Soliton based χ(2) combs in high-Q optical microresonators.

Investigations of the frequency combs in χ(3) microresonators have passed a critical point when the soliton based regimes are well established and realized on different platforms. For χ(2) microresonators, where the first harmonic (FH) and second harmonic (SH) envelopes are coupled via the SH generation and optical parametric oscillation, the comb-soliton studies are just starting. Here we report on a vast accessible dual χ(2) soliton-comb family in high-Q microresonators with the SH and FH combs centered at the pump frequency ωp and its half ωp/2. Vicinity of the point of equal FH and SH group velocities λc, available via proper radial poling, is found to be the most advantageous for the generation of spectrally broad dual FH-SH combs. Our predictions as applied to lithium niobate resonators include the dependence of comb and dissipative soliton parameters on the pump power, the deviation λp - λc, the modal quality factors and frequency detunings, and the necessary parameters of radial poling of the resonator. These predictions form a solid basis for the realization of χ(2) frequency combs.

Walk-off controlled self-starting frequency combs in χ(2) optical microresonators.

Investigations of frequency combs in χ(3) optical microresonators are burgeoning nowadays. Changeover to χ(2) resonators promises further advances and brings new challenges. Here, the comb generation entails not only coupled first and second harmonics (FHs and SHs) and two dispersion coefficients but also a substantial difference in the group velocities - the temporal walk-off. We predict walk-off controlled highly stable comb generation, which is drastically different from that known in the χ(3) case. This includes the general notion of antiperiodic states; formation of localized coherent antiperiodic steady states (solitons), where the FH and SH envelopes move with a common velocity without shape changes; characterization of a new vast family of antiperiodic solitons; and the dependence of comb spectra on the pump power and the group velocity difference.

Whispering gallery resonators with broken axial symmetry: Theory and experiment.

Axial symmetry is the cornerstone for theory and applications of high-Q optical whispering gallery resonators (WGRs). Nevertheless, research on birefringent crystalline material persistently pushes towards breaking this symmetry. We show theoretically and experimentally that the effect of broken axial symmetry, caused by optical anisotropy, is modest for the resonant frequencies and Q-factors of the WGR modes. Thus, the most important equatorial whispering gallery modes can be quantitatively described and experimentally identified. At the same time, the effect of broken axial symmetry on the light field distribution of the whispering gallery modes is typically very strong. This qualitatively modifies the phase-matching for the χ(2) nonlinear processes and enables broad-band second harmonic generation and optical parametric oscillation. The effect of weak geometric ellipticity in nominally symmetric WGRs is also considered. Altogether our findings pave the way for an extensive use of numerous birefringent (uniaxial and biaxial) crystals with broad transparency window and large χ(2) coefficients in nonlinear optics with WGRs.

Strong forward-backward asymmetry of stimulated Raman scattering in lithium-niobate-based whispering gallery resonators.

We show experimentally and prove theoretically that the pump-power thresholds of stimulated Raman scattering (SRS) in lithium-niobate-based whispering gallery resonators (WGRs) are strongly different for the signal waves propagating in the backward and forward directions with respect to the pump wave. This feature is due to a strong polaritonic effect. It leads to a cascade of alternating forward-backward Raman lines with increasing pump power. The measured polarization and spectral properties of SRS are in good agreement with theory. Similar properties have to be inherent in other WGRs made of polar crystals.

Strong polarization effects in photothermal common-path interferometry.

We show experimentally and theoretically that heating of highly transparent materials by continuous-wave pump beams induces strong optical anisotropy for probe beams in primarily optically isotropic configurations. This is due to a uniaxial thermally induced strain and the elasto-optic effect. The cases of glasses and lithium niobate crystals are considered. The discovered effect is important for the development of techniques aimed at the analysis of absorptive properties of transparent optical materials.

Structure of pump resonances during optical parametric oscillation in whispering gallery resonators.

In optical parametric oscillators, the line shape of the pump resonance becomes strongly distorted above the oscillation threshold. We model this behavior and find good agreement with the literature data and our original experimental data. A fit of the model to the data provides valuable information about the loss mechanisms in the parametric process. In particular, the modal properties of the parametric waves can be gained, which is important for both classical and quantum aspects of optical parametric oscillation.

Whispering gallery modes at the rim of an axisymmetric optical resonator: analytical versus numerical description and comparison with experiment.

Optical whispering gallery modes (WGMs) of mm-sized axisymmetric resonators are well localized at the equator. Employing this distinctive feature, we obtain simple analytical relations for the frequencies and eigenfunctions of WGMs which include the major radius of the resonator and the curvature radius of the rim. Being compared with results of finite-element simulations, these relations show a high accuracy and practicability. High-precision free-spectral-range measurements with a millimeter-sized disc resonator made of MgF(2) allow us to identify the WGMs and confirm the applicability of our analytical description.

Hidden reservoir of photoactive electrons in LiNbO3 crystals.

We show that a continuous-wave (cw) pump beam at a wavelength of 532 nm produces substantial light-induced (LI) absorption in the visible range in initially transparent undoped LiNbO3 crystals. The LI absorption coefficient stays linear in the pump intensity I(p) up to I(p)(max)=48 kW/cm2. Together with other features including long-term stretched-exponential relaxation of the LI absorption, it indicates that the present concept of LI electron processes in this important optical material must be revised: the amount of photoactive electrons increases already within the cw intensity range. A quantitative model is proposed that explains the experimental data and employs two-step excitations from filled localized states near the valence band via intermediate deep centers into the conduction band. The introduced localized states serve as a hidden reservoir of electrons.

Highly tunable low-threshold optical parametric oscillation in radially poled whispering gallery resonators.

Whispering-gallery resonators (WGR's), based on total internal reflection, possess high quality factors in a broad spectral range. Thus, nonlinear-optical processes in such cavities are ideally suited for the generation of broadband or tunable electromagnetic radiation. Experimentally and theoretically, we investigate the tunability of optical parametric oscillation in a radially structured WGR made of lithium niobate. With a 1.04 µm pump wave, the signal and idler waves are tuned from 1.78 to 2.5 µm--including the point of degeneracy--by varying the temperature between 20 and 62 °C. A weak off centering of the radial domain structure extends considerably the tuning capabilities. The oscillation threshold lies in the mW-power range.

Kinetics of photorefractive recording for circular light beams.

We show, theoretically and experimentally, that the buildup of the space-charge field in photorefractive crystals is far from monoexponential for circular light beams. This is a general property of the two-dimensional (2D) case, in contrast to the one-dimensional case. The results form a basis for determination of the photoelectric parameters of photorefractive crystals within a wide intensity range, which is important, e.g., for solving of the optical-damage problem in LiNbO3 and LiTaO3 crystals.

Ultraslow shock waves of electron density in LiNbO3 crystals.

We show, experimentally and theoretically, that the application of modest voltages, U0=(0.1-1) kV, to LiNbO3ratioFe crystals at sufficiently high temperatures, T approximately (550-700) degrees C, leads to the formation of ultraslow shock waves (moving discontinuities) of the electron density owing to the removal of electrons from Fe2+ centers. Behind the sharp wave front, almost all iron centers are in the Fe3+ state, the sample is optically transparent, and its transport properties are strongly modified. The front velocity decreases during the propagation; it is controlled by the electron mobility.

Bragg selectivity of space-charge gratings in multidomain lithium niobate crystals.

It is shown experimentally and theoretically that a partial domain reversal in ferroelectric lithium niobate crystals containing a previously imprinted photorefractive space-charge grating results in a highly unusual change of the angular Bragg selectivity. This carries important in situ information about domain structures, including the quality of periodically poled samples.

Long-living currents induced by nanosecond light pulses in LiNbO(3) crystals.

We have obtained first solid evidence of strong charge separation that is caused by relaxing localized electrons in a polar medium: Space-charge gratings induced in highly-doped LiNbO(3):Fe crystals by interfering nanosecond light pulses at 532 nm show a highly peculiar long term behavior (buildup or/and decay) in the dark. It depends strongly on the applied electric field E(0) (ranging from -140 to +640 kV/cm) and occurs on a time scale of (1 - 100) s which is much larger than the relaxation time of photo-electrons and smaller than the dark dielectric relaxation time. All peculiarities observed are fully described by a charge-transport model that incorporates the energy relaxation of electrons within a band of localized Fe(2+) states and a long-living, field-gradient-independent "polar current" directed along the polar axis.

Investigation of nonlinear absorption processes with femtosecond light pulses in lithium niobate crystals.

The propagation of high-power femtosecond light pulses in lithium niobate crystals (LiNb O3 ) is investigated experimentally and theoretically in collinear pump-probe transmission experiments. It is found within a wide intensity range that a strong decrease of the pump transmission coefficient at wavelength 388 nm fully complies with the model of two-photon absorption; the corresponding nonlinear absorption coefficient is beta(p) approximately = 3.5 cm/GW. Furthermore, strong pump pulses induce a considerable absorption for the probe at 776 nm. The dependence of the probe transmission coefficient on the time delay Delta t between probe and pump pulses is characterized by a narrow dip (at Delta t approximately = 0) and a long (on the picosecond time scale) lasting plateau. The dip is due to direct two-photon transitions involving pump and probe photons; the corresponding nonlinear absorption coefficient is beta(r) approximately = 0.9 cm/GW. The plateau absorption is caused by the presence of pump-excited charge carriers; the effective absorption cross section at 776 nm is sigma(r) approximately = 8 x 10(-18) cm(2). The above nonlinear absorption parameters are not strongly polarization sensitive. No specific manifestations of the relaxation of hot carriers are found for a pulse duration of approximately = 0.24 ps.

Regimes of feedback-controlled beam coupling.

The introduction of certain electronic feedback loops into photorefractive wave-coupling schemes makes them noise free and leads to dramatic changes of the whole nonlinear behavior. The familiar steady states can be transformed into periodic states that are characterized by ultimately high and low values of the diffraction efficiency eta of the recorded index grating or into quasisteady states with small values of eta. These transformations possess thresholds with respect to controllable experimental parameters like the coupling strength and the input intensity ratio. We present a general analysis of the threshold behavior for different modes of the feedback operation and different types of the nonlinear photorefractive response. The results obtained (analytical and numerical) allow one to predict the regions of stability for feedback-controlled steady states and the observable characteristics of the system, including the output amplitudes and diffraction efficiency of the spatial grating, beyond these regions. They extend strongly the potentialities of the feedback-controlled wave coupling.

Femtosecond time-resolved absorption processes in lithium niobate crystals.

Femtosecond pump pulses are strongly attenuated in lithium niobate owing to two-photon absorption; the relevant nonlinear coefficient beta(p) ranges from approximately 3.5 cm/GW for lambda(p) = 388 nm to approximately 0.1 cm/GW for 514 nm. In collinear pump-probe experiments the probe transmission at the double pump wavelength 2lambda(p) = 776 nm is controlled by two different processes: A direct absorption process involving pump and probe photons (beta (r) = 0.9 cm/GW) leads to a pronounced short-duration transmission dip, whereas the probe absorption by pump-excited charge carriers results in a long-duration plateau. Coherent pump-probe interactions are of no importance. Hot-carrier relaxation occurs on the time scale of < or approximately equal to 0.1 ps.

Description of readout processes during strong beam coupling.

We show, using the symmetry properties of the coupled-wave equations for the transmission and reflection geometries, that any readout characteristic of dynamic spatially nonuniform index gratings in photorefractive crystals can be explicitly expressed through the characteristics of the recording light beams. This approach is applied to describe the impact of beam coupling on the diffraction efficiency of dynamic gratings and on the output intensities of the light beams at instantaneous input phase changes (light grating translation). Further implications of this general approach are discussed.

Slowing down of light in photorefractive crystals with beam intensity coupling reduced to zero.

A considerable deceleration of light pulses in crystals with nearly compensated space-charge field proves that the strong dispersion of dynamic photorefractive gratings in the vicinity of Bragg resonance is of primary importance for light slowing down.

Origin of stretched exponential relaxation for hopping-transport models.

We propose a novel geometric approach to the description of the relaxation phenomena in complex condensed-matter systems. It is shown within a fairly general random site hopping model that the stretched exponential decay law, exp([-(t/tau)(beta)], originates from the simple and general geometric features of a random distribution of transport and trapping sites in the 3D space. The value of the variable stretching index beta is determined by the localization radius of hopping electrons. The possibilities for generalization of the obtained results and interpretation of the relevant experimental data are discussed.

Solutions for vectorial beam coupling under ac field in cubic photorefractive crystals.

We develop a theory of vectorial wave coupling in cubic photorefractive crystals placed in an alternating ac field to enhance the nonlinear response. It is proven in the general case that despite essential differences between the diffusion and the ac nonlocal responses, the latter keeps the light interference fringes straight during the interaction. This fundamental feature allows, under certain restrictions, to reduce the nonlinear problem of vectorial coupling to the known linear problem of vectorial Bragg diffraction from a spatially uniform grating, which admits an exact solution. As a result, the nonlinear vectorial problem can be effectively solved for a number of practically important cases. These cases include nontrivial polarization effects and also the high-contrast effects. The presence of conservation laws involving the polarization degrees of freedom is shown. A number of particular cases relevant to experiments with BTO crystals are considered.