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The color density images (in log scale) of the intensity reflection and transmission coefficients as functions of normalized detuning δ and incident intensity I: (a) log 10 R l , (b) log 10 T l , (c) log 10 Rr and (d) log 10 Tr. The zeros of the reflection coefficients Rr and R l are shown by blue lines. For comparison, they are reproduced as thin lines in the right panels. The contour T l = 1 (Tr = 1) is shown as heavy (black) lines in panel (b) (panel (d)).
Source publication
Spectral singularities are ubiquitous with PT-symmetry leading to infinite
transmission and reflection coefficients. Such infinities imply the divergence
of the fields in the medium thereby breaking the very assumption of the
linearity of the medium used to obtain such singularities. We identify
saturable nonlinearity retaining contributions from a...
Contexts in source publication
Context 1
... now show how the gain/loss domain boundary given by S = 1 gets distorted by increasing power levels. The color density plot in Fig. 4 shows the dependence of the transmission and reflection coefficients as functions of δ and the incident intensity I. The domain boundaries for left and right incidence characterized by R l = 0 and R r = 0 are shown by blue lines in (a) and (c), respec- tively. The case T = 1 are depicted by the black heavy lines in (b) and (d) for left ...
Context 2
... this nonreciprocity can be amplified to the extent that system allows predominantly only one way transmission (optical isolation). It allows light to pass through for left incidence while it is blocked for light coming from the other side leading to the optical diode action. Another interesting feature that need be noted from the black line in Fig. 4(b) is that the same power level corresponds to three distinct values of δ (say at I = 2.2). This is a typ- ical signature of a nonlinear system and normally gets manifested in bistable or multi-stable response. In what follow we show both diode action and bistability in our system. To this goal we choose a system with L = 3L 0 , which ...
Citations
... It has been shown from these investigations that a remarkable feature of the PT-symmetric system is that the Hamiltonians possess a real eigenvalue spectrum despite the fact that they are non-Hermitian. Such nontrivial characteristics offer the potential to dramatically improve the performance of optical systems in a wide range of fields, including low-power optical isolation [36] or sensors [37,38], unidirectional invisibility [39,40], slow and fast light [41], high-sensitivity metrology Research Article [42], active control of light propagation [43], etc. Up to now, the PT-symmetric optical structures have been successfully realized in experiment via a variety of physical systems, including synthetic waveguides [44][45][46], the vapor of multilevel atoms [47], and optical or optomechanical microcavities [43,[48][49][50][51]. ...
The photon transport in a pair of parallel waveguides mediated by a parity-time- (PT-) symmetric trimer QED system is investigated. We demonstrate that the transport behaviors of the incident photons transferring between different waveguides can be actively controlled by the PT symmetry. The efficiency of such photon transport can be tuned to be much larger than 100% when the optical gain is introduced, and the transfer intensity is robust against the weak coupling among the atom, the cavity modes, their corresponding coupling mismatch, as well as the atomic dissipation. Furthermore, we demonstrate that when the system is excited by two input fields, the relative phase of the two input signals can serve as a sensitive control parameter for manipulating the photon transport, and controllable directional amplification of the incident signal photons with a fixed frequency can be realized by modulating the relative phase. The obtained results can be useful for designing phase-dependent active nonreciprocal devices, i.e., a phase-sensitive directional amplifier.
... Expressing the refractive index of the slab as = + , substituting it into Eqs. (18) and (19), and multiplying them by their complex conjugates give the reflection and transmission coefficients as follows ...
We study spectral singularities of an infinite planar slab of homogeneous optically active material in focus of a thin lens under illumination of a Gaussian beam. We describe the field distribution of the Gaussian beam under this configuration as a plane wave propagated near the optical axis which its phase and amplitude vary with distance from center of the beam. Based on this approximation, we carry out the transfer matrix for the slab. We explore the consequences of this configuration on determining the threshold gain of the active medium and tuning the resonance frequencies related to spectral singularities. We show that the spectral singularities and the threshold gain besides that vary with distance from center of the Gaussian beam, also they change with relative aperture of the focusing lens. As a result, using a thin lens with higher relative aperture, the spectral singularities corresponding resonances shift to the higher frequencies (lower wavelengths). Numerical results confirm the theoretical findings
... The threshold could be regarded as the PTsymmetric phase transition point or exceptional point (EP). At the EP, a number of novel optical phenomena were reported, such as optical isolation [9][10][11], nonlinear effect [12,13], unidirectional reflectionless (UR) [14,15], coherent perfect absorption (CPA) [16,17], loss induced transparency [18,19]. Especially, the UR and CPA were widely studied in both the PT-symmetric and non-PT-symmetric systems [20][21][22][23][24][25][26][27][28][29][30]. ...
The unidirectional reflectionless (UR) light propagation is investigated in the waveguide coupled to gain and loss resonators by using a developed coupled mode-scattering matrix theory. The results show that there is almost no reflection in the case of the backward incidence, but total reflection in the case of the forward incidence under the condition of balancing gain and loss in the gain resonator for the proposed waveguide when the indirect coupling phase θ ranges from 0.8 rad to 2.3 rad and from 4 rad to 5.5 rad. Moreover, the coherent perfect absorption (CPA) can be observed at the same time. Especially, the UR light propagation appears when the absolute value of detuning δ is smaller than 1 1013 rad s-1. Based on the findings above, we propose a metal-insulator-metal non-parity-time symmetric plasmonic waveguide and obtain the UR plasmonic propagation and CPA. The theoretical results are in excellent agreement with the finite-difference time-domain simulations. These results will provide a new pathway for the realization of unidirectional propagation and absorption of light at the nanoscale. © 2021 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft.
... In the unbroken PT -symmetric phase, there are also real eigenvalues for the Hamilton of such a non-Hermitian system [33,34]. The PT -symmetric system shows unique characteristics different from other non-Hermitian ones [35,36,37,38,39,40], such as the nonreciprocity [41,42]. It is indicated that the PT -symmetric optomechanical system can be used to achieve directional amplification of signal fields [43], in which the amplification is originated from the gain or the coupling by the blue-detuned pumping field [21,44,45,46,47,48]. ...
We explore nonreciprocal transmission behaviors in an optomechanical system, in which two dissipative cavity modes are coupled with each other and also with two parity-time-symmetric mechanical modes. Two cavities, one of which is probed by a weak field, are driven by two strong control fields, respectively. With the active-passive mechanical-resonator scheme, such a closed-loop four-mode system can show an amplification behavior of the probe field with three transmission windows based on optomechanically induced transparency (OMIT). Due to the breaking of the time-reversal symmetry corresponding to the relative phase between two control fields, the amplified nonreciprocal transmission can be realized in the middle OMIT window and its direction can be controlled via the phase modulation. In addition, the system can also show asymmetric group velocities of light propagation, i.e. the tunable asymmetric fast–slow light effects, for example, slow lights along a direction and fast lights along the other one. It is of interest that the dynamic asymmetric fast-to-slow light conversion can be realized periodically by phase modulation. Such a system of three OMIT windows, acting as the schemes of the directional amplifier and all-optical switch of the direction and velocity of light, may provide underlying applications in the photonic network and information communicating process involving multi-signal transmission.
... EPs have been found in a variety of non-Hermitian systems, such as optomechanical systems, atomic systems, laser systems, electronic circuit systems, plasmonic systems, [1][2][3][4][5][6][7] and so on. In the recent two decades, people have found that many unusual phenomena in PT-symmetric and non-PT-symmetric optical systems around EPs, [8][9][10][11][12][13] such as novel optical switching, 14) loss induced transparency, 15) power oscillation, 16) coherent perfect absorption, 17,18) nonreciprocal light propagation or nonreciprocal reflection (NR), 13,[19][20][21][22] nonlinear effects, 23,24) and so on. Particularly, NR has been widely studied in PT-symmetric and non-PT-symmetric optical systems owing to its important application in nonreciprocal optical devices. ...
We investigated optical responses in a non-PT-symmetric plasmonic resonator coupled waveguide by using developed coupled mode theory and the finite-difference time-domain simulation. A nonreciprocal reflection (NR) can be achieved by tuning the direct coupling and the dissipation, which can be used to design nonreciprocal optical devices. The results show that the direct coupling can reduce the nonreciprocal degree of reflection, and especially, greatly discrepant dissipation in the two resonators can give rise to obvious NR. Moreover, the simulation results are in good agreement with the theoretical results. These results will pave a way for realization of stable nonreciprocal devices.
... For a recent experiment on optomechanical circulators see [9]. Some of the underlying physical effects utilized in these devices include optical nonlinearity [10], magneto-optical crystal based Faraday rotation [11,12], reservoir engineering [13] and photonic Aharonov-Bohm effect [14]. ...
We study the optical transmission characteristics of coupled spinning optomechanical resonators with pump-probe driven lasers. Under the steady-state conditions, we focus on how changing the optical Sagnac effect due to same or opposite spinning directions of the resonators can give rise to non-reciprocal and delayed probe light transmission. We find that coupled resonators can exhibit distinct transmission features, can generate negative group delays (slow as well as fast light) and offer additional control of the probe light transmission as compared to the case of a single spinning resonator. Our results can be useful in achieving chiral light propagation in quantum communication technologies without using traditional magneto-optical means.
... Second and most importantly, a properly tuned -symmetric guide can have a spectral singularity, leading to blown up scattering amplitudes for both reflection and transmission. Though infinities are not encountered in realistic nonlinear systems [30,31], there is always a significant field enhancement. We show that the resonances of 'null' width of the -symmetric system can lead to dramatic enhancement of the transverse spin. ...
We study the transverse spin and the Belinfante spin momentum in a gain–loss balanced waveguide, known to be one of the first and most studied examples of PT-symmetric systems. Such a guide supports the spectral singularities leading to infinite scattering amplitudes for both reflection and transmission. We show that near the spectral singularity there can be dramatic enhancement of the transverse spin and the transverse spin momentum. Note that these exotic spin and spin momentum have recently been observed experimentally despite having tiny magnitudes, making it worthy to explore ways and means to enhance these fundamentally important elusive quantities.
... Recently, PT-symmetric arrangements with gain and loss have attracted extensive research on the field of optics [1][2][3][4]. Such systems exhibit non-Hermitian degeneracies also known as exceptional points (EPs), where both the eigenvalues and their corresponding eigenfrequencies simultaneously coalesce in parameter space [5][6][7][8]. ...
... furthermore, we substitute the ansatz ℵ א= + δℵ into the nonlinear Langevin equations (2). According to ignoring the nonlinear terms, we can get the evolution equations of the perturbation terms: ...
Recently, the conception of P T symmetry has attracted considerable attention in various fields such as optics, acoustics, and atomic physics because of the existence of exceptional point (EP) and its importance in understanding non-Hermitian physics. Here, we propose a new scheme of investigating the mechanical-EP-induced transparency and tunable fast-to-slow light phenomena in P T -symmetric mechanical systems. We find that (i) the transmission of the probe field changes from singleto double transparency windows via the transition from a broken mechanical P T -symmetric phase to an unbroken mechanical P T -symmetric phase; (ii) the efficiency of transparency can be significantly enhanced about three orders of magnitude in the vicinity of the mechanical EP, compared to passive mechanical resonators system; and (iii) the mechanical EP can not only amplify the group delay, but also manipulate the switch from slow light to fast light, which may offer an approach to achieve the practical application of slow light and relevant to the optical switcher and communication network. Our results reveal that the exotic properties of the mechanical EP can result in enormous enhancement of the transmitted probe power and novel steering of fast and slow light.
... They lead to distinct spectral degeneracies where the reflection and transmission of the system tend to infinity and have extremely narrow resonant bandwidth [15]. This interesting feature can be used for potential applications relevant to superscattering [16,17], coherent perfect absorption and lasing [18][19][20], and saturable nonlinearity [21]. Note that the majority of the previous works are focused on asymmetric nanoscale structures and the realization of EPs in symmetric plasmonic configurations has not been presented so far. ...
... The calculated normalized electric-field enhancement distribution in this case is depicted in Fig. 2(d). It is expected that the inherent nonlinear response of the gain material used in the proposed active system will eventually saturate the spectral singularity [21]. This study is outside of the scope of the current paper and will be performed in the future. ...
The intriguing physics of exceptional points (EPs) and spectral singularities in open (non-Hermitian) active photonic systems has recently sparked increased interest among the research community. These spectral degeneracies have been obtained in asymmetric active and passive photonic configurations but their demonstration with symmetric active plasmonic structures still remains elusive. In this paper, we present a nanoscale active plasmonic waveguide system consisting of an array of periodic slits that can exhibit exceptional points and spectral singularities leading to several functionalities. The proposed symmetric active system operates near its cutoff wavelength and behaves as an effective epsilon-near-zero (ENZ) medium. We demonstrate the formation of an EP that is accessed with very low gain coefficient values, a unique feature of the proposed nanoscale symmetric plasmonic configuration. Reflectionless ENZ transmission and perfect loss compensation are realized at the EP which coincides with the effective ENZ resonance wavelength of the proposed array of active plasmonic waveguides. When we further increase the gain coefficient of the dielectric material loaded in the slits, a spectral singularity occurs at the ENZ resonance leading to superscattering (lasing) response at both forward and backward directions. These interesting effects are achieved by materials characterized by very small gain coefficients with practical values and at subwavelength scales due to the strong and homogeneous field enhancement inside the active slits at the ENZ resonance leading to enhanced light-matter interaction. We theoretically analyze the obtained EP, as well as the divergent spectral singularity, using a transmission line model, and investigate the addition of a second incident wave and nonlinearities in the response of the proposed active ENZ plasmonic system. Our findings provide a route towards interesting nanophotonic applications, such as reflectionless active ENZ media, unidirectional coherent perfect absorbers, nanolasers, and strong optical bistability and all-optical switching nanodevices.
... If we substitute (26) in (7), we can relate A + (k) and B + (k) to A − (k) and B − (k). This gives (14) with the following formula for the transfer matrix of the system. ...
... We can determine its transfer matrix using (8), (26), and (27) with c = 0. This gives ...
... A brief review of the physical aspects of spectral singularities is provided in [49]. For a discussion of the spectral singularities of nonlinear Schrödinger equation and their applications in optics, see [44,26,12,9]. ...
We outline a global approach to scattering theory in one dimension that allows for the description of a large class of scattering systems and their \(\mathbb {P}\)-, \(\mathbb {T}\)-, and \(\mathbb {P}\mathbb {T}\)-symmetries. In particular, we review various relevant concepts such as Jost solutions, transfer and scattering matrices, reciprocity principle, unidirectional reflection and invisibility, and spectral singularities. We discuss in some detail the mathematical conditions that imply or forbid reciprocal transmission, reciprocal reflection, and the presence of spectral singularities and their time-reversal. We also derive generalized unitarity relations for time-reversal-invariant and \(\mathbb {P}\mathbb {T}\)-symmetric scattering systems, and explore the consequences of breaking them. The results reported here apply to the scattering systems defined by a real or complex local potential as well as those determined by energy-dependent potentials, nonlocal potentials, and general point interactions.
