We review quantum mechanical and optical pseudo-Hermitian systems with an emphasis on PT-symmetric systems important for optics and electrodynamics. One of the most interesting and much discussed consequences of PT symmetry is a phase transition under which the system eigenvalues lose their PT symmetry. We show that although this phase transition is difficult to realize experimentally, a similar transition can be observed in quasi-PT-symmetric systems. Other effects predicted for PT-symmetric systems are not specific for these systems and can be observed in ordinary fully passive systems.

Optical bistability of a spaser and criteria of its appearance are studied theoretically. The effective transmission coefficient of a spaser is calculated. This allows for considering a "mirrorless" spaser bistability in the same way as that of a nonlinear Fabry-Perot cavity. It is shown that at sufficiently high losses in a spaser, due to the bistability, kink waves may propagate along a one-dimensional chain of spasers. This wave propagates even if the pumping is below the threshold of spasing. At low losses in spaser, quasiperiodic dissipative structures emerge in the spaser chain. The dynamics of the origin of such structures has a self-assembling character.

We discuss phase transitions in - symmetric optical systems. We show that due to frequency dispersion of the dielectric permittivity, an optical system can have - symmetry at isolated frequency points only. An assumption of the existence of a - symmetric system in a continuous frequency interval violates the causality principle. Therefore, the ideal symmetrybreaking transition cannot be observed by simply varying the frequency.In the last decade, there has been rising interest in optics of artificial materials. Among such materials, the systems with balanced loss and gain regions have attracted particular attention [1][2][3]. The concept of these systems stems from the idea of the extension of quantum mechanics to non-Hermitian Hamiltonians possessing - symmetry [4,5].- symmetrical systems are invariant with respect to the simultaneous spatial inversion and time inversion In optics, - symmetry is usually studied in the frequency domain by considering solutions of the scalar Helmholtz equation for the z-component of the electric field E:

Light propagation through a single gain layer and a multilayer system with gain layers is studied. Results obtained using the Fresnel formulas, Airy's series summation, and the numerical solution of the nonlinear Maxwell±Bloch equations by the finite difference time domain (FDTD) method are analyzed and compared. Normal and oblique propagation of a wave through a gain layer and a slab of a photonic crystal are examined. For the latter problem, the gain line may be situated in either the pass or stop band of the photonic crystal. It is shown that the monochromatic plane-wave approximation is generally inapplicable for active media, because it leads to results that violate causality. But the problem becomes physically meaningful and correct results can be obtained for all three approaches once the structure of the wavefront and the finite aperture of the beam are taken into account.

We consider exciting surface plasmon polaritons in the Kretschmann configuration.Contrary to common belief, we show that a plane wave incident at an angle greater than the angle of total internal reflection does not excite surface plasmon polaritons. These excitations do arise, however, if the incident light forms a narrow beam composed of an infinite number of plane waves.The surface plasmon polariton is formed at the geometrical edge of the beam as a result of interference of reflected plane waves.

In the approach to the stationary regime, a spaser exhibits complicated and highly nonlinear dynamics with anharmonic oscillations. 1 We demonstrate that these oscillations are due to Rabi oscillations of the quantum dot in the field of the nanoparticle. We show that the oscillations may or may not arise dependent on the initial conditions.

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