We show that a dynamic gain-loss modulation in an optical structure can lead to a direction-dependent parity-time (PT) phase transition. The phase transition can be made thresholdless in the forward direction, and yet remains with a non-zero threshold in the backward direction. As a result, non-reciprocal directional amplification can be realized.
In a non-reciprocal optical amplifier, gain depends on whether the light propagates forwards or backwards through the device. Typically, one requires either the magneto-optical effect, a temporal modulation, or an optical nonlinearity to break reciprocity. By contrast, here, we demonstrate non-reciprocal amplification of fibre-guided light using Raman gain provided by spin-polarized atoms that are coupled to the nanofibre waist of a tapered fibre section. The non-reciprocal response originates from the propagation direction-dependent local polarization of the nanofibre-guided mode in conjuncti…
We present a topological approach to the input-output relations of photonic driven-dissipative lattices acting as directional amplifiers. Our theory relies on a mapping from the optical non-Hermitian coupling matrix to an effective topological insulator Hamiltonian. This mapping is based on the singular value decomposition of non-Hermitian coupling matrices, whose inverse matrix determines the linear input-output response of the system. In topologically non-trivial regimes, the input-output response of the lattice is dominated by singular vectors with zero singular values that are the equivale…
Green's functions are fundamental quantities that determine the linear responses of physical systems. The recent developments of non-Hermitian systems, therefore, call for Green's function formulas of non-Hermitian bands. This task is complicated by the high sensitivity of energy spectrums to boundary conditions, which invalidates the straightforward generalization of Hermitian formulas. Here, based on the non-Bloch band theory, we obtain simple Green's function formulas of general one-dimensional non-Hermitian bands. Furthermore, in the large-size limit, these formulas dramatically reduce to …
Photons excited into ground state modes at finite temperature display partitioning among photon phases, lifetimes and distances travelled since creation. These distributions set the distance from an interface a created photon has some chance of emission. Excited photons at each frequency have a phase velocity set by each mode propagation index which determines mode density and internal energy contribution. All photons emitted after striking an interface obliquely are refracted. Their exit intensities are then irreversible except when weak internal attenuation occurs. At low temperature attenua…
Non-reciprocal devices, which allow the non-reciprocal signal routing, serve as the fundamental elements in photonic and microwave circuits and are crucial in both classical and quantum information processing. The radiation-pressure-induced coupling between light and mechanical motion in traveling wave resonators has been exploited to break the Lorentz reciprocity, realizing non-reciprocal devices without magnetic materials. Here, we experimentally demonstrate a reconfigurable nonreciprocal device with alternative functions of either a circulator or a directional amplifier via the optomechanic…
We provide a theoretical description of light scattering by a spherical particle whose permittivity is modulated in time at twice the frequency of the incident light. Such a particle acts as a finite-sized photonic time crystal and, despite its sub-wavelength spatial extent, can host optical parametric amplification. Conditions of parametric Mie resonances in the sphere are derived. We show that time-modulated materials provide a route to tailor directional light amplification, qualitatively different from that in scatterers made from a gain media. We design two characteristic time-modulated s…
Recent studies demonstrated the violation of reciprocity in optical processes in low-symmetry magnetic crystals. In these crystals the speed of light can be different for counter-propagating beams. Correspondingly, they can show strong directional anisotropies such as direction dependent absorption also called directional dichroism[S. Bordács et al., Nat. Phys. 8, 734 (2012); M. Saito et al., J. Phys. Soc. Jpn. 77, 013705 (2008)]. Based on symmetry considerations, we identify the magnetic point groups of materials which can host such directional anisotropies and also provide a list of possible…
The non-Hermitian skin effect (NHSE) is a phenomenon whereby certain non-Hermitian lattice Hamiltonians, particularly those with nonreciprocal couplings, can host an extensive number of eigenmodes condensed to the boundary, called skin modes. Although the NHSE has mostly been studied in the classical regime, we show that it can also manifest in quantum systems containing boson number nonconserving processes arising from uniform parametric driving. We study lattices of coupled nonlinear resonators that can function as reciprocal quantum amplifiers. A one-dimensional chain exhibiting NHSE can pe…
We describe the use of fiber Brillouin amplification (FBA) for the coherent transmission of optical frequencies over a 480 km long optical fiber link. FBA uses the transmission fiber itself for efficient, bi-directional coherent amplification of weak signals with pump powers around 30 mW. In a test setup we measured the gain and the achievable signal-to-noise ratio (SNR) of FBA and compared it to that of the widely used uni-directional Erbium doped fiber amplifiers (EDFA) and to our recently built bi-directional EDFA. We measured also the phase noise introduced by the FBA and used a new and si…
Non-reciprocal devices, which have different transmission coefficients for propagating waves in opposite directions, are crucial components in many low noise quantum measurements. In most schemes, magneto-optical effects provide the necessary non-reciprocity. In contrast, the proof-of-principle device presented here, consists of two on-chip coupled Josephson parametric converters (JPCs), which achieves directionality by exploiting the non-reciprocal phase response of the JPC in the trans-gain mode. The non-reciprocity of the device is controlled in-situ by varying the amplitude and phase diffe…
Amplification/attenuation of light waves in artificial materials with a gain/loss modulation on the wavelength scale can be sensitive to the propagation direction. We give a numerical proof of the high anisotropy of the gain/loss in two dimensional periodic structures with square and rhombic lattice symmetry by solving the full set of Maxwell's equations using the finite difference time domain method. Anisotropy of amplification/attenuation leads to the narrowing of the angular spectrum of propagating radiation with wavevectors close to the edges of the first Brillouin Zone. The effect provide…
Improving and controlling the efficiency of a gain medium is one of the most challenging problems of laser research. By measuring the gain length in an opal based photonic crystal doped with laser dye, we demonstrate that optical amplification is more than twenty-fold enhanced along the Gamma-K symmetry directions of the face centered cubic photonic crystal. These results are theoretically explained by directional variations of the density of states, providing a quantitative connection between density of the states and light amplification.
Non-reciprocal components are essential in photonic systems for protecting light sources and for signal routing functions. Acousto-optic methods to produce non-reciprocal devices offer a foundry-compatible alternative to magneto-optic solutions and are especially important for photonic integration. In this paper, we experimentally demonstrate a dynamically reconfigurable non-reciprocal acousto-optic modulator at telecom wavelength. The modulator can be arranged in a multitude of reciprocal and non-reciprocal configurations by means of an external RF input. The dynamic reconfigurability of the …
Engineering phonon transport in physical systems is a subject of interest in the study of materials and plays a crucial role in controlling energy and heat transfer. Of particular interest are non-reciprocal phononic systems, which in direct analogy to electric diodes, provide a directional flow of energy. Here, we propose an engineered nanostructured material, in which tunable non-reciprocal phonon transport is achieved through optomechanical coupling. Our scheme relies on breaking time-reversal symmetry by a spatially varying laser drive, which manipulates low-energy acoustic phonons. Furthe…
Non-reciprocal devices, such as circulators and isolators, are indispensable components in classical and quantum information processing in an integrated photonic circuit. Aside from those applications, the non-reciprocal phase shift is of fundamental interest for exploring exotic topological photonics, such as the realization of chiral edge states and topological protection. However, incorporating low optical-loss magnetic materials into a photonic chip is technically challenging. In this study, we experimentally demonstrate non-magnetic non-reciprocity using optomechanical interactions in a w…
We propose a mechanism to achieve the group velocity control of bifurcation light via an imaginary coupling effect in the non-reciprocal lattice. The physical model is composed of two-layer photonic lattices with non-reciprocal coupling in each unit cell, which can support a real energy spectrum with a pair of Dirac points in the first Brillouin zone due to the Hermicity. Furthermore, we show that the systems experience topological phase transition at the Dirac points by tuning the coupling strength, allowing the existence of topological edge states on the left or right boundaries of respectiv…
An optical signal that propagates along a conventional waveguide is back reflected at waveguide terminations. If the waveguide permits only one-way propagation, this back reflection cannot take place; the optical signal undergoes a nearly 100% conversion to radiation modes. Hence, a terminated one-way waveguide may serve as a matched nano-antenna with a natural guiding and feeding mechanism. We examine the termination effect in a recently suggested nano-scale one-way plasmonic waveguide, and its properties as a matched nano antenna are shown. Since one-way structures are inherently non-recipro…
Breaking the symmetry between forward and backward propagating optical modes is of fundamental scientific interest and enables crucial functionalities, such as isolators, circulators, and duplex communication systems. Whereas there has been progress in achieving optical isolation on-chip, integrated broadband non-reciprocal signal processing functionalities that enable transmitting and receiving via the same low-loss planar waveguide, without altering the frequency or mode of the signal, remain elusive. Here, we demonstrate a non-reciprocal delay scheme based on the uni-directional transfer of…
The transportation of photons and phonons typically obeys the principle of reciprocity. Breaking reciprocity of these bosonic excitations will enable the corresponding non-reciprocal devices, such as isolators and circulators. Here, we use two optical modes and two mechanical modes in a microresonator to form a four-mode plaquette via radiation pressure force. The phase-controlled non-reciprocal routing between any two modes with completely different frequencies is demonstrated, including the routing of phonon to phonon (MHz to MHz), photon to phonon (THz to MHz), and especially photon to phot…
We describe the application of Raman Optical-fiber Amplification (ROA) for the phase coherent transfer of optical frequencies in an optical fiber link. ROA uses the transmission fiber itself as a gain medium for bi-directional coherent amplification. In a test setup we evaluated the ROA in terms of on-off gain, signal-to-noise ratio, and phase noise added to the carrier. We transferred a laser frequency in a 200 km optical fiber link with an additional 16 dB fixed attenuator (equivalent to 275 km of fiber on a single span), and evaluated both co-propagating and counter-propagating amplificatio…
We produce transmission and reflection spectra of the anti-directional coupler (ADC) composed of linearly-coupled positive- and negative-refractive-index arms, with intrinsic Kerr nonlinearity. Both reflection and transmission feature two highly amplified peaks at two distinct wavelengths in a certain range of values of the gain, making it possible to design a wavelength-selective mode-amplification system. We also predict that a blend of gain and loss in suitable proportions can robustly enhance reflection spectra which are detrimentally affected by the attenuation, in addition to causing red…
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…
In this study, we propose the application of non-Hermitian photonic crystals (PCs) with anisotropic emissions. Unlike a ring of exceptional points (EPs) in isotropic non-Hermitian PCs, the EPs of anisotropic non-Hermitian PCs appear as lines symmetrical about the $Γ$ point. The non-Hermitian Hamiltonian indicates that the formation of EPs is related to the non-Hermitian strength. The real spectrum appears in the $Γ$Y direction and has been validated as the complex conjugate medium (CCM) by effective medium theory (EMT). But for the $Γ$X direction, EMT indicates that the effective refractive in…
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…
Space-time modulation induced non-reciprocity in EM metasurfaces is proposed and numerically demonstrated using rigorous Generalized Sheet Transitions Conditions (GSTCs) under oblique plane-wave incidence. It is phenomenologically shown that the space-time modulation of surface susceptibilities create an inherent asymmetry with respect to the directional perturbation on the metasurface and the transverse wave momentum of the input wave, between forward and backward propagations, resulting in non-reciprocal wave transmission. Exploiting the periodicity of the surface susceptibilities in both ti…
Static metasurfaces have shown to be prominent compact structures for reciprocal and frequency-invariant transformation of electromagnetic waves in space. However, incorporating temporal variation to static metasurfaces would result in dynamic apparatuses which are capable of four-dimensional tailoring of both the spatial and temporal characteristics of electromagnetic waves, leading to functionalities that are far beyond the capabilities of conventional static metasurfaces. This includes nonreciprocal full-duplex wave transmission, pure frequency conversion, parametric wave amplification, spa…
We introduce a class of non-Hermitian systems that break electromagnetic reciprocity while preserving time-reversal symmetry, and describe its novel polarization dynamics. We show that this class of systems can be realized using van der Waals heterostructures involving transition-metal dichalcogenides (TMDs). Our work provides a path towards achieving strong optical nonreciprocity and polarization-dependent directional amplification using compact, large-area and magnet-free structures.
Space-time modulated metamaterials support extraordinary rich applications, such as parametric amplification, frequency conversion and non-reciprocal transmission. However, experimental realization of space-time modulation is highly non-trivial, hindering many interesting physics that are theoretically predicted to be experimentally demonstrated. Here, based on the proposed virtualized metamaterials with software-defined impulse response, we experimentally realize non-Hermitian space-time varying metamaterials for efficient and asymmetric frequency conversion by allowing material gain and loss…
