ABCD matrix for reflection and refraction of Gaussian beams at the surface of a parabola of revolution

We report the formulation of an ABCD matrix for reflection and refraction of Gaussian light beams at the surface of a parabola of revolution that separate media of different refractive indices based on optical phase matching. The equations for the spot sizes and wave-front radii of the beams are also obtained by using the ABCD matrix. With these matrices, we can more conveniently design and evaluate some special optical systems, including these kinds of elements. (c) 2005 Optical Society of America

Effect of recording conditions on the anisotropic diffraction of volume holographic gratings

The anisotropic Bragg diffraction of the volume holographic gratings in photorefractive crystals are investigated based on the model of anisotropic coupled-wave theory. The effect of the initial intensity ratio and the recording angles of the two recording waves on the anisotropic Bragg diffraction properties is discussed. It is shown that both the ratio of the initial intensity and the incident angles of the recording waves are selective action for the anisotropic Bragg diffraction efficiency of the volume holographic gratings, while these two recording conditions are not selective action for the isotropic Bragg diffraction. Furthermore, the Bragg phase matching condition of anisotropic diffraction is analyzed when the recording angles change. (C) 2006 Elsevier GmbH. All rights reserved.

光谱相位相干技术测量飞秒脉冲的倍频误差

从理论上推导了第Ⅱ类相位匹配下宽带飞秒脉冲的二次谐波光场,分析输入飞秒脉冲的非共线相位匹配方式、脉冲带宽引起相位失配与群速失配对测量的影响。结果表明,为了消除飞秒脉冲的带宽影响,需要对测量记录的光强乘以一个调制因子;测量相位误差与非共线相位匹配的夹角和晶体长度成正比;相位失配与群速失配产生相位测量误差,且第Ⅱ类相位匹配方式下脉冲附加相位值较大;强度和相位误差需要在脉冲重建结果中补偿。

Wavelength conversion based on degenerate-four-wave-mixing with continuous-wave pumping in silicon nanowire waveguide

We present a comprehensive numerical study on the all-optical wavelength conversion based on the degenerate four-wave-mixing with continuous-wave pumping in the silicon nanowire waveguide. It is well known that the conversion efficiency and the 3-dB bandwidth can be greatly affected by the phase-matching condition. Through proper design of the waveguide cross-section, its dispersion property can be adjusted to satisfy the phase-matching condition and therefore effective wavelength conversion can be achieved in a large wavelength range. Generally, the group velocity dispersion plays a dominant role in the wavelength conversion. However, the fourth-order dispersion takes an important effect on the wavelength conversion when the group velocity dispersion is near the zero-point. Furthermore, the conversion efficiency and the 3-dB bandwidth can also be affected by the interactive length and the initial pump power. Through the numerical simulation, the optimal values for the interactive length and the initial pump power, which are functions of the propagation loss, are obtained to realize the maximum conversion efficiency. (C) 2008 Elsevier B.V. All rights reserved.

Design and Fabrication of a Photonic Crystal Channel Drop Filter Based on an Asymmetric Silicon-on-Insulator Slab

We report on the design and fabrication of a photonic crystal (PC) channel drop filter based on an asymmetric silicon-on-insulator (SOI) slab. The filter is composed of two symmetric stick-shape micro-cavities between two single-line-defect (W1) waveguides in a triangular lattice, and the phase matching condition for the filter to improve the drop efficiency is satisfied by modifying the positions and radii of the air holes around the micro-cavities. A sample is then fabricated by using electron beam lithography (EBL) and inductively coupled plasma (ICP) etching processes. The measured 0 factor of the filter is about 1140, and the drop efficiency is estimated to be 73% +/- 5% by fitting the transmission spectrum.

Second-harmonic generation of Bogoliubov excitations in a two-component Bose-Einstein condensate

A second-harmonic generation (SHG) is predicted for the Bogoliubov excitations in a two-component Bose-Einstein condensate. It is shown that, because the linear dispersion curve of the excitations displays two branches, the phase-matching condition for the SHG can be fulfilled if the wave vectors and frequencies of fundamental and second-harmonic waves are selected suitably from different branches. The nonlinearly coupled envelope equations for the SHG are derived by using a method of multiple scales. The explicit solutions of these envelope equations are provided and the conversion efficiency of the SHG is also discussed.

Optical characteristics of DBR with inhomogeneous graded interfaces

Optical properties of Al0.9Ga0.1As/Al gamma Ga1-gamma As/GaAs/Al chi Ga1-chi As DBR with inhomogeneous graded interfaces has been investigated by using characteristic matrix method. The refractive index model and the analytic characteristic matrix of graded interfaces are obtained. The reflectance spectrum and the reflective phase shift are calculated for GaAs/Al-0.9 Ga-0.1 As DBR and graded interfaces DBR by using characteristic matrix method. The effect of graded interfaces on the optical properties of DBR is discussed. The result shows an extra graded phase matching layer must he added in front of the graded interfaces DBR to fulfil the conditions of phase matching at central wavelength. The accurate thickness of phase matching layer is calculated by optical thickness approximation method.

Theory and experiment of two-photon 'direct' interference for type-II spontaneous parametric down-conversion with an ultrafast pulse laser pump

Fourth-order spatial interference of entangled photon pairs generated in the process of spontaneous parametric down-conversion pumped by a femtosecond pulse laser has been performed for the first time. In theory, it takes into account the transverse correlation between the two photons and is used to calculate the dependence of the visibility of the interference pattern obtained in Young's double-slit experiment. In this experiment, a short focal length tens and two narrow band interference filters were adopted to eliminate the effects of the broadband pump laser and improve the visibility of the interference pattern under the condition of nearly collinear light and degenerate phase matching.

Design and Fabrication of a Photonic Crystal Channel Drop Filter Based on an Asymmetric Silicon-on-Insulator Slab

We report on the design and fabrication of a photonic crystal (PC) channel drop filter based on an asymmetric silicon-on-insulator (SOI) slab. The filter is composed of two symmetric stick-shape micro-cavities between two single-line-defect (W1) waveguides in a triangular lattice, and the phase matching condition for the filter to improve the drop efficiency is satisfied by modifying the positions and radii of the air holes around the micro-cavities. A sample is then fabricated by using electron beam lithography (EBL) and inductively coupled plasma (ICP) etching processes. The measured 0 factor of the filter is about 1140, and the drop efficiency is estimated to be 73% +/- 5% by fitting the transmission spectrum.

Tunable parametric fluorescence using a single crystal

In this paper, we investigate the mechanism of tunable parametric superfluorescence (PS) based on the second harmonic generation and parametric processes taking place in the same nonlinear crystal (BBO). The tunable spectra of PS has been generated between 480 nm and 530 nm, which is pumped by the second-harmonic from the high-power Ti: sapphire laser system at 1 kHz repetition rate. We present the generation mechanism of PS theoretically and simulate the process of PS ring using the amplification transfer function. The experiment and the theory show that PS will appear when the phase matching angle for second-harmonic generation is close to the optimal pump angle for optical parametric generation, and then the tunable spectra of PS are generated by slightly adjusting the crystal angle. The result provides a theoretical basis for controlling the generation of PS and quantum entanglement states, which is of great significance for the development of quantum imaging, quantum communications and other applieations.

Supercontinuum generation in air-silica microstructured fibers with nanosecond and femtosecond pulse pumping

We study the generation of supercontinua in air-silica microstructured fibers by both nanosecond and femtosecond pulse excitation. In the nanosecond experiments, a 300-nm broadband visible continuum was generated in a 1.8-m length of fiber pumped at 532 nm by 0.8-ns pulses from a frequency-doubled passively Q-switched Nd:YAG microchip laser. At this wavelength, the dominant mode excited under the conditions of continuum generation is the LP 11 mode, and, with nanosecond pumping, self-phase modulation is negligible and the continuum generation is dominated by the interplay of Raman and parametric effects. The spectral extent of the continuum is well explained by calculations of the parametric gain curves for four-wave mixing about the zero-dispersion wavelength of the LP11 mode. In the femtosecond experiments, an 800-nm broad-band visible and near-infrared continuum has been generated in a 1-m length of fiber pumped at 780 nm by 100-fs pulses from a Kerr-lens model-locked Ti:sapphire laser. At this wavelength, excitation and continuum generation occur in the LP01 mode, and the spectral width of the observed continuum is shown to be consistent with the phase-matching bandwidth for parametric processes calculated for this fiber mode. In addition, numerical simulations based on an extended nonlinear Schrödinger equation were used to model supercontinuum generation in the femtosecond regime, with the simulation results reproducing the major features of the experimentally observed spectrum. © 2002 Optical Society of America.

Wave mixing of hybrid Bogoliubov modes in a Bose-Einstein condensate

Mode-mixing of coherent excitations of a trapped Bose-Einstein condensate is modeled using the Bogoliubov approximation. Calculations are presented for second-harmonic generation between the two lowest-lying even-parity m=0 modes in an oblate spheroidal trap. Hybridization of the modes of the breather (l=0) and surface (l=4) states leads to the formation of a Bogoliubov dark state near phase-matching resonance so that a single mode is coherently populated. Efficient harmonic generation requires a strong coupling rate, sharply-defined and well-separated frequency spectrum, and good phase matching. We find that in all three respects the quantal results are significantly different from hydrodynamic predictions. Typically the second-harmonic conversion rate is half that given by an equivalent hydrodynamic estimate.

Simulação do comportamento espectral de redes de período longo em fibra óptica

Esta tese é dedicada às redes de período longo, LPG’s, em fibra óptica, escritas por exposição a radiação ultravioleta (UV) ou por exposição a descargas eléctricas, e às suas aplicações em comunicações ópticas e em sistemas sensores. Numa primeira fase estudaram-se os aspectos teóricos fundamentais para a compreensão das LPG, nomeadamente os dois modelos matemáticos propostos na literatura, para a transmissão espectral de uma LPG, o modelo de duas camadas e o modelo de três camadas. Em seguida, estudou-se o deslocamento do comprimento de onda ressonante perante mudanças de parâmetros externos. Aqui, verificou-se que para variações da temperatura no exterior da LPG, o deslocamento do comprimento de onda ressonante é linear. Por outro lado, para variações de índice de refracção exterior, verificou-se que à medida que o índice exterior se aproxima dos valores do índice de refracção da bainha, o comprimento de onda ressonante tende para valores mais baixos. Por último, realizou-se um estudo da transmissão espectral de duas aplicações que envolvem LPG’s, nomeadamente dois tipos de interferómetros e filtros ópticos. Numa segunda fase, foi desenvolvida uma ferramenta de simulação destes modelos, que permitia não só a obtenção dos espectros de transmissão das LPG’s mas também a obtenção das curvas de phase matching em função do período da rede e do comprimento de onda ressonante. A aplicação permitia também a obtenção das curvas do deslocamento do comprimento de onda ressonante, perante variações do índice de refracção exterior ou da temperatura. Para além disso, essa ferramenta realiza a simulação dos espectros de transmissão de filtros ópticos e de interferómetros de Michelson e de Mach-Zehnder construídos com base em LPG’s. A última fase do trabalho, a componente laboratorial, foi realizada na Unidade de Optoelectrónica e Sistemas Electrónicos do INESC Porto, onde foram construídos e testados os dispositivos estudados anteriormente, com o intuito de validar a aplicação desenvolvida. A ferramenta de simulação demonstrou ser capaz de simular de forma adequada os diversos aspectos do comportamento das LPG’s que foram estudados. A comparação dos resultados obtidos permitiu concluir que o modelo mais correcto para o estudo das LPG’s é o modelo de três camadas, o que está de acordo com o esperado.

Eine kontinuierliche Lyman-alpha-Quelle basierend auf Festkörperlasersystemen

In dieser Arbeit wird eine schmalbandige kontinuierliche kohärente Lyman-α-Quelle basierend auf Festkörperlasersystemen zur zukünftigen Kühlung von Antiwasserstoff vorgestellt. Die fundamentalen Festkörperlasersysteme ermöglichen es im Vier-Wellen-Misch-Prozess zur Erzeugung der Lyman-α-Strahlung nicht nur die 6^1S – 7^1S-Zwei-Photonen-Resonanz des Quecksilbers sondern erstmals auch die 6^1S – 6^3P-Ein-Photonen-Resonanz zur Erhöhung der Konversionseffizienz optimal zu nutzen. In ersten Messungen wurden 0,063nW Leistung bei Lyman-α erzeugt. Mit dieser Lyman-α-Quelle war es, durch die Nähe des ersten fundamentalen Lasers zur Ein-Photonen-Resonanz, erstmals möglich den kompletten Verlauf der Phasenanpassungskurve des Vier-Wellen- Misch-Prozesses aufzunehmen. Neben den fundamentalen Lasersystemen und der Lyman-alpha-Erzeugung selbst, wird in dieser Arbeit die Detektion der produzierten Lyman-α-Strahlung mit einem Photomultiplier vorgestellt, die soweit optimiert wurde, dass eine zuverlässige Abschätzung der erzeugten Leistung möglich ist. Für diesen Zweck wurde zudem ein Teststand aufgebaut, mit dem die Transmissivität der Optiken, welche in der Lyman-α-Apparatur verwendet werden, bei 121,56nm gemessen wurde. Des Weiteren wird hier eine vielseitige Rechnung vorgestellt, mit der die erzeugte Leistung bei Lyman-α, unter anderem in Abhängigkeit von der Temperatur, der Absorption des ersten fundamentalen Laserstrahls, dem Dichteprofil des Quecksilberdampfes und unter dem Einfluss eines Puffergases, bestimmt wird.

Einfluss der 6 1 S - 6 3 P-Resonanz auf die Lyman-alpha-Erzeugung in Quecksilber

In dieser Arbeit wird eine kontinuierliche, kohärente Strahlungsquelle bei 121,56nm, der Lyman-alpha Linie in Wasserstoff, vorgestellt. Diese Lyman-alpha Quelle soll zur zukünftigen Laserkühlung von Antiwasserstoff dienen. Die Strahlung wird durch Vier-Wellen-Mischen in Quecksilberdampf produziert. Dabei wird ein Festkörperlasersystem zur Erzeugung der Fundamentalstrahlen eingesetzt. Zur Erhöhung der nichtlinearen Suszeptibilität wird die 6^1S-7^1S Zwei-Photonen-Resonanz ausgenutzt. Zusätzlich wird mit Hilfe eines durchstimmbaren ultravioletten Lasersystems die 6^1S-6^3P Ein-Photon-Resonanz genutzt, was es erlaubt, die nichtlineare Suszeptibilität des Mischprozesses um Größenordnungen zu erhöhen. Um den Einfluss der 6^1S-6^3P Ein-Photon-Resonanz zu untersuchen, wurden zunächst die Phasenanpassungstemperaturen bei verschiedenen Verstimmungen der ultravioletten Strahlung zur 6^3P Resonanz vermessen und festgestellt, dass kleinere Verstimmungen zu niedrigeren Phasenanpassungstemperaturen führen. Es konnte sowohl theoretisch wie auch experimentell gezeigt werden, dass diese niedrigeren Phasenanpassungstemperaturen bei kleinen Verstimmungen der Erhöhung der Lyman-alpha Erzeugung durch die größere nichtlineare Suszeptibilität bei kleinen Verstimmungen entgegenwirken. Bei immer kleineren Verstimmungen zur 6^3P Resonanz limitiert die Absorption der ultravioletten Strahlung die Lyman-alpha Erzeugung. Ein positiver Effekt der niedrigeren Phasenanpassungstemperaturen ist, dass es möglich wird, auf das bisher nötige Puffergas in der Quecksilber-Dampfzelle zu verzichten, was die Lyman-alpha Erzeugung um einen Faktor 1,7 erhöht. Damit war es möglich, die bisherige Effizienz der Lyman-alpha Erzeugung zu verbessern. Es wurde eine Lyman-alpha Leistung von 0,3nW erreicht. Zusätzlich zum Einfluss der 6^3P Resonanz auf die Lyman-alpha Erzeugung wurde ein weiterer Effekt beobachtet. Durch die Nähe der 6^1S-6^3P Ein-Photon-Resonanz wird auch mehr Besetzung in das obere 7^1S Niveau der Zwei-Photonen-Resonanz gepumpt. Dadurch konnte erstmals eine kontinuierliche Lasertätigkeit auf der 6^1P-7^1S Linie in Quecksilber bei 1014nm beobachtet werden.