Parity-time-symmetric ($\mathcal{PT}$-symmetric) optical waveguide couplers offer a great potential for future applications in integrated optics. Studies of nonlinear $\mathcal{PT}$-symmetric couplers present new possibilities for ultracompact configurable all-optical signal processing. Here, we predict nonlinearly triggered transition from a full to a broken $\mathcal{PT}$-symmetric regime in finite-size systems described by smooth permittivity profiles and, in particular, in a conventional discrete waveguide directional coupler configuration with a rectangular permittivity profile. These results suggest a practical route for experimental realization of such systems.
Parity-time-symmetric ($\mathcal{PT}$-symmetric) optical waveguide couplers have become a key component for integrated optics. They offer new possibilities for fast, ultracompact, configurable, all-optical signal processing. Here, we study nonlinear properties of finite-size multimode $\mathcal{PT}$-symmetric couplers and report a peculiar type of dispersion relation in couplers made of more than one dimer. Moreover, we predict a $\mathcal{PT}$ transition triggered by nonlinearity in these structures, and we demonstrate that with the increase of the number of dimers in the system, the transiti…
Despite the benefits that directional coupler based parity-time symmetric systems may offer to the field of integrated optics, the realization of such couplers relies on rather strict design constraints on the waveguide parameters. Here, we investigate directional couplers built of asymmetric waveguides that do not fulfill parity-time symmetry. Nevertheless, we demonstrate that for properly designed parameters, at least one mode of such couplers shows a behavior similar to the one observed in parity-symmetric systems. We find an analytical condition relating gain and loss that enables such a b…
We propose a mechanism for realization of exact control of parity-time (PT) symmetry by using a periodically modulated nonlinear optical coupler with balanced gain and loss. It is shown that for certain appropriately chosen values of the modulation parameters, we can construct a family of exact analytical solutions for the two-mode equations describing the dynamics of such nonlinear couplers. These exact solutions give explicit examples that allow us to precisely manipulate the system from nonlinearity-induced symmetry breaking to PT symmetry, thus providing an analytical approach to the all-o…
We demonstrate the existence of stable collective excitation in the form of "supersolitons" propagating through chains of solitons with alternating signs (i.e., Newton's cradles built of solitons) in nonlinear optical couplers, including the PT-symmetric version thereof. In the regular coupler, stable supersolitons are created in the cradles composed of both symmetric solitons and asymmetric ones with alternating polarities. Collisions between moving supersolitons are investigated too, by the means of direct simulations in both the regular and PT-symmetric couplers.
We introduce a stochastic ${\cal PT}$-symmetric coupler, which is based on dual-core waveguides with fluctuating parameters, such that the gain and the losses are exactly balanced in average. We consider different parametric regimes which correspond to the broken and unbroken ${\cal PT}$ symmetry, as well as to the exceptional point of the underlying deterministic system. We demonstrate that in all the cases the statistically averaged intensity of the field grows. This result holds for either linear or nonlinear coupler and is independent on the type of fluctuations.
We investigate the nonlinear parity-time (PT) symmetric coupler from a dynamical perspective. As opposed to linear PT-coupler where the PT threshold dictates the evolutionary characteristics of optical power in the two waveguides, in a nonlinear coupler, the PT threshold governs the existence of stationary points. We have found that the stability of the ground state undergoes a phase transition when the gain/loss coefficient is increased from zero to beyond the PT threshold. Moreover, we found that instabilities in initial conditions can lead to aperiodic oscillations as well as exponential gr…
We study analytically the polarization behaviour of directional couplers composed of birefringent waveguides, showing that they can induce polarization transformations that depend on the specific input-output path considered. On the basis of this study, we propose and demonstrate experimentally, by femtosecond laser writing, directional couplers that are free from this problem and also yield a polarization independent power-splitting ratio. More in detail, we devise two different approaches to realize such devices: the first one is based on local birefringence engineering, while the second one…
Controlling the balanced gain and loss in a PT-symmetric system is a rather challenging task. Utilizing Floquet theory, we explore the constructive role of periodic modulation in controlling the gain and loss of a PT-symmetric optical coupler. It is found that the gain and loss of the system can be manipulated by applying a periodic modulation. Further, such an original non-Hermitian system can even be modulated into an effective Hermitian system derived by the high-frequency Floquet method. Therefore, compared with other PT symmetry control schemes, our protocol can modulate the unbroken PT-s…
We reveal a generic connection between the effect of time-reversals and nonlinear wave dynamics in systems with parity-time (PT) symmetry, considering a symmetric optical coupler with balanced gain and loss where these effects can be readily observed experimentally. We show that for intensities below a threshold level, the amplitudes oscillate between the waveguides, and the effects of gain and loss are exactly compensated after each period due to {periodic time-reversals}. For intensities above a threshold level, nonlinearity suppresses periodic time-reversals leading to the symmetry breaking…
We consider the existence and stability of solitons in a $χ^{(2)}$ coupler. Both the fundamental and second harmonics undergo gain in one of the coupler cores and are absorbed in the other one. The gain and losses are balanced creating a parity-time (${\cal PT}$) symmetric configuration. We present two types of families of ${\cal PT}$-symmetric solitons, having equal and different profiles of the fundamental and second harmonics. It is shown that gain and losses can stabilize solitons. Interaction of stable solitons is shown. In the cascading limit the model is reduced to the ${\cal PT}$-symme…
In addition to the implementation of parity-time ($\mathcal{PT}$)-symmetric optical systems by carefully and actively controlling the gain and loss, we show that a $2\times 2$ $\mathcal{PT}$-symmetric Hamiltonian has a unitarily equivalent representation without complex optical potentials in the resulting optical coupler. Through the Naimark dilation in operator algebra, passive $\mathcal{PT}$-symmetric couplers can thus be implemented with a refractive index of real values and asymmetric coupling coefficients. This opens up the possibility to implement general $\mathcal{PT}$-symmetric systems…
We theoretically investigate the solitary waves and their switching dynamics in a $\mathcal{PT}$-symmetric directional fiber coupler, exhibiting Kerr nonlinearity, by developing a variational analysis. We analyze the fundamental switching characteristics of the $\mathcal{PT}$-symmetric Kerr coupler in the picosecond timescale by considering the coupled-mode equation for the unperturbed nonlinear Schrödinger equation, which we compare to its conventional counterpart. The impacts of higher-order perturbations (intrapulse Raman scattering, self-steepening, and third-order dispersion) are investig…
Dynamics of symmetric and antisymmetric 2-solitons and 3-solitons is studied in the model of the nonlinear dual-core coupler and its PT-symmetric version. Regions of the convergence of the injected perturbed symmetric and antisymmetric N-solitons into symmetric and asymmetric quasi-solitons are found. In the PT-symmetric system, with the balanced gain and loss acting in the two cores, borders of the stability against the blowup are identified. Notably, in all the cases the stability regions are larger for antisymmetric 2-soliton inputs than for their symmetric counterparts, on the contrary to …
We consider a dual-core nonlinear waveguide with the parity-time (PT) symmetry, realized in the form of equal gain and loss terms carried by the coupled cores. To expand a previously found stability region for solitons in this system, and explore possibilities for the development of dynamical control of the solitons, we introduce "management" in the form of periodic sinusoidal variation of the loss-gain (LG) coefficients, along with synchronous variation of the inter-core coupling (ICC) constant. This system, which can be realized in optics (in the temporal and spatial domains alike), features…
We analyze the stability of a non-Hermitian coupler with respect to modulational inhomogeneous perturbations in the presence of unbalanced gain and loss. At the parity-time (PT) symmetry point the coupler is unstable. Suitable symmetry breakings lead to an asymmetric coupler, which hosts nonlinear supermodes. A subset of those broken symmetry cases finally yields nonlinear supermodes which are stable against modulational perturbations. The lack of symmetry requirements will facilitate experimental implementations and relevant photonics applications.
We investigate the switching dynamics in a $\mathcal{PT}$-symmetric fiber coupler composed of a saturable nonlinear material as the core. In such a saturable nonlinear medium, bistable solitons may evolve due to the balance between dispersion and saturable nonlinearity, which we extend in the context of the $\mathcal{PT}$-symmetric coupler. Our investigations of power-controlled and phase-sensitive switching show richer soliton switching dynamics than the currently existing conventional counterparts, which may lead to ultrafast and efficient all-optical switching dynamics at very low power owi…
The concept of quasi-PT symmetry in optical wave guiding system is elaborated by comparing the evolution dynamics of a PT-symmetric directional coupler and a passive directional coupler. In particular we show that in the low loss regime, apart for an overall exponentially damping factor that can be compensated via a dynamical renormalization of the power flow in the system along the propagation direction, the dynamics of the passive coupler fully reproduce the one of the PT-symmetric system.
We report a detailed study on soliton steering dynamics in a parity-time-symmetric directional coupler in the femtosecond domain, which requires incorporation of higher-order perturbative effects such as third-order and fourth-order dispersions, self-steepening, and intrapulse Raman scattering. With a high gain/loss, the combination of all these effects is found to stabilize the soliton pulse evolution in the coupler from the chaotic behavior of unperturbed evolution. This work demonstrates that efficient soliton steering can be achieved at very low critical power and a relatively higher gain/…
The Zeno effect is investigated for soliton type pulses in a nonlinear directional coupler with dissipation. The effect consists in increase of the coupler transparency with increase of the dissipative losses in one of the arms. It is shown that localized dissipation can lead to switching of solitons between the arms. Power losses accompanying the switching can be fully compensated by using a combination of dissipative and active (in particular, parity-time -symmetric) segments.
We study wave propagation in linear arrays composed of pairs of conjugate waveguides with balanced gain and loss, i.e. arrays of the PT-symmetric couplers, where the linear spectrum is known to feature high-frequency and low-frequency branches. We introduce a domain wall by switching the gain and loss in a half of the array, and analyze the scattering of linear waves on this defect. The analysis reveals two major effects: amplification of both reflected and transmitted waves, and excitation of the reflected and transmitted low-frequency and high-frequency waves by the incident high-frequency a…
We consider the asymmetric active coupler (AAC) consisting of two coupled dissimilar waveguides with gain and loss. We show that under generic conditions, not restricted by parity-time symmetry, there exist finite-power, constant-intensity nonlinear supermodes (NS), resulting from the balance between gain, loss, nonlinearity, coupling and dissimilarity. The system is shown to possess nonreciprocal dynamics enabling directed power transport and optical isolation functionality.
Families of analytical solutions are found for symmetric and antisymmetric solitons in the dual-core system with the Kerr nonlinearity and PT-balanced gain and loss. The crucial issue is stability of the solitons. A stability region is obtained in an analytical form, and verified by simulations, for the PT-symmetric solitons. For the antisymmetric ones, the stability border is found in a numerical form. Moving solitons of both types collide elastically. The two soliton species merge into one in the "supersymmetric" case, with equal coefficients of the gain, loss and inter-core coupling. These …
A dual-core waveguide with balanced gain and loss in different arms and with intermodal coupling is considered. The system is not invariant under the conventional $PT$ symmetry but obeys $CPT$ symmetry where an additional spatial inversion $C$ corresponds to swapping the coupler arms. We show that second-order dispersion of coupling allows for unbroken $CPT$ symmetry and supports propagation of stable vector solitons along the coupler. Small-amplitude solitons are found in explicit form. The combined effect of gain-and-loss and dispersive coupling results in several interesting features which …
We design and optimize a waveguide structure consisted of three segments of PT-symmetric coupler. It can amplify the difference mode with the attenuation of the sum mode, so performs an asymmetric optical amplifier. Also, the dependence of the amplification factor for the difference mode and the attenuation factor for the sum mode on the gain/loss is illustrated.
We study spatial and temporal solitons in the $\mathcal{PT}$ symmetric coupler with gain in one waveguide and loss in the other. Stability properties of the high- and low-frequency solitons are found to be completely determined by a single combination of the soliton's amplitude and the gain/loss coefficient of the waveguides. The unstable perturbations of the high-frequency soliton break the symmetry between its active and lossy components which results in a blowup of the soliton or a formation of a long-lived breather state. The unstable perturbations of the low-frequency soliton separate its…
We introduce one- and two-dimensional (1D and 2D) models of parity-time ($% \mathcal{PT}$) -symmetric couplers with the mutually balanced linear gain and loss applied to the two cores, and cubic-quintic (CQ) nonlinearity acting in each one. The 2D and 1D models may be realized in dual-core optical waveguides, in the spatiotemporal and spatial domains, respectively. Stationary solutions for $\mathcal{PT}$-symmetric solitons in these systems reduce to their counterparts in the usual coupler. The most essential problem is the stability of the solitons, which become unstable against symmetry break…
We describe the process of parametric amplification in a directional coupler of quadratically nonlinear and lossy waveguides, which belong to a class of optical systems with spatial parity-time (PT) symmetry in the linear regime. We identify a distinct spectral parity-time anti-symmetry associated with optical parametric interactions, and show that pump-controlled symmetry breaking can facilitate spectrally selective mode amplification in analogy with PT lasers. We also establish a connection between breaking of spectral and spatial mode symmetries, revealing the potential to implement unconve…
We show that the parity-time (PT) symmetric coupled optical waveguides with gain and loss support localised oscillatory structures similar to the breathers of the classical $ϕ^4$ model. The power carried by the PT-breather oscillates periodically, switching back and forth between the waveguides, so that the gain and loss are compensated on the average. The breathers are found to coexist with solitons and be prevalent in the products of the soliton collisions. We demonstrate that the evolution of the small-amplitude breather's envelope is governed by a system of two coupled nonlinear Schrödinge…
Families of coupled solitons of $\mathcal{PT}$-symmetric physical models with gain and loss in fractional dimension and in settings with and without cross-interactions modulation (CIM), are reported. Profiles, powers, stability areas, and propagation dynamics of the obtained $\mathcal{PT}$-symmetric coupled solitons are investigated. By comparing the results of the models with and without CIM, we find that the stability area of the model with CIM is much broader than the one without CIM. Remarkably, oscillating $\mathcal{PT}$-symmetric coupled solitons can also exist in the model of CIM with t…
In general the ubiquitous χ^{(2)} nonlinear directional coupler, where nonlinearity and evanescent coupling are intertwined, is nonintegrable. We rigorously demonstrate that matching excitation to the even or odd fundamental supermodes yields dynamical analytical solutions for any phase matching in a symmetric coupler. We analyze second harmonic generation and optical parametric amplification regimes and study the influence of fundamental fields parity and power on the operation of the device. These fundamental solutions are useful to develop applications in classical and quantum fields such a…
We introduce a 2D network built of $\mathcal{PT}$-symmetric dimers with on-site cubic nonlinearity, the gain and loss elements of the dimers being linked by parallel square-shaped lattices. The system may be realized as a set of $\mathcal{PT}$-symmetric dual-core waveguides embedded into a photonic crystal. The system supports $\mathcal{PT}$-symmetric and antisymmetric fundamental solitons (FSs) and on-site-centered solitary vortices (OnVs). Stability of these discrete solitons is the central topic of the consideration. Their stability regions in the underlying parameter space are identified t…
We study effects of nonlocality of the cubic self-focusing nonlinearity on the stability and symmetry-breaking bifurcation (SBB) of solitons in the model of a planar dual-core optical waveg- uide with nonlocal (thermal) nonlinearity. In comparison with the well-known coupled systems with the local nonlinearity, the present setting is affected by the competition of different spatial scales, viz., the coupling length and correlation radius of the nonlocality, $\sqrt{d}$. By means of numer- ical methods and variational approximation (VA, which is relevant for small d), we find that, with the incr…
We introduce the notion of a ${\cal PT}$-symmetric dimer with a $χ^{(2)}$ nonlinearity. Similarly to the Kerr case, we argue that such a nonlinearity should be accessible in a pair of optical waveguides with quadratic nonlinearity and gain and loss, respectively. An interesting feature of the problem is that because of the two harmonics, there exist in general two distinct gain/loss parameters, different values of which are considered herein. We find a number of traits that appear to be absent in the more standard cubic case. For instance, bifurcations of nonlinear modes from the linear soluti…
Optics has proved a fertile ground for the experimental simulation of quantum mechanics. Most recently, optical realizations of $\mathcal{PT}$-symmetric quantum mechanics have been shown, both theoretically and experimentally, opening the door to international efforts aiming at the design of practical optical devices exploiting this symmetry. Here, we focus on the optical $\mathcal{PT}$-symmetric dimer, a two-waveguide coupler were the materials show symmetric effective gain and loss, and provide a review of the linear and nonlinear optical realizations from a symmetry based point of view. We …
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 …
Following the concept of $\mathcal{PT}$-symmetric couplers, we propose a linearly coupled system of nonlinear waveguides, made of positive- and negative-index materials, which carry, respectively, gain and loss. We report novel bi- and multi-stability states pertaining to transmitted and reflective intensities, which are controlled by the ratio of the gain and loss coefficients, and phase mismatch between the waveguides. These states offer transmission regimes with extremely low threshold intensities for transitions between coexisting states, and very large amplification ratio between the inpu…
Polymer based electro-optic modulators have shown great potentials in high frequency analog optical links. Existing commercial LiNibO3 Mach-Zehnder modulators have intrinsic drawbacks in linearity to provide high fidelity communication. In this paper, we present the design, fabrication and characterization of a traveling wave directional coupler modulator based on electro-optic polymer, which is able to provide high linearity, high speed, and low optical insertion loss. A silver ground electrode is used to reduce waveguide sidewall roughness due to the scattering of UV light in photolithograph…
We numerically study the nonlocal gap solitons in parity-time (PT) symmetric optical lattices built into a nonlocal self-focusing medium. We state the existence, stability, and propagation dynamics of such PT gap solitons in detail. Simulated results show that there exist stable gap soltions. The influences of the degree of nonlocality on the soliton power, the energy flow density and the stable region of the PT gap solitons are also examined.
We investigate wave transport properties of Parity-Time (PT) symmetric lattices that are periodically modulated along the direction of propagation. We demonstrate that in the regime of unbroken PT-symmetry the system Floquet-Bloch modes may interfere constructively leading to either controlled oscillations or linear power absorption and amplification occurring exactly at the phase transition point. The differential power response is effected by the overlap of the gain and loss system distribution with wave intensity pattern that is formed through Rabi oscillations engaging the coupled Floquet-…
Based on the reciprocity theorem, we put forward a generalized parametric space for an arbitrary transfer matrix with parity time (PT) symmetry. Through this space, one can extract complete information involving PT phases, reflectances, transmittance and known extraordinary scattering phenomena. We demonstrate a PT heterostructure with coherent perfect absorption-lasing, anisotropic transmission resonance, and parity symmetry of reflection coefficients at the frequencies of interest. In addition, with the parametric space and the analytical formula, the corresponding complex dielectric permitt…
We report a study on a closed-form nonlinear parity-time symmetric optical quadrimer waveguides system with a specific coupling scheme. The system yields power saturation behavior in the modes, which may be attributed to the inherent attractor in the system. A detailed analysis has been provided to confirm the attractor aspect of the system. This work also addresses a crucial issue regarding choice of initial conditions while carrying out numerical simulation for such systems.
Paraxial linear propagation of light in an optical waveguide with material gain and loss is governed by a Schrödinger equation with a complex potential. Properties of parity-time-symmetric complex potentials have been heavily studied before. In this article, new classes of non-parity-time-symmetric complex potentials featuring conjugate-pair eigenvalue symmetry in its spectrum are constructed by operator symmetry methods. Due to this eigenvalue symmetry, it is shown that the spectrum of these complex potentials is often all-real. Under parameter tuning in these potentials, phase transition can…
We introduce an optical system (a coupler) obeying parity-time ($PT$) symmetry with odd-time reversal, $T^2=-1$. It is implemented with two birefringent waveguides embedded in an anti-$PT$-symmetric medium. The system possesses properties which are untypical for most physical systems with the conventional even-time reversal. Having symmetry-protected degeneracy of the linear modes, the coupler allows for realization of a coherent switch operating with a superposition of binary states which are distinguished by their polarizations. When a Kerr nonlinearity is taken into account, each linear sta…
We carry out a modulation instability (MI) analysis in nonlinear complex parity-time (PT) symmetric periodic structures. All the three regimes defined by the PT-symmetry breaking point or threshold, namely, below threshold, at threshold and above threshold are discussed. It is found that MI exists even beyond the PT-symmetry threshold indicating the possible existence of solitons or solitary waves, in conformity with some recent reports. We find that MI does not exist at the PT-symmetry breaking point in the case of normal dispersion below a certain nonlinear threshold. However, in the case of…
We propose a parity-time symmetric dielectric-nanofilm-dielectric multilayered structure that could facilitate highly amplified transmission of optical power in the infrared spectrum. We have theoretically studied our model using the transfer matrix formalism. The reflection and the transmission coefficients of the S-matrix are evaluated. The theoretical results are validated by FDTD numerical simulation. We have shown how the thickness of the layers and the gain/loss coefficient of the active layers could generate spectral singularities in the S-matrix and how these singularities could be exp…
We theoretically investigate a nanoscale mode-division multiplexing scheme based on parity-time (PT) symmetric coaxial plasmonic waveguides. Coaxial waveguides support paired degenerate modes corresponding to distinct orbital angular momentum states. PT symmetric inclusions of gain and loss break the degeneracy of the paired modes and create new hybrid modes without orbital angular momentum. This process can be made thresholdless by matching the mode order with the number of gain and loss sections within the coaxial ring. Using both a Hamiltonian formulation and degenerate perturbation theory,…
We demonstrate single transverse-mode operation of broad-area coupled waveguide lasers enabled by parity-time (PT) symmetry. The PT symmetric laser operates on coupled waveguide cavities with electrically tuned gain and loss. Such counterintuitive waveguide design enables PT symmetric breaking, causing unique mode selection and ultimately enabling single mode operation. By electrically tuning the loss in the loss region of the coupled waveguide cavity, several different PT-symmetric regimes are analyzed theoretically, and the corresponding PT symmetric phase transition is demonstrated experime…
A class of structures based on PT PT-symmetric Bragg gratings in the presence of both gain and loss is studied. The basic concepts and properties of parity and time reversal in one-dimensional structures that possess idealised material properties are given. The impact of realistic material properties on the behaviour of these devices is then investigated. Further extension to include material non-linearity is used to study an innovative all-optical memory device.
We investigate the properties of multidimensional parity-time symmetric periodic systems whose non-Hermitian periodicity is an integer multiple of the underlying Hermitian system's periodicity. This creates a natural set of degeneracies which can undergo thresholdless $\mathcal{PT}$ transitions. We derive a $\mathbf{k} \cdot \mathbf{p}$ 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 $\mathcal{PT}$ transitions are shown to yield significant control over the band structure…
The combination of the interference with the amplification of modes in a waveguide with gain and losses can result in a giant amplification of the propagating beam, which propagates without distortion of its average amplitude. An increase of the gain-loss gradient by only a few times results in a magnification of the beam by a several orders of magnitude.
We study light-beam propagation in a nonlinear coupler with an asymmetric double-channel waveguide and derive various analytical forms of optical modes. The results show that the symmetry-preserving modes in a symmetric double-channel waveguide are deformed due to the asymmetry of the two-channel waveguide, yet such a coupler supports the symmetry-breaking modes. The dispersion relations reveal that the system with self-focusing nonlinear response supports the degenerate modes, while for self-defocusingmedium the degenerate modes do not exist. Furthermore, nonlinear manipulation is investigate…
Parity-time(PT) symmetric lattices have been widely studied in controlling the flow of waves, and recently moiré superlattices, connecting the periodic and non-periodic potentials, are introduced for exploring unconventional physical properties in physics; while the combination of both and nonlinear waves therein remains unclear. Here, we report a theoretical survey of nonlinear wave localizations in PT symmetric moiré optical lattices, with the aim of revealing localized gap modes of different types and their stabilization mechanism. We uncover the formation, properties, and dynamics of funda…
Parity-Time (PT) symmetric optical structures exhibit several unique and interesting characteristics with the most popular being exceptional points. While the emerging concept of PT-symmetry has been extensively investigated in bulky photonic designs, its exotic functionalities in nanophotonic non-Hermitian plasmonic systems still remain relatively unexplored. Towards this goal, in this work we analyze the unusual properties of a plasmonic Huygens metasurface composed of an array of active metal-dielectric core-shell nanoparticles. By calculating the reflection and transmission coefficients of…
We study electromagnetic field propagation through a planar three-waveguide coupler with linear gain and loss, in a configuration that is the optical analog of a quantum $\mathcal{PT}$-symmetric system, and provide its closed-form analytic propagator. At an specific propagation length, we show that the device provides all-optical amplitude to phase modulation with a $π$ modulation range, if an extra binary phase is allowed in the reference signal, as well as phase to amplitude modulation, with an amplitude modulation range that depends linearly on the gain-to-coupling ratio of the system.
Non-Hermitian optical systems with parity-time (PT) symmetry have recently revealed many intriguing prospects that outperform conservative structures. The prevous works are mostly rooted in complex arrangements with controlled gain-loss interplay. Here, we demonstrate anti-PT symmetry inherent in nonlinear optical interactions based upon forward optical four-wave mixing in a laser-cooled atomic ensemble with negligible linear gain and loss. We observe the pair of frequency modes undergo a nontrivial anti-PT phase transition between coherent power oscillation and optical parametric amplificatio…
