Supplemental Document

Designing open channels in random scatteringmedia for on-chip spectrometers: supplementTIANRAN LIU∗ AND ANDREA FIORE

Department of Applied Physics and Institute for Photonic Integration, Eindhoven University of Technology,P.O. Box 513, 5600MB Eindhoven, The Netherlands∗Corresponding author: t.liu@tue.nl

This supplement published with The Optical Society on 5 August 2020 by The Authors under theterms of the Creative Commons Attribution 4.0 License in the format provided by the authorsand unedited. Further distribution of this work must maintain attribution to the author(s) and thepublished article’s title, journal citation, and DOI.

Supplement DOI: https://doi.org/10.6084/m9.figshare.12649316

Parent Article DOI: https://doi.org/10.1364/OPTICA.391612

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This document provides supplementary information to "Designing open channels in random scattering media for on-chip spectrometers," https://doi.org/10.1364/OPTICA.391612.

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pplied to optimizss, as shown ansmission mathannel that mandeed, comparedhe transmittanceroadened, as shhannels, the spepectral broaden3(e). If the loss lr stronger scattansmittance at ahat case.

g. S3. Transmissifractive index ovistribution of thptimization. (b) aussian beam. Thled area) along when light is injecormalized transmhannel with k = 0shown in the inrget mode (Gausal transmittance ptimization forhe method discuolarization of in

ze the transmittain Fig S3(b) atrix, and in thisatches the targed to the losslesse of first channelhown in Fig S3ectra of the tarning and transmlevel is much higtering, there coall and the prop

ion properties wver the entire sihe transmission |E| field distribuhe wavefront at twith the field discted as the 1st mmittance spectra (black) and k = nset. (e) Normassian beam) withis shown in the inr TE polarizatioussed in this panput light. He

ance with the prand (c). The l case, it is the et mode after s case, we obserl is lower, but al3(d). Like the hrget mode expemission reductiogher either due ould be no chaposed method w

with loss. The imamulation domaineigenvalues befution when lighthe input boundastribution. (c) |Emaximal transmia of the 1st max0.005 (red), absoalized transmittanh k = 0 (black) annset. on aper can be appere we show t

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zation for a demation (with elecn Fig. S4. The of the holes, for thereby the tranation.

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with TE polarizatmodel with TE warefractive index oc field intensitysion spectra of theoretical correlutput discussed d mode (of singlle-resolved trann other words, een as a speckleions in the speckas C ( ) =and M is the where denosing), is the abD is the diffusioe v is the speed medium for a roee path. tion due to fabrany real applicventional way, iof inverse dess and large tivity to fabricaassume two difhole has a lostribution with ose fluctuationsng electron beashare a uniform posure, commony. Fig. S5(a) sthe outputs whf samples with ded with each set a minor averageariance of radius to 0.25 in avf uniform radiuseparately from

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rication imperfecation. Compareit is difficult toigned devices number of vation errors offferent scenarioocal radius unca common vars, electromagnetam lithography. m radius offset, usn problems in bshows the dishen a local undifferent varianct containing 100e transmission tus increases toverage and shous offset, the tram -30 nm (under

e having a TE plane of the erent average cross-section ends on the

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ections needs ed to devices o predict thedue to their variables. To f the device os: In the first ertainty that riance, which tic noise and In a second sually caused both electron- stribution of ncertainty is ce from 5 nm 0 samples. An to drop from o 15 nm, theows a larger ansmission in exposure) to

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g. S5. Tolerancstribution of traoles. Different ouaussian distributind 15 nm, plottedre Gaussian fit to niform radius offhannels are markeeference 1. S. Feng, C. Ka

Fluctuations oMedia," Phys. R

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xposure) with asure shows moure and channerable to exposequired tolerancbeam lithograph

ce to fabricationansmission withutputs are plottedion with zero med in blue, green athe distribution. fset induced by ed in different coane, P. A. Lee, aof Coherent WavRev. Lett. 61, 834–, ed., Photonic Banr US, 1993), Vol. 30

a 10nm step in ore damage to els at the longersure error thances are well why or deep-UV op

n errors (a) Ph radius uncertad together. Radiuean and a varianand olive respec(b) Transmissionunder- or over-elors. and A. D. Stoneve Transmission –837 (1988). nd Gaps and Localiz08.

Fig. S5(b). In ththe performanr wavelength sin the others. within the limit ptical lithograph

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