---
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
_id: '21639'
abstract:
- lang: eng
  text: Traditional optical elements and conventional metasurfaces obey shift-invariance
    in the paraxial regime. For imaging systems obeying paraxial shift-invariance,
    a small shift in input angle causes a corresponding shift in the sensor image.
    Shift-invariance has deep implications for the design and functionality of optical
    devices, such as the necessity of free space between components (as in compound
    objectives made of several curved surfaces). We present a method for nanophotonic
    inverse design of compact imaging systems whose resolution is not constrained
    by paraxial shift-invariance. Our method is end-to-end, in that it integrates
    density-based full-Maxwell topology optimization with a fully iterative elastic-net
    reconstruction algorithm. By the design of nanophotonic structures that scatter
    light in a non-shift-invariant manner, our optimized nanophotonic imaging system
    overcomes the limitations of paraxial shift-invariance, achieving accurate, noise-robust
    image reconstruction beyond shift-invariant resolution.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: William F.
  full_name: Li, William F.
  last_name: Li
- first_name: Gaurav
  full_name: Arya, Gaurav
  last_name: Arya
- first_name: Charles
  full_name: Roques-Carmes, Charles
  id: e2e68fc9-6505-11ef-a541-eb4e72cc3e82
  last_name: Roques-Carmes
- first_name: Zin
  full_name: Lin, Zin
  last_name: Lin
- first_name: Steven G.
  full_name: Johnson, Steven G.
  last_name: Johnson
- first_name: Marin
  full_name: Soljačić, Marin
  last_name: Soljačić
citation:
  ama: Li WF, Arya G, Roques-Carmes C, Lin Z, Johnson SG, Soljačić M. Transcending
    shift-invariance in the paraxial regime via end-to-end inverse design of freeform
    nanophotonics. <i>Optics Express</i>. 2023;31(15):24260-24272. doi:<a href="https://doi.org/10.1364/oe.492553">10.1364/oe.492553</a>
  apa: Li, W. F., Arya, G., Roques-Carmes, C., Lin, Z., Johnson, S. G., &#38; Soljačić,
    M. (2023). Transcending shift-invariance in the paraxial regime via end-to-end
    inverse design of freeform nanophotonics. <i>Optics Express</i>. Optica Publishing
    Group. <a href="https://doi.org/10.1364/oe.492553">https://doi.org/10.1364/oe.492553</a>
  chicago: Li, William F., Gaurav Arya, Charles Roques-Carmes, Zin Lin, Steven G.
    Johnson, and Marin Soljačić. “Transcending Shift-Invariance in the Paraxial Regime
    via End-to-End Inverse Design of Freeform Nanophotonics.” <i>Optics Express</i>.
    Optica Publishing Group, 2023. <a href="https://doi.org/10.1364/oe.492553">https://doi.org/10.1364/oe.492553</a>.
  ieee: W. F. Li, G. Arya, C. Roques-Carmes, Z. Lin, S. G. Johnson, and M. Soljačić,
    “Transcending shift-invariance in the paraxial regime via end-to-end inverse design
    of freeform nanophotonics,” <i>Optics Express</i>, vol. 31, no. 15. Optica Publishing
    Group, pp. 24260–24272, 2023.
  ista: Li WF, Arya G, Roques-Carmes C, Lin Z, Johnson SG, Soljačić M. 2023. Transcending
    shift-invariance in the paraxial regime via end-to-end inverse design of freeform
    nanophotonics. Optics Express. 31(15), 24260–24272.
  mla: Li, William F., et al. “Transcending Shift-Invariance in the Paraxial Regime
    via End-to-End Inverse Design of Freeform Nanophotonics.” <i>Optics Express</i>,
    vol. 31, no. 15, Optica Publishing Group, 2023, pp. 24260–72, doi:<a href="https://doi.org/10.1364/oe.492553">10.1364/oe.492553</a>.
  short: W.F. Li, G. Arya, C. Roques-Carmes, Z. Lin, S.G. Johnson, M. Soljačić, Optics
    Express 31 (2023) 24260–24272.
date_created: 2026-03-30T12:22:48Z
date_published: 2023-07-10T00:00:00Z
date_updated: 2026-04-27T07:32:36Z
day: '10'
ddc:
- '530'
doi: 10.1364/oe.492553
extern: '1'
external_id:
  arxiv:
  - '2302.01712'
  pmid:
  - '37475257'
intvolume: '        31'
issue: '15'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.1364/OE.492553
month: '07'
oa: 1
oa_version: Published Version
page: 24260-24272
pmid: 1
publication: Optics Express
publication_identifier:
  eissn:
  - 1094-4087
publication_status: published
publisher: Optica Publishing Group
quality_controlled: '1'
scopus_import: '1'
status: public
title: Transcending shift-invariance in the paraxial regime via end-to-end inverse
  design of freeform nanophotonics
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 31
year: '2023'
...