Research interests

I am interested in theoretical and numerical nanophotonics, including basic theory, novel simulation methods, and design optimization. I am in Shanhui Fan's group.

Compact bends for multi-mode photonic crystal waveguides with high transmission and suppressed modal crosstalk
We demonstrate an extremely compact bend for a photonic crystal waveguide supporting three spatial modes. The bend exhibits nearly 100% transmission over a relative bandwidth of 1% with less than 1% crosstalk. We show that our design is robust with respect to fabrication errors. Our design method is applied to create a structure consisting of dielectric rods, as well as a structure consisting of air holes in a dielectric background.
Highly Tailored Computational Electromagnetics Methods for Nanophotonic Design and Discovery
The use of computational electromagnetics (CEM) techniques has greatly advanced nanophotonics. The applications of nanophotonics in turn motivates the development of efficient highly tailored algorithms for specific application domains. In this paper, we will discuss some specific considerations in seeking to advance CEM for nanophotonic design and discovery, with examples drawn from the design of aperiodic nanophotonic structures for on-chip information processing applications.
Ultra-compact photonic crystal waveguide spatial mode converter and its connection to the optical diode effect
We design an extremely compact photonic crystal waveguide spatial mode converter which converts the fundamental even mode to the higher order odd mode with nearly 100% efficiency. We adapt a previously developed design and optimization process that allows these types of devices to be designed in a matter of minutes. We also present an extremely compact optical diode device and clarify its general properties and its relation to spatial mode converters. Finally, we connect the results here to a general theory on the complexity of optical designs.
S4: A free electromagnetic solver for layered periodic structures
We describe S4, a free implementation of the Fourier Modal Method (FMM), which has also been commonly referred to as Rigorous Coupled Wave Analysis (RCWA), for simulating electromagnetic propagation through 3D structures with 2D periodicity. We detail design aspects that allow S4 to be a flexible platform for these types of simulations. In particular, we highlight the ability to select different FMM formulations, user scripting, and extensibility of program capabilities for eigenmode computations.
Ultra-compact non-reciprocal optical isolator based on guided resonance in a magneto-optical photonic crystal slab
We design an ultracompact optical isolator with normal incident geometry that operates with a bandwidth that is substantial for a device of this size. For operation in a telecommunication wavelength of 1.55 um, the thickness of the device is less than 1?Ám and the device supports an operating bandwidth of 400 GHz over which the minimum contrast ratio exceeds 25 dB. Our design utilizes guided resonance in a photonic crystal slab to enhance magneto-optical effects, and exploits interference effects among multiple resonances to create desired transmission spectral line shapes.
Efficient computation of equifrequency surfaces and density of states in photonic crystals using Dirichlet-to-Neumann maps
We present an efficient method for computing the equifrequency surfaces (EFSs) and density of states of a photonic crystal. The method is based on repeatedly solving a small nonlinear eigenvalue problem formulated using the Dirichlet-to-Neumann map of the unit cell. A simple contouring algorithm is presented for sampling EFSs as well as computing group velocity vectors. We compare our method with several published results to demonstrate its efficiency and accuracy.
Design methodology for compact photonic-crystal-based wavelength division multiplexers
We present an extremely compact wavelength division multiplexer design, as well as a general framework for designing and optimizing frequency selective devices embedded in photonic crystals satisfying arbitrary design constraints. Our method is based on the Dirichlet-to-Neumann simulation method and uses low rank updates to the system to efficiently scan through many device designs.
Sensitivity enhancement in photonic crystal slab biosensors
Mohamed El Beheiry, Victor Liu, Shanhui Fan, and Ofer Levi
Refractive index sensitivity of guided resonances in photonic crystal slabs is analyzed. We show that modal properties of guided resonances strongly affect spectral sensitivity and quality factors, resulting in substantial enhancement of refractive index sensitivity. A three-fold spectral sensitivity enhancement is demonstrated for suspended slab designs, in contrast to designs with a slab resting over a substrate. Spectral sensitivity values are additionally shown to be unaffected by quality factor reductions, which are common to fabricated photonic crystal nano-structures. Finally, we determine that proper selection of photonic crystal slab design parameters permits biosensing of a wide range of analytes, including proteins, antigens, and cells. These photonic crystals are compatible with large-area biosensor designs, permitting direct access to externally incident optical beams in a microfluidic device.
Resonance-enhanced optical forces between coupled photonic crystal slabs
The behaviors of lateral and normal optical forces between coupled photonic crystal slabs are analyzed. We show that the optical force is periodic with displacement, resulting in stable and unstable equilibrium positions. Moreover, the forces are strongly enhanced by guided resonances of the coupled slabs. Such enhancement is particularly prominent near dark states of the system, and the enhancement effect is strongly dependent on the types of guided resonances involved. These structures lead to enhancement of light-induced pressure over larger areas, in a configuration that is directly accessible to externally incident, free-space optical beams.
I had originally wondered about the topological structure of the dark states in our 3-parameter space. Our suspicion that they are 1D analytic curves appears to be confirmed by Shipman & Tu

Undergraduate research

At Caltech, I worked in the Caltech Nanofabrication Group under the direction of Axel Scherer. It was there that I first became interested in nanophotonics and getting involved with fabrication work. I did SURFs during the summers of 2004 and 2005, where I worked with Joerg Schilling on Silicon photonics and light emitters. Later for my senior thesis project, I worked with Zhaoyu Zhang on making tiny lasers. I believe the resulting publication was (is?) a record-holder for the smallest laser.

Visible submicron microdisk lasers
The authors describe the performance of submicron microdisk lasers fabricated within InGaP/InGaAlP quantum well material working at room temperature. The smallest lasers, with diameters of approximately 600 nm, feature ultrasmall mode volumes and exhibit single mode operation at low threshold powers. Their small cavity volumes of approximately 0.03 cubic microns enable microdisk lasers to be used as spectroscopic sources. Here the authors demonstrate the fabrication and characterization of visible, monolithically fabricated, submicron microdisk lasers.