Parity-time Symmetric Waveguide Research Articles

Directional coupling with parity-time symmetric Bragg gratings.

Parity-time symmetric Bragg gratings produce unidirectional reflection around the exceptional point. We propose and explore directional coupling of gain and loss modulated waveguide Bragg gratings operating at around 880 nm with long-range surface plasmon polaritons. Step-in-width modulation of a Ag stripe supporting long-range plasmons combined with a periodic modulation of the cladding were used to balance the real and imaginary index perturbation of the gratings. IR140 dye molecules in solvent forms a portion of the uppercladding, providing gain under optical pumping. We investigate directional coupling between a pair of parity-time symmetric waveguide Bragg gratings operating near their exceptional point, arranged in various configurations - duplicate, duplicate-shifted and duplicate-flipped. We also investigate coupling to a bus waveguide and to a conventional waveguide Bragg grating. Unidirectional multi-wavelength reflection and coupled supermode conversion are predicted.

Propagation of dark solitons in parity-time symmetric waveguides

We study the propagation of dark solitons in the Kerr nonlinearity and parity-time (PT)-symmetric waveguides with Gaussian distribution. Fundamental characters of the dark solitons during the transportation are carefully checked in different parameter regions by the split-time-step Crank–Nicolson method. The results show that the dark solitons are bound to the center of the PT-symmetric waveguide when the central refractive index of the PT-symmetric potential is strong, and the dark soliton tends to deflect toward the gain region due to the gain/loss effect of PT-symmetric waveguide. We also find that when the dark soliton is introduced from the gain region of the PT-symmetric potential, the low-speed dark soliton is reflected by the gain region, and the high-speed dark soliton is bound to the center of the PT-symmetric potential in the corresponding parameter interval.

高斯型PT对称波导中高斯光波的控制

高斯型PT对称波导中高斯光波的控制

The broken condition and regulation of a non-conjugated PT symmetric waveguide system

In this paper, a modified method to analyze and regulate the broken condition of a general parity-time symmetric waveguide system with non-conjugated refractive index profile ( nr1-jni1 and nr2+jni2) is proposed. The broken condition can be regulated by altering the width of waveguide. For the general PT symmetric waveguide system, this method provides a simple design to reduce the requirement of gain medium. This finally makes it easier to design a waveguide system on the basis of a now available material and to achieve broken condition. The analysis of a non-conjugate refractive index double channel waveguides is carried out as an example, and the calculation error is less than 4% compared with the result of FDTD simulation.

Light Stops at Exceptional Points.

Almost twenty years ago, light was slowed down to less than 10^{-7} of its vacuum speed in a cloud of ultracold atoms of sodium. Upon a sudden turn-off of the coupling laser, a slow light pulse can be imprinted on cold atoms such that it can be read out and converted into a photon again. In this process, the light is stopped by absorbing it and storing its shape within the atomic ensemble. Alternatively, the light can be stopped at the band edge in photonic-crystal waveguides, where the group speed vanishes. Here, we extend the phenomenon of stopped light to the new field of parity-time (PT) symmetric systems. We show that zero group speed in PT symmetric optical waveguides can be achieved if the system is prepared at an exceptional point, where two optical modes coalesce. This effect can be tuned for optical pulses in a wide range of frequencies and bandwidths, as we demonstrate in a system of coupled waveguides with gain and loss.

Discrete dark solitons in parity–time-symmetric waveguide arrays with gain and loss

We demonstrate that discrete dark solitons can be self-trapped in binary self-defocusing parity–time-symmetric waveguide arrays with gain and loss. The discrete dark solitons appear in the form of a localized dip on the Bloch-wave background. When the appropriate boundary condition is satisfied in such finite arrays, the analytical and numerical solutions of discrete dark solitons exist and can both be stable in the one-dimensional case; the stable fundamental discrete vortex solitons can be numerically gained in the two-dimensional case. Interestingly, such one-dimensional discrete dark solitons do not exhibit displacement properties.

Electrical tunability due to coalescence of exceptional points in parity-time symmetric waveguides.

We demonstrate theoretically the electric tunability due to the coalescence of exceptional points in PT-symmetric waveguides bounded by imperfect conductive layers. Owing to the competition effect of multimode interaction, multiple exceptional points and PT phase transitions could be attained in such a simple system, and their occurrences are strongly dependent on the boundary conductive layers. When the conductive layers become very thin, it is found that the oblique transmittance and reflectance of the same system can be tuned between zero and one by a small change in the carrier density. The results may provide an effective method for fast tuning and modulation of optical signals through electrical gating.

Towards nanoscale multiplexing with parity-time-symmetric plasmonic coaxial waveguides

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 show how the wavevectors and fields evolve with increased loss/gain and derive sufficient conditions for thresholdless transitions. As a multiplexing filter, this PT symmetric coaxial waveguide could help double density rates in on-chip nanophotonic networks.

General coupled mode theory in non-Hermitian waveguides.

In the presence of loss and gain, the coupled mode equation on describing the mode hybridization of various waveguides or cavities, or cavities coupled to waveguides becomes intrinsically non-Hermitian. In such non-Hermitian waveguides, the standard coupled mode theory fails. We generalize the coupled mode theory with a properly defined inner product based on reaction conservation. We apply our theory to the non-Hermitian parity-time symmetric waveguides, and obtain excellent agreement with results obtained by finite element fullwave simulations. The theory presented here is typically formulated in space to study coupling between waveguides, which can be transformed into time domain by proper reformulation to study coupling between non-Hermitian resonators. Our theory has the strength of studying non-Hermitian optical systems with inclusion of the full vector fields, thus is useful to study and design non-Hermitian devices that support asymmetric and even nonreciprocal light propagations.

Transmission and control of bright solitons in parity-time symmetric waveguide

Based on the theoretical model of optical wave propagation in parity-time (PT) symmetric waveguide, the transmission and control of bright solitons in PT symmetric Kerr nonlinear planar waveguide with Gaussian distribution are studied numerically. The PT symmetric waveguide requires that the refractive index distribution of waveguide should have to be an even symmetry, whereas the gain/loss distribution should be odd. The results show that when the strength of refractive index distribution of waveguide is positive, the refractive index has a maximum value in the center of the PT symmetric waveguide. Without the self-focusing Kerr nonlinear effect, the waveguide can also restrict optical wave to form the wavy light beam and transmit with long distance. When the strength of refractive index distribution is negative, the refractive index has a minimum value in the center of the PT symmetric waveguide. The transmission direction of optical wave is shifted. The gain/loss distribution can control the transmission direction of optical wave: if the strength of gain/loss distribution is positive, the optical wave is shifted toward the left; if the strength is negative, the optical wave is shifted toward the right; if the strength equals zero, the optical wave is divided into two beams. And when the refractive index distribution is negative, the interaction between adjacent bright solitons can be suppressed very well. The results of this research can provide a theoretical basis for the application of PT symmetric waveguide in all-optical control in the future.

Asymmetric Evolution of Interacting Solitons in Parity Time Symmetric Cells

We show the evolution of two fundamental bright solitons after being simultaneously launched into nonlinear triangular parity time (PT) symmetric waveguides, at mirrored transverse input positions. Numerical simulations show, whether below or above the phase transition, in general the retarded soliton propagating along the gain side and the advanced soliton evolving along the loss side of either waveguide interfere incoherently, within the interacting regime. In non-interacting regime, however, each soliton evolves as it has been launched individually. When beyond the phase transition, the unstable solitons become self-trapped after traversing relatively short distances. The incoherent interference alters the projectile of each soliton from that of the one launched individually at the same initial input position. The temporal dynamics of interacting solitons along PT symmetric waveguide, due to the interplay of nonlinearity and the active elements, are not periodic. This is in contrast to the interaction dynamics along the purely index guided cell. The results suggest that appropriately designed nonlinear PT symmetric waveguides, below or above the phase transition, can play the role of key elements in design and fabrication of optical gates, isolators, and switches.

Giant amplification of modes in parity-time symmetric waveguides

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.