coupling loss when optical fiber and waveguide coupling.
Background technology
Silicon photon technology is under the driving of low cost and low-power consumption, based on SOI (silicon-on-insulator) platform, having prepared multiple silicon photonic device up to now and achieved integreted phontonics, silicon photon technology is considered as solve the most potential technology of power consumption and bandwidth problem in current integrated circuit.The significant challenge that current silicon photon technology faces is how introduced by LASER Light Source and derive integreted phontonics loop, grating coupler is high due to its high coupling efficiency, cost is low and compatible with CMOS technology, without die terminals mirror polish, the advantages such as optical signal input and output can be realized Anywhere at chip surface, become maximally effective LASER Light Source coupling scheme in silicon integreted phontonics loop.
The method improving grating coupler coupling efficiency has a lot, as increased bottom multilayer diel, back bonding metallic mirror and cover layer etc., these methods or enhancing directivity, or reduce the reflection loss between grating coupler and optical fiber, but owing on usual grating coupler, grating is equally distributed, and equally distributed grating coupler to the optical power distribution of external diffraction along the direction of propagation according to index decreased, i.e. P=P0Exp (-2 α x), P0For incident optical power, 2 α are the Power leakage factor (constant) of grating, there is pattern and do not mate between diffraction mould field and the Gaussian mode field of single-mode fiber of this decay, and the coupling efficiency limiting grating coupler improves further.In order to realize mating of grating diffraction mould field upwards and single-mode fiber Gaussian mode field, can realizing the non-uniform Distribution of leakage factor by longitudinal non-homogeneous grating and obtain output field distribution G (x) of gaussian shape, the Power leakage factor of grating must is fulfilled for:
In formulaFor normalized Gauss distribution, wherein w0=5.2 μm, w0Size is corresponding with single-mode fiber spot size 5.2 μm, utilizes energy normalized condition to obtain
Current non-homogeneous grating is to carry out light engraving erosion at SOI top silicon layer to generate the grating of non-homogeneous dutycycle in the vertical, or utilize the preparation of the hesitation in sense coupling technique to have non-homogeneous dutycycle and the grating of non-homogeneous groove depth simultaneously, and then realize the non-uniform Distribution of leakage factor.The shortcoming of current scheme is in that the refractive index of material is fixed；Additionally needing secondarily etched, namely also need to generate wire grating groove, complex process in the erosion of silicon waveguide surface light engraving after carving saturating SOI and pushing up silicon layer generation silicon waveguide, preparation cost is high；The problem that non-homogeneous grating exists process repeatability difference is prepared also with hesitation.
The present invention proposes a kind of adjustable grating coupler of refractive index and preparation method thereof.This bonder at the sub-wavelength rectangular channel (or groove of other shapes such as square, circular) of the longitudinally different horizontal dutycycles of different grating groove location etchings thus being distributed at the grating groove being longitudinally formed different equivalent refractive index, and then grating diffration characteristic can be regulated so that output field is distributed as the Gauss distribution mated with fiber mode.Non-homogeneous grating in the present invention is SOI to be pushed up silicon layer carve the grating groove thoroughly generating sub-wavelength structure, and waveguiding structure and sub-wavelength structure only can generate with an etching technics.Method in the present invention overcomes the conventional optical media nonadjustable shortcoming of thin-film material refractive index simultaneously.
Summary of the invention
In order to solve the unmatched problem of inter mode of generic homogeneous grating coupler output mould field and the single-mode fiber mode field existed in prior art, it is an object of the invention to provide adjustable grating coupler for realizing high efficiency broadband couple device of a kind of refractive index and preparation method thereof, it can realize coupling between single-mode fiber with planar optical waveguide.
Obtain output field distribution G (x) of gaussian shape in order to obtain the α (x) relevant to the direction of propagation (longitudinal direction) x, adopt the grating groove distribution heterogeneous of x direction to realize.Different transverse direction (y direction) dutycycle f is utilized at longitudinally different x positionyRegulate grating groove equivalent refractive index nLDistribution is thus realizing grating radiation upwards is the Gaussian beam mated with fiber mode.
EFFECTIVE MEDIUM THEORY according to sub-wavelength structure, when light wave is by sub-wavelength structure, sub-wavelength structure can be used as the uniform dielectric of an equivalence, the situation of non-homogeneous grating groove distribution under polarizing for TE, and the refractive index of EFFECTIVE MEDIUM is:
(2) in formula, nairThe refractive index that=1 is waveguide etch areas (air), n1Refractive index for the non-etch areas of waveguide core layer.The cycle of fixed lateral (y direction) is sub-wavelength magnitude, by different longitudinal direction (x direction) position adjustments transverse direction dutycycle fy(that is: waveguide core layer is in xoy plane, and the dutycycle of the y-axis direction etching sub-wavelength structure corresponding in core layer surface difference x coordinate position is fy, there is different f different x coordinate positionsy) can longitudinally obtain the grating groove distribution of different equivalent refractive index.
Volume fraction according to grating groove Yu grating tooth, can calculate the equivalent refractive index of grating layer:
neq=(1-fx)nsub+fxn1(3)
(3) f in formulaxFor longitudinal direction (x direction) dutycycle of grating, fxValue between (0,1).
TE modal eigenvalue equation according to slab guide:
Wherein H is the thickness of waveguide core layer, n2For the refractive index of waveguide lower limit layer, n3The refractive index of the index-matching fluid added above for waveguide (in the reflection of fiber end face and then improves upwards coupling efficiency between diffraction light and optical fiber in order to reduce grating upwards diffraction light, experiment test needs add index-matching fluid at grating surface, fiber end face immerses in matching fluid), neffFor the effective refractive index of the grating waveguide with sub-wavelength structure, m=0 is mode step number.When λ is incident illumination wavelength in a vacuum, the effective refractive index n of TE pattern grating waveguide can be calculated according to equation (4)eff。
Screen periods can draw according to following optical grating diffraction Bragg condition,
qλ=Λx[neff-n1sin(θ)](5)
Wherein q=-1 is the order of diffraction time, ΛxFor grating cycle at direction of propagation x, θ is the angle of optical fiber offset from perpendicular.
The leakage factor expression formula of grating coupler is:
2α=(Pup+Pdown)/Pin(6)
(6) P in formulainFor the luminous power of input waveguide, PupAnd PdownThe respectively luminous power of diffraction up and down, in the analog simulation to grating coupler, PinNormalization is equal to 1, PupAnd PdownSimulation calculation can be passed through out.By to the uniform grating bonder under different grating groove refractive indexs to the outside leakage power P of certain wavelength lightupAnd Pdownα can be calculated.
According to formula (6) under the premise that other structural parameters of grating coupler are fixed, change different horizontal dutycycle fyWith longitudinal periods lambdaxParameter combination can pass through simulation software and calculate and obtain different α value, i.e. the Power leakage factor-alpha of adjustable light barrier, and ΛxParameter value is with n in formula (5)effChange and change, neffAgain with n in formula (4)eqChange and change, neqAgain with n in formula (3)subChange and change, nsub is again with f in formula (2)yChange and change.Therefore can retrodict according to this series of variation relation and obtain: by regulating fy(fixing the sub-wavelength structure any value that the cycle is sub-wavelength magnitude in y direction) regulates leakage factor distribution α (x) and then to realize the field distribution of diffraction output be Gaussian field distribution G (x).
According to the α distribution that the uniform grating bonder under different grating groove refractive indexs is corresponding, in conjunction with different horizontal dutycycle fyThe distribution of corresponding grating groove equivalent refractive index and the output field in order to obtain gaussian shape are distributed grating Power leakage factor-alpha distribution necessary to G (x), can be obtained by different horizontal dutycycle fyRegulate grating groove refractive index and realize the output field distribution of gaussian shape.
Summing up the concrete thinking that regulates is: regulate the f in equation (2)yRegulate nsub, then by nsubRegulate the n in equation (3)eq, then by neqRegulate the n in equation (4)eff, then by neffRegulate the Λ in equation (5)x, by one group of fyAnd ΛxParameter value can obtain a α value, different fyAnd ΛxParameter combination can obtain different α value, i.e. the Power leakage factor-alpha of adjustable light barrier, then by equation (1) according to specific α (x) distribution in x direction, it may be achieved output field distribution G (x) of gaussian shape.
For reaching above-mentioned purpose, the technical solution of the present invention is:
A kind of adjustable grating coupler of refractive index, it is characterised in that including:
One substrate layer；
One lower limit layer, this lower limit layer is on substrate layer；
One waveguide core layer, this waveguide core layer is on lower limit layer, including a submicron waveguide core layer, a tapered transmission line sandwich layer, a slab waveguide sandwich layer, with the narrow end that submicron waveguide core layer junction is tapered transmission line sandwich layer, the wide end junction of tapered transmission line sandwich layer is slab waveguide sandwich layer, make the grating having non-homogeneous grating groove to be distributed on the surface of this slab waveguide sandwich layer, grating is for realizing the coupling from the incident illumination in slab waveguide sandwich layer is exported；
One optical fiber, this optical fiber is directly over grating, and this optical fiber is for receiving diffraction light upwards.
Waveguide core layer (grating layer is etched in this core layer surface), limiting layer, substrate layer.Waveguiding structure is connected in the horizontal direction by a slab waveguide, tapered transmission line and submicron waveguide and forms.What be connected with slab waveguide is tapered transmission line, and what be connected with tapered transmission line is submicron waveguide, at grating arranged above with being used for receiving the optical fiber of upwards diffraction light.
The present invention utilizes grating can will go out waveguide by the optical diffraction of waveguide core layer, and the light that diffraction goes out is placed in the optical fiber above grating and receives.
The manufacture method of the adjustable grating coupler of a kind of refractive index, concretely comprises the following steps:
Step 1: make upper limiting layer and waveguide core layer on substrate slice successively；
Step 2: the sheet minor structure made in cleaning step 1, dries；
Step 3: the slice, thin piece of drying is put in sol evenning machine, spin coating photoresist layer, dry；
Step 4: adopt electron beam exposure technique that the photoresist on waveguide core layer surface is exposed, form the photoresist mask pattern of slab waveguide, tapered transmission line and submicron waveguide；
Step 5: adopt sense coupling, forms the sandwich layer of slab waveguide, tapered transmission line and submicron waveguide three；
Step 6: put into by slice, thin piece in sol evenning machine, at core layer surface spin coating photoresist；
Step 7: adopt electron beam exposure technique to be exposed in slab waveguide core layer surface, form the photoresist mask pattern of grating；
Step 8: the device architecture after exposure is carried out developing fixing；
Step 9: adopt sense coupling, forms grating；
Step 10: clean the slice, thin piece having formed grating, dries.
Wherein said grating is the horizontal cycle be sub-wavelength magnitude and have different transverse direction (y direction) dutycycle f at longitudinal direction (x direction) different x positionyGrating.
Accompanying drawing explanation
Fig. 1 is the structural representation of the adjustable grating coupler of refractive index of the present invention.
Fig. 2 is the schematic cross-section of the adjustable grating coupler structure of refractive index.
Fig. 3 (a)-Fig. 3 (f) is the adjustable grating coupler preparation method schematic diagram of refractive index.Fig. 3 (a) makes limiting layer 6 and silicon waveguide core layer 7 successively on silicon substrate 8 in embodiment step 1, form the figure of SOI sheet；The SOI sheet making the sandwich layer having slab waveguide, tapered transmission line and submicron waveguide three is put in sol evenning machine in embodiment step 6 by Fig. 3 (b), the figure after spin coating photoresist layer 9；Fig. 3 (c) adopts electron beam exposure technique to be exposed in slab waveguide 3 core layer surface in embodiment step 7, form the figure after grating 5 figure；Fig. 3 (d) is the figure after the SOI sheet after exposing in embodiment step 8 carries out developing fixing；Fig. 3 (e) is employing sense coupling in embodiment step 9, the figure after silicon waveguide core layer 7 surface forms grating 4；Fig. 3 (f) is the silicon waveguide core layer 7 on the SOI sheet surface cleaned in embodiment step 10 and form grating 4, the figure after drying.
Fig. 4 is normalized Gauss distribution G (x) and makes the output field of grating coupler be distributed as grating coupler leakage factor distribution α (x) required for G (x).
Fig. 5 is the situation that in the present invention, the adjustable grating coupler of refractive index is distributed for non-homogeneous grating groove under TE polarization, grating groove equivalent refractive index nsubCorresponding horizontal dutycycle fy, longitudinal grating period AxAnd leakage factor α.According to the curve in Fig. 5, to when realizing different output field distribution (such as Gaussian field distribution), required x direction leakage factor distribution α (x), corresponding grating coupler parameter value situation can be found, i.e. the horizontal dutycycle f of non-homogeneous grating groove corresponding with α (x)yWith longitudinal grating period AxThe value distribution situation of the two.
Fig. 6 is the relation schematic diagram in the specific embodiment of the invention between coupling efficiency and the wavelength of the adjustable grating coupler of refractive index.
Fig. 7 is the adjustable grating coupler of refractive index distribution schematic diagram of the electromagnetic wave electric field component in each layer of grating coupler when lambda1-wavelength is 1550nm in the specific embodiment of the invention.
Detailed description of the invention
Below in conjunction with drawings and Examples, the structure and features of the present invention is described in further detail.As shown in Figure 1 and Figure 2, for based on SOI material, a kind of adjustable grating coupler of refractive index, including:
One substrate silicon layer 8；
The lower limit layer 6 of one silicon waveguide, this limiting layer 6 is earth silicon material；
One silicon waveguide core layer 7, this waveguide core layer 7 is produced on below upper limiting layer 6；This waveguide core layer 7 includes: the sandwich layer of submicron waveguide 1, tapered transmission line 2 and slab waveguide 3 three；Submicron waveguide 1 is cuboid；The narrow end of tapered transmission line 2 is connected with submicron waveguide 1, and the other end is connected with slab waveguide 3；The width of this tapered transmission line 2 is between submicron waveguide 1 and slab waveguide 3, for reducing the loss between submicron waveguide 1 and slab waveguide 3；Make on the surface of slab waveguide 3 and have grating 4；
One optical fiber 5, this optical fiber 5 is for receiving the upwards diffraction light of grating 4, axis runout grating 4 surface normal 10 ° of optical fiber 5.
Heretofore described grating is the horizontal cycle be sub-wavelength magnitude and have different transverse direction (y direction) dutycycle f at longitudinal direction (x direction) different x positionyGrating.
Owing to grating 4 is produced on silicon ducting layer in the present invention, it is possible to couple light out from the optical fiber outside silicon waveguide entrance.Incident illumination in submicron waveguide 1 enters the grating region in slab waveguide 3 through tapered transmission line 2, by grating 4 diffraction, diffraction light is divided into: the upwards diffraction caused by negative First order diffraction and downward diffraction, wherein diffraction light upwards is received by optical fiber 5, downward diffraction light some after burying the reflection of oxide layer and substrate interface more upwards outgoing received by optical fiber 5.By above-mentioned measure, it is possible to obtain have the grating coupler of high coupling efficiency.
The present invention provides the manufacture method of the adjustable grating coupler of a kind of refractive index, as it is shown on figure 3, comprise the steps:
Step 1: make upper limiting layer 6 and silicon waveguide core layer 7 on silicon substrate 8 successively, forms SOI sheet, as shown in Fig. 3 (a)；
Step 2: clean the silicon waveguide core layer 7 on SOI sheet surface, dries；
Step 3: the SOI sheet of drying is put in sol evenning machine, spin coating photoresist layer, dry；
Step 4: adopt electron beam exposure technique that the photoresist on SOI sheet surface is exposed, form the photoresist mask pattern of slab waveguide 3, tapered transmission line 2 and submicron waveguide 1；
Step 5: adopt sense coupling, forms the sandwich layer of slab waveguide 3, tapered transmission line 2 and submicron waveguide 1 three, as shown in fig. 1；
Step 6: have the SOI sheet of slab waveguide 3, tapered transmission line 2 and submicron waveguide 1 to put in sol evenning machine by making, spin coating photoresist layer 9, as shown in Figure 3 (b)；
Step 7: adopt electron beam exposure technique to be exposed on slab waveguide 3 surface, form the figure of grating 4, as shown in Figure 3 (c)；Wherein said grating 4 is the non-homogeneous grating of two dimension of sub-micrometer scale；
Step 8: the SOI sheet after exposure carries out developing fixing, as shown in Fig. 3 (d)；
Step 9: adopt sense coupling, forms grating 4, as shown in Fig. 3 (e) on silicon ducting layer 7 surface；
Step 10: clean the silicon ducting layer 7 on the SOI sheet surface having formed grating 4, dries, as shown in Fig. 3 (f).
Fig. 4 is normalized Gauss distribution G (x) and makes the output field of grating coupler be distributed as grating coupler leakage factor distribution α (x) required for G (x).Fig. 5 is the situation that in the present invention, the adjustable grating coupler of refractive index is distributed for non-homogeneous grating groove under TE polarization, grating groove equivalent refractive index nsubCorresponding horizontal dutycycle fy, longitudinal grating period AxAnd leakage factor α.Utilize Fig. 5 longitudinally the adjustable non-homogeneous grating coupler of grating groove refractive index can carried out 0 to 0.5 μm-1Between arbitrary leakage factor distribution design, and then available Fig. 5 realizes leakage factor distribution α (x) in Fig. 4, can obtain Gaussian output field distribution G (x) in Fig. 4.Fig. 6 is the simulation curve of the adjustable grating coupler specific embodiment coupling efficiency of refractive index of the present invention.Curve transverse axis is wavelength, and the longitudinal axis is coupling efficiency, that is to say that in silicon waveguide core layer 7, input optical power is coupled into the luminous power in optical fiber 5 when being 1, and when wavelength is 1550nm, coupling efficiency is up to 62%, three dB bandwidth 87nm.Fig. 7 is the distribution of the electromagnetic wave electric field component in each layer of grating coupler when lambda1-wavelength is 1550nm of refractive index of the present invention adjustable grating coupler specific embodiment, incident illumination is incident from the left side of silicon waveguide core layer 7, upwards diffraction is realized through grating 4, Fig. 7 can be seen that, major part incident illumination all achieves upwards couple, and diffraction mode distributions upwards is Gauss distribution form.The emulation tool that Fig. 6 and Fig. 7 adopts is based on the full vector open source software Camfr of eigen mode method of deploying, and the concrete structure parameter adopted in emulation is: the refractive index n of substrate silicon layer 81=3.476, thickness 1 μm (, on simulation result without impact, in emulation, value is more much smaller than actual substrate silicon layer thickness for this layer thickness)；The refractive index n of silicon dioxide layer 62=1.444, thickness 2.2 μm；The refractive index n of silicon waveguide core layer 71=3.476, thickness 220nm；Waveguide core layer 7 refractive index matching layers (corresponding in actual experiment test to reduce the fiber end face reflection to upwards diffraction light, the index-matching fluid that will add at grating surface) refractive index n above3=1.46；The etching depth of grating 5 is 220nm, and longitudinal dutycycle is fx=0.5, longitudinal cycle is followed successively by 606nm, 608nm, 611nm, 616nm, 620nm, 625nm, 631nm, 637nm, 644nm, 651nm, 658nm, 667nm, 675nm, 683nm, 692nm, 702nm, 716nm, 726nm, 742nm, 753nm, 735nm, 708nm, 677nm, 651nm, 632nm, 619nm, 609nm, 605nm；The cycle of horizontal sub-wavelength structure is 400nm, and etching depth is 220nm, equivalent refractive index (the corresponding horizontal dutycycle f of longitudinal grating grooveynull) be followed successively by 3.4(0.95)、3.3824(0.94)、3.356(0.93)、3.3161(0.9)、3.2794(0.88)、3.24(0.86)、3.1916(0.83)、3.143(0.8)、3.0897(0.78)、3.0406(0.75)、2.9853(0.71)、2.9231(0.68)、2.8649(0.65)、2.8062(0.62)、2.7448(0.59)、2.6734(0.55)、2.5856(0.51)、2.5188(0.48)、2.4211(0.44)、2.3531(0.41)、2.4626(0.46)、2.6359(0.53)、2.8479(0.64)、3.0404(0.75)、3.1887(0.82)、3.2929(0.89)、3.371(0.94)、3.4112(0.96).
The above; being only the detailed description of the invention in the present invention, but protection scope of the present invention is not limited thereto, any people being familiar with this technology is under the premise without departing from the technology of the present invention principle; can also making some improvements and modifications, these improvements and modifications also should be regarded as protection scope of the present invention.
Claims (1)
1. a manufacture method for the adjustable grating coupler of refractive index, grating groove is the sub-wavelength structure of different horizontal dutycycle, and grating is have different transverse directions and y direction dutycycle f at the x position that longitudinal direction and x direction are differentyGrating；Grating is at longitudinal dutycycle fxValue is a definite value between (0,1)；Constitute the sub-wavelength structure of longitudinally upper different x position grating groove, its horizontal dutycycle fyValue by export required for Gaussian field distribution G (x) leakage factor distribution α (x) determine；
It is characterized in that: in order to obtain Gaussian field distribution G (x) in formula (1), need to regulate leakage factor distribution α (x), output field distribution G (x) of gaussian shape, the Power leakage factor of grating must is fulfilled for:
In formulaFor normalized Gauss distribution, wherein w0=5.2 μm, w0Size is corresponding with single-mode fiber spot size 5.2 μm；
According to formula (6) under the premise that other structural parameters of grating coupler are fixed, change different horizontal dutycycle fyWith longitudinal periods lambdaxParameter be combined through simulation software and calculate and obtain different α value, i.e. the Power leakage factor-alpha of adjustable light barrier,
The leakage factor expression formula of grating coupler is:
2 α=(Pup+Pdown)/Pin(6)
(6) P in formulainFor the luminous power of input waveguide, PupAnd PdownThe respectively luminous power of diffraction up and down, in the analog simulation to grating coupler, PinNormalization is equal to 1；By to the uniform grating bonder under different grating groove refractive indexs to the outside leakage power P of certain wavelength lightupAnd PdownCalculating obtains α；
By regulating fy, fyFor the fixing sub-wavelength structure any value that the cycle is sub-wavelength magnitude in y direction, regulate leakage factor distribution α (x) and then to realize the field distribution of diffraction output be Gaussian field distribution G (x).
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| US11474294B2 (en) * | 2021-01-29 | 2022-10-18 | Globalfoundries U.S. Inc. | Grating couplers with segments having sections of inverted curvature |
| US11448828B2 (en) * | 2021-02-22 | 2022-09-20 | Taiwan Semiconductor Manufacturing Company, Ltd. | Optical device for coupling light |
| CN113126204A (en) * | 2021-04-13 | 2021-07-16 | 中山大学 | Visible light waveband thin-film lithium niobate grating coupler and preparation method thereof |
| CN113534342B (en) * | 2021-06-22 | 2024-03-15 | 北京工业大学 | High coupling efficiency segmented uniform grating coupler based on lithium niobate thin film waveguide |
| CN115343805A (en) * | 2022-08-31 | 2022-11-15 | 天津大学 | Sub-wavelength grating coupler with high manufacturing tolerance |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101556356A (en) * | 2009-04-17 | 2009-10-14 | 北京大学 | Grating coupler and application thereof in polarization and wave length beam splitting |
| CN102713706A (en) * | 2010-01-29 | 2012-10-03 | 惠普发展公司，有限责任合伙企业 | Grating-based optical fiber-to-waveguide interconnects |
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Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101556356A (en) * | 2009-04-17 | 2009-10-14 | 北京大学 | Grating coupler and application thereof in polarization and wave length beam splitting |
| CN102713706A (en) * | 2010-01-29 | 2012-10-03 | 惠普发展公司，有限责任合伙企业 | Grating-based optical fiber-to-waveguide interconnects |
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