Optical Nonlinear Interactions In Dielectric Nano-suspensions

This work is divided into two main parts. In the first part (chapters 2-7) we consider the nonlinear response of nano-particle colloidal systems. Starting from the Nernst-Planck and Smoluchowski equations, we demonstrate that in these arrangements the underlying nonlinearities as well as the nonlinear Rayleigh losses depend exponentially on optical intensity. Two different nonlinear regimes are identified depending on the refractive index contrast of the nanoparticles involved and the interesting prospect of self-induced transparency is demonstrated. Soliton stability is systematically analyzed for both 1D and 2D configurations and their propagation dynamics in the presence of Rayleigh losses is examined. We also investigate the modulation instability of plane waves and the transverse instabilities of soliton stripe beams propagating in nonlinear nano-suspensions. We show that in these systems, the process of modulational instability depends on the boundary conditions. On the other hand, the transverse instability of soliton stripes can exhibit new features as a result of 1D collapse caused by the exponential nonlinearity. Many-body effects on the systems\u27 nonlinear response are also examined. Mayer cluster expansions are used in order to investigate particle-particle interactions. We show that the optical nonlinearity of these nano-suspensions can range anywhere from exponential to polynomial depending on the initial concentration and the chemistry of the electrolyte solution. The consequence of these inter-particle interactions on the soliton dynamics and their stability properties are also studied. The second part deals with linear and nonlinear properties of optical nano-wires and the coupled mode formalism of parity-time (PT) symmetric waveguides. Dispersion properties of AlGaAs nano-wires are studied and it is shown that the group velocity dispersion in such waveguides can be negative, thus enabling temporal solitons. We have also studied power flow in nano-waveguides and we have shown that under certain conditions, optical pulses propagating in such structures will exhibit power circulations. Finally PT symmetric waveguides were investigated and a suitable coupled mode theory to describe these systems was developed

On-Chip Multi 4-Port Optical Circulators

We present a new geometry for on-chip optical circulators based on waveguide arrays. The optical array is engineered to mimic the Fock space representation of a noninteracting two-site Bose–Hubbard Hamiltonian. By introducing a carefully tailored magnetooptic nonreciprocity to these structures, the array operates in the perfect transfer and surface Bloch oscillation modes in the forward and backward propagation directions, respectively. We show that an array made of ð2N þ 1Þ waveguide channels can function as N 4-port optical circulators with very large isolation ratios and low forward losses. Numerical analysis using beam propagation method indicates a large bandwidth of operation

Non-Hermitian matter-wave mixing in Bose-Einstein condensates: Dissipation-induced amplification

We investigate the nonlinear scattering dynamics in interacting atomic Bose-Einstein condensates under non-Hermitian dissipative conditions. We show that, by carefully engineering a momentum-dependent atomic loss profile, one can achieve matter-wave amplification through four-wave mixing in a quasi-one-dimensional nearly-free-space setup—a process that is forbidden in the counterpart Hermitian systems due to energy mismatch. Additionally, we show that similar effects lead to rich nonlinear dynamics in higher dimensions. Finally, we propose a physical realization for selectively tailoring the momentum-dependent atomic dissipation. Our strategy is based on a two-step process: (i) exciting atoms to narrow Rydberg or metastable excited states, and (ii) introducing loss through recoil; all while leaving the bulk condensate intact due to protection by quantum interference

Supersymetric laser arrays

We introduce the concept of supersymmetric laser arrays that consists of a main optical lattice and its superpartner structure, and we investigate the onset of their lasing oscillations. Due to the coupling of the two constituent lattices, their degenerate optical modes form doublets, while the extra mode associated with unbroken supersymmetry forms a singlet state. Singlet lasing can be achieved for a wide range of design parameters either by introducing stronger loss in the partner lattice or by pumping only the main array. Our findings suggest the possibility of building single-mode, high-power laser arrays and are also important for understanding light transport dynamics in multimode Parity-Time symmetric photonic structures

Non-Hermitian engineering for brighter broadband pseudothermal light

We show that non-Hermitian engineering can play a positive role in quantum systems. This is in contrast to the widely accepted notion that optical losses are a foe that must be eliminated or, at least, minimized. We take advantage of the interplay between nonlinear interactions and loss to show that spectral-loss engineering can relax phase-matching conditions, enabling generation of broadband pseudothermal states at new frequencies. This opens the door for utilizing the full potential of semiconductor materials that exhibit giant nonlinearities but lack the necessary ingredients for achieving quasi-phase matching. This in turn may pave the way for building on-chip quantum light sources.Comment: 11 pages (6 pages main text); 4 figure

Exceptional points and lasing self-termination in photonic molecules

We investigate the rich physics of photonic molecule lasers using a non-Hermitian dimer model. We show that several interesting features, predicted recently using a rigorous steady state ab-initio laser theory (SALT), can be captured by this toy model. In particular, we demonstrate the central role played by exceptional points in both pump-selective lasing and laser self-terminations phenomena. Due to its transparent mathematical structure, our model provides a lucid understanding for how different physical parameters (optical loss, modal coupling between microcavities and pump profiles) affect the lasing action. Interestingly, our analysis also confirms that, for frequency mismatched cavities, operation in the proximity of exceptional points (without actually crossing the square root singularities) can still lead to laser self-termination. We confirm this latter prediction for two coupled slab cavities using scattering matrix analysis and SALT technique. In addition, we employ our model to investigate the pump-controlled lasing action and we show that emission patterns are governed by the locations of exceptional points in the gain parameter space. Finally we extend these results to multi-cavity photonic molecules, where we found the existence of higher-order EPs and pump-induced localization.Comment: 21 pages, 8 figure

Optomechanical interactions in non-Hermitian photonic molecules

We study optomechanical interactions in non-Hermitian photonic molecules that support two photonic states and one acoustic mode. The nonlinear steady-state solutions and their linear stability landscapes are investigated as a function of the system\u27s parameters and excitation power levels. We also examine the temporal evolution of the system and uncover different regimes of nonlinear dynamics. Our analysis reveals several important results: (1) parity-time () symmetry is not necessarily the optimum choice for maximum optomechanical interaction. (2) Stable steady-state solutions are not always reached under continuous wave optical excitations. (3) Accounting for gain saturation effects can regulate the behavior of the otherwise unbounded oscillation amplitudes. Our study provides a deeper insight into the interplay between optical non-Hermiticity and optomechanical coupling and can thus pave the way for new device applications

Symmetry in optics and photonics: a group theory approach

Group theory (GT) provides a rigorous framework for studying symmetries in various disciplines in physics ranging from quantum field theories and the standard model to fluid mechanics and chaos theory. To date, the application of such a powerful tool in optical physics remains limited. Over the past few years however, several quantum-inspired symmetry principles (such as parity-time invariance and supersymmetry) have been introduced in optics and photonics for the first time. Despite the intense activities in these new research directions, only few works utilized the power of group theory. Motivated by this status quo, here we present a brief overview of the application of GT in optics, deliberately choosing examples that illustrate the power of this tool in both continuous and discrete setups. We hope that this review will stimulate further research that exploits the full potential of GT for investigating various symmetry paradigms in optics, eventually leading to new photonic devices.Comment: 20 page, 5 figure

The dawn of non-Hermitian optics

Recent years have seen a tremendous progress in the theory and experimental implementations of non-Hermitian photonics, including all-lossy optical systems as well as parity-time symmetric systems consisting of both optical loss and gain. This progress has led to a host of new intriguing results in the physics of light–matter interactions with promising potential applications in optical sciences and engineering. In this comment, we present a brief perspective on the developments in this field and discuss possible future research directions that can benefit from the notion of non-Hermitian engineering