Abstract

On-chip spectrometers with tailored spectral range and compact footprint have been pursued widely in the last decade. Splitting different frequencies typically requires a propagation length that scales inversely with the frequency resolution, which leads to a trade-off between resolution and size. Scattering media in the diffusive regime provide a long light path and multipath interference in a compact area, resulting in strong dispersive properties that can be used for on-chip compressive spectrometry. However, the performance suffers from the low light transmission through the diffusive medium. It has been found that there exist “open channels” such that light with certain wavefronts can pass through the medium with high transmission. Here we show that a scattering structure can be designed so that open channels match target input/output channels in order to maximize transmission while keeping the dispersive properties typical of diffusive media. Specifically, we use inverse design to generate a scattering structure where the open channels match the output waveguides at desired wavelengths. For a proof of concept, we propose a ${{1}} \times {{10}}$ multiplexer covering a band of 500 nm in the mid-infrared spectrum, with a footprint of only ${9.4}\;\unicode{x00B5}{\rm m} \times {14.4}\;\unicode{x00B5}{\rm m}$. We also show that filters with nearly arbitrary spectral response can be designed, enabling a new degree of freedom in on-chip spectrometer design, and we investigate the ultimate resolution limits of these structures. The structures can also be designed based on a simple geometry consisting of circular holes with diameters from 200 to 700 nm etched in a dielectric slab, making them highly suited for fabrication. With the help of compressive sensing, the proposed method represents an important tool in the quest towards integrated lab-on-a-chip spectroscopy.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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2018 (4)

H. Podmore, A. Scott, and R. Lee, “On-chip compressed sensing Fourier-transform visible spectrometer,” IEEE Photon. J. 10, 6602010 (2018).
[Crossref]

D. M. Kita, B. Miranda, D. Favela, D. Bono, J. Michon, H. Lin, T. Gu, and J. Hu, “High-performance and scalable on-chip digital Fourier transform spectroscopy,” Nat. Commun. 9, 4405 (2018).
[Crossref]

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[Crossref]

S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12, 659–670 (2018).
[Crossref]

2017 (3)

Ž. Zobenica, R. W. van der Heijden, M. Petruzzella, F. Pagliano, R. Leijssen, T. Xia, L. Midolo, M. Cotrufo, Y. Cho, F. W. M. van Otten, E. Verhagen, and A. Fiore, “Integrated nano-opto-electro-mechanical sensor for spectrometry and nanometrology,” Nat. Commun. 8, 2216 (2017).
[Crossref]

H. Podmore, A. Scott, P. Cheben, A. V. Velasco, J. H. Schmid, M. Vachon, and R. Lee, “Demonstration of a compressive-sensing Fourier-transform on-chip spectrometer,” Opt. Lett. 42, 1440–1443 (2017).
[Crossref]

Z. Yu, H. Cui, and X. Sun, “Genetic-algorithm-optimized wideband on-chip polarization rotator with an ultrasmall footprint,” Opt. Lett. 42, 3093–3096 (2017).
[Crossref]

2016 (6)

J. C. C. Mak, C. Sideris, J. Jeong, A. Hajimiri, and J. K. S. Poon, “Binary particle swarm optimized 2 × 2 power splitters in a standard foundry silicon photonic platform,” Opt. Lett. 41, 3868–3871 (2016).
[Crossref]

J. Bosch, S. A. Goorden, and A. P. Mosk, “Frequency width of open channels in multiple scattering media,” Opt. Express 24, 26472–26478 (2016).
[Crossref]

M. Nedeljkovic, A. V. Velasco, A. Z. Khokhar, A. Delâge, P. Cheben, and G. Z. Mashanovich, “Mid-infrared silicon-on-insulator Fourier-transform spectrometer chip,” IEEE Photon. Technol. Lett. 28, 528–531 (2016).
[Crossref]

R. Sarma, A. G. Yamilov, S. Petrenko, Y. Bromberg, and H. Cao, “Control of energy density inside a disordered medium by coupling to open or closed channels,” Phys. Rev. Lett. 117, 086803 (2016).
[Crossref]

T. Zhu, Y. Hu, P. Gatkine, S. Veilleux, J. Bland-Hawthorn, and M. Dagenais, “Arbitrary on-chip optical filter using complex waveguide Bragg gratings,” Appl. Phys. Lett. 108, 101104 (2016).
[Crossref]

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
[Crossref]

2015 (1)

B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4  µm 2 footprint,” Nat. Photonics 9, 378–382 (2015).
[Crossref]

2014 (5)

B. Gérardin, J. Laurent, A. Derode, C. Prada, and A. Aubry, “Full transmission and reflection of waves propagating through a maze of disorder,” Phys. Rev. Lett. 113, 173901 (2014).
[Crossref]

A. C. R. Niederberger, D. A. Fattal, N. R. Gauger, S. Fan, and R. G. Beausoleil, “Sensitivity analysis and optimization of sub-wavelength optical gratings using adjoints,” Opt. Express 22, 12971–12981 (2014).
[Crossref]

A. Y. Piggott, J. Lu, T. M. Babinec, K. G. Lagoudakis, J. Petykiewicz, and J. Vučković, “Inverse design and implementation of a wavelength demultiplexing grating coupler,” Sci. Rep. 4, 7210 (2014).
[Crossref]

F. Meng, R.-J. Shiue, N. Wan, L. Li, J. Nie, N. C. Harris, E. H. Chen, T. Schröder, N. Pervez, I. Kymissis, and D. Englund, “Waveguide-integrated photonic crystal spectrometer with camera readout,” Appl. Phys. Lett. 105, 051103 (2014).
[Crossref]

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light Sci. Appl. 3, e203 (2014).
[Crossref]

2013 (3)

C. M. Lalau-Keraly, S. Bhargava, O. D. Miller, and E. Yablonovitch, “Adjoint shape optimization applied to electromagnetic design,” Opt. Express 21, 21693–21701 (2013).
[Crossref]

B. Redding, S. F. Liew, R. Sarma, and H. Cao, “Compact spectrometer based on a disordered photonic chip,” Nat. Photonics 7, 746–751 (2013).
[Crossref]

M. F. Duarte and R. G. Baraniuk, “Spectral compressive sensing,” Appl. Comput. Harmon. Anal. 35, 111–129 (2013).
[Crossref]

2012 (3)

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6, 581–585 (2012).
[Crossref]

C. Peroz, C. Calo, A. Goltsov, S. Dhuey, A. Koshelev, P. Sasorov, I. Ivonin, S. Babin, S. Cabrini, and V. Yankov, “Multiband wavelength demultiplexer based on digital planar holography for on-chip spectroscopy applications,” Opt. Lett. 37, 695–697 (2012).
[Crossref]

X. Gan, N. Pervez, I. Kymissis, F. Hatami, and D. Englund, “A high-resolution spectrometer based on a compact planar two dimensional photonic crystal cavity array,” Appl. Phys. Lett. 100, 231104 (2012).
[Crossref]

2011 (2)

2010 (2)

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

A. Kshorshidahmad and A. G. Kirk, “Composite superprism photonic crystal demultiplexer: analysis and design,” Opt. Express 18, 20518–20528 (2010).
[Crossref]

2009 (1)

S. Babin, A. Bugrov, S. Cabrini, S. Dhuey, A. Goltsov, I. Ivonin, E.-B. Kley, C. Peroz, H. Schmidt, and V. Yankov, “Digital optical spectrometer-on-chip,” Appl. Phys. Lett. 95, 041105 (2009).
[Crossref]

2008 (1)

I. M. Vellekoop and A. P. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101, 120601 (2008).
[Crossref]

2007 (1)

2006 (1)

2005 (1)

M. Burger and S. J. Osher, “A survey on level set methods for inverse problems and optimal design,” Eur. J. Appl. Math. 16, 263–301 (2005).
[Crossref]

2004 (2)

T. Fukazawa, F. Ohno, and T. Baba, “Very compact arrayed-waveguide-grating demultiplexer using Si photonic wire waveguides,” Jpn. J. Appl. Phys. 43, L673 (2004).
[Crossref]

S. Janz, A. Balakrishnan, S. Charbonneau, P. Cheben, M. Cloutier, A. Delage, K. Dossou, L. Erickson, M. Gao, P. A. Krug, B. Lamontagne, M. Packirisamy, M. Pearson, and D.-X. Xu, “Planar waveguide echelle gratings in silica-on-silicon,” IEEE Photon. Technol. Lett. 16, 503–505 (2004).
[Crossref]

2003 (1)

2000 (1)

1998 (1)

1992 (1)

M. Zirngibl, C. Dragone, and C. H. Joyner, “Demonstration of a 15*15 arrayed waveguide multiplexer on InP,” IEEE Photon. Technol. Lett. 4, 1250–1253 (1992).
[Crossref]

Adibi, A.

Akkermans, E.

E. Akkermans and G. Montambaux, Mesoscopic Physics of Electrons and Photons (Cambridge University, 2007).

Andreoli, D.

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
[Crossref]

Askari, M.

Aubry, A.

B. Gérardin, J. Laurent, A. Derode, C. Prada, and A. Aubry, “Full transmission and reflection of waves propagating through a maze of disorder,” Phys. Rev. Lett. 113, 173901 (2014).
[Crossref]

Baba, T.

T. Fukazawa, F. Ohno, and T. Baba, “Very compact arrayed-waveguide-grating demultiplexer using Si photonic wire waveguides,” Jpn. J. Appl. Phys. 43, L673 (2004).
[Crossref]

Babin, S.

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light Sci. Appl. 3, e203 (2014).
[Crossref]

C. Peroz, C. Calo, A. Goltsov, S. Dhuey, A. Koshelev, P. Sasorov, I. Ivonin, S. Babin, S. Cabrini, and V. Yankov, “Multiband wavelength demultiplexer based on digital planar holography for on-chip spectroscopy applications,” Opt. Lett. 37, 695–697 (2012).
[Crossref]

S. Babin, A. Bugrov, S. Cabrini, S. Dhuey, A. Goltsov, I. Ivonin, E.-B. Kley, C. Peroz, H. Schmidt, and V. Yankov, “Digital optical spectrometer-on-chip,” Appl. Phys. Lett. 95, 041105 (2009).
[Crossref]

Babinec, T. M.

A. Y. Piggott, J. Lu, T. M. Babinec, K. G. Lagoudakis, J. Petykiewicz, and J. Vučković, “Inverse design and implementation of a wavelength demultiplexing grating coupler,” Sci. Rep. 4, 7210 (2014).
[Crossref]

Balakrishnan, A.

S. Janz, A. Balakrishnan, S. Charbonneau, P. Cheben, M. Cloutier, A. Delage, K. Dossou, L. Erickson, M. Gao, P. A. Krug, B. Lamontagne, M. Packirisamy, M. Pearson, and D.-X. Xu, “Planar waveguide echelle gratings in silica-on-silicon,” IEEE Photon. Technol. Lett. 16, 503–505 (2004).
[Crossref]

Baraniuk, R. G.

M. F. Duarte and R. G. Baraniuk, “Spectral compressive sensing,” Appl. Comput. Harmon. Anal. 35, 111–129 (2013).
[Crossref]

Bartek, M.

J. H. Correia, M. Bartek, and R. F. Wolffenbuttel, “High-selectivity single-chip spectrometer for operation at visible wavelengths,” in International Electron Devices Meeting, Technical Digest (1998), pp. 467–470.

Beausoleil, R. G.

Bhargava, S.

Bland-Hawthorn, J.

T. Zhu, Y. Hu, P. Gatkine, S. Veilleux, J. Bland-Hawthorn, and M. Dagenais, “Arbitrary on-chip optical filter using complex waveguide Bragg gratings,” Appl. Phys. Lett. 108, 101104 (2016).
[Crossref]

Boccara, A. C.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

Bono, D.

D. M. Kita, B. Miranda, D. Favela, D. Bono, J. Michon, H. Lin, T. Gu, and J. Hu, “High-performance and scalable on-chip digital Fourier transform spectroscopy,” Nat. Commun. 9, 4405 (2018).
[Crossref]

Bosch, J.

Brady, D. J.

Bromberg, Y.

R. Sarma, A. G. Yamilov, S. Petrenko, Y. Bromberg, and H. Cao, “Control of energy density inside a disordered medium by coupling to open or closed channels,” Phys. Rev. Lett. 117, 086803 (2016).
[Crossref]

Bugrov, A.

S. Babin, A. Bugrov, S. Cabrini, S. Dhuey, A. Goltsov, I. Ivonin, E.-B. Kley, C. Peroz, H. Schmidt, and V. Yankov, “Digital optical spectrometer-on-chip,” Appl. Phys. Lett. 95, 041105 (2009).
[Crossref]

Burger, M.

M. Burger and S. J. Osher, “A survey on level set methods for inverse problems and optimal design,” Eur. J. Appl. Math. 16, 263–301 (2005).
[Crossref]

Busch, K.

Cabrini, S.

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light Sci. Appl. 3, e203 (2014).
[Crossref]

C. Peroz, C. Calo, A. Goltsov, S. Dhuey, A. Koshelev, P. Sasorov, I. Ivonin, S. Babin, S. Cabrini, and V. Yankov, “Multiband wavelength demultiplexer based on digital planar holography for on-chip spectroscopy applications,” Opt. Lett. 37, 695–697 (2012).
[Crossref]

S. Babin, A. Bugrov, S. Cabrini, S. Dhuey, A. Goltsov, I. Ivonin, E.-B. Kley, C. Peroz, H. Schmidt, and V. Yankov, “Digital optical spectrometer-on-chip,” Appl. Phys. Lett. 95, 041105 (2009).
[Crossref]

Calafiore, G.

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light Sci. Appl. 3, e203 (2014).
[Crossref]

Calo, C.

Cao, H.

R. Sarma, A. G. Yamilov, S. Petrenko, Y. Bromberg, and H. Cao, “Control of energy density inside a disordered medium by coupling to open or closed channels,” Phys. Rev. Lett. 117, 086803 (2016).
[Crossref]

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E. Akkermans and G. Montambaux, Mesoscopic Physics of Electrons and Photons (Cambridge University, 2007).

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J. Bosch, S. A. Goorden, and A. P. Mosk, “Frequency width of open channels in multiple scattering media,” Opt. Express 24, 26472–26478 (2016).
[Crossref]

I. M. Vellekoop and A. P. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101, 120601 (2008).
[Crossref]

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M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
[Crossref]

Nedeljkovic, M.

M. Nedeljkovic, A. V. Velasco, A. Z. Khokhar, A. Delâge, P. Cheben, and G. Z. Mashanovich, “Mid-infrared silicon-on-insulator Fourier-transform spectrometer chip,” IEEE Photon. Technol. Lett. 28, 528–531 (2016).
[Crossref]

Nie, J.

F. Meng, R.-J. Shiue, N. Wan, L. Li, J. Nie, N. C. Harris, E. H. Chen, T. Schröder, N. Pervez, I. Kymissis, and D. Englund, “Waveguide-integrated photonic crystal spectrometer with camera readout,” Appl. Phys. Lett. 105, 051103 (2014).
[Crossref]

Niederberger, A. C. R.

Ohno, F.

T. Fukazawa, F. Ohno, and T. Baba, “Very compact arrayed-waveguide-grating demultiplexer using Si photonic wire waveguides,” Jpn. J. Appl. Phys. 43, L673 (2004).
[Crossref]

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M. Burger and S. J. Osher, “A survey on level set methods for inverse problems and optimal design,” Eur. J. Appl. Math. 16, 263–301 (2005).
[Crossref]

Packirisamy, M.

S. Janz, A. Balakrishnan, S. Charbonneau, P. Cheben, M. Cloutier, A. Delage, K. Dossou, L. Erickson, M. Gao, P. A. Krug, B. Lamontagne, M. Packirisamy, M. Pearson, and D.-X. Xu, “Planar waveguide echelle gratings in silica-on-silicon,” IEEE Photon. Technol. Lett. 16, 503–505 (2004).
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Ž. Zobenica, R. W. van der Heijden, M. Petruzzella, F. Pagliano, R. Leijssen, T. Xia, L. Midolo, M. Cotrufo, Y. Cho, F. W. M. van Otten, E. Verhagen, and A. Fiore, “Integrated nano-opto-electro-mechanical sensor for spectrometry and nanometrology,” Nat. Commun. 8, 2216 (2017).
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M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6, 581–585 (2012).
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Parker, M. C.

Pearson, M.

S. Janz, A. Balakrishnan, S. Charbonneau, P. Cheben, M. Cloutier, A. Delage, K. Dossou, L. Erickson, M. Gao, P. A. Krug, B. Lamontagne, M. Packirisamy, M. Pearson, and D.-X. Xu, “Planar waveguide echelle gratings in silica-on-silicon,” IEEE Photon. Technol. Lett. 16, 503–505 (2004).
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Pernice, W.

Peroz, C.

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light Sci. Appl. 3, e203 (2014).
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C. Peroz, C. Calo, A. Goltsov, S. Dhuey, A. Koshelev, P. Sasorov, I. Ivonin, S. Babin, S. Cabrini, and V. Yankov, “Multiband wavelength demultiplexer based on digital planar holography for on-chip spectroscopy applications,” Opt. Lett. 37, 695–697 (2012).
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S. Babin, A. Bugrov, S. Cabrini, S. Dhuey, A. Goltsov, I. Ivonin, E.-B. Kley, C. Peroz, H. Schmidt, and V. Yankov, “Digital optical spectrometer-on-chip,” Appl. Phys. Lett. 95, 041105 (2009).
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F. Meng, R.-J. Shiue, N. Wan, L. Li, J. Nie, N. C. Harris, E. H. Chen, T. Schröder, N. Pervez, I. Kymissis, and D. Englund, “Waveguide-integrated photonic crystal spectrometer with camera readout,” Appl. Phys. Lett. 105, 051103 (2014).
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X. Gan, N. Pervez, I. Kymissis, F. Hatami, and D. Englund, “A high-resolution spectrometer based on a compact planar two dimensional photonic crystal cavity array,” Appl. Phys. Lett. 100, 231104 (2012).
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R. Sarma, A. G. Yamilov, S. Petrenko, Y. Bromberg, and H. Cao, “Control of energy density inside a disordered medium by coupling to open or closed channels,” Phys. Rev. Lett. 117, 086803 (2016).
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Ž. Zobenica, R. W. van der Heijden, M. Petruzzella, F. Pagliano, R. Leijssen, T. Xia, L. Midolo, M. Cotrufo, Y. Cho, F. W. M. van Otten, E. Verhagen, and A. Fiore, “Integrated nano-opto-electro-mechanical sensor for spectrometry and nanometrology,” Nat. Commun. 8, 2216 (2017).
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S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12, 659–670 (2018).
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A. Y. Piggott, J. Lu, T. M. Babinec, K. G. Lagoudakis, J. Petykiewicz, and J. Vučković, “Inverse design and implementation of a wavelength demultiplexing grating coupler,” Sci. Rep. 4, 7210 (2014).
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Podmore, H.

Polson, R.

B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4  µm 2 footprint,” Nat. Photonics 9, 378–382 (2015).
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Popoff, S. M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
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Post, E.

Prada, C.

B. Gérardin, J. Laurent, A. Derode, C. Prada, and A. Aubry, “Full transmission and reflection of waves propagating through a maze of disorder,” Phys. Rev. Lett. 113, 173901 (2014).
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Rakhshandehroo, M.

Redding, B.

B. Redding, S. F. Liew, R. Sarma, and H. Cao, “Compact spectrometer based on a disordered photonic chip,” Nat. Photonics 7, 746–751 (2013).
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S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12, 659–670 (2018).
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R. Sarma, A. G. Yamilov, S. Petrenko, Y. Bromberg, and H. Cao, “Control of energy density inside a disordered medium by coupling to open or closed channels,” Phys. Rev. Lett. 117, 086803 (2016).
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B. Redding, S. F. Liew, R. Sarma, and H. Cao, “Compact spectrometer based on a disordered photonic chip,” Nat. Photonics 7, 746–751 (2013).
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G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light Sci. Appl. 3, e203 (2014).
[Crossref]

C. Peroz, C. Calo, A. Goltsov, S. Dhuey, A. Koshelev, P. Sasorov, I. Ivonin, S. Babin, S. Cabrini, and V. Yankov, “Multiband wavelength demultiplexer based on digital planar holography for on-chip spectroscopy applications,” Opt. Lett. 37, 695–697 (2012).
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Schmid, J. H.

Schmidt, H.

S. Babin, A. Bugrov, S. Cabrini, S. Dhuey, A. Goltsov, I. Ivonin, E.-B. Kley, C. Peroz, H. Schmidt, and V. Yankov, “Digital optical spectrometer-on-chip,” Appl. Phys. Lett. 95, 041105 (2009).
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F. Meng, R.-J. Shiue, N. Wan, L. Li, J. Nie, N. C. Harris, E. H. Chen, T. Schröder, N. Pervez, I. Kymissis, and D. Englund, “Waveguide-integrated photonic crystal spectrometer with camera readout,” Appl. Phys. Lett. 105, 051103 (2014).
[Crossref]

Scott, A.

Shen, B.

B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4  µm 2 footprint,” Nat. Photonics 9, 378–382 (2015).
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F. Meng, R.-J. Shiue, N. Wan, L. Li, J. Nie, N. C. Harris, E. H. Chen, T. Schröder, N. Pervez, I. Kymissis, and D. Englund, “Waveguide-integrated photonic crystal spectrometer with camera readout,” Appl. Phys. Lett. 105, 051103 (2014).
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Sigmund, O.

J. S. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser Photon. Rev. 5, 308–321 (2011).
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Sullivan, M. E.

Sun, X.

Vachon, M.

van der Heijden, R. W.

Ž. Zobenica, R. W. van der Heijden, M. Petruzzella, F. Pagliano, R. Leijssen, T. Xia, L. Midolo, M. Cotrufo, Y. Cho, F. W. M. van Otten, E. Verhagen, and A. Fiore, “Integrated nano-opto-electro-mechanical sensor for spectrometry and nanometrology,” Nat. Commun. 8, 2216 (2017).
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Ž. Zobenica, R. W. van der Heijden, M. Petruzzella, F. Pagliano, R. Leijssen, T. Xia, L. Midolo, M. Cotrufo, Y. Cho, F. W. M. van Otten, E. Verhagen, and A. Fiore, “Integrated nano-opto-electro-mechanical sensor for spectrometry and nanometrology,” Nat. Commun. 8, 2216 (2017).
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Veilleux, S.

T. Zhu, Y. Hu, P. Gatkine, S. Veilleux, J. Bland-Hawthorn, and M. Dagenais, “Arbitrary on-chip optical filter using complex waveguide Bragg gratings,” Appl. Phys. Lett. 108, 101104 (2016).
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I. M. Vellekoop and A. P. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101, 120601 (2008).
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Ž. Zobenica, R. W. van der Heijden, M. Petruzzella, F. Pagliano, R. Leijssen, T. Xia, L. Midolo, M. Cotrufo, Y. Cho, F. W. M. van Otten, E. Verhagen, and A. Fiore, “Integrated nano-opto-electro-mechanical sensor for spectrometry and nanometrology,” Nat. Commun. 8, 2216 (2017).
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M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
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S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12, 659–670 (2018).
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A. Y. Piggott, J. Lu, T. M. Babinec, K. G. Lagoudakis, J. Petykiewicz, and J. Vučković, “Inverse design and implementation of a wavelength demultiplexing grating coupler,” Sci. Rep. 4, 7210 (2014).
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F. Meng, R.-J. Shiue, N. Wan, L. Li, J. Nie, N. C. Harris, E. H. Chen, T. Schröder, N. Pervez, I. Kymissis, and D. Englund, “Waveguide-integrated photonic crystal spectrometer with camera readout,” Appl. Phys. Lett. 105, 051103 (2014).
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B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4  µm 2 footprint,” Nat. Photonics 9, 378–382 (2015).
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J. H. Correia, M. Bartek, and R. F. Wolffenbuttel, “High-selectivity single-chip spectrometer for operation at visible wavelengths,” in International Electron Devices Meeting, Technical Digest (1998), pp. 467–470.

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Ž. Zobenica, R. W. van der Heijden, M. Petruzzella, F. Pagliano, R. Leijssen, T. Xia, L. Midolo, M. Cotrufo, Y. Cho, F. W. M. van Otten, E. Verhagen, and A. Fiore, “Integrated nano-opto-electro-mechanical sensor for spectrometry and nanometrology,” Nat. Commun. 8, 2216 (2017).
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P. Cheben, J. H. Schmid, A. Delâge, A. Densmore, S. Janz, B. Lamontagne, J. Lapointe, E. Post, P. Waldron, and D.-X. Xu, “A high-resolution silicon-on-insulator arrayed waveguide grating microspectrometer with sub-micrometer aperture waveguides,” Opt. Express 15, 2299–2306 (2007).
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S. Janz, A. Balakrishnan, S. Charbonneau, P. Cheben, M. Cloutier, A. Delage, K. Dossou, L. Erickson, M. Gao, P. A. Krug, B. Lamontagne, M. Packirisamy, M. Pearson, and D.-X. Xu, “Planar waveguide echelle gratings in silica-on-silicon,” IEEE Photon. Technol. Lett. 16, 503–505 (2004).
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Xu, Z.

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Yamilov, A. G.

R. Sarma, A. G. Yamilov, S. Petrenko, Y. Bromberg, and H. Cao, “Control of energy density inside a disordered medium by coupling to open or closed channels,” Phys. Rev. Lett. 117, 086803 (2016).
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G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light Sci. Appl. 3, e203 (2014).
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C. Peroz, C. Calo, A. Goltsov, S. Dhuey, A. Koshelev, P. Sasorov, I. Ivonin, S. Babin, S. Cabrini, and V. Yankov, “Multiband wavelength demultiplexer based on digital planar holography for on-chip spectroscopy applications,” Opt. Lett. 37, 695–697 (2012).
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S. Babin, A. Bugrov, S. Cabrini, S. Dhuey, A. Goltsov, I. Ivonin, E.-B. Kley, C. Peroz, H. Schmidt, and V. Yankov, “Digital optical spectrometer-on-chip,” Appl. Phys. Lett. 95, 041105 (2009).
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M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6, 581–585 (2012).
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M. Zirngibl, C. Dragone, and C. H. Joyner, “Demonstration of a 15*15 arrayed waveguide multiplexer on InP,” IEEE Photon. Technol. Lett. 4, 1250–1253 (1992).
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Ž. Zobenica, R. W. van der Heijden, M. Petruzzella, F. Pagliano, R. Leijssen, T. Xia, L. Midolo, M. Cotrufo, Y. Cho, F. W. M. van Otten, E. Verhagen, and A. Fiore, “Integrated nano-opto-electro-mechanical sensor for spectrometry and nanometrology,” Nat. Commun. 8, 2216 (2017).
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T. Zhu, Y. Hu, P. Gatkine, S. Veilleux, J. Bland-Hawthorn, and M. Dagenais, “Arbitrary on-chip optical filter using complex waveguide Bragg gratings,” Appl. Phys. Lett. 108, 101104 (2016).
[Crossref]

F. Meng, R.-J. Shiue, N. Wan, L. Li, J. Nie, N. C. Harris, E. H. Chen, T. Schröder, N. Pervez, I. Kymissis, and D. Englund, “Waveguide-integrated photonic crystal spectrometer with camera readout,” Appl. Phys. Lett. 105, 051103 (2014).
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[Crossref]

S. Babin, A. Bugrov, S. Cabrini, S. Dhuey, A. Goltsov, I. Ivonin, E.-B. Kley, C. Peroz, H. Schmidt, and V. Yankov, “Digital optical spectrometer-on-chip,” Appl. Phys. Lett. 95, 041105 (2009).
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H. Podmore, A. Scott, and R. Lee, “On-chip compressed sensing Fourier-transform visible spectrometer,” IEEE Photon. J. 10, 6602010 (2018).
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IEEE Photon. Technol. Lett. (3)

M. Nedeljkovic, A. V. Velasco, A. Z. Khokhar, A. Delâge, P. Cheben, and G. Z. Mashanovich, “Mid-infrared silicon-on-insulator Fourier-transform spectrometer chip,” IEEE Photon. Technol. Lett. 28, 528–531 (2016).
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J. Lightwave Technol. (2)

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T. Fukazawa, F. Ohno, and T. Baba, “Very compact arrayed-waveguide-grating demultiplexer using Si photonic wire waveguides,” Jpn. J. Appl. Phys. 43, L673 (2004).
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J. S. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser Photon. Rev. 5, 308–321 (2011).
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G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light Sci. Appl. 3, e203 (2014).
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Ž. Zobenica, R. W. van der Heijden, M. Petruzzella, F. Pagliano, R. Leijssen, T. Xia, L. Midolo, M. Cotrufo, Y. Cho, F. W. M. van Otten, E. Verhagen, and A. Fiore, “Integrated nano-opto-electro-mechanical sensor for spectrometry and nanometrology,” Nat. Commun. 8, 2216 (2017).
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Nat. Photonics (4)

B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4  µm 2 footprint,” Nat. Photonics 9, 378–382 (2015).
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[Crossref]

B. Redding, S. F. Liew, R. Sarma, and H. Cao, “Compact spectrometer based on a disordered photonic chip,” Nat. Photonics 7, 746–751 (2013).
[Crossref]

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6, 581–585 (2012).
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M. Cui, “A high speed wavefront determination method based on spatial frequency modulations for focusing light through random scattering media,” Opt. Express 19, 2989–2995 (2011).
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P. Cheben, J. H. Schmid, A. Delâge, A. Densmore, S. Janz, B. Lamontagne, J. Lapointe, E. Post, P. Waldron, and D.-X. Xu, “A high-resolution silicon-on-insulator arrayed waveguide grating microspectrometer with sub-micrometer aperture waveguides,” Opt. Express 15, 2299–2306 (2007).
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B. Momeni, J. Huang, M. Soltani, M. Askari, S. Mohammadi, M. Rakhshandehroo, and A. Adibi, “Compact wavelength demultiplexing using focusing negative index photonic crystal superprisms,” Opt. Express 14, 2413–2422 (2006).
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J. Bosch, S. A. Goorden, and A. P. Mosk, “Frequency width of open channels in multiple scattering media,” Opt. Express 24, 26472–26478 (2016).
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Opt. Lett. (5)

Phys. Rev. Lett. (5)

I. M. Vellekoop and A. P. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101, 120601 (2008).
[Crossref]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
[Crossref]

B. Gérardin, J. Laurent, A. Derode, C. Prada, and A. Aubry, “Full transmission and reflection of waves propagating through a maze of disorder,” Phys. Rev. Lett. 113, 173901 (2014).
[Crossref]

R. Sarma, A. G. Yamilov, S. Petrenko, Y. Bromberg, and H. Cao, “Control of energy density inside a disordered medium by coupling to open or closed channels,” Phys. Rev. Lett. 117, 086803 (2016).
[Crossref]

Sci. Rep. (1)

A. Y. Piggott, J. Lu, T. M. Babinec, K. G. Lagoudakis, J. Petykiewicz, and J. Vučković, “Inverse design and implementation of a wavelength demultiplexing grating coupler,” Sci. Rep. 4, 7210 (2014).
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Other (2)

E. Akkermans and G. Montambaux, Mesoscopic Physics of Electrons and Photons (Cambridge University, 2007).

J. H. Correia, M. Bartek, and R. F. Wolffenbuttel, “High-selectivity single-chip spectrometer for operation at visible wavelengths,” in International Electron Devices Meeting, Technical Digest (1998), pp. 467–470.

Supplementary Material (1)

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» Supplement 1       supplemental document

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Figures (4)

Fig. 1.
Fig. 1. (a) Scattering structure with uniform holes in a golden spiral distribution and its transmission spectra in all the output waveguides. Black and white areas in the left image have refractive indices of 1 and 3.43, respectively. (b) Optimized scattering structure and its transmission spectra in all the output waveguides. (c) Average and minimum transmittance at target wavelengths as a function of the number of iterations, for 2D (continuous lines) and 3D (dashed lines) models. Details of the 3D optimization are given in Supplement 1. (d) Distribution of electric field intensity at first target wavelength (3000 nm). The TM polarization is assumed in the simulations throughout this paper.
Fig. 2.
Fig. 2. Diffusive waveguide (a) before and (e) after optimization. $|{{E}}|$ field distribution when light is injected as a Gaussian beam (b) before and (f) after optimization. The $|{{E}}|$ distribution of the second maximal transmission channel (c) before and (g) after optimization. The wavefront at the input boundary is plotted (red-filled area) along with the field distribution. Distribution of the transmission eigenvalues (d) before and (h) after optimization. The black line indicates the theoretical bimodal distribution.
Fig. 3.
Fig. 3. (a)–(d) Optimized filters and their transmissions spectra (red) and corresponding target spectra (black). A low-pass filter spectrum with step widths of (a) 150 nm and (b) 60 nm. A sinusoidal spectrum with period of (c) 150 nm and (d) 60 nm. (e) FoM as a function of the number of iterations for sinusoidal spectra with different FSR from 30 nm (purple) to 100 nm (barn red). (f) The spectral correlation function of transmission of the filter with initial structure (black) with the structures in (c) (red) and in (d) (blue) averaged over all the detection channels. The theoretical correlation function C1 is plotted as a green line.
Fig. 4.
Fig. 4. (a) Optimized scattering structure with deformation limited to the radius and position of holes. Black and white areas have refractive indices of 1 and 3.43, respectively. (b) Overlapped distribution of electric field intensity at the target wavelengths. (c) Average and minimum transmittance at the target wavelengths as a function of the iteration. (d) Transmission spectra of the 10 outputs.

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