Inverse-designed photonic fibers and metasurfaces
for nonlinear frequency conversion [Invited]
CHAWIN SITAWARIN,
1
WEILIANG JIN,
1
ZIN LIN,
2
AND ALEJANDRO W. RODRIGUEZ
1,
*
1
Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
2
John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
*Corresponding author: arod@princeton.edu
Received 22 November 2017; revised 19 March 2018; accepted 20 March 2018; posted 21 March 2018 (Doc. ID 313902);
published 20 April 2018
Typically, photonic waveguides designed for nonlinear frequency conversion rely on intuitive and established
principles, including index guiding and bandgap engineering, and are based on simple shapes with high degrees
of symmetry. We show that recently developed inverse-design techniques can be applied to discover new kinds of
microstructured fibers and metasurfaces designed to achieve large nonlinear frequency-conversion efficiencies. As
a proof of principle, we demonstrate complex, wavel ength-scale chalcogenide glass fibers and gallium phosphide
three-dimensional metasurfaces exhibiting some of the largest nonlinear conversion efficiencies predicted thus far,
e.g., lowering the power requirement for third-harmonic generation by 10
4
and enhancing second-harmonic
generation conversion efficiency by 10
7
. Such enhancements arise because, in addition to enabling a great degree
of tunability in the choice of design wavelengths, these optimization tools ensure both frequency- and
phase-matching in addition to large nonlinear overlap factors.
© 2018 Chinese Laser Press
OCIS codes: (050.1755) Computational electromagnetic methods; (060.4370) Nonlinear optics, fibers; (190.2620) Harmonic
generation and mixing; (190.4360) Nonlinear optics, devices; (350.4238) Nanophotonics and photonic crystals.
https://doi.org/10.1364/PRJ.6.000B82
1. INTRODUCTION
Nonlinear frequency conversion plays a crucial role in many
photonic applications, including ultra-short pulse shaping
[1,2], spectroscopy [3], generation of novel optical states
[4–6], and quantum information processing [7–9]. Although
frequency conversion has been studied exhaustively in bulky
optical systems, including large ring resonators [10] and etalon
cavities [11], it remains largely unstudied in micro- and nano-
scale structures where light can be confined to lengthscales of
the order of or even smaller than its wavelength. By confining
light over long a time and to small volumes, such highly com-
pact devices greatly enhance light – matter interactions, enabling
similar as well as new [12] functionalities compared to those
available in bulky systems but at much lower power levels.
Several proposals have been put forward based on the premise
of observing enhanced nonlinear effects in structures capable of
supporting multiple resonances at far-away frequencies
[13–21], among which are micro-ring resonators [22,23]
and photonic crystal (PhC) cavities [24,25]. However, to date,
these conventional designs fall short of simultaneously meeting
the many design challenges associated with resonant frequency
conversion, chief among them being the need to support multi-
ple modes with highly concentrated fields, exactly matched
resonant frequencies, and strong mode overlaps [26]. Recently,
we proposed to leverage powerful, large-scale optimization
techniques (commonly known as inverse design) to allow
computer-aided photonic designs that can address all of these
challenges.
Our recently demonstrated optimization framework allows
automatic discovery of novel cavities that support tightly local-
ized modes at several desired wavelengths and exhibit large non-
linear mode overlaps. As a proof-of-concept, we proposed
doubly resonant structures, including multi-layered, aperiodic
micro-post cavities and multi-track ring resonators, capable of
realizing second-harmonic generation efficiencies exceeding
10
4
W
−1
[27,28]. In this paper, we extend and apply this op-
timization approach to design extended structures, including
micro-structured optical fibers and PhC three-dimensional
metasurfaces, as shown in Fig. 1, for achieving high-efficiency
(second- and third-harmonic) frequency conversion. Harmonic
generation, which underlies numerous applications in science,
including coherent light sources [29], optical imaging and
microscopy [30,31], and entangled-photon generation [32],
is now feasible at lower power requirements thanks to the avail-
ability of highly nonlinear χ
2
and χ
3
materials such as III–V
semiconductor compounds [33,34] and novel types of
chalcogenide glasses [35]. In combination with advances in
materials synthesis, emerging fabrication technologies have also
B82
Vol. 6, No. 5 / May 2018 / Photonics Research
Research Article
2327-9125/18/050B82-08 Journal © 2018 Chinese Laser Press
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