Alexander Cerjan

Exceptional contours and band structure design in parity-time symmetric photonic crystals

We investigate the properties of two-dimensional parity-time symmetric periodic systems whose non-Hermitian periodicity is an integer multiple of the underlying Hermitian systems periodicity. This creates a natural set of degeneracies that can undergo thresholdless PT transitions. We derive a k·p perturbation theory suited to the continuous eigenvalues of such systems in terms of the modes of the underlying Hermitian system. In photonic crystals, such thresholdless PT transitions are shown to yield significant control over the band structure of the system, and can result in all-angle supercollimation, a PT-superprism effect, and unidirectional behavior.

Achieving Arbitrary Control over Pairs of Polarization States Using Complex Birefringent Metamaterials

We demonstrate that the key to realizing arbitrary control over pairs of polarization states of light, i.e., transforming an arbitrarily polarized pair of input states to an arbitrarily polarized pair of output states, is the ability to generate pairs of states with orthogonal polarizations from nonorthogonal pairs of initial states. Then, we develop a new class of non-Hermitian metamaterials, termed complex birefringent metamaterials, which are able to do exactly this. Such materials could facilitate the detection of small polarization changes in scattering experiments as well as enable new polarization multiplexing schemes in communications networks.

Eigenvalue dynamics in the presence of non-uniform gain and loss

We introduce a general set of conditions for observing reverse pump dependence in lasers and other counterintuitive phenomena, which demonstrate that any irreducible system with patterned gain and loss can exhibit such exotic behaviors.

Evidence of Anderson localization effects in random Raman lasing

Anderson localization, also known as strong localization, is the absence of diffusion in turbid media resulting from wave interference. The effect was originally predicted for electron motion, and is widely known to exist in systems of less than 3 dimensions. However, Anderson localization of optical photons in 3 dimensional systems remains an elusive and controversial topic. Random Raman lasing offers the unique combination of large gain and virtually zero absorption. The lack of absorption makes long path length, localized modes preferred. The presence of gain offsets what little absorption is present, and preferentially amplifies localized modes due to their large Q factors compared with typical low Q modes present in complex media. Random Raman lasers exhibit several experimentally measured properties that diverge from classical, particle-like, diffusion. First, the temporal width of the emission being 1 to a few nanoseconds in duration when it is pumped with a 50 ps laser is a full order of magnitude longer than is predicted by Monte Carlo simulations. Second, the random Raman laser emission is highly multi-mode, consisting of hundreds of simultaneous lasing modes. This is in contrast to early theoretical results and back of the envelope arguments that both suggest that only a few modes should be present. We will present the evidence that suggests a divergence from classical diffusion theory. One likely explanation, that is consistent with all of these anomalies, is the presence of high-Q localized modes consistent with Anderson localization.

Controlling mode competition by tailoring the spatial pump distribution in a laser: a resonance-based approach

We introduce a simplified version of the steady-state ab initio laser theory for calculating the effects of mode competition in continuous wave lasers using the passive cavity resonances. This new theory harnesses widely available numerical methods that can efficiently calculate the passive cavity resonances, with negligible additional computational overhead. Using this theory, we demonstrate that the pump profile of the laser cavity can be optimized both for highly multi-mode and single-mode emission. An open source implementation of this method has been made available.

Invited Article: Acousto-optic finite-difference frequency-domain algorithm for first-principles simulations of on-chip acousto-optic devices

We introduce a finite-difference frequency-domain algorithm for coupled acousto-optic simulations. First-principles acousto-optic simulation in time domain has been challenging due to the fact that the acoustic and optical frequencies differ by many orders of magnitude. We bypass this difficulty by formulating the interactions between the optical and acoustic waves rigorously as a system of coupled nonlinear equations in frequency domain. This approach is particularly suited for on-chip devices that are based on a variety of acousto-optic interactions such as the stimulated Brillouin scattering. We validate our algorithm by simulating a stimulated Brillouin scattering process in a suspended waveguide structure and find excellent agreement with coupled-mode theory. We further provide an example of a simulation for a compact on-chip resonator device that greatly enhances the effect of stimulated Brillouin scattering. Our algorithm should facilitate the design of nanophotonic on-chip devices for the harnessi...