Micro/Nanofabrication and Instrumentation Laboratory EECE 403. Dr. Lukas Chrostowski

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1 Micro/Nanofabrication and Instrumentation Laboratory EECE 403 Dr. Lukas Chrostowski 1

2 Design cycle Design & Modelling Mask Layout Fabrication (outside) Final Test Fabrication (UBC) Midprocess test

3 Today 1) GDS Design review ) MZI Matlab model 3) Waveguide Lumerical MODE 3

4 Draft merged GDS from HW3 4

5 Homework #4 Due September 6 Goal: Final GDS design will be submitted for fabrication Optical Model for your design solution to lukasc@ece.ubc.ca, subject: EECE403-HW4 Report: PDF only. Design description, Matlab model, simulation graphs, discussion, etc. GDS file ref: Silicon Photonics Design book 5

6 Homework #4 Optical model for your specific GDS design neff vs. wavelength (Lumerical), with curve-fit equation (Matlab) Plot transmission vs. wavelength, for T = 0 K T = [ 1,, 10 ] K (tuning one arm only) T = [ 1,, 10 ] K (tuning both arms, i.e., ambient temp) Determine the spectral shift vs. temperature (track a peak/dip) Plot lambda vs. T, find the slope For one arm, and both arms Plot transmission vs. temperature ( T = 0-50 K) for a fixed wavelength What is the impact of the wavelength dependance of neff (vs. constant neff)? What is the impact of L on the MZI response? 6

7 Design & Modeling Matlab model of optical circuit Components: Optical input & output y-branch splitters interferometer electrical-thermal tuning Simulation Optical output spectrum Optical waveguide calculations optical field profile propagation constant / effective index using Lumerical MODE Solutions Design & Modelling 7

8 Interferometer Zehnder_interferometer 8

9 Monochromatic Laser Light Plane wave: Propagation constant of light Index of refraction, n E = E 0 e i(!t z) = n 9

10 Mach Zehnder Interferometer Two y-branches, two optical paths Constructive vs. Destructive interference /JSTQE

11 be Ii = I 1 /, and the field will be E i = E 1 /p. Thus, the y-branch functions as a 50/50% beam-splitter in Y Branch Splitter fundamental mode of the waveguide and the nd order mode (or radiation mode). Thus the light at the combined port will For the splitter, we begin with an input intensity, I i, with electric field, E i. The light is split equally into the two branches. Thus each output has intensity I 1 = I = I i /, and electric field, E 1 = E = E i / p (sincei / E ). to combine two incoherent beams of light using a y-branch in possible not is it that is point important An directions. both coherent beams in Section 4.3. will treat the interference of We power. the increase to order E i E 1 E Figure 4.14: Y-Branch splitter/combiner, layout example. 11

12 Y Branch Combiner e- For the combiner, the same equations apply, namely that light input in one waveguide, I 1, is split equally between the fundamental mode of the waveguide and the nd order mode (or radiation mode). Thus the light at the combined port will be I i = I 1 /, and the field will be E i = E 1 / p. Thus, the y-branch functions as a 50/50% beam-splitter in both directions. An important point is that it is not possible to combine two incoherent beams of light using a y-branch in order to increase the power. We will treat the interference of coherent beams in Section

13 Mach Zehnder Interferometer E i E 1 Light is split into the two arms. Propagation in the arms: E Figure 4.15: Mach-Zehnder Interferometer, layout example. 1 = n 1 At the end of the waveguides: = n the waveguides have lengths L 1 and L = L 1 + L, E o1 =E 1 e i 1L 1 1 L 1 = E i p e i 1L 1 1 L 1 E o1 E o E o =E e i L L = E i p e i L L 13

14 Mach Zehnder Interferometer E o1 E o Figure 4.15: Mach-Zehnder Interferometer, layout example. Light is combined in the y-branch. The output of the y-branch is E o = 1 p (E o1 + E o )= E i E o e i 1L 1 1 L 1 + e i L L Intensity is: I o = I i 4 e i 1L 1 1 L 1 + e i L L 14

15 Mach Zehnder Interferometer For the lossless case: I o = I apple i 1L 1 L cos apple 4 apple =I i cos apple 1L 1 L = I i [1 + cos( 1L 1 L )] The output of the interferometer is thus a sinusoidallyvarying function of wavelength (via 1 and )foranimbalanced interferometer (L 1 6= L ). It also varies sinusoidally with the waveguide e ective index (n 1 and n ), which can be changed by the thermo-optic e ect (Section 3.1.1), plasma dispersion e ect (Section 7.1.1), etc. 15

16 Matlab Model Define a wavelength sweep: lambda = 1.540:1e-6:1.560 neff is wavelength dependant (start with n=const) neff =... (lambda) beta1, beta =... Define constants: L1, L, alpha Write expression for output, Io Plot: plot(lambda, Io, '-', 'LineWidth',3); 16

17 Transmission vs. wavelength 1 ΔT = 0 K Transfer function (I o /I i ) Wavelength [µm] 17

18 4.3. Thermally-Tuned MZI 4.3. Thermally-Tuned MZI The Mach-Zehnder Inteferometer can function as an thermotheoptic Mach-Zehnder Inteferometer can function an thermoswitch if a temperature di erence is appliedas between the opticarms. switch if can a temperature di erence This be implemented by usingisaapplied resistivebetween heater onthe onethis of the arms Let us consider a temperature increase of on arms. can be [7]. implemented by using a resistive heater applied thelet lower and aa thermo-optic one oftdn the armsto[7]. us arm, consider temperaturecoefficient increase of 4 1 of = K. The propagation constantcoefficient in the dt T applied to the lower arm, and a thermo-optic lower arm is: dn dn of dt = K 1. The propagation constant in the n + T dt = (4.15) lower arm is: n + Inserting this in Eq. = 4.14, the perature dependant: dn T dt optical output is thus tem(4.15) Inserting this in Eq. 4.14, the optical output is thus tem"!# Fig perature dependant: dn Ii Io ( T ) = 1 + cos " Ii Io ( T ) = 1 + cos 1 L1 n + dt n + 1 LUBC 1 EECE dn dt T L T!# (4.16a) L per 500 dep 18

19 Inserting this in Eq. 4.14, the optical output is thus Thermally-Tuned MZI perature dependant: Silicon Photonics can be Optical output " 4.3. Thermally-Tuned MZI 0 (off) or can 1 function (on) Ii as an thermothe Mach-Zehnder Inteferometer Io ( T ) = Arm cos optic switch if a temperature di erence is applied between the arms. This can be implemented by using a resistive heater on one of the arms [7]. Let us consider a temperature increase of T applied to the lower arm, and a thermo-optic coefficient dn of dt = K 1. The propagation constant in the lower arm is: dn n + dt T (4.15) = or anything in between Controlled by: Inserting this in Eq. 4.14, the optical output is thus temperature dependant: Transfer function (Io/Ii) L1 Mach-Zehnder Interferometer n + ΔT = 0 K ΔT = 5 K dn dt!# Output T L 0.6 Input 0.4 Arm 0. (4 from: Silicon Photonics, Deen, Kumar Basu, Figure Mach Zehnder interferometer. Wavelength [µm], L. L1identical For waveguide cross-sections (n1 = n ), thi Phase shift (thermo-optic effect) external field it may be converted into an active optical device, as discussed comes Wavelength (via beta) There are also other active guided wave devices that may be used a " interferometers,!# and filters. References dnworking of an interferomet We shall discuss in this subsection the dtused asta passive and also an Ii n Mach Zehnder interferometer (MZI), that is Io ( T ) = 1+ cos L L already bee (4 by utilizing the EO effect. Its use as a light modulator has Chapter 7. The basic structure is shown in Figure Assume that the inpu " Ii Io ( T ) = 1 + cos!# (4.16a) Figure 4.16: Optical transmission spectrum of an MZI for a temperature di erence applied on the nd arm (L ). Parameters: L1 = 500µm, L = 100µm, = 3dB/cm, lossless y-branch. Wavelengthdependant e ective index for both waveguides as per Eq For identical waveguide cross-sections (n1 = n ), this becomes "!# dn dt T Ii n Io ( T ) = 1 + cos L L (4.17a) [1] Amnon Yariv and Pochi Yeh. Optical Electronics in Modern Communications. sixth edition Oxford University Press, 006 (cit. on p. 58). Fundamentals and Devices 1 L1 n + dn dt T L [] A. Yariv. Coupled-mode theory for guided-wave ophere, we explicitly see that the output of the interferometer tics. Quantum Electronics, IEEE Journal of 9.9 is a sinusoidally-varying function of wavelength and temper(1973), pp. issn: (cit. on p. 58). ature. This is illustrated in Figures 4.16 and 4.17 loss in(with the input waveguide is split equally by a Y-splitter. The input intensities in a included). [3] N. Rouger, L. Chrostowski, and R. Vafaei. Temperaare then equal, ande ects the propagating electric fields are expressed as 19 EECE 011 tureubc on484 silicon-on-insulator (SOI) racetrack resonators: A coupled analytic and -D finite di erence ap- Here, we explicitly see that the output of the interferom

20 Matlab Model Recalculate beta, including T Write expression for output, Io Plot: hold all lot(lambda, Io, '--', 'LineWidth',3); 0

21 Transmission vs. wavelength Transfer function (I o /I i ) ΔT = 0 K ΔT = 5 K Wavelength [µm] 1

22 MZI Modulator IME L = 100 µm Leads to oscillations vs. wavelength Voltage causes a shift in spectrum IME paper: Liow, et. al, JSTQE, vol 16, no 1, p. 307, Jan/Feb 010 Constructive Interference Destructive Interference

23 Transmission vs. T Transfer function (I o /I i ) One arm Both arms Temperature Increase [K] 3

24 neff Effective Index Average index of refraction of a waveguide. Light travels partly in silicon, partly in air, partly in oxide Index will depend on geometry (relative to wavelength) Thus neff is wavelength dependant y Position [ m] x Position [ m] (a) E-field intensity, linear scale 4

25 Optical waveguide calculations Lumerical MODE Solutions Software package that calculates mode profiles includes wavelength sweeps calculates the effective index of refraction / beta / speed of light 5

26 Optical waveguide calculations Mode profile 6

27 Optical waveguide calculations Wavelength sweeps 7

28 neff Effective Index (vs. wavelength) Export the data, Curve-fit to a polynomial n = (λ 1.55) 0.183(λ 1.55) 0.000(λ 1.55) 3 eff n = (λ 1.55) 0.35(λ 1.55) 0.000(λ 1.55) 3 eff 3D FDTD 3D FDTD curve fit 600 nm neff.4.3 n eff = (λ 1.55) 0.304(λ 1.55) 0.000(λ 1.55) 3 n = (λ 1.55) 0.391(λ 1.55) 0.000(λ 1.55) 3 eff 500 nm increasing width. 400 nm.1 n eff = (λ 1.55) 0.453(λ 1.55) 0.000(λ 1.55) Wavelength x

29 Matlab Model Define a wavelength sweep: lambda = 1.540:1e-6:1.560 neff is wavelength dependant neff = *(lambda-1.55) *(lambda-1.55).^; Write expression for output, Io Plot: plot(lambda, Io, '-', 'LineWidth',3); 9

30 Oxide on Optical Waveguides Model both waveguides, since you will measure both in this class first without oxide then with oxide Si 0 nm Cladding oxide Si 0 nm Buried Oxide (BOX) Buried Oxide (BOX) Si substrate Si substrate 30