One-dimensional lattices with chiral symmetry are known to possess quantized Zak phase and nontrivial topological phases. Here it is shown that quantized Zak phase and nontrivial edge states, partially protected by inversion symmetry rather than chiral symmetry, can be observed and probed in the bulk exploiting continuous-time photonic quantum walk in zig-zag waveguide arrays. Averaged beam displacement measurements can detect quantized Zak phase and non-trivial topological phases in the extended Su-Schrieffer-Heeger model with broken chiral symmetry.
We experimentally investigate the decoherence of single surface plasmon polaritons in metal stripe waveguides. In our study we use a Mach-Zehnder configuration previously considered for measuring decoherence in atomic, electronic and photonic systems. By placing waveguides of different length in one arm we are able to measure the amplitude damping time T_1 = 1.90 +/- 0.01 x 10^-14 s, pure phase damping time T_2^* = 11.19 +/- 4.89 x 10^-14 s and total phase damping time T_2 = 2.83 +/- 0.32 x 10^-14 s. We find that decoherence is mainly due to amplitude damping and thus loss arising from inelast…
One-dimensional superlattices with modulated coupling constants show rich topological properties and tunable edge states. Beyond the dimeric case, probing the topological properties of superlattices is a challenge. Here we suggest a rather general method of bulk probing topological invariants in waveguide superlattices based on spatial displacement of discretized beams. A judiciously tailored initial beam excitation of the lattice, corresponding to superposition of Wannier functions, provides a direct measure of the band gap topological numbers. For a quadrimeric superlattice, a simple bulk pr…
We study theoretically two vibrating quantum emitters trapped near a one-dimensional waveguide and interacting with propagating photons. We demonstrate, that in the regime of strong optomechanical interaction the light-induced coupling of emitter vibrations can lead to formation of spatially localized vibration modes, exhibiting parity-time (PT ) symmetry breaking. These localized vibrations can be interpreted as topological defects in the quasiclassical energy spectrum.
On-chip chiral quantum light-matter interfaces, which support directional interactions, provide a promising platform for efficient spin-photon coupling, non-reciprocal photonic elements, and quantum logic architectures. We present full-wave three-dimensional calculations to quantify the performance of conventional and topological photonic crystal waveguides as chiral emitter-photon interfaces. Specifically, the ability of these structures to support and enhance directional interactions while suppressing subsequent backscattering losses is quantified. Broken symmetry waveguides, such as the non…
We experimentally investigate the suitability of a multi-path waveguide interferometer with mechanical shutters for performing a test for hypercomplex quantum mechanics. Probing the interferometer with coherent light we systematically analyse the influence of experimental imperfections that could lead to a false-positive test result. In particular, we analyse the effects of detector nonlinearity, input-power and phase fluctuations on different timescales, closed-state transmissivity of shutters and crosstalk between different interferometer paths. In our experiment, a seemingly small shutter t…
We propose two non-Hermitian arrays consisting of $N=2l+1$ waveguides and exhibiting parity-time ($\mathcal{PT}$) or anti-$\mathcal{PT}$ symmetry for investigating light transfer dynamics based on $N$th-order exceptional points (EPs). The $\mathcal{PT}$-symmetric array supports two $N$th-order EPs separating an unbroken and a broken phase with real and imaginary eignvalues, respectively. Light transfer dynamics in this array exhibits radically different behaviors, i.e. a unidirectional oscillation behavior in the unbroken phase, an edge-towards localization behavior in the broken phase, and a …
The photonic local density of states (PLDOS) determines the light matter interaction strength in nanophotonic devices. For standard dielectric devices, the PLDOS is fundamentally limited by diffraction, but its precise dependence on the size parameter $s$ of a device can be non-trivial. Here, we measure the PLDOS dependence on the size parameter in a waveguide using a new technique - nanowaveguide coupled cathode luminescence (CL). We observe that depending on the position within the waveguide cross-section, the effective diffraction limit of the PLDOS varies, and the PLDOS peak shape changes.…
We consider a periodic waveguide array whose unit cell consists of a $\mathcal{PT}$-symmetric quadrimer with two competing loss/gain parameter pairs which lead to qualitatively different symmetry-broken phases. It is shown that the transitions between the phases are described by a symmetry-adapted nonlocal current which maps the spectral properties to the spatially resolved field, for the lattice as well as for the isolated quadrimer. Its site-average acts like a natural order parameter for the general class of one-dimensional $\mathcal{PT}$-symmetric Hamiltonians, vanishing in the unbroken ph…
We study the transport of a single photon in two coupled one-dimensional semi-infinite coupled-resonator waveguides (CRWs), in which both end sides are coupled to a dissipative cavity. We demonstrate that a single photon can transfer from one semi-infinite CRW to the other nonreciprocally. Based on such nonreciprocity, we further construct a three-port single-photon circulator by a T-shaped waveguide, in which three semi-infinite CRWs are pairwise mutually coupled to each other. The single-photon nonreciprocal transport is induced by the breaking of the time-reversal symmetry and the optimal c…
On-chip optical waveguides with low propagation losses and precisely engineered group velocity dispersion (GVD) are important to nonlinear photonic devices such as soliton microcombs. Yet, despite intensive research efforts, nonlinear integrated photonic platforms still feature propagation losses orders of magnitude higher than in standard optical fiber. The tight confinement and high index contrast of integrated waveguides make them highly susceptible to fabrication induced surface roughness. Therefore, microresonators with ultra-high Q factors are, to date, only attainable in polished bulk c…
We study a photonic analog of a modified Fano-Anderson model -- a waveguide array with two additional waveguides and by using the coupled mode theory we calculate its spectral and scattering properties. We classify eigenomodes according to vertical symmetry of the structure given by self-coupling coefficients of the additional waveguides and establish the conditions for BIC existence. We use the Weierstrass factorization theorem and interpret the scattering spectra of the systems with broken symmetry in terms of the eigenmodes. The Fano resonance related with excitation of quasi-BIC is explain…
Dynamically encircling an exceptional point (EP) in parity-time (PT) symmetric systems shows an interesting chiral dynamics, leading to asymmetric mode switching in which the output modes are different when the encircling direction is reversed. Here we show that the dynamical encircling of an EP in anti-PT-symmetric systems can also result in chiral dynamics if the starting/end point lies in the PT-broken phase, in contrast to PT-symmetric systems where chiral dynamics emerges if the starting/end point lies in the PT-unbroken phase. For many applications, such as signal processing using wavegu…
Selective on-chip optical filters with high rejection levels are key components for a wide range of advanced photonic circuits. However, maximum achievable rejection in state-of-the-art on-chip devices is seriously limited by phase errors arising from fabrication imperfections. Due to coherent interactions, unwanted phase-shifts result in detrimental destructive interferences that distort the filter response, whatever the chosen strategy (resonators, interferometers, Bragg filters, etc.). Here we propose and experimentally demonstrate a radically different approach to overcome this fundamental…
We propose a scheme comprising an array of anisotropic optical waveguides, embedded in a gas of cold atoms, which can be tuned from a Hermitian to an odd-PT -- symmetric configuration through the manipulation of control and assistant laser fields. We show that the system can be controlled by tuning intra -- and inter-cell coupling coefficients, enabling the creation of topologically distinct phases and linear topological edge states. The waveguide array, characterized by a quadrimer primitive cell, allows for implementing transitions between Hermitian and odd-PT -symmetric configurations, brok…
Parity-time (PT) symmetry and broken in micro/nano photonic structures have been investigated extensively as they bring new opportunities to control the flow of light based on non-Hermitian optics. Previous studies have focused on the situations of PT-symmetry broken in loss-loss or gain-loss coupling systems. Here, we theoretically predict the gain-gain and gain-lossless PT-broken from phase diagram, where the boundaries between PT-symmetry and PT-broken can be clearly defined in the full-parameter space including gain, lossless and loss. For specific micro/nano photonic structures, such as c…
We address dissipative soliton formation in modulated PT-symmetric continuous waveguide arrays composed from waveguides with amplifying and absorbing sections, whose density gradually increases (due to decreasing waveguide separation) either towards the center of the array or towards its edges. In such a structure the level of gain/loss at which PT-symmetry gets broken depends on the direction of increase of the waveguide density. Breakup of the PT-symmetry occurs when eigenvalues of modes localized in the region, where waveguide density is largest, collide and move into complex plane. In this…
We investigate the influence of non-Hermiticity on the adiabatic elimination in coupled waveguides. We show that adiabatic elimination is not affected when the system is in parity-time symmetric phase. However, in the broken phase the eliminated waveguide loses its darkness namely its amplitude starts increasing, which means adiabatic elimination does not hold in the broken phase. Our results can advance the control of the dynamics in coupled laser cavities, and help the design of controllable absorbers.
One-way edge states at the surface of photonic topological insulators are of significant interest for communications, nonlinear and quantum optics. Moreover, when reciprocity is broken in a photonic topological insulator, these states provide protection against disorder, which is of particular importance for slow light applications. Achieving such a one-way edge state, however, requires the construction of a two-dimensional structure. Here, we show how unidiriectional Floquet bands can arise in purely one-dimensional, adiabatically-modulated dynamic systems, in contrasts with the higher dimens…
We theoretically and numerically investigate the scattering behavior of a periodic parity-time (PT)-symmetric waveguide network composed of a finite number of unit cells. Specifically, we put forward rigorous and formally exact expressions for wave propagation, bi-directional reflectionless, and coherent perfect absorption and lasing (CPAL) occuring in a finite periodic optical waveguide network. Through the use of the generalized parametric space derived from observation of PT-symmetric transfer matrix, Lorentz reciprocity theorem and non-imaginary Bloch phase, we observe that when the unit c…
The paper addresses the bistability caused by spontaneous symmetry breaking bifurcation in a one-dimensional periodically corrugated nonlinear waveguide pumped by coherent light at normal incidence. The formation and the stability of the switching waves connecting the states of different symmetries are studied numerically. It is shown that the switching waves can form stable resting and moving bound states (dissipative solitons). The protocols of the creation of discussed nonlinear localized waves are suggested and verified by numerical simulations.
Manipulating the global $PT$ symmetry of a non-Hermitian composite system is a rather significative and challenging task. Here, we investigate Floquet control of global $PT$ symmetry in 2D arrays of quadrimer waveguides with transverse periodic structure along $x$-axis and longitudinal periodic modulation along $z$-axis. For unmodulated case with inhomogeneous inter- and intra- quadrimer coupling strength $κ_1\neqκ$, in addition to conventional global $PT$-symmetric phase and $PT$-symmetry-breaking phase, we find that there is exotic phase where global $PT$ symmetry is broken under open bounda…
The existence of a frozen mode in a periodic serpentine waveguide with broken longitudinal symmetry is demonstrated numerically. The frozen mode is associated with a stationary inflection point (SIP) of the Bloch dispersion relation, where three Bloch eigenmodes collapse on each other, as it is an exceptional point of order three. The frozen mode regime is characterized by vanishing group velocity and enhanced field amplitude, which can be very attractive in various applications including dispersion engineering, lasers, and delay lines. Useful and simple design equations that lead to realizati…
The demand for nonlinear effects within a silicon platform to support photonic circuits requiring phase-only modulation, frequency doubling, and/or difference frequency generation, is becoming increasingly clear. However, the symmetry of the silicon crystal inhibits second order optical nonlinear susceptibility, $χ^{(2)}$. Here, we show that the crystalline symmetry is broken when a DC field is present, inducing a $χ^{(2)}$ in a silicon waveguide that is proportional to the large $χ^{(3)}$ of silicon. First, Mach-Zehnder interferometers using the DC Kerr effect optical phase shifters in silico…
Topological matter and topological optics have been studied in many systems, with promising applications in materials science and photonics technology. These advances motivate the study of the interaction between topological matter and light, as well as topological protection in light-matter interactions. In this work, we study a waveguide-interfaced topological atom array. The light-matter interaction is nontrivially modified by topology, yielding novel optical phenomena. We find topology-enhanced photon absorption from the waveguide for large Purcell factor, i.e., $Γ/Γ_0\gg 1$, where $Γ$ and…
Parity-time (PT) symmetry in non-Hermitian optical systems promises distinct optical effects and applications not found in conservative optics. Its counterpart, anti-PT symmetry, subscribes another class of intriguing optical phenomena and implies complementary techniques for exotic light manipulation. Despite exciting progress, so far anti-PT symmetry has only been realized in bulky systems or with optical gain. Here, we report an on-chip realization of non-Hermitian optics with anti-PT symmetry, by using a fully-passive, nanophotonic platform consisting of three evanescently coupled waveguid…
High-harmonic generation (HHG) provides short-wavelength light that is useful for precision spectroscopy and probing ultrafast dynamics. We report efficient, phase-coherent harmonic generation up to 9th-order (333 nm) in chirped periodically poled lithium niobate waveguides driven by phase-stable $\leq$12-nJ, 100 fs pulses at 3 $μ$m with 100 MHz repetition rate. A mid-infrared to ultraviolet-visible conversion efficiency as high as 10% is observed, amongst an overall 23% conversion of the fundamental to all harmonics. We verify the coherence of the harmonic frequency combs despite the complex …
We present a transmission line theory of exceptional points of degeneracy (EPD) in coupled-mode guiding structures, i.e., a theory that illustrates the characteristics of coupled electromagnetic modes under a special dispersion degeneracy condition, yet unexplored in the contest of gain and loss. We demonstrate the concept of Parity-Time ($\cal{PT}$)-symmetry in coupled uniform waveguides with balanced and symmetric gain and loss and how this condition is associated with a second order EPD. We show that by introducing gain into naturally lossy structures provides for the conditions whereby exc…
Waveguide arrays offer enormous potential to design circuit elements essential to fabricate optical devices capable to processing information codified by light. In this work we study the existence and stability of localized beams in one dimensional photonic lattices composed by a Kerr type waveguide array. We analyzed the case where discrete translation symmetry is broken in as much as one of the waveguides lacks a nonlinear response. Specifically, we determined the space of parameters where a coherent and robust mobility across the lattice is achieved. Moreover, we calculate the reflection an…
Thermo-optic microheater is indispensable in silicon photonic devices for smart and reconfigurable photonic networks. Much efforts have been made to improve the metallic microheater performance in the past decades. However, because of the metallic nature of light absorption, placing the metallic microheater very close to the waveguide for fast response is impractical and has not been done experimentally. Here, we experimentally demonstrate a metallic microheater placed very close to the waveguide based on parity-time (PT) symmetry breaking. The intrinsic high loss of metallic heater ensures th…
Waveguiding structures made of anisotropic media support bound states in the continuum (BICs) that arise when the radiation channel of otherwise semi-leaky modes is suppressed. Hitherto, only structures with optical axes aligned in symmetric orientations inside the waveguide plane, where BICs appear as lines in the momentum-frequency dispersion diagram, have been considered. Here we address settings where such symmetry is broken and unveil a number of fundamental new features. Weak and strong symmetry-breaking regimes are identified, corresponding to azimuthal and polar optical axes orientatio…
Cholesky factorization provides photonic lattices that are the isospectral partners or the square root of other arrays of coupled waveguides. The procedure is similar to that used in supersymmetric quantum mechanics. However, Cholesky decomposition requires initial positive definite mode coupling matrices and the resulting supersymmetry is always broken. That is, the isospectral partner has the same range than the initial mode coupling matrix. It is possible to force a decomposition where the range of the partner is reduced but the characteristic supersymmetric intertwining is lost. As an exam…
Topological photonics, featured by stable topological edge states resistant to perturbations, has been utilized to design robust integrated devices. Here, we present a study exploring the intriguing topological rotated Weyl physics in a 3D parameter space based on quaternary waveguide arrays on lithium niobate-on-insulator (LNOI) chips. Unlike previous works that focus on the Fermi arc surface states of a single Weyl structure, we can experimentally construct arbitrary interfaces between two Weyl structures whose orientations can be freely rotated in the synthetic parameter space. This intrigu…
We address a two-dimensional parity-time (PT)-symmetric structure built as a chain of waveguides, where all waveguides except for the central one are conservative, while the central one is divided into two halves with gain and losses. We show that such a system admits bound states in the continuum (BICs) whose properties vary drastically with the orientation of the line separating amplifying and absorbing domains, which sets the direction of internal energy flow. When the flow is perpendicular to the chain of the waveguides, narrow BICs emerge when the standard defect mode, which is initially …
