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Register a new userUnidirectional Nonlinear PT-symmetric Optical Structures
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Authors
Hamidreza Ramezani
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We show that non-linear optical structures involving a balanced gain-loss profile, can act as unidirectional optical valves. This is made possible by exploiting the interplay between the fundamental symmetries of parity (P) and time (T), with optical nonlinear effects. This novel unidirectional dynamics is specifically demonstrated for the case of an integrable PT-symmetric nonlinear system.
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Unidirectional reflectionless propagation (or transmission) is an interesting wave phenomenon observed in many $mathcal{PT}$-symmetric optical structures. Theoretical studies on unidirectional reflectionless transmission often use simple coupled-mode models. The coupled-mode theory can reveal the most important physical mechanism for this wave phenomenon, but it is only an approximate theory, and it does not provide accurate quantitative predictions with respect to geometric and material parameters of the structure. In this paper, we rigorously study unidirectional reflectionless transmission for two-dimensional (2D) $mathcal{PT}$-symmetric periodic structures sandwiched between two homogeneous media. Using a scattering matrix formalism and a perturbation method, we show that real zero-reflection frequencies are robust under $mathcal{PT}$-symmetric perturbations, and unidirectional reflectionless transmission is guaranteed to occur if the perturbation (of the dielectric function) satisfies a simple condition. Numerical examples are presented to validate the analytical results, and to demonstrate unidirectional invisibility by tuning the amplitude of balanced gain and loss.
In this work we first examine transverse and longitudinal fluxes in a $cal PT$-symmetric photonic dimer using a coupled-mode theory. Several surprising understandings are obtained from this perspective: The longitudinal flux shows that the $cal PT$ transition in a dimer can be regarded as a classical effect, despite its analogy to $cal PT$-symmetric quantum mechanics. The longitudinal flux also indicates that the so-called giant amplification in the $cal PT$-symmetric phase is a sub-exponential behavior and does not outperform a single gain waveguide. The transverse flux, on the other hand, reveals that the apparent power oscillations between the gain and loss waveguides in the $cal PT$-symmetric phase can be deceiving in certain cases, where the transverse power transfer is in fact unidirectional. We also show that this power transfer cannot be arbitrarily fast even when the exceptional point is approached. Finally, we go beyond the coupled-mode theory by using the paraxial wave equation and also extend our discussions to a $cal PT$ diamond and a one-dimensional periodic lattice.
We reveal a generic connection between the effect of time-reversals and nonlinear wave dynamics in systems with parity-time (PT) symmetry, considering a symmetric optical coupler with balanced gain and loss where these effects can be readily observed experimentally. We show that for intensities below a threshold level, the amplitudes oscillate between the waveguides, and the effects of gain and loss are exactly compensated after each period due to {periodic time-reversals}. For intensities above a threshold level, nonlinearity suppresses periodic time-reversals leading to the symmetry breaking and a sharp beam switching to the waveguide with gain. Another nontrivial consequence of linear PT-symmetry is that the threshold intensity remains the same when the input intensities at waveguides with loss and gain are exchanged.
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.
We explore the consequences of incorporating parity and time reversal ($mathcal{PT}$) symmetries on the dynamics of nonreciprocal light propagation exhibited by a class of nonuniform periodic structures known as chirped $mathcal{PT}$-symmetric fiber Bragg gratings (FBGs). The interplay among various grating parameters such as chirping, detuning, nonlinearities, and gain/loss gives rise to unique bi- and multi-stable states in the unbroken as well as broken $mathcal{PT}$-symmetric regimes. The role of chirping on the steering dynamics of the hysteresis curve is influenced by the type of nonlinearities and the nature of detuning parameter. Also, incident directions of the input light robustly impact the steering dynamics of bistable and multistable states both in the unbroken and broken $mathcal{PT}$-symmetric regimes. When the light launching direction is reversed, critical stable states are found to occur at very low intensities which opens up a new avenue for an additional way of controlling light with light. We also analyze the phenomenon of unidirectional wave transport and the reflective bi- and multi-stable characteristics at the so-called $mathcal{PT}$-symmetry breaking point.
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