Anatoly S. Chirkin

Entangled photon states in consecutive nonlinear optical interactions

Quantum theory of two consecutive light-wave parametric interactions with aliquant frequencies produced by a common pump wave in a crystal is developed. Using the differentiation method, the unitary evolution operator of the system is reduced to an ordered form that allows the calculation of the field state and the statistical characteristics of interacting waves. It is shown that, for the initial vacuum field state, the created photons obey the super-Poisson statistics at the interacting frequencies and are in a multiparticle entangled state.

Investigations in the nonlinear behavior of dielectrics by using ultrashort pulses (Best Oral Presentation)

Ultra-short pulse systems are considered as innovative laser sources for a variety of applications in micro material structuring, medicine and diagnostics. Current commercial systems are still lacking in output power limiting the throughput and the economic efficiency within a production line. In the optimization of ultra short pulse sources of the next generation, special effects in optical components during interaction with ultra-short pulses play a major role. Especially, low damage thresholds and non-linear absorptance have already been observed within the activities of the EUREKA-project CHOCLAB II, which are concentrated on the evaluation of multiple-pulse damage and the absorptance of fs-optical components according to the International Standards ISO 11254-2 and ISO 11551. In this paper, a theoretical model on the basis of photo- and avalanche ionization is presented describing the incidence of damage as a consequence of a sufficient high density of conduction band electrons. Furthermore, the influence of the Kerr-effect and conduction band electrons on the optical properties of dielectrics is investigated theoretically. From our calculations, a significant increase in reflectance due to the dominant Kerr-effect can be deduced as well as a noticeable increase in absorptance induced by free electron heating already at energy density values clearly below the damage threshold. Finally, results of an experimental investigation in the influence of the internal field strength in a dielectric layer stack on the damage threshold are described. The experiments clearly support the assumption already stated in other publications, that the field intensity formed by the optical design plays a key role for damage resistance of optical coatings for ultrashort pulses.

Tripartite entanglement in coupled three-wave interactions

We study the three-mode entanglement properties in a new kind of the coupled nonlinear optical interactions consisting of two parametric down-conversion processes and one up-conversion. Approach, based on partial scaling transformation of the covariant matrix, is used to reveal tripartite entanglement. It is established that the three-mode field is in the true entangled state.

Generalized expression for the natural width of the radiation spectrum of quantum oscillators

A simple method for calculating the linewidth of sources of stimulated coherent radiation caused by spontaneous noise and thermal fluctuations has been proposed in the framework of the two-level model of the active medium. An expression for the spectral width has been derived beyond the adiabatic approximation under an arbitrary relation between relaxation times in a self-sustained oscillation system, taking into account a finite spectral band of spontaneous radiation. The result is applicable for a wide class of coherent radiation sources.

Quantum holographic teleportation of entangled two-color optical images

We introduce and theoretically investigate a scheme for teleportation of two-frequency entangled optical images in which the quantum channel is formed by four-frequency multimode states, generated in a single nonlinear photonic crystal by coupled parametric interactions. We study in detail the performance of the scheme. Namely, we evaluate its fidelity and the spatial-frequency spectra of the quadrature components characterizing the deterioration of the entanglement in the initial images due to the teleportation process. We analyze the influence of the spatial bandwidth of entanglement on the fidelity of teleportation. We investigate the performance of the scheme both in the near and the far diffraction field. Our analysis suggests that bandwidth matching of the quantum channel field with that of the images is generally necessary for high-quality teleportation. We show that entangled images are more fragile and more difficult to teleport than their coherent counterparts.

Simultaneous parametric generation and up-conversion of entangled optical images

A quantum theory of parametric amplification and frequency conversion of an optical image in coupled nonlinear optical processes that include one parametric amplification process at high-frequency pumping and two up-conversion processes in the same pump field is developed. The field momentum operator that takes into account the diffraction and group velocities of the waves is used to derive the quantum equations related to the spatial dynamics of the images during the interaction. An optical scheme for the amplification and conversion of a close image is considered. The mean photon number density and signal-to-noise ratio are calculated in the fixed-pump-field approximation for images at various frequencies. It has been established that the signal-to-noise ratio decreases with increasing interaction length in the amplified image and increases in the images at the generated frequencies, tending to asymptotic values for all interacting waves. The variance of the difference of the numbers of photons is calculated for various pairs of frequencies. The quantum entanglement of the optical images formed in a high-frequency pump field is shown to be converted to higher frequencies during the generation of sum frequencies. Thus, two pairs of entangled optical images are produced in the process considered.

On the Possibility of the Nondegenerate Parametric Amplification of Optical Waves at Low-Frequency Pumping

It is shown that parametric amplification at low-frequency pumping can be implemented in coupled nonlinear optical interactions in aperiodic nonlinear photonic crystals created by the method of the superposition of the modulation of the second-order susceptibility. In this process, the intensities of waves with frequencies higher than the pump frequency increase monotonically with the interaction length as in the case of the traditional process of parametric amplification at high-frequency pumping. The dependence of the gain factor on the coupling constants of interacting waves is obtained. The process under consideration makes it possible to ensure the tuning of the generated frequency in the ultraviolet range upon pumping in the visible range. Analysis of the process is performed on the example of aperiodic nonlinear photonic crystals of lithium niobate.

Multiple quasi-phase-matching in nonlinear Raman-Nath diffraction.

The method of the superposition of a nonlinearity modulation is employed to design a two-dimensional (2D) nonlinear photonic lattice for efficient multiple quasi-phase-matched second harmonic generation in the process of nonlinear Raman-Nath diffraction (NRND). An analytical solution is proposed to calculate the second harmonic intensity in rectangular 2D lattices. This approach can be useful for the generation of multiple second harmonic beams with the efficiency a few orders of magnitude higher than in the case of nonphase-matched generation via NRND.

Dynamics of the Amplitude and Phase of a Signal in the Process of Quasi-Phase-Matched Parametric Interaction

The parametric amplification of a light wave in nonlinear optical crystals under a high-frequency pump and a periodic spatial modulation of the coefficient of nonlinear coupling of the waves is considered. The value of the period of modulation of the nonlinear coefficient that corresponds to the maximum gain is found. The behavior of the phase and intensity of the amplified wave is studied using the matrix approach. For the case of the optimum phase relation between the interacting waves, the expression for the intensity of the amplified wave is obtained, which, in the limit, gives the result for a homogeneous nonlinear crystal.

Theory of second-harmonic generation in a chirped 2D nonlinear optical superlattice under nonlinear Raman-Nath diffraction

We analyze second-harmonic generation (SHG) in a two-dimensional nonlinear optical superlattice (NLOS) with its modulation period being chirped in the propagation direction and constant in the transverse direction. This results in efficient multiple SHG via nonlinear Raman–Nath diffraction. We obtain exact analytical expressions for a SH amplitude generated in chirped 2D NLOSs and for its quasi-phase-matching bandwidth. The results of analytical calculations are in excellent agreement with the numerical ones. We show that the process is robust to angular deviations of NLOS and it can be applied to enable tunable and broadband frequency conversion.