New approaches for the fabrication of photonic structures of nonlinear optical materials

We revisited two different strategies to fabricate 1D photonic crystals of nonlinear optical dielectric materials based on ultrafast laser ablation of the surface of an RbTiOPO₄ crystal, and selective etching of ferroelectric domains of the surface of a periodically poled LiNbO₄ crystal. We evaluated their behaviour as Bragg diffraction gratings. We also presented the recent advances we developed in a new procedure of fabrication of 2D and 3D photonic crystals of KTiOPO₄ (KTP) grown on the surface of a KTP substrate by liquid phase epitaxial means within the pores of a silicon macroporous template. Optical, structural, morphological, and compositional characterization for the photonic crystals produced through this technique are presented.     

Influence of Kerr nonlinearity on the band structures of two-dimensional photonic crystals

Dynamic modifications of the band structures of two-dimensional photonic crystals composed of Kerr-nonlinear dielectric rods in air forming hexagonal, square and honeycomb lattices are investigated. Calculations are carried out by the method based on the finite-difference time-domain (FDTD) technique for both TM and TE polarizations. The bands in all cases are observed to red-shift with the introduction of nonlinearity. Inspection of the variation of the mid-gap frequencies with source intensity reveals that the red-shift increases as gap number increases, in a manner proportional to the mid-gap frequency in linear regime. The red-shift of mid-gap frequencies is also found to follow the adopted saturable model for the change of relative permittivity with source intensity. Either the so-called dielectric or the air band edges of the gaps are found to be more sensitive to nonlinearity resulting in broadening or shrinking of the gaps. Possible utilizations of the present observations for all-optical device applications, such as wavelength multiplexing, are discussed.     

Ultrasensitive UV-tunable grating in all-solid photonic bandgap fibers

We study the shift of a long period grating’s resonance wavelength with UV induced refractive index changes in an all-solid photonic bandgap fiber. A long period grating is mechanically imprinted in an all-solid photonic bandgap fiber with Germanium doped silica high-index rods in a lower-index silica background. The index of the high-index rods is modified through UV exposure, and we observe that the long period grating’s resonance shifts with the bandgaps. With a sensitivity of 21,000 nanometers per refractive index unit and a 8.8 nm resonance width changes of refractive index of 3 × 10⁻⁶ are in principle detectable     

Ultra fast third-order non-linear response of amino-triazole donor-acceptor derivatives by optical Kerr effect

We report the study of the temporal dependence of the non-linear optical response of novel organic materials in solution. The experimental results of the optical Kerr gate using 70 fs pulses show a quasi-instantaneous response for three derivatives of an amino-triazole donor-acceptor system. The non-linearity of the compounds is identified as arising from the electronic contribution to the third-order non-linear susceptibility. The non-linear parameters of each sample were obtained using the optical Kerr response of CS₂ as reference.     

Phase matched vectorial three-wave mixing in isotropic Kerr media

A theoretical analysis of vectorial three-wave mixing in isotropic Kerr media is presented. The analysis based on the coupled-wave equations describes the amplification of a weak wave by coupling with a strong pump wave phase matched by optically induced change of average refractive index. The phase matching condition for interacting waves with different polarizations is calculated, allowing a large amplification of a weak wave by three-wave mixing in thick Kerr media. The main conclusions of our theoretical analysis are supported by the results of experiments in CS₂ liquid medium.     

Superprism effect in 1D photonic crystal

It is shown that superprism effect can be observed not only in 2D and 3D photonic crystal but also in 1D photonic crystal. To observe the effect a diffraction grating should be put on the top of the 1D PC. It is shown that the band gap more dramatically appears in 1D PC than in 2D PC. This effect makes all PBG effects including superprism effect more pronounced and also weakens the influence of losses.     

Analytical solution for the field in photonic structures containing cubic nonlinearity

In this work, we consider the exact solution of the stationary cubic nonlinear equation in a semi-infinite nonlinear medium in contact with a one-dimensional photonic crystal. Two kinds of analytical solutions are found for an arbitrary magnitude of the nonlinearity: a standing-wave-like one containing the inverse elliptic function Eli(?∣m), and a one-wave-type solution for transmitted TE-polarized waves. An approximate two-wave solution is proposed to describe the field propagation through the nonlinear film covering the photonic crystal. It is shown that the problem of a mixed linear-nonlinear structure may be reduced to a transcendental kernel equation determining the field inside the nonlinear part of the medium. The light reflection from a Si/SiO₂ layered structure in contact with an optically nonlinear medium is calculated. The angular-frequency photonic band diagram and power dependency are investigated. Local interface waveguide modes are considered.     

Tamm states and nonlinear surface modes in photonic crystals

We predict the existence of surface gap modes, known as Tamm states for electronic systems, in truncated photonic crystals formed by two types of dielectric rods. We investigate the energy threshold, dispersion, and modal symmetries of the surface modes, and also demonstrate the existence and tunability of nonlinear Tamm states in binary photonic crystals with nonlinear response.     

Tunable double-channel filter based on two-dimensional ferroelectric photonic crystals

A tunable double-channel filter is presented, which is based on a two-dimensional nonlinear ferroelectric photonic crystal made of cerium doped barium titanate. The filtering properties of the photonic crystal filter can be tuned by adjusting the defect structure or by a pump light. The influences of the structure disorders caused by the perturbations in the radius or the position of air holes on the filtering properties are also analyzed.     

Design and simulation of a novel 32 × 32 photonic bandgap power switch based on SOI waveguide

In this paper, we propose a novel 32 × 32 photonic bandgap (PBG) power switch based on silicon-on-insulator (SOI) substrate. The 32 × 32 PBG power switch merges the design concept of PBG structure and multimode interference (MMI) structure. With controlling the voltages of 256 blocks for changing the refractive index, we can demonstrate that the light propagation direction can be switched to the assigned output port as a 32 × 32 power switch. According to the simulations, the power switching control tables are searched and selected for successful switching. The size of our designed 32 × 32 PBG switch can be reduced to 252 × 6040 μm which is much smaller than the conventional opto-electronic switches.     

Influence of cubic nonlinearity on laser radiation transmission in a photonic crystal with spatially modified media properties

The transfer matrix method was modified to explore the Kerr nonlinearity influence on laser radiation propagation in a one‐dimensional photonic crystal. The suggested spatial distribution of the refractive index allows to remove minibands and to make the transmission curve much steeper. Plain and steep photonic band gap edges are effective in creation of transmission anisotropy of powerful laser radiation. The investigated photonic crystal has a strong anisotropic optical transmission and acts as an optical analog of the electronic diode. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Isotropic photonic bandgap in Penrose textured metallic mircocavity

Photonic microcavity has modified photonic modes that have intense localized electric field, which can couple strongly with the embedded emission centers. In this work, we fabricated 2D photonic microcavities with Penrose quasicrystal pattern with 10-fold symmetry. Organic luminescence material tris(8-hydroxyquinoline) aluminum (Alq₃) was embedded into the microcavity and the angle resolved transmission (ART) and photoluminescence (ARPL) spectra of the microcavity were measured. The results showed that the normal Gaussian photoluminescence spectrum of Alq₃ has been strongly modified by the microcavity dispersion characteristic. In addition, omni-directional photonic band gap exists in the microcavity. The higher symmetry of Penrose quasicrystal pattern means that there was minimal difference in the directional dispersion characteristics.     

Thermodynamics of Phase Transitions of a Kerr Nonlinear Blackbody

We study the thermodynamics of phase transitions of a blackbody whose interior is filled by a Kerr nonlinear crystal. There is a transition temperature To, above which the Kerr nonlinear blackbody is in the normal thermal radiation state, and below which it is in the squeezed thermal radiation state. At To, the Gibbs free energy of the two phases is continuous but the entropy density of the two phases is discontinuous. Hence, there is a jump in the entropy density and this leads to a latent heat density. The photon system undergoes a first-order phase transition from the normal to the squeezed thermal radiation state.     

Propagation of Gaussian beams in negative-index metamaterials with cubic nonlinearity

Propagation of Gaussian beams in the negative-index metamaterials (NIMs) with cubic nonlinearities is investigated, both theoretically and numerically. The role of the status of the incident Gaussian beam, which is scaled by a converging parameter in this paper, in beam self-focusing and self-defocusing in NIMs is specially identified. The expressions for beam self-focusing and self-defocusing for different converging parameter cases, and the dependence of the critical power and the focus location of self-focusing in NIMs on the converging parameter are obtained. It is found that it is the divergent rather than convergent incident beams which are self-focused more quickly in NIMs with defocusing nonlinearities, in sharp contrast with the propagation property of Gaussian beams in conventional Kerr media, in which beam self-focusing only occurs in the media with focusing nonlinearities and a convergent incident beam self-focuses more quickly than a divergent one. By adjusting the converging parameter of incident Gaussian beam or the controllable magnetic permeability of NIM, or both, one can manipulate the beam self-focusing in NIMs at will.     

Impact of chromatic dispersion and group delay ripple on self-phase modulation based optical regenerators

We demonstrate that chromatic dispersion and group delay ripple limit the performance of all-optical regeneration based on self-phase modulation. The level of degradation depends in detail on the type of phase distortions introduced. The regenerator performance is measured using the optical signal to noise ratio (OSNR) margin provided to the system for a given bit error ratio. The addition of chromatic dispersion and group delay ripple induces a significant reduction in this OSNR margin.     

Nonlinear three-wave interaction in photonic crystals

We present a multi-scale analysis of nonlinear three-wave-interaction processes in photonic crystals. Based on photonic Bloch functions as carrier waves, we derive the effective nonlinear coupled wave equations that govern pulse propagation in these systems and obtain the corresponding effective photonic crystal parameters directly from photonic band-structure computations. As an illustration, we show how hitherto inaccessible radiation-conversion processes such as wave-front reversal of optical pulses can be realized. Furthermore, we describe a novel regime of nonlinear three-wave interaction in photonic crystals associated with the nearly degenerate case and show how these results may be utilized to study experimentally certain problems from plasma physics and hydrodynamics in the context of nonlinear photonic crystals.     

Strong nonlinear optical refractive effect of self-assembled multilayer films containing tetrasulfonated iron phthalocyanine

Multilayer films containing anionic iron phthalocyanine tetrasulfonate (FePcTsNa₄) and cationic poly(diallydimethyl ammonium chloride) were prepared using electrostatic self-assembled layer-by-layer technique. The growth of the film was monitored by ultraviolet-visible absorption spectroscopy, and the morphology of the film was characterized by atomic force microscopy. Polarized visible spectra showed that macrocycles of FePcTsNa₄ in the film presented a flat orientation relative to the plane of the solid substrates. The third-order nonlinear optical properties of the film were studied by using Z-scan technique with laser duration of 21 ps at the wavelength of 532 nm. The FePcTsNa₄/PDDA film exhibited strong self-focusing effect with n₂ value of 4.13 × 10⁻¹⁵ m²/W, which is 4 orders larger than that of FePcTsNa₄ aqueous solution.     

Photonic bandgap properties of 8-fold symmetric photonic quasicrystals

The bandgap properties of 2D 8-fold symmetric photonic quasicrystals (PQCs) composed of a set of rods are numerically investigated for various fill factors, dielectric constants and propagation angles using the finite difference time domain (FDTD) method. Some interesting properties are found besides the known results: (i) the central frequency of the bandgap shifts to low frequency as r/a increases; (ii) an optimum fill factor to obtain the largest gap width exists, which decreases with increasing dielectric constant; (iii) compared with the behavior for a given fill factor, the variation of bandgap width for the optimum fill factor increases much more significantly with the dielectric constant. Selection guidelines for 8-fold symmetric PQC designs are provided for optimum fill factors and variation of the relative bandgap width at different dielectric constants.     

Superbending effect in two-dimensional graded photonic crystals

We study the superbending effect in a two-dimensional graded photonic crystal (GPC) for both TE and TM modes. We show that the lateral beam shift is extremely sensitive to the wavelength for the TM mode but not TE mode, indicating the potential in designing some special superbending devices, for example, TE/TM splitter and polarization-indifference waveguide at prescribed wavelengths.     

Quantitative analysis of subdiffractive light propagation in photonic crystals

We present a qualitative study of the subdiffractive light beam propagation in photonic crystals, based on the theoretical analysis of full Maxwell equation system beyond the slowly varying envelope and paraxial approximations. We calculate the zero diffraction curve in the parameter space, we calculate the weak asymptotical broadening (spreading in transverse direction), and we also analyze the dependence of subdiffractive propagation on the polarization orientation (both for TM and TE polarization).