Absar U. Hassan

Enhanced sensitivity at higher-order exceptional points

Non-Hermitian degeneracies, also known as exceptional points, have recently emerged as a new way to engineer the response of open physical systems, that is, those that interact with the environment. They correspond to points in parameter space at which the eigenvalues of the underlying system and the corresponding eigenvectors simultaneously coalesce. In optics, the abrupt nature of the phase transitions that are encountered around exceptional points has been shown to lead to many intriguing phenomena, such as loss-induced transparency, unidirectional invisibility, band merging, topological chirality and laser mode selectivity. Recently, it has been shown that the bifurcation properties of second-order non-Hermitian degeneracies can provide a means of enhancing the sensitivity (frequency shifts) of resonant optical structures to external perturbations. Of particular interest is the use of even higher-order exceptional points (greater than second order), which in principle could further amplify the effect of perturbations, leading to even greater sensitivity. Although a growing number of theoretical studies have been devoted to such higher-order degeneracies, their experimental demonstration in the optical domain has so far remained elusive. Here we report the observation of higher-order exceptional points in a coupled cavity arrangement—specifically, a ternary, parity–time-symmetric photonic laser molecule—with a carefully tailored gain–loss distribution. We study the system in the spectral domain and find that the frequency response associated with this system follows a cube-root dependence on induced perturbations in the refractive index. Our work paves the way for utilizing non-Hermitian degeneracies in fields including photonics, optomechanics, microwaves and atomic physics.

Nonlinear reversal of thePT-symmetric phase transition in a system of coupled semiconductor microring resonators

A system of two coupled semiconductor-based resonators is studied when lasing around an exceptional point. We show that the presence of nonlinear saturation effects can have important ramifications on the transition behavior of this system. In sharp contrast with linear PT-symmetric configurations, nonlinear processes are capable of reversing the order in which the symmetry breaking occurs. Yet, even in the nonlinear regime, the resulting non-Hermitian states still retain the structural form of the corresponding linear eigenvectors expected above and below the phase transition point. The conclusions of our analysis are in agreement with experimental data.

Dynamically Encircling Exceptional Points: Exact Evolution and Polarization State Conversion

We show that a two-level non-Hermitian Hamiltonian with constant off-diagonal exchange elements can be analyzed exactly when the underlying exceptional point is perfectly encircled in the complex plane. The state evolution of this system is explicitly obtained in terms of an ensuing transfer matrix, even for large encirclements, regardless of adiabatic conditions. Our results clearly explain the direction-dependent nature of this process and why in the adiabatic limit its outcome is dominated by a specific eigenstate-irrespective of initial conditions. Moreover, numerical simulations suggest that this mechanism can still persist in the presence of nonlinear effects. We further show that this robust process can be harnessed to realize an optical omnipolarizer: a configuration that generates a desired polarization output regardless of the input polarization state, while from the opposite direction it always produces the counterpart eigenstate.

Parity-time-symmetric coupled microring lasers operating around an exceptional point

The behavior of a parity-time-symmetric coupled microring system is studied when operating in the vicinity of an exceptional point. Using the abrupt phase transition around this point, stable single-mode lasing is demonstrated in spectrally multimoded microring arrangements.

Dark-state lasers: mode management using exceptional points

By exploiting the inherent characteristics of dark-state resonators, we experimentally realize a single-frequency integrated microring laser system. This semiconductor laser can remain single-mode, even at high pump power levels, while allowing tunability over a wide spectral range. Our results demonstrate the potential of exceptional points as a versatile tool for mode selection in micro-cavity laser configurations.

Chiral state conversion without encircling an exceptional point

Dynamically varying system parameters along a path enclosing an exceptional point is known to lead to chiral mode conversion. But is it necessary to include this non-Hermitian degeneracy inside the contour for this process to take place? We show that a sufficiently slow variation of parameters, even away from the systems exceptional point, can also lead to a robust asymmetric state exchange. To study this process, we consider a prototypical two-level non-Hermitian Hamiltonian with a constant coupling between elements. Closed-form solutions are obtained when the amplification or attenuation coefficients in this arrangement are varied in conjunction with the resonance detuning along a circular contour. Using asymptotic expansions, this input-independent mode conversion is theoretically proven to take place irrespective of whether the exceptional point is enclosed upon encirclement. Our results significantly broaden the range of parameter space required for the experimental realization of such chiral mode conversion processes.

Ultrasensitive micro-scale parity-time-symmetric ring laser gyroscope.

We propose a new scheme for ultrasensitive laser gyroscopes that utilizes the physics of exceptional points. By exploiting the properties of such non-Hermitian degeneracies, we show that the rotation-induced frequency splitting becomes proportional to the square root of the gyration speed (Ω), thus enhancing the sensitivity to low angular rotations by orders of magnitudes. In addition, at its maximum sensitivity limit, the measurable spectral splitting is independent of the radius of the rings involved. This Letter paves the way toward a new class of ultrasensitive miniature ring laser gyroscopes on chip.

Integrable nonlinear parity-time-symmetric optical oscillator.

The nonlinear dynamics of a balanced parity-time-symmetric optical microring arrangement are analytically investigated. By considering gain and loss saturation effects, the pertinent conservation laws are explicitly obtained in the Stokes domain, thus establishing integrability. Our analysis indicates the existence of two regimes of oscillatory dynamics and frequency locking, both of which are analogous to those expected in linear parity-time-symmetric systems. Unlike other saturable parity-time-symmetric systems considered before, the model studied in this work first operates in the symmetric regime and then enters the broken parity-time phase.

Statistical parity-time-symmetric lasing in an optical fibre network

Parity-time (PT)-symmetry in optics is a condition whereby the real and imaginary parts of the refractive index across a photonic structure are deliberately balanced. This balance can lead to interesting optical phenomena, such as unidirectional invisibility, loss-induced lasing, single-mode lasing from multimode resonators, and non-reciprocal effects in conjunction with nonlinearities. Because PT-symmetry has been thought of as fragile, experimental realisations to date have been usually restricted to on-chip micro-devices. Here, we demonstrate that certain features of PT-symmetry are sufficiently robust to survive the statistical fluctuations associated with a macroscopic optical cavity. We examine the lasing dynamics in optical fibre-based coupled cavities more than a kilometre in length with balanced gain and loss. Although fluctuations can detune the cavity by more than the free spectral range, the behaviour of the lasing threshold and the laser power is that expected from a PT-stable system. Furthermore, we observe a statistical symmetry breaking upon varying the cavity loss.Parity-time-symmetric optical systems have so far only been realized using microscopic cavities because the necessary gain-loss balance is thought to be fragile with regard to statistical fluctuations. Here, Jahromi et al.. demonstrate PT-symmetric lasing using kilometre-long fibre cavities.

Tunable parity-time-symmetric microring lasers

Wavelength tuning in a single mode parity-time (PT) symmetric semiconductor microring laser is demonstrated. Stable continuous tuning over a spectral range of 4 nm has been obtained at telecom wavelengths by adjusting the ambient temperature.