Controlling the disorder properties of quadratic nonlinear photonic crystals

We experimentally demonstrate a modulation scheme for disordered nonlinear crystals that combines periodic modulation and disordered sections. The crystal is divided into a set of identical periodically poled building blocks, whereby each block is followed by a short section of random length. We use this scheme to achieve broadband second harmonic generation in KTiOPO4 nonlinear crystals while independently controlling the bandwidth and the center of the converted wavelengths as well as the efficiency of conversion. The trade-off between bandwidth and efficiency is improved in comparison with periodically poled crystals.     

Switchable two-dimensional gratings based on field-induced layer undulations in cholesteric liquid crystals

We propose switchable two-dimensional (2D) diffractive gratings with periodic refractive-index modulation arising from layer undulations in cholesteric liquid crystals. The cholesteric cell can be switched between two states: (1) flat layers of a planar cholesteric texture and (2) a square lattice of periodic director modulation associated with layer undulations that produces 2D diffraction patterns. The intensities of the diffraction maxima can be tuned by changing the applied field. The diffractive properties can be optimized for different wavelengths by appropriately choosing cholesteric pitch, cell thickness, and surface treatment.     

Nonreciprocity of waves in 1D photonic quasiperiodic crystals

Optical properties of one-dimensional quasiperiodic crystals with a linear profile of the modulation parameters are studied. It is shown that such systems possess a wider photonic forbidden band than the ideally periodic systems. The asymmetric profile of variation of the system parameters leads to nonreciprocity, which allows one to use these systems as optical diodes.     

Periodic,quasi‐periodic,and random quadratic nonlinear photonic crystals

Quadratic nonlinear photonic crystals are materials in which the second order susceptibility χ⁽²⁾ is spatially modulated while the linear susceptibility remains constant. These structures are significantly different than the more common photonic crystals, in which the linear susceptibility is modulated. Nonlinear processes in nonlinear photonic crystals are governed by the phase matching requirements, which are determined by the reciprocal lattice of these crystals. Therefore, the modulation of the nonlinear susceptibility enables to engineer the spatial and spectral response in various three‐wave mixing processes. It enables to support the efficient generation of new optical frequencies at multiple directions. We analyze three wave mixing processes in nonlinear photonic crystals in which the modulation is either periodic, quasi‐periodic, radially symmetric or even random. We discuss both one‐dimensional and two‐dimensional modulations. In addition to harmonic generations, we outline several new possibilities for all‐optical control of the spatial and polarization properties of optical beams in specially designed nonlinear photonic crystals.     

Modulated crystals and almost periodic measures

Modulated crystals and quasicrystals can simultaneously be described as modulated quasicrystals, a class of point sets introduced by de Bruijn in 1987. With appropriate modulation functions, modulated quasicrystals themselves constitute a substantial subclass of strongly almost periodic point measures. We re-analyze these structures using methods from modern mathematical diffraction theory, thereby providing a coherent view over that class. Similar to de Bruijn’s analysis, we find stability with respect to almost periodic modulations.

     

A highly stable holographic medium based on CaF<Subscript>2</Subscript>:Na crystals with colloidal color centers: II. Mechanisms of hologram recording and erasure

The mechanisms of formation and erasure of holographic gratings recorded in calcium fluoride crystals with a low sodium content have been considered. It is found that in the case of recording by UV radiation, an effective holographic grating is formed due to the spatial modulation of the colloidal centers arising under the action of the radiation at temperatures about 200°C. The decisive role of photoinduced diffusion of anion vacancies in this modulation is demonstrated.     

Diffraction of Light Beams at Parametric Interaction in Nonlinear Photonic Crystals

We consider the parametric amplification of a light beam in nonlinear photonic crystals (NLPCs) under a high-frequency pump and periodic spatial modulation of the coefficient of nonlinear coupling of the waves. We study the behavior of the intensity of the amplified diffracting beam using the matrix approach. We compare our results with the parametric interaction of beams in homogeneous nonlinear optical crystals. We show that the analysis of diffraction effects at nonlinear optical interaction in NLPCs, taking into account only noncompensated quasi-phase mismatching, is incorrect.     

Formation of defect density superlattices in binary compounds under nuclear irradiation

Manifestation of antisite defects in crystals under irradiation is studied. Calculations show that the concentration of such defects can reach high levels under typical irradiation intensities and temperatures. It is shown that buildup of antisite defects and interaction between them can result in instability of the system during irradiation with respect to spatially nonuniform perturbations. The instability should give rise to a periodic modulation of the density of antisite defects. The region of instability as a function of crystal parameters and irradiation has been obtained.     

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.     

Microwave-induced transient parametric gratings

We propose a new method for the formation of light-induced transient gratings in microwave-biased semiconductor crystals that exhibit a negative differential resistivity. Nonuniform heating of the electron gas in alternating electric fields induces spatially periodic modulation of the refractive index with spacing that is tunable by the external field frequency. Numerical simulations performed on a bulk GaAs sample prove that transient parametric gratings of both free-carrier and electro-optic origin can be triggered by a spatially modulated light pattern or by uniform photoexcitation.     

A method for studying the multipolarity and orientation of elementary oscillators in cubic crystals on the basis of axially periodic dependence of the luminescence intensity

A new method for determining the multipolarity and orientation of elementary quantum oscillators in cubic crystals is proposed. This method is based on studying the spatially periodic dependences of the intensity of luminescence observed in crystals with an induced anisotropy. The method was experimentally verified on LiF crystals containing F ₂ and F ₃ ⁺ color centers. It is shown that the observed spatially periodic dependences are in good agreement with the calculated dependences. The proposed method supplements the known methods for studying polarized luminescence (the methods of azimuthal dependences and polarization ratios and their various modifications). However, the new method, in contrast to the known ones, does not require measurements of the polarization ratios (for example, the degree of luminescence polarization), which in some cases significantly simplifies the experiment. Another advantage of the proposed method is its universality; i.e., it can be applied with equal success to both anisotropic and cubic crystals.     

Micro- and nanostructures for the spatially periodic orientation of liquid crystals obtained by focused ion beam milling

Micro- and nanostructured surfaces creating spatially periodic boundary conditions of the alignment of nematic liquid crystals in two mutually orthogonal directions perpendicular and parallel to the surface are obtained by focused ion beam milling. It is shown that ion milling provides an easy axis along the normal and sufficiently strong anchoring energy. The value of this energy can noticeably exceed the energy of the planar anchoring of liquid crystals with typical orienting surfaces on the basis of polymer films. Using the numerical simulation, the anchoring energy values necessary for an implementation of a deep modulation of the director field with a spatial period of hundreds of nanometers are determined, which is important for creation of photonic liquid-crystal systems.     

Resonance behaviour near Hopf bifurcations in the electrical conductivity of BSN crystals

The amplitude of the ac-voltage resulting from an external periodic modulation of the current density applied to BSN crystals exhibits a Lorentzian type resonance prior to a Hopf bifurcation. The resonance peak is near the internal oscillation frequency which would appear at the bifurcation. As the bifurcation point is approached the resonance peak becomes narrower and higher, in fair agreement with theoretical predictions. Increasing the amplitude of the modulation signal results in a loss of the frequency selectivity and a saturation of the gain.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Subbarrier interaction of channeling particles under the self-similar excitation of correlated states in a periodically deformed crystal

It has been shown that application of the periodic modulation of parabolic potential well parameters (in the case of charged particle channeling in crystals, i.e., periodic spatial modulation of the wall height of a potential well in the crystal channel) leads to the formation of the coherent channeling state in particles in this well. The formation of this state changes the interaction process between these particles and nuclei, and increases the barrier transparency by many times. For channeling this mode can be formed using, e.g., the longitudinal acoustic wave running along the channel axis. This wave changes the distance between nuclei and, accordingly, modulates the height of channel walls.     

On the theory of diffraction of light in photonic crystals with allowance for interlayer disordering

Electrodynamic Green’s functions are used to construct an analytical theory of the Bragg diffraction of polarized light in photonic crystals having a close-packed structure. For opal-based photonic crystals, the Bragg diffraction intensity is calculated with allowance for permittivity periodic modulation and for the presence of an optical crystal boundary and interlayer disordering, which usually appears during sample growth. A comprehensive study is made of the effect of the structure disorder caused by the random packing of growth layers on diffraction. For a random constructed twinned fcc structure, the average structure factor and the scattering (diffraction) cross sections (which are dependent on the linear polarization of the incident and scattered waves) are calculated. Numerical examples are used to show that the theory developed can be applied to analyze and process experimental diffraction patterns of real photonic crystals having a close-packed structure disordered in one direction.     

Discrete nonlinear Schrödinger equation with arbitrary nonlocality: Linear stability analysis and localized solution

The modulational instability of a plane wave for a discrete nonlinear Schrödinger equation with arbitrary nonlocality is analyzed. This model describes light propagation in a thin film planar waveguide arrays of nematic liquid crystals subjected to a periodic transverse modulation by a low frequency electric field. It is shown that nonlocality can both suppress and promote the growth rate and bandwidth of instability, depending on the type of a response function of a discrete medium. A solitary wave (breather-like) solution is built by the variational approximation and its stability is demonstrated.     

One-dimensional photonic crystal fabricated by the photochemical etching of silicon

The formation of periodic wall arrays on an n-type (100) Si substrate with V-shaped seed grooves on the surface was investigated. The influence of silicon sidewall roughness on the optical properties of onedimensional (1D) of photonic crystals obtained on the basis of the arrays was studied. The reflection spectra of the 1D photonic crystals exhibit a high modulation level of up to 95% and photonic band gaps of a high order that are in good agreement with calculations over a wide spectral range (1.5—15 μm).     

BPM simulation of SNOM measurements of waveguide arrays induced by periodically poled BNN crystals

The simulation of light propagation using standard beam propagation techniques, in periodically inverted domains in Ba₂NaNb₅O₁₂ crystals is presented. The poled domains pattern gives rise to periodic modulation of the refractive index in the crystal, which can be observed with diffraction experiments and simulated by one-dimensional beam propagation methods. The micro-domains are characterized by Scanning Near Field Microscopy, using both transmission and collection modes. In particular, under the collection mode, micro- pictures have been obtained with unexpected high optical contrast between positive and negative domains of up to 80%. Using a beam simulation method, the results are explained considering that the ferroelectric domains operate as a periodic array of planar waveguides.     

Model of periodic superstructure formation induced by mobile defects on a semiconductor surface

A model for forming a periodic superstructure on a semiconductor surface with mobile defects is proposed. It is shown that a self-organized system of such defects could lead to considerable modulation of incommensurate phase parameters in near-surface layers under the conditions of defect interaction with an incommensurate displacement wave. This type of defect system could induce a substantial energy decrease for the incommensurate phase and its additional stabilization on the one hand, and an increase in modulation amplitude that might be accompanied by a soliton-like nonsinusoidal incommensurate displacement wave on the other. The model allows us to explain the experimental results regarding the periodic superstructure discovered by G.V. Benemanskaya et al. on the surface of a GaN semiconductor. In particular, the model enables us to explain the nature of such superstructures based on the self-organization of mobile neutral triad-type defects, composed of negatively charged (3−) vacancies of the host lattice centers of Ga³⁺ and surface impurity ions of Cs⁺ and Ba²⁺, under conditions of triad interaction with an incommensurate displacement wave.