polarization splitting rotator (psr) based on sub ... · fig. 1. schematic of swg waveguide: w is...

Oscar Yun Wang Dr. Lukas Chrostowski

Ref.Textbook:

L. Chrostowski, M. Hochberg,

“Silicon Photonics Design”, Cambridge

University Press, 2015

Si-EPIC CREATE

Polarization Splitting Rotator (PSR) based on Sub-Wavelength Grating (SWG) waveguides

© 2016 L. ChrostowskiSi-EPIC CREATE

Outline – Polarization splitter rotators

• Design polarization splitting rotator based on sub-wavelength grating (SWG) waveguides. • introduction to SWG waveguides• introduction to polarization splitting rotators• using the effective medium theory to simulate a polarization rotating

directional coupler, • calculating the band-structure diagrams of SWG waveguides, • verifying our design using 3D-FDTD, • designing the experiment, • creating a layout.

2

Dr. Lukas Chrostowski

Si-EPIC CREATE

Sub-Wavelength Grating (SWG)Silicon Photonics


Sub-wavelength grating materials

• No diffraction in gratings when the period is << wavelength.• First observed in nature in moths – C. G. Bernhard, Endeavour 26, p. 79, 1967

• graded index• used in Canon lenses as an AR coating

4



• What can you do with them?

• The optical response of the material becomes the weighted average of the original materials.

• Analogous to Pulse-Width Modulation in electrical engineering

• Can create arbitrary index of refraction values by digital modulation (in the mask layout) rather than analog modulation (e.g., varying the material composition, like in graded index fibres)

• Extra degree of freedom in PIC design

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• What can you do with them?

• Graded index• lens• anti-reflection

• Anisotropic materials• Mirrors• Waveguides• Edge couplers• Grating couplers• Waveguide crossing• MMI• Directional couplers

• Ring resonators• Sensors• Filters (e.g., Bragg gratings)• …

• Lots of publications in the field.

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SWG Edge Coupler

• Mode profile of a large ∆n vs. small ∆n waveguide.• Can engineer a gradual (adiabatic) change from a large ∆n high-contrast

(high-confinement) silicon photonic waveguide, to a low-contrast (low confinement) SWG waveguide, that is well matched to the optical fibre.

• ~ 90% efficiency

7

P. Cheben et al., Optics Express, vol. 14, p. 4695 (2006) P. Cheben et al., Opt. Lett., vol. 35, p. 2526 (2010)

P. Cheben et al., US Patent 7,680,371

Light Propagation

© 2015 IBM CorporationTymon Barwicz et al.,

Cost-Efficient Photonic Packaging August, 2015

V-groove Undercut regionVenting

hole

Metamaterial converter for coupling to cleaved standard fiber

• Coupler embedded in suspended oxide membrane for isolation to Si handle• First use of hybrid waveguide transition in Cheben et al., Optics Lett. 2010

Fiber coupler Hybrid waveguide Solid waveguide

Metamaterial converter

UndercutregionSiSi

SiO2SiO2

Tapered up

12

Si SiO2

Non-linear taper Linear tapersButt-junction

S-band metamaterial converter



Optical measurements of metamaterial converter performance

13

Wavelength (um)

Loss

to fi

ber (

dB)

1.26 1.28 1.3 1.32 1.34 1.36

-3

-2

-1

TETM

0.8 dB

-1.3 dB

O-band converter response

Measurement setup

Jig for pressing fibers into grooves

• Manual assembly to V-grooves, no active alignment (OFC’15, Th3F.3).

• Spread on single wafer: -1.1 dB to -2.6 dB• V-groove variability expected to dominate spread

in this early production tools implementation

Chip ID 1 2 3 4 5

Max in polarization -1.1 dB -1.2 dB -1.1 dB -2.4 dB -1.9 dB

Min in polarization -1.4 dB -1.5 dB -1.4 dB -2.6 dB -2.1 dB

Position on wafer random random random edge edge

1.31 um measurement with water immersion (n~1.31)



Fibersbutted

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Parallelized fiber assembly: automated assembly results

• Sliding base enables fiber butting on coupler with pure vertical pick-tip movement.• Coupler in suspended membrane with undercut filled with adhesive at assembly.

Pho

toni

c di

e

12 fiber array

Polymer lidShort MT ferrule

Side-view polished cross-section

FiberLid

Si Adhesive

Coupler in suspendedmembrane

100 um

Pick-tip

Sliding base

Fiber core

Si

Adhesive

100 um

Polymer lid

Cross-section of an assembly, all 12 fibers seated.


Focusing Sub-Wavelength Grating Coupler – Lines

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Ref: Y. Wang, “Focusing sub-wavelength grating couplers with low back reflections for rapid prototyping of silicon photonics circuits”, OE, 2014


SWG Waveguides

• Light propagation in a periodic medium:• Λ < λ/2: The sub-wavelength zone. Diffraction is suppressed. The periodic

structure supports a true lossless mode in this case. The waveguide behaves like conventional waveguide. This is in analogy to the electron distribution in periodic potentials (semiconductor).

• Λ ~ λ/2: The wavelength range corresponding to the photonic bandgap where the propagation constant becomes complex and Bragg reflections occur.

• Λ > λ/2: Radiation out of the waveguide. The propagation loss is determined by reflection and diffraction at the segment boundaries due to the high index contrast.

• SWG waveguides are attractive as they allow to tailor propagation properties – mode shape and dispersion – by varying the duty cycle, η, period, Λ, the waveguide width, w, and the waveguide thickness, h.

• Invented at the National Research Council of Canada (NRC).

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P. Cheben, et al., “Subwavelength waveguide grating for mode conversion and light coupling in integrated optics”, Optics Express, 2006

to period ratio lL is high enough and the waveguide behaves like conventional waveguide. The

periodic structure supports a true lossless mode in this case [37]; 2) The wavelength rangecorresponding to the photonic bandgap where the propagation constant becomes complex andBragg reflections occur; and 3) the wavelength range shorter than the Bragg wavelength wherethe Bloch wave becomes leaky and part of the energy is radiated out of the waveguide and thepropagation loss is determined by reflection and diffraction at the segment boundaries due tothe high index contrast [38]. By having L ⌧ l the mode is without loss because reflection anddiffraction effects are suppressed. This is in analogy to the electron distribution in periodic po-tentials. For a photonic integrated circuit designer SWG waveguides are attractive as they allowto tailor propagation properties (namely the mode shape and dispersion) by varying the dutycycle (h), period (L), the waveguide width (w), and the waveguide thickness (t). Long periodic

Fig. 1. Schematic of SWG waveguide: w is the waveguide width and t the thickness; L isthe SWG period and the length of the Si blocks is determined by the duty cycle h .

modulation of the refractive index along the axis of propagation has been achieved by dopingLiNbO3 [39, 40], etching GaAs [41], and InP [37] but these methods are not suitable for subwavelength gratings. SWG gratings in SOI waveguides have recently been proposed by the Na-tional Research Council of Canada (NRC) [33, 42, 43]. The guiding waveguide is divided intosmall segments (blocks of Si with refractive index ncore) with length Lh , where L is the periodand h is the duty cycle. The cross-section is comparable to traditional waveguides. Figure 1shows the schematic of a SWG waveguide. The substrate material with refractive index, nsub,is SiO2 and as cladding material, nclad we used water since most biological applications requirean aqueous solution. SWG structures have been used to control the lateral and vertical modeshape for tapers in fiber-to-chip couplers [30, 31] to minimize mode mismatch loss, metamate-rial lenses [32], or waveguide crossings [33]. Wanguemert-Perez et al. propose the use of SWGwaveguides for biosensing [44]. They are using a Fourier-type 2D vectorial simulation tool toanalyze the effect of a varying duty cycle on the sensing performance. To confirm their theoreti-cal sensitivity enhancement they also perform a full 3D FDTD simulation. However their paperonly focuses on the theoretical analysis and is not showing any experimental results. Wang etal. demonstrates both theoretically and experimentally the use of SWG wavguides in ring res-onators for filtering applications [45]. Our group demonstrated experimentally optical buildingblocks such as waveguides, directional couplers, and strip to SWG waveguide converters [46].We also demonstrated the fabrication and measurement of ring resonators and investigated the-oretically their sensing performance [47]. Preliminary experimental results of ring resonatorshave also been published [47]. Here we extend the theoretical analysis of SWG waveguides assensors and we confirm experimentally the sensitivity of SWG ring resonators with salt solu-tions at different concentrations. Furthermore we show the result of a model sandwich assay.

J. Flueckiger, et al., “Sub-wavelength grating for enhanced ring resonator biosensor”, submitted Optics Express, 2015


Propagation: SWG waveguide

• Propagation just like in a regular waveguide, except the field profile is periodic• Field enhancement in the gaps, just like in slot waveguides

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Light Propagation

Cross-section fields:Top-view field:


SWG Ring Sensors

• Evanescent field sensors, with improved sensitivity ~ 400 - 490 nm / RIU

14


Sensitivity calibration (salt steps)

Bio sandwich assay experiments

Oscar Yun Wang Dr. Lukas Chrostowski

Ref.Textbook:

L. Chrostowski, M. Hochberg,

“Silicon Photonics Design”, Cambridge

University Press, 2015

Si-EPIC CREATE

Polarization Splitting Rotator (PSR)

© 2015 Y. Wang

Outline

• What is a polarization splitter rotator (PSR) ?

• How does it work?

• State-of-the-art

• Remaining Issues?

• Why we need sub-wavelength gratings?

• How to design a PSR with SWG?

• Based on paper from Carleton, NRC, Malaga:

• Yule Xiong, J. Gonzalo Wangüemert-Pérez, Dan-Xia Xu, Jens H. Schmid, Pavel Cheben, Winnie N. Ye, “Polarization splitter and rotator with subwavelength grating for enhanced fabrication tolerance”, Optics Letters 12/2014.

• What can be improved?

16

© 2015 Y. Wang

What is a PSR? — Motivation• Due to the high index contrast of the SOI platform, components are polarization

dependent (dispersion, loss), which makes it inconvenient to integrate with other polarization insensitive systems, such as optical fibre networks;

• PSRs are fundamental building blocks in polarization diversity systems [1] and polarization multiplexing devices [2];

• The required components are polarization splitters and polarization rotators:

• a PSR combines the two functionalities

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[1]. D. Dai, L. Liu, S. Gao, D.-X. Xu, and S. He, Laser Photon. Rev. 7, 303 (2013). [2].T. Barwicz, M. R. Watts, M. A. Popović, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, Nat. Photonics 1, 57 (2007).[3] L. Chrostowski, and M. Hochberg, “Silicon Photonics Design” Cambridge University Press (2015)

[3] [3]

© 2015 Y. Wang

How Does It Work?

• Phase match condition:

The widths of the two waveguides are adjusted so that the effective index of the fundamental quasi-TM mode in waveguide 1 is equal to that of the fundamental quasi-TE mode in waveguide 2.

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DC-based PSR

[1] L. Liu, et.al,``Silicon-on-insulator polarization splitting and rotating device for polarization diversity circuits ”, OE, 2011

[1]

Fig.1 Schematic of the cross section of a PSR based on directional coupler. [1]

n1,TMe↵ = n2,TE

e↵

© 2015 Y. Wang

Numerous PSR implementations

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[1] L. Liu, et.al,``Silicon-on-insulator polarization splitting and rotating device for polarization diversity circuits ”, OE, 2011 [2] Y. Ding, et.al, “Fabrication tolerant polarization splitter and rotator based on a tapered directional coupler “, OE, 2012 [3] D. Dai, et. al.``Novel concept for ultracompact polarization splitter-rotator based on silicon nanowires”, OE, 2011 [4] Y. Xiong, et. al, ``Fabrication tolerant and broadband polarization splitter and rotator based on a taper-etched directional coupler”, OE, 2014 [5] Y. Ding, et. al, ``Wideband polarization splitter and rotator with large fabrication tolerance and simple fabrication process”, OL, 2013 [6] W. D. Sacher, ``Polarization rotator-splitters in standard active silicon photonics platforms”, OE, 2014 [7] J. Wang, et. al, ``Novel ultra-broadband polarization splitter- rotator based on mode-evolution tapers and a mode-sorting asymmetric Y-junction”, OE, 2014 [8]Y. Xiong, et. al, ``Polarization splitter and rotator with subwavelength grating for enhanced fabrication tolerance”, OL, 2014

[1] [2] [3][4]

[5] [6] [7] [8]

© 2015 Y. Wang

Remaining Issues

• DC-based PSR: sensitive to fabrication errors, strict constraints on waveguide width and coupler length. The coupling wavelength shifts with a rate of about 15 nm/nm with respect to the variation of the waveguide width;

• MMI-based PSR: complex structure: includes a mode-evolution taper, a Y- junction, a phase shifter and an MMI.

• Mode-evolution PSR: large size (~500 um): including a bi-level taper and a adiabatic coupler;

• Ideally, we need a PSR with high conversion coefficient, large extinction ratio, compact size, and low insertion loss.

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[1] L. Liu, et.al,``Silicon-on-insulator polarization splitting and rotating device for polarization diversity circuits ”, OE, 2011 [2] Y. Ding, et.al, “Fabrication tolerant polarization splitter and rotator based on a tapered directional coupler “, OE, 2012 [3] D. Dai, et. al.``Novel concept for ultracompact polarization splitter-rotator based on silicon nanowires”, OE, 2011

© 2015 Y. Wang

Why we need sub-wavelength gratings?

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Conventional DC-based PSR:

The two waveguides of the conventional DC-based PSR have the same material index, therefore, the mode effective indices changes with different slopes, which leads to high sensitivity to fabrication errors.The coupling wavelength shifts with a rate of about 15 nm/nm with respect to the variation of w1.

DC-based PSR with SWG:

The SWG approach allows the two waveguides in the DC to have different material indices. By doing so, the mode effective indices of both waveguides change equally when the waveguide width fluctuates, therefore maintaining the phase-matching condition.

Fig.2 Effective indices of the fundamental modes of (a) the silicon wire waveguide A and (b) the SWG waveguide B with different equivalent refractive indices nB 3.476, 2.525, 2.4, and 2.3, as a function of the waveguide widths WA and WB. Red circles represent the phase-matching condition where the width WA is set to 450 nm. [1]

[1]Y. Xiong, et. al, ``Polarization splitter and rotator with subwavelength grating for enhanced fabrication tolerance”, OL, 2014

waveguides. The height of both waveguides is H and thecoupling length is L. Here we setH to 220 nm since this isthe value commonly used by photonic foundries [12]. Ans–bend with a radius RS is used near the output ports todecouple the waveguides. The superstrate medium is airin order to achieve an efficient cross-polarization cou-pling by breaking the vertical symmetry. Specifically,waveguide B is considered as a SWG waveguide com-prised of alternating media with high- (silicon) andlow (air)-refractive indices, with a subwavelength pitchΛ along the direction of propagation (z). Segment lengthsof the high- and low-refractive index media along thepropagation direction are a and Λ − a, respectively, asshown in Fig. 1(a). An SWG–wire transition taper [13] isused to couple light between the SWGwaveguide and thesilicon wire. Due to the properties of SWGs, waveguide Bcan be considered as an equivalent wire waveguide withan engineered material refractive index nB [Fig. 1(c)],which can be controlled by selecting a specific duty ratioη ! a∕Λ. Within a considerable range of waveguidewidths (WB ! "50 nm), nB can be well approximatedas a constant.The operation principle of the PSR is similar to those

based on conventional photonic wire directional cou-plers: the widths of the waveguides are chosen such thatthe effective index of the quasi-TMmode (referred simplyas TM mode hereafter) in waveguide A is similar to thatof the quasi-TE mode in waveguide B (i.e., nTM

A ∼ nTEB ), as

shown in Fig. 2(a). At the same time, nTEA ≫ nTE

B . Underthese conditions, the TE mode injected in the input portA1 propagates to the through port A2 with a minimalcross-coupling to the SWG waveguide B; while the TMmode injected into the port A1 couples to the fundamen-tal TE Bloch mode of the waveguide B. The cross-coupling between the two polarizations is facilitatedby the two orthogonal hybrid modes supported in thecoupling region, in which the horizontal and verticalasymmetries are created by the asymmetric DC geometryand the difference between the upper and bottom clad-ding indices [6,7].As it can be observed in Fig. 2(a), the effective

index dependence on waveguide width for the TE andTM modes (with slopes of STE

wire and STMwire) are signifi-

cantly different in conventional wire waveguides. Conse-quently, the phase-matching condition for TM–TE

polarization conversion can be easily lost due to fabrica-tion variations of the waveguide’s width [7]. This is themain reason that DC-based photonic wire PSRs arehighly sensitive to variations in waveguide dimensions.Indeed, the phase-matching condition could be preservedif the effective indices for waveguides A and B have thesame waveguide width dependence. This is, however,impossible to achieve with conventional silicon photonicwire waveguides. The solution we propose in this reportis to utilize an SWG waveguide as the second waveguide(B). By adjusting the SWG equivalent material refractiveindex, not only the mode effective index but also theslope STE

SWG can be modified, as illustrated in Fig. 2(b).When setting the width (WA ! 450 nm) for waveguideA, we can satisfy the phase-matching condition for arange of widths (WB) of waveguide B by manipulatingthe SWG equivalent material refractive index nB. Inaddition, when nB is reduced from 3.476 (i.e., a wirewaveguide) to 2.3, the slope STE

SWG for waveguide Bdecreases correspondingly. In particular, the slopeSTESWG in waveguide B with nB ! 2.4 is similar to STM

wirein waveguide A at the phase-matching position. In otherwords, the phase-matching condition can still be main-tained if the widths of both waveguides vary similarly,thereby improving the fabrication tolerance.

When the width of an SWG waveguide varies, a changein the duty ratio is generally expected. Based on ourexperience, the correlation between the width and dutyratio fluctuations for a particular fabrication process isnot known a priori. Here we have chosen to primarilyfocus on the waveguide width variation to illustratethe working principle. A more sophisticated design strat-egy may be adopted to include the experimentally deter-mined relations between the waveguide width and theSWG duty ratio. However, it is an advantage of ourapproach that it is possible to find a combination ofWA, WB and η, as an extra design freedom, to satisfythe phase-matching condition.

We evaluate the general characteristics of the PSR byusing the full-vectorial eigenmode expansion (EME)method [14]. The SWG waveguide B is first consideredas an equivalent wire waveguide with an engineeredmaterial refractive index nB, which is a convenientapproximation to limit the computation time. Then 3D–FDTD simulations of the PSR with the actual periodicSWG configuration are carried out to determine the per-formance of the PSR. We assume a free-space centralwavelength of λ0 ! 1550 nm. The refractive indices ofsilicon and the bottom oxide are nSi ! 3.476 and nSiO2 !1.444, respectively, the bend radius of the s–bend isRS ! 50 μm; the width of the waveguide A is WA !450 nm; and the pitch of the SWG waveguide B isΛ ! 300 nm. These feature sizes are compatible withstandard processing in silicon photonics foundries [15].The coupling gapD is set to 100 nm to achieve a short cou-pling length, i.e., 25 μmfor the engineered refractive indexnB ! 2.4 andWB ! 685 nm. A larger gap may be used forease of fabrication using deep ultraviolet (DUV) lithogra-phy, but it will result in a slightly longer PSR.

The required value of the duty ratio η for an SWGwave-guide with an engineered refractive index nB can be es-timated using the effective medium approximation [11].

Fig. 2. Effective indices of the fundamental modes of (a) thesilicon wire waveguide A and (b) the SWG waveguide B withdifferent equivalent refractive indices nB ! 3.476, 2.525, 2.4,and 2.3, as a function of the waveguide widths WA and WB.Red circles represent the phase-matching condition wherethe width WA is set to 450 nm.

6932 OPTICS LETTERS / Vol. 39, No. 24 / December 15, 2014

© 2015 Y. Wang

Principles

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Fig. 1. Schematics of the polarization splitter and rotator based on an asymmetric directional coupler with a subwavelength grating (SWG) waveguide. (a) Top view, (b) 3D view, and (c) with the SWG waveguide represented as an equivalent wire waveguide with an engineered refractive index nB. [1]


© 2015 Y. Wang

How Does It Work?

• What is a polarization splitter rotator (PSR)?


• Why do we need sub-wavelength gratings (SWG) in a PSR?


23

© 2015 Y. Wang

How Does It Work?

24

• What is a polarization splitter rotator (PSR)?


• Why do we need sub-wavelength gratings (SWG) in a PSR?


© 2015 Y. Wang

How to design a PSR with SWG?

• Step 1: Choose the geometry of the regular waveguide (WG width, WG height), and calculate the mode effective indices as a function of waveguide width;

• Step 2: Calculate the mode effective index as a function of waveguide width for SWG waveguide with various refractive index, and decide the refractive index, , of the SWG waveguide;

• Step 3: Design a SWG waveguide with an equivalent refractive index to ;

• Step 4: Design a taper to connect the SWG waveguide to the regular waveguide;

• Step 5: 3D FDTD simulation for the whole structure.

25

nB

nB


Fig. 1. Schematics of the polarization splitter and rotator based on an asymmetric directional coupler with a subwavelength grating (SWG) waveguide. (a) Top view, (b) 3D view, and (c) with the SWG waveguide represented as an equivalent wire waveguide with an engineered refractive index nB. [1]

© 2015 Y. Wang

Step1: WG geometry and mode effective index

• In Mode Solution, run WG_mode.lsf;

• run sweep_width.lsf;

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WG width (nm)300 350 400 450 500 550 600

Effe

ctiv

e in

dex

1.4

1.6

1.8

2

2.2

2.4

2.6

TM slope =0.74/um

TETM

Fig. Effective indices of the fundamental TE & TM mode as a function of waveguide width for a strip waveguide with a silicon thickness of 220nm.

Fig. Mode distribution of the fundamental TE (TE0) mode in a strip waveguide with 220nm Si thickness and 450 nm width.

Fig. Mode distribution of the fundamental TM (TM0) mode in a strip waveguide with 220nm Si thickness and 450 nm width.

The effective index of the fundamental TM0 mode for a 450 nm waveguide width is 1.545, indicated by the dash line. It is close to a linear relation between the effective index and the waveguide for the TM mode with a slope of 0.74/um

© 2015 Y. Wang

Step 2: Choose n for the SWG waveguide

• In Mode Solution, run sweep_index_width.lsf

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WG width (nm)300 400 500 600 700 800 900 1000

Effe

ctiv

e in

dex

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8n=2.3, slope=0.5/umn=2.4, slope=0.75/umn=2.5, slope=0.89/umn=3.447, slope=3.25/um

Fig. Effective indices of the TE0 mode as a function of waveguide width for SWG waveguides with various refractive index.

§ In this step, we use refractive index to approximate the SWG waveguide;

§ We are trying to come up with a SWG waveguide in which the TE0 mode meet the phase match condition with the TM0 of the strip waveguide;

§ We also want the slope of the SWG waveguide to be close to that of the TM0 mode in the strip waveguide

From the above graph we can see that the TE0 mode of a SWG waveguide with n=2.4, width=685nm meet the phase match condition with the TM0 in the strip waveguide, and they have similar slope, which is the key to make fabrication insensitive design.

© 2015 Y. Wang

Step 3: Design SWG waveguide with required n

• Using 3D-FDTD with Bloch boundary conditions to calculate the band structure of SWG waveguide and determine the SWG waveguide period and fill factor;

28

© 2015 Y. Wang

Step 4: Design a SWG taper• SWG taper connecting the SWG waveguide to a strip waveguide can be designed following the

method shown[1];• open SWG_taper.fsp

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[1]P. Bock, et. al, ``Subwavelength grating crossings for silicon wire waveguides ”, OE, 2010

© 2015 Y. Wang

Step 5: 3D simulation for the whole structure

• The final step is to simulate the whole structure in 3D FDTD to confirm the confirm the final design.

• The gap between the two waveguide was 100nm;

• Coupling length used in the simulation was 25um.

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Fig. Input TE0 in the strip waveguide, power at the output of the through port and cross port.

Fig. Input TM0 in the strip waveguide, power at the output of the through port and cross port.

§ The reported polarization conversion loss (PCL) was 0.13dB, and To maintain a low polarization conversion loss with PCL better than −1 dB at the central wavelength of 1550 nm, it is required δW≤+/-40nm.

§ The PCL of the draft design was 1.2 dB. Extra loss came from the taper design (50 um vs. 3 um), and the highlighted region (50 um S_bend vs. 3 um S_bend).


Experimental results

• Test the same device twice• TE input• TM input

• Use Y-Branches to combine/split• But introduces reflections and

Fabry-Perot cavities.

31

TE

TE

TE

TM

TM

TE

PSR


Experimental results – TM input

32

TM-TE (Cross)

TM-TM(Through)


Experimental results – TE input

33

TE-TE (Through)

TE-TE (Cross)

© 2015 Y. Wang

What can be improved?

• The polarization conversion loss need to be reduced

• better SWG taper, S_bend with larger radius;

• The bandwidth need to be enlarged

• overlay with another set of SWG?

34

© 2016 L. ChrostowskiSi-EPIC CREATE 35

Tutorial on SWG Waveguide analysis using Effective Medium Theory using Lumerical MODE’s eigensolver

Lukas Chrostowski James Pond


SWG Waveguide – Approximation using Effective Medium Theory

• Replace 3D periodic waveguide structure with an equivalent 2D uniform waveguide

• Volumetric weighted average of the sub-wavelength materials’ index of refractions

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3.47 3.47

2.45

3.47 3.47 3.47 3.471.44 1.44 1.44 1.44 1.44 1.44

1.44

1.44

1.44

1.44


SWG Waveguide analysis using Effective Medium Theory using Lumerical MODE’s eigensolver

• Geometry:• SiO2 BOX 3 µm• SiO2 cladding 2 µm• waveguide 220 thick, 500 nm wide

• n = 3.47 (solid silicon), or• n = 2.45 (SWG 50% Si / SiO2)

• 2D Eigensolver• 6 µm span in both dimensions

• Run simulations• Plot settings for mode profile:

• Energy density• Log scale• “Plot in New Window”• Settings | Set Color Bar Limits

• Min = -10• Max = -20

• Frequency analysis• Track selected mode• start/stop 1.55 µm• # points = 1• # test modes = 1• detailed dispersion calculation• run “Frequency Sweep”• look in “Frequency Plot” | group

index

• Repeat calculations twice:• solid silicon• SWG EMT

37


Oxide Geometry

38

Z = oxide thickness

X = waveguide length

Y = oxide width


Waveguide Geometry

39

Solid waveguideSWG waveguide

Z = waveguide thickness

X = waveguide length

Y = waveguide width


Simulation – Eigenmode solver

40


Run

41


Run – Eigensolver Analysis

42


Run – Eigensolver Analysis Frequency Analysis tab

43


Results

• neff = 2.44• ng = 4.04

• Note: we neglected material dispersion (ng = 4.18 with Si dispersion)

• neff = 1.58• ng = 2.21

• Note: we neglected material dispersion; and approx. using EMT

44


SWG Waveguide analysis using Effective Medium Theory using Lumerical MODE’s eigensolver

• Conclusions about Effective Medium Theory approach:• This technique works well only if you are use that the wavelength is very

large compared to the structure’s period. You need to be sure you are far away from the Bragg resonance.

• Good for estimating things like:• effective index• mode size• mode overlap with an optical fibre• estimating evanescent sensor’s sensitivity

45


Tutorial on SWG Waveguide analysis using 3D-FDTD with Bloch boundary conditions and dispersion diagrams

James Pond Lukas Chrostowski


SWG Waveguide – Analysis using 3D FDTD and Bloch Boundaries

• 3D FDTD (time domain) simulations of a unit cell• Band diagram: sweep simulations for different wave vectors (k) and find the

frequency supported (f)• Calculate neff, ng.

• Top-view of the unit cell:

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3.47 3.47 3.47 3.47 3.47 3.471.44 1.44 1.44 1.44 1.44 1.44

1.44

1.44

Bandstructure can be simulated with FDTD

Bandgap

Bandgapatk=0.5

©LUMERICALSOLUTIONSINC

We are operating in the SW regime

49

Inthisregion,theSWGbehaveslikeawaveguide.

Whatweneedistogettheeffectiveindexandgroupindex


Correct neff and ngIntroduceapitch(forexamplea=300nm)Beta=k0*neff=2*pi/lambda*1.452Expressedinunitsof2*pi/awehaveBeta=1.452*a/lambda=1.452*300nm/1550nm=0.28▪ Aslongasbeta<0.5weareoperatingbelowthebandgap

PerformafrequencysweepfromBeta=0.28to0.38Wemustbecautiousasweareclosetocutoff!Simulationregionmustbequitelarge▪ Finemeshonlyrequirednearwaveguide50

Configure the SWG waveguideDutycycle,pitch(period),width1,width2

51

pitch (period) w1 w2


Set frequency range to studyConfigurethey-axis(frequency)rangeforbanddiagram:range=150to240THz

52


Setup bandstructure sweep

53


Source settings

54


Run bandstructure sweep

55


Analyze resultsRunscriptfileanalyze_bandstructure.lsfItwillcreatethefollowingresults…

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Image of bandstructure, log scale

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Plot of w vs beta Theextracted5pointsofdataarefittoa4thorderpolynomial

Thefitteddataisresampledathighresolution

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Plot of neff and ng vs lambda

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• Effective Index, neff.• ~ 1.65

• Group index, ng.• ~ 2.7

ne↵ =c

vphase, vphase =

!

�ng

=c

vgroup

, vgroup

=d!

d�

Plot of wavelength vs k

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ExercisesRepeatwith▪FinerFDTDmesh▪ Setgridaccuracysliderto2or3▪ Usethemeshoverrideforwaveguide▪ Reducemeshsizearoundwaveguidebyfactorof2(dy=dz=10nm)

▪Increasesimulationtimefrom500fsto1000fs▪Increasenumberofsweeppointofbandstructureto10▪IncludetheSiliconsubstratebelowthe3µmBOX

▪Makesurethatyourresultsareaccurate▪Performconvergencetests.

Extractthe3DBlochmodeprofileat1550nm▪Seehttps://kb.lumerical.com/en/index.html?diffractive_optics_pc_bloch_mode_profile.html

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https://kb.lumerical.com/en/index.html?diffractive_optics_pc_bloch_mode_profile.html

https://kb.lumerical.com/en/index.html?diffractive_optics_pc_bloch_mode_profile.html


SWG Waveguide – Analysis using 3D FDTD and Bloch Boundaries

• time – improves the spectral resolution of the dispersion diagram. Longer times needed to resolve the two solutions near the bandgap. For SWG waveguides, we don’t need high resolution, hence we can do a fast simulation (e.g., 500 fs).

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1000 fs 500 fs


SWG Waveguide – Exercises

• Create a map of neff, ng, versus parameters of interest:• duty cycle• period• width 1• width 2

• e.g., find neff vs. width2, and use it to develop an SWG edge coupler.

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Lightline, cut-off

• When you have an oxide cladding (below and above), the SWG core index is always greater than the cladding. So there is no cut-off.

• If you have air, or water, the SWG index can be lower than the BOX lower cladding.

• The lightline:• The waveguide is cutoff for all points of the curve above the lightline because light

simply leaks into the substrate

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Cut-offGuided

Lightline


Lightline, cut-off

• Oxide • Air cladding (or water) for sensors• more challenging to design

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Lightline, cut-off

• Oxide • Air cladding (or water) for sensors• more challenging to design

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SWG in Oxide

SWG in Air


FDTD for Band Structures

• One advantage of using FDTD for bandstructure calculations is that you can easily calculate the bandstructure for dispersive media. • Dispersion for both:

• Silicon dispersion, and the waveguide mode group index• Whether or not you are cutoff because the substrate index is also changing with

wavelength (i.e., the lightline is not perfectly straight). • You can tell you are cutoff just by watching the autoshutoff value of the FDTD

simulation (approaches 0 when cut-off).

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Configure the materials

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Results – dispersion

• For pitch = 0.3, duty = 0.5, w1 = 0.5, w2 = 0• with dispersive silicon & oxide materials

Mesh accuracy 2, disabled mesh override• neff at 1550 = 1.64695• ng at 1550 = 2.6879

• with dispersive silicon & oxide materialsMesh accuracy 3, enabled mesh override• neff at 1550 = 1.64922• ng at 1550 = 2.70196

• with constant index materialsMesh accuracy 3, enabled mesh override• neff at 1550 = 1.6493• ng at 1550 = 2.64047 (3-5% error)

• In a strip waveguide, neglecting material dispersion results in larger group index errors.

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polarization splitting rotator (psr) based on sub ... · fig. 1. schematic of swg waveguide: w is...

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