Advancements in transformation optics-enabled gradient-index lens design

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

Transformation Optics (TO) provides the mathematical framework for representing the behavior of electromagnetic radiation in a given geometry by â€transformingâ€it to an alternative, usually more desirable, geometry through an appropriate mapping of the constituent material parameters. Using a quasi-conformal mapping, the restrictions on the required material parameters can be relaxed allowing isotropic inhomogeneous all-dielectric materials to be employed. This approach has led to the development of a new and powerful design tool for gradient-index (GRIN) optical systems. Using TO, aspherical lenses can be transformed to simpler spherical and flat geometries or even rotationally-Asymmetric shapes which result in true 3D GRIN profiles. TO can also potentially be extended to collapse an entire lens system into a representative GRIN profile thus reducing its physical dimensions while retaining the optical performance of the original system. However, dispersion effects of the constituent materials often limit the bandwidth of metamaterial and TO structures thus restricting their potential applicability. Nonetheless, with the proper pairing of GRIN profile and lens geometry to a given material system, chromatic aberrations can be minimized. To aid in the GRIN construction, we employ advanced multi-objective optimization algorithms which allow the designer to explicitly view the trade-offs between all design objectives such as RMS spot size, field-of-view (FOV), lens thickness, and focal drift due to chromatic aberrations. We present an overview of our TO-enabled GRIN lens design process and analysis techniques while demonstrating designs which minimize the presence of mono-and poly-chromatic aberrations and discuss their requisite material systems.

Original languageEnglish (US)
Title of host publicationNovel Optical Systems Design and Optimization XVIII
EditorsG. Groot Gregory, Cornelius F. Hahlweg, Cornelius F. Hahlweg, Arthur J. Davis, G. Groot Gregory, Arthur J. Davis
PublisherSPIE
ISBN (Electronic)9781628417456, 9781628417456
DOIs
StatePublished - Jan 1 2015
Event18th Conference of Novel Optical Systems Design and Optimization - San Diego, United States
Duration: Aug 10 2015Aug 12 2015

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
Volume9579
ISSN (Print)0277-786X
ISSN (Electronic)1996-756X

Other

Other18th Conference of Novel Optical Systems Design and Optimization
CountryUnited States
CitySan Diego
Period8/10/158/12/15

Fingerprint

Gradient index optics
gradient index optics
Lens Design
lens design
Optics
Lenses
Gradient
gradients
Aberrations
lenses
Lens
optics
aberration
Aberration
Geometry
geometry
profiles
Conformal mapping
conformal mapping
Dispersion Effect

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

Cite this

Campbell, S., Brocker, D., Nagar, J., Easum, J. A., Werner, D. H., & Werner, P. L. (2015). Advancements in transformation optics-enabled gradient-index lens design. In G. G. Gregory, C. F. Hahlweg, C. F. Hahlweg, A. J. Davis, G. G. Gregory, & A. J. Davis (Eds.), Novel Optical Systems Design and Optimization XVIII [95790E] (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 9579). SPIE. https://doi.org/10.1117/12.2187513
Campbell, Sawyer ; Brocker, Donovan ; Nagar, Jogender ; Easum, John A. ; Werner, Douglas Henry ; Werner, Pingjuan Li. / Advancements in transformation optics-enabled gradient-index lens design. Novel Optical Systems Design and Optimization XVIII. editor / G. Groot Gregory ; Cornelius F. Hahlweg ; Cornelius F. Hahlweg ; Arthur J. Davis ; G. Groot Gregory ; Arthur J. Davis. SPIE, 2015. (Proceedings of SPIE - The International Society for Optical Engineering).
@inproceedings{10df85180e6246acb4c7da480fd7753c,
title = "Advancements in transformation optics-enabled gradient-index lens design",
abstract = "Transformation Optics (TO) provides the mathematical framework for representing the behavior of electromagnetic radiation in a given geometry by {\^a}€transforming{\^a}€it to an alternative, usually more desirable, geometry through an appropriate mapping of the constituent material parameters. Using a quasi-conformal mapping, the restrictions on the required material parameters can be relaxed allowing isotropic inhomogeneous all-dielectric materials to be employed. This approach has led to the development of a new and powerful design tool for gradient-index (GRIN) optical systems. Using TO, aspherical lenses can be transformed to simpler spherical and flat geometries or even rotationally-Asymmetric shapes which result in true 3D GRIN profiles. TO can also potentially be extended to collapse an entire lens system into a representative GRIN profile thus reducing its physical dimensions while retaining the optical performance of the original system. However, dispersion effects of the constituent materials often limit the bandwidth of metamaterial and TO structures thus restricting their potential applicability. Nonetheless, with the proper pairing of GRIN profile and lens geometry to a given material system, chromatic aberrations can be minimized. To aid in the GRIN construction, we employ advanced multi-objective optimization algorithms which allow the designer to explicitly view the trade-offs between all design objectives such as RMS spot size, field-of-view (FOV), lens thickness, and focal drift due to chromatic aberrations. We present an overview of our TO-enabled GRIN lens design process and analysis techniques while demonstrating designs which minimize the presence of mono-and poly-chromatic aberrations and discuss their requisite material systems.",
author = "Sawyer Campbell and Donovan Brocker and Jogender Nagar and Easum, {John A.} and Werner, {Douglas Henry} and Werner, {Pingjuan Li}",
year = "2015",
month = "1",
day = "1",
doi = "10.1117/12.2187513",
language = "English (US)",
series = "Proceedings of SPIE - The International Society for Optical Engineering",
publisher = "SPIE",
editor = "Gregory, {G. Groot} and Hahlweg, {Cornelius F.} and Hahlweg, {Cornelius F.} and Davis, {Arthur J.} and Gregory, {G. Groot} and Davis, {Arthur J.}",
booktitle = "Novel Optical Systems Design and Optimization XVIII",
address = "United States",

}

Campbell, S, Brocker, D, Nagar, J, Easum, JA, Werner, DH & Werner, PL 2015, Advancements in transformation optics-enabled gradient-index lens design. in GG Gregory, CF Hahlweg, CF Hahlweg, AJ Davis, GG Gregory & AJ Davis (eds), Novel Optical Systems Design and Optimization XVIII., 95790E, Proceedings of SPIE - The International Society for Optical Engineering, vol. 9579, SPIE, 18th Conference of Novel Optical Systems Design and Optimization, San Diego, United States, 8/10/15. https://doi.org/10.1117/12.2187513

Advancements in transformation optics-enabled gradient-index lens design. / Campbell, Sawyer; Brocker, Donovan; Nagar, Jogender; Easum, John A.; Werner, Douglas Henry; Werner, Pingjuan Li.

Novel Optical Systems Design and Optimization XVIII. ed. / G. Groot Gregory; Cornelius F. Hahlweg; Cornelius F. Hahlweg; Arthur J. Davis; G. Groot Gregory; Arthur J. Davis. SPIE, 2015. 95790E (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 9579).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

TY - GEN

T1 - Advancements in transformation optics-enabled gradient-index lens design

AU - Campbell, Sawyer

AU - Brocker, Donovan

AU - Nagar, Jogender

AU - Easum, John A.

AU - Werner, Douglas Henry

AU - Werner, Pingjuan Li

PY - 2015/1/1

Y1 - 2015/1/1

N2 - Transformation Optics (TO) provides the mathematical framework for representing the behavior of electromagnetic radiation in a given geometry by â€transformingâ€it to an alternative, usually more desirable, geometry through an appropriate mapping of the constituent material parameters. Using a quasi-conformal mapping, the restrictions on the required material parameters can be relaxed allowing isotropic inhomogeneous all-dielectric materials to be employed. This approach has led to the development of a new and powerful design tool for gradient-index (GRIN) optical systems. Using TO, aspherical lenses can be transformed to simpler spherical and flat geometries or even rotationally-Asymmetric shapes which result in true 3D GRIN profiles. TO can also potentially be extended to collapse an entire lens system into a representative GRIN profile thus reducing its physical dimensions while retaining the optical performance of the original system. However, dispersion effects of the constituent materials often limit the bandwidth of metamaterial and TO structures thus restricting their potential applicability. Nonetheless, with the proper pairing of GRIN profile and lens geometry to a given material system, chromatic aberrations can be minimized. To aid in the GRIN construction, we employ advanced multi-objective optimization algorithms which allow the designer to explicitly view the trade-offs between all design objectives such as RMS spot size, field-of-view (FOV), lens thickness, and focal drift due to chromatic aberrations. We present an overview of our TO-enabled GRIN lens design process and analysis techniques while demonstrating designs which minimize the presence of mono-and poly-chromatic aberrations and discuss their requisite material systems.

AB - Transformation Optics (TO) provides the mathematical framework for representing the behavior of electromagnetic radiation in a given geometry by â€transformingâ€it to an alternative, usually more desirable, geometry through an appropriate mapping of the constituent material parameters. Using a quasi-conformal mapping, the restrictions on the required material parameters can be relaxed allowing isotropic inhomogeneous all-dielectric materials to be employed. This approach has led to the development of a new and powerful design tool for gradient-index (GRIN) optical systems. Using TO, aspherical lenses can be transformed to simpler spherical and flat geometries or even rotationally-Asymmetric shapes which result in true 3D GRIN profiles. TO can also potentially be extended to collapse an entire lens system into a representative GRIN profile thus reducing its physical dimensions while retaining the optical performance of the original system. However, dispersion effects of the constituent materials often limit the bandwidth of metamaterial and TO structures thus restricting their potential applicability. Nonetheless, with the proper pairing of GRIN profile and lens geometry to a given material system, chromatic aberrations can be minimized. To aid in the GRIN construction, we employ advanced multi-objective optimization algorithms which allow the designer to explicitly view the trade-offs between all design objectives such as RMS spot size, field-of-view (FOV), lens thickness, and focal drift due to chromatic aberrations. We present an overview of our TO-enabled GRIN lens design process and analysis techniques while demonstrating designs which minimize the presence of mono-and poly-chromatic aberrations and discuss their requisite material systems.

UR - http://www.scopus.com/inward/record.url?scp=84951144793&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84951144793&partnerID=8YFLogxK

U2 - 10.1117/12.2187513

DO - 10.1117/12.2187513

M3 - Conference contribution

AN - SCOPUS:84951144793

T3 - Proceedings of SPIE - The International Society for Optical Engineering

BT - Novel Optical Systems Design and Optimization XVIII

A2 - Gregory, G. Groot

A2 - Hahlweg, Cornelius F.

A2 - Hahlweg, Cornelius F.

A2 - Davis, Arthur J.

A2 - Gregory, G. Groot

A2 - Davis, Arthur J.

PB - SPIE

ER -

Campbell S, Brocker D, Nagar J, Easum JA, Werner DH, Werner PL. Advancements in transformation optics-enabled gradient-index lens design. In Gregory GG, Hahlweg CF, Hahlweg CF, Davis AJ, Gregory GG, Davis AJ, editors, Novel Optical Systems Design and Optimization XVIII. SPIE. 2015. 95790E. (Proceedings of SPIE - The International Society for Optical Engineering). https://doi.org/10.1117/12.2187513