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Register a new user$N$-channel comb filtering and lasing in $mathcal{PT}$-symmetric superstructures
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Added by
Arjunan Govindarajan
Publication date
2020
fields
Physics
and research's language is
English
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A comb spectrum generating device based on Bragg grating superstructures with gain and loss is suggested in this paper. It includes a comprehensive analysis of the device formulation, generation and manipulation of the comb spectrum with a number of degrees of freedom such as duty cycle, sampling period and gain-loss parameter. For applications such as RF traversal filters and tunable multi-wavelength laser sources, the reflected intensities of the comb resulting from the superstructures should have uniform intensities, and this is guaranteed by optimizing the physical length of the device, gain and loss in the unbroken $mathcal{PT}$-symmetric regime. Alternatively, it can be accomplished by reducing the duty cycle ratio of the superstructure to extremely small values in the broken $mathcal{PT}$-symmetric regime. Such a customization will degrade the reflectivity of the conventional grating superstructures, while it gives rise to narrow spectral lines with high reflectivity in the proposed system. Remarkably, combs with an inverted envelope are generated for larger values of gain and loss.
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We report the spectral features of a phase-shifted parity and time ($mathcal{PT}$)-symmetric fiber Bragg grating (PPTFBG) and demonstrate its functionality as a demultiplexer in the unbroken $mathcal{PT}$-symmetric regime. The length of the proposed system is of the order of millimeters and the lasing spectra in the broken $mathcal{PT}$-symmetric regime can be easily tuned in terms of intensity, bandwidth and wavelength by varying the magnitude of the phase shift in the middle of the structure. Surprisingly, the multi-modal lasing spectra are suppressed by virtue of judiciously selected phase and the gain-loss value. Also, it is possible to obtain sidelobe-less spectra in the broken $mathcal{PT}$-symmetric regime, without a need for an apodization profile, which is a traditional way to tame the unwanted sidelobes. The system is found to show narrow band single-mode lasing behavior for a wide range of phase shift values for given values of gain and loss. Moreover, we report the intensity tunable reflection and transmission characteristics in the unbroken regime via variation in gain and loss. At the exceptional point, the system shows unidirectional wave transport phenomenon independent of the presence of phase shift in the middle of the grating. For the right light incidence direction, the system exhibits zero reflection wavelengths within the stopband at the exceptional point. We also investigate the role of multiple phase shifts placed at fixed locations along the length of the FBG and the variations in the spectra when the phase shift and gain-loss values are tuned. In the broken $mathcal{PT}$-symmetric regime, the presence of multiple phase shifts aids in controlling the number of reflectivity peaks besides controlling their magnitude.
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 solitons feature a subexponential instability, which may be suppressed by periodic switching (management).
The capability to temporarily arrest the propagation of optical signals is one of the main challenges hampering the ever more widespread use of light in rapid long-distance transmission as well as all-optical on-chip signal processing or computations. To this end, flat-band structures are of particular interest, since their hallmark compact eigenstates do not only allow for the localization of wave packets, but importantly also protect their transverse profile from deterioration without the need for additional diffraction management. In this work, we experimentally demonstrate that, far from being a nuisance to be compensated, judiciously tailored loss distributions can in fact be the key ingredient in synthesizing such flat bands in non-Hermitian environments. We probe their emergence in the vicinity of an exceptional point and directly observe the associated compact localised modes that can be excited at arbitrary positions of the periodic lattice.
We construct dark solitons in the recently introduced model of the nonlinear dual-core coupler with the mutually balanced gain and loss applied to the two cores, which is a realization of parity-time symmetry in nonlinear optics. The main issue is stability of the dark solitons. The modulational stability of the CW (continuous-wave) background, which supports the dark solitons, is studied analytically, and the full stability is investigated in a numerical form, via computation of eigenvalues for modes of small perturbations. Stability regions are thus identified in the parameter space of the system, and verified in direct simulations. Collisions between stable dark solitons are briefly considered too.
We introduce the notion of a ${cal PT}$-symmetric dimer with a $chi^{(2)}$ 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 solutions occur in two different ways depending on whether the first or the second harmonic amplitude is vanishing in the underlying linear eigenvector. Moreover, a host of interesting bifurcation phenomena appear to occur including saddle-center and pitchfork bifurcations which our parametric variations elucidate. The existence and stability analysis of the stationary solutions is corroborated by numerical time-evolution simulations exploring the evolution of the different configurations, when unstable.
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