Structural and optical characterization of photonic crystals synthesized using the inward growing self-assembling method

We present a systematic analysis of three-dimensionally (3D) ordered photonic crystals fabricated using the recently reported inward growing self-assembling method. The structural and optical characterizations reveal extremely high quality features in these crystals. These include the high reflectance values in the first order stop band and the high energy optical response observed in all the samples, irrespective of the diameter of the spheres, even though the time for fabrication is less than three hours. The photonic stop band is tuned by varying the angle of incidence of light. The peak reflectance and the width of the photonic stop band are unaffected up to an angle of incidence of 45°. At higher angles of incidence, the involvement of other planes in the Bragg reflection is qualitatively demonstrated, emphasizing the extent of ordering and the quality of photonic crystals.     

Analysis of femtosecond optical pulse propagation in one-dimensional nonlinear photonic crystals using finite-difference time-domain method

In this paper, we have used the finite-difference time-domain (FDTD) method to analyze the optical pulse propagation in a nonlinear, one-dimensional photonic crystal (1DPC). Hyperbolic secant pulses with various carrier wavelengths are utilized in this study. In a nonlinear regime, a 1DPC introduces a photonic band-gap whose central wavelength and width depend on the input pulse intensity. In the present work, three different cases are considered. These correspond to the carrier wavelengths of the incident pulses being out of, near to, and partially in the band-gap. For each case, the effect of nonlinearity on pulse propagation is investigated. Also, we have analyzed the two-frequency regime, in which each of the two pulses has a different carrier frequency (wavelength). This kind of study can be done directly with FDTD without any further computational burden but it is somewhat complicated using nonlinear coupled-mode equations (NLCME) and nonlinear Schrödinger equation (NLSE), which require separate treatments for each carrier wavelength.     

Optical interference in nonlinear photonic crystals

A model to analyze the interaction of the parametric fields being generated in a two-dimensional nonlinear photonic crystal has been developed. The analysis provides details of the interference of the generated wave(s) both inside and in the region just outside the crystal. The results are verified by second-harmonic generation in a LiNbO3 crystal that has been poled with a tetragonal inverted domain structure.     

Vorticity cutoff in nonlinear photonic crystals

Using group-theory arguments, we demonstrate that, unlike in homogeneous media, no symmetric vortices of arbitrary order can be generated in two-dimensional (2D) nonlinear systems possessing a discrete-point symmetry. The only condition needed is that the nonlinearity term exclusively depends on the modulus of the field. In the particular case of 2D periodic systems, such as nonlinear photonic crystals or Bose-Einstein condensates in periodic potentials, it is shown that the realization of discrete symmetry forbids the existence of symmetric vortex solutions with vorticity higher than two.     

Optical chaos in nonlinear photonic crystals

We examine the spatial evolution of lightwaves in a nonlinear photonic crystal with a quadratic nonlinearity, when a second harmonic and a sum-frequency generation are simultaneously quasi-phase-matched. We find the conditions for a transition to Hamiltonian chaos for different amplitudes of lightwaves at the crystal boundary.     

Electromagnetic-field amplification in finite one-dimensional photonic crystals

The electromagnetic-field distribution in a finite one-dimensional photonic crystal is studied using the numerical solution of Maxwell’s equations by the transfer-matrix method. The dependence of the transmission coefficient T on the period d (or the wavelength λ) has the characteristic form with M–1 (M is the number of periods in the structure) maxima with T = 1 in the allowed band of an infinite crystal and zero values in the forbidden band. The field-modulus distribution E(x) in the structure for parameters that correspond to the transmission maxima closest to the boundaries of forbidden bands has maxima at the center of the structure; the value at the maximum considerably exceeds the incident-field strength. For the number of periods M ~ 50, more than an order of magnitude increase in the field amplification is observed. The numerical results are interpreted with an analytic theory constructed by representing the solution in the form of a linear combination of counterpropagating Floquet modes in a periodic structure.     

Group-velocity-matched multistep cascading in nonlinear photonic crystals

We demonstrate that simultaneous phase- and group-velocity-matched cascaded parametric processes can be achieved in two-dimensional quadratic nonlinear photonic crystals by proper matching of noncollinear processes with front tilting of the fundamental pulse. We present examples of cascaded third- and fourth-harmonic generation in a poled LiNbO3 planar structure.     

Multifrequency gap solitons in nonlinear photonic crystals

We predict the existence of multifrequency gap solitons (MFGSs) in both one- and two-dimensional nonlinear photonic crystals. A MFGS is a single intrinsic mode possessing multiple frequencies inside the gap. Its existence is a result of synergic nonlinear coupling among solitons or soliton trains at different frequencies. Its formation can either lower the threshold fields of the respective frequency components or stabilize their excitations. These MFGSs form a new class of stable gap solitons.     

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.     

Terahertz modulator using photonic crystals

In this letter, a novel terahertz wave modulator based on a silicon oxide/polyaniline photonic crystal is proposed. The modulation mechanism of the novel modulator is based on a dynamic shift of the photonic band gap by the applied external electric field. Its performances were investigated with the finite-difference time-domain method. The novel modulator has 3 dB modulation bandwidth of 10 kHz, a size as small as 20 mm and its extinction ratio larger than 30 dB at the frequency of 1 THz.     

Band-structure determination for finite 3-D photonic crystals

The partial band structure from a finite photonic crystal is determined using a model based on light diffraction and the transfer-matrix formalism. The predictions from such a model are compared to an experimental measurement of the bands in the LU direction of a face centered cubic colloidal crystal. Then, both the theoretical predictions and the experimental measurements are compared with the usual band-structure calculation based on a plane-wave expansion with perfectly periodic boundary conditions. As in measurements performed in the past, discrepancies between the predictions of this later model and the experimentally determined bands are observed. On the contrary, using the model presented based on light propagation through a finite crystal, where no periodicity is imposed in the direction perpendicular to any of the set of planes considered to determine a specific branch of the band structure, we found a very good agreement between the experimentally determined and the predicted bandwidths.     

Photoacoustic method for orientation and optical characterization of nonlinear crystals

Second-harmonic conversion of the 532-nm pulsed output of a doubled Nd:YAG laser in KDP was characterized by analyzing the changes in the acoustic signals generated in the crystal at different orientation conditions and for several incident fluences. Using a piezoelectric transducer, phase-matching condition was determined by maximizing the amplitude of the acoustic signals detected. The angular orientation for optimum harmonic efficiency was obtained with the same precision compared with the conventional optical procedure. The origin of the photoacoustic signals is the relaxed energy following the absorption of 266-nm photons. To determine the mechanisms of the 266-nm absorption processes, we also performed experiments under direct illumination with the 266-nm emission of the quadrupled Nd:YAG laser. A combination of a linear and nonlinear process occurs. Direct absorption by KDP as well as the participation of transient defects produced in the material were analyzed. Received: 27 July 1998 / Revised version: 19 March 1999 / Published online: 19 August 1999     

Optically tunable superprism effect in nonlinear photonic crystals

An analysis of the tunable superprism effect in a two-dimensional nonlinear photonic crystal is presented. We show that, by shifting the photonic bands of the crystal through the Kerr effect induced by a pump beam, one can tune the refraction angle of a transmitted signal beam over tens of degrees. We also demonstrate that the optical power required to tune the refracted angle is dramatically reduced if the frequency of the pump beam is close to a bandgap edge.     

Ultrafast optical switching in Kerr nonlinear photonic crystals

Nonlinear photonic crystals made from polystyrene materials that have Kerr nonlinearity can exhibit ultrafast optical switching when the samples are pumped by ultrashort optical pulses with high intensity due to the change of the refractive index of polystyrene and subsequent shift of the band gap edge or defect state resonant frequency. Polystyrene has a large Kerr nonlinear susceptibility and almost instantaneous response to pump light, making it suitable for the realization of ultrafast optical switching with a response time as short as a few femtoseconds. In this paper, we review our experimental progress on the continual improvement of all-optical switching speed in two-dimensional and three-dimensional polystyrene nonlinear photonic crystals in the past years. Several relevant issues are discussed and analyzed, including different mechanisms for all-optical switching, preparation of nonlinear photonic crystal samples by means of microfabrication and self-assembly techniques, characterization of optical switching performance by means of femtosecond pump-probe technique, and different ways to lower the pump power of optical switching to facilitate practical applications in optical information processing. Finally, a brief summary and a perspective of future work are provided.     

Quasi phase matching in two-dimensional nonlinear photonic crystals

We analyze quasi-phase-matched (QPM) conversion efficiency of the five possible types of periodic two-dimensional nonlinear structures: Hexagonal, square, rectangular, centered-rectangular, and oblique. The frequency conversion efficiency, as a function of the two-dimensional quasi-phase-matching order, is determined for the general case. Furthermore, it is demonstrated for two basic feasible motifs, a circular motif and a rectangular motif. This enables to determine the optimal motif dimensions for achieving the highest conversion efficiency. We find that a rectangular motif is more efficient than a circular motif for quasi-phase-matched processes that rely on a single reciprocal lattice vector (RLV), and that under optimal choice of motif dimensions, it converges into a one-dimensional periodic structure. In addition, in a few specific cases we found that higher order QPM can be significantly more efficient than lower order QPM.     

Ultrafast optical switching in Kerr nonlinear photonic crystals

Nonlinear photonic crystals made from polystyrene materials that have Kerr nonlinearity can exhibit ultrafast optical switching when the samples are pumped by ultrashort optical pulses with high intensity due to the change of the refractive index of polystyrene and subsequent shift of the band gap edge or defect state resonant frequency. Polystyrene has a large Kerr nonlinear susceptibility and almost instantaneous response to pump light, making it suitable for the realization of ultrafast optical switching with a response time as short as a few femtoseconds. In this paper, we review our experimental progress on the continual improvement of all-optical switching speed in two-dimensional and three-dimensional polystyrene nonlinear photonic crystals in the past years. Several relevant issues are discussed and analyzed, including different mechanisms for all-optical switching, preparation of nonlinear photonic crystal samples by means of microfabrication and self-assembly techniques, characterization of optical switching performance by means of femtosecond pump-probe technique, and different ways to lower the pump power of optical switching to facilitate practical applications in optical information processing. Finally, a brief summary and a perspective of future work are provided.     

有限开敞介质光子晶体的模式及其带结构分析

针对光子晶体在行波管中的应用,对有限开敞介质光子晶体的模式和带结构进行了分析和计算. 分析表明,有限开敞介质光子晶体中所能存在的模式包括EH和HE混合模式,如果是二维光子晶体,还存在E模式,E₁模式即为无限光子晶体中的E极化. 计算表明,被用作行波管慢波电路的光子晶体可以不必拥有完全带隙,而只需要具有带间隙即可. 关键词： 光子晶体 本征值方程 行波管 带结构     

Study of electromagnetic field surface states in photonic crystals using the finite-difference method

Bulletin of the Lebedev Physics Institute - The properties of electromagnetic field surface states in globular photonic crystals are analyzed using numerical solution of Maxwell equations by the...