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)     

Anisotropy of nonlinear optical transmission at the edge of the photonic band gap of an apodized layered medium

The effect of Kerr nonlinearity on the transmission of laser radiation in a one-dimensional photonic crystal has been investigated by the transfer-matrix method, modified to describe nonlinear effects. The crystal under study is a thin-film multilayer structure with a spatial distribution of the refractive index, which makes it possible to eliminate side bands in the transmission spectrum at each side of the photonic band gap and significantly increase the slope of the transmission curve. The transmission spectrum of such a photonic crystal structure has been studied for two opposite directions of laser radiation propagation. The anisotropy of nonlinear transmission is most pronounced near the edge of the photonic crystal band gap, which lies in the near-IR region. The proposed structure, having strong transmission anisotropy and sufficiently low reflection in the forward direction, can operate as an optical diode (analog of an electron diode).     

Transient gain in photonic crystals

Using the optical response formula for photonic crystals and the Bloch equations, we analyze coherent emission in arbitrary two-dimensional photonic crystals. The transient emission depends not only on the photon density of the states, but also on the intensity and duration of the pump laser pulses. A transient gain exists if the pump pulse area is a certain value and the transition frequency is tuned to the band edge. The sharp structure of the density of states near the band edge leads to a dramatic enhancement of the transient emission intensity and an abrupt change in the oscillation of the emission field. PACS 42.70.Qs; 32.80.-t; 42.25.Bs     

A way for enhancing second harmonic generation in one-dimensional nonlinear photonic crystals

We investigate one-dimensional nonlinear photonic crystals consisting of ferroelectric domains with the modulated polarization directions. Significant enhancement of second harmonic generation (SHG) is observed from numerical simulations when the frequency of fundamental wave is aimed at the photonic band edge. We devise the model structure with optimal configuration of the polarization directions of the ferroelectric domains in terms of simulated annealing algorithm. The conversion efficiencies of the ‘forward’ and ‘backward’ SHGs can be engineered.     

Inertia of the bound-electron Kerr-type optical nonlinearity in transparent solids

The inertia of the Kerr-type nonlinear-optical response of bound electrons in solids is analyzed. It is shown that, in the case of wide-gap materials, away from the mid-gap frequency E_g/2?, E_g being the band gap, the inertia of this response becomes noticeable only for attosecond pulse features. However, near E_g/2?, where the inertia of bound-electron Kerr-type optical nonlinearity is enhanced by a strong dispersion of two-photon absorption and where the nonlinear refraction is especially strong, light pulses as long as tens and even hundreds of femtoseconds are expected to experience self-steepening and an asymmetric spectral broadening due to the retarded Kerr effect.     

Femtosecond third-harmonic generation:. self-phase matching through a transient. Kerr grating and the way to ultrafast computing

The third harmonic of 810-nm 100-fs pulses at 130 μJ is generated very efficiently when ultrashort pulses from two noncollinear beams interfere in an optical medium to create an instantaneous transient grating via the optical Kerr effect. The grating couples two pathways for third-harmonic generation, each taking two photons from one beam and one photon from the other beam, respectively. The coupling enables self-phase matching in the complete process, resulting in a conversion efficiency of ≈3%. Scattering an independent beam at the transient grating confirms a lifetime limited by the pulse duration, with a reaction on the order of one optical cycle. Using the second harmonic of a Ti-sapphire laser at 405 nm, it is shown that the generation of the transient Kerr grating is a general feature, requiring less than 20 μJ/pulse. By introducing a third femtosecond beam we are able to emulate various digital logic units with femtosecond response. Received: 16 October 2001 / Published online: 6 June 2002     

光子晶体线缺陷波导中的折射率相位移调制增强效应

在传统的基于全内反射原理的低折射率比介质波导所构建的相位移调制型光学器件中,调制区域的长度通常在毫米到厘米量级.由于器件横向尺寸保持在微米量级,因此狭长结构成为了传统光波导器件的典型特征,这限制了光学器件集成度的提高,严重制约了集成光路的进一步发展.光子晶体的出现为高密集成光路的发展提供了一条新的途径.本文使用平面波展开方法计算了光子晶体线缺陷波导中的色散曲线.研究发现:在色散曲线下边缘处,材料折射率的一个微小变化可以引起传输常数的较大变化,如果工作频率点选择在带下边缘附近,则可以大幅度减小相位移调制型器件调制区域的长度.本文使用时域有限差分方法进一步验证这种增强效应,计算结果表明,对于0.46%的折射率变化,光子晶体线缺陷波导中的相位调制长度仅为均匀媒质中相位移调制长度的11.7%.通过以进一步研究,这种增强效应有望应用与高密度集成光路.     

Cross-phase modulation in one-dimensional photonic crystals: applications to all-optical devices

We present a numerical study of a finite photonic band gap structure with a χ⁽³⁾ nonlinearity that couples two input pump beams at frequencies ω₁ and ω₂. We show that in this configuration a variety of all-optical devices can be obtained: an optical transistor, a double switch, and a dynamical switch.     

Optical bistability at angular incidence in a one-dimensional photonic crystal containing single negative materials

Nonlinear wave propagation is studied theoretically in a one-dimensional photonic band gap structure containing single negative materials. It is found that Kerr nonlinearity is greatly enhanced near the lower edge of a recently explored angular gap for transverse magnetic polarized light. Consequently, optical bistability is achieved at very low values of input intensity in a periodic structure composed of only a few repeating units. The characteristics of optical bistability are affected only slightly with the variation of the incident angle and thickness ratio of the layers. The effect of losses is also found to be relatively insignificant in such a small structure.     

Optical switching applications of ZnSe/MgF2 photonic band gap structures based on thermal nonlinearities

We investigate a thermo-optical device based on a ZnSe/MgF₂ multilayer and demonstrate the modulation of its optical reflectance around the band edge. An electrically induced temperature increase is responsible for the change of the refractive indices of the layers. As a result, the reflection spectrum shifts and the reflected signal decreases. The structure was grown using a thermal evaporation technique, and was designed in such a way that a band edge appears at 632.8 nm, i.e. accessible to a low-power He–Ne laser. The reflection characteristics were investigated as a function of the applied voltage and we found that the photonic band edge shifts by a maximum of 7 nm for an applied voltage of 90 V. Furthermore, different sets of measurements have shown that the spectral shift depends on the voltage squared, thus allowing experimental data analysis in terms of the thermally driven optical nonlinearity.     

Transient-mode excitation, terahertz generation and wavelength shifting in a photonic band gap

Dynamic responses of photonic crystal microcavities in nonlinear media are analyzed via both a finite-difference code and coupled-mode theory in the time domain. Optical frequency generation in both second- and third-order nonlinear materials is demonstrated based on the transient evolution of cavity modes. Terahertz waves can be generated in quadratically nonlinear crystals by optical rectification, whereas state generation inside the band gap can be linked to a Rabi-like splitting in cubic media. An all-optical ultra-fast wavelength shifter is proposed.     

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.     

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.     

Spectral Analysis using Linearly Chirped Gaussian Pulse Stacking

We analyze the spectrum of a stacked pulse with the technique of linearly chirped Gaussial2 pulse stacking. Our results show that there are modulation structures in the spectrum of the stacked pulse. The modulation frequencies are discussed in detail. By applying spectral analysis, we find that the intensity fluctuation cannot be smoothed by introducing an optical amplitude filter.     

Giant Kerr nonlinearities and slow optical solitons in coupled double quantum-well nanostructure

We investigate the enhancement of Kerr nonlinearities in an asymmetric coupled double quantum-well (CQW) by analyzing the nonlinear optical response. With the consideration of real parameters in AlGaAs-based CQWs, we indicate the possibility to obtain the giant Kerr nonlinearities with the cancellation of linear absorption simultaneously. We also reveal both analytically and numerically that under appropriate conditions a probe field with very low intensity can evolve into a stable shape-preserving waveform that propagates with a slow group velocity. The stability of such slow optical solitons is also demonstrated numerically.     

Optimization of two-photon absorption enhancement in one-dimensional photonic crystals with defect states

One-dimensional photonic crystals with a defect layer of CdS were fabricated. The observed enhancement of two-photon absorption (TPA) in the CdS layer can be attributed to the intensified optical field confined within the defect layer of the photonic crystal. The results show that the enhancement of TPA coefficient depends basically on the number of periods of the photonic crystal and the defect mode position in the photonic band gap. The observation agrees qualitatively with the expectations of a computation by matrix transfer formulation.     

Optical confinement of spatial frequencies in the photonic crystal waveguide

The optical confinement of spatial frequencies in the photonic crystal waveguide has been investigated theoretically and simulated numerically. It is found that the enhanced gap confinement is at frequency close to the upper band edge, in contrary to the conventional concept that the strongest optical confinement is found at frequencies near the mid-gap. The anomalous phenomenon may be attributed to a Van Hove saddle point singularity in a band adjacent to a photonic crystal band gap. In general, the saddle point favors the appearance of a very flat band, which in turn causes an enhanced confinement at band-gap frequencies.     

Two-dimensional photonic crystals with pure germanium-on-insulator

We have investigated pure germanium two-dimensional photonic crystals. The photonic crystals which exhibit resonances in the near infrared spectral range were fabricated on germanium-on-insulator substrates using standard silicon-based processing. The germanium-on-insulator substrate consists of a thin layer of pure germanium-on-oxide deposited on a silicon substrate. The optical properties are probed by the direct band gap optical recombination of pure germanium at room temperature. Resonant optical modes are evidenced between 1.68 and 1.53 μm in different type of hexagonal cavities (H1-H5). The spectral position of the modes is controlled by the lattice periodicity and air filling factor of the photonic crystals. Close to the Ge band edge, the quality factors are limited by the bulk material absorption.     

染料掺杂光子晶体荧光带隙边缘的激射研究

利用激光全息光刻技术, 在重铬酸盐明胶 感光材料中制备了掺杂有机染料的层状光子晶体. 在532 nm纳秒脉冲激光激励下, 样品的荧光光谱表现出良好的带隙特征; 随着抽运能量的增加, 在荧光带隙带边位置获得了激射光, 并进一步研究了光子晶体的带边位置与染料荧光峰的匹配对激射的影响.带边位置越靠近染料的荧光峰, 激射阈值越低, 反之则不易产生激射.该研究为超低阈值光子晶体激光器的发展提供了思路和方法. 关键词： 全息光刻 光子晶体 荧光带隙 低阈值激射