高斯束射线追踪

Using the approximate high-frequency asymptotic methods to solve the scalar wave equation, we can get the eikonal equation and transport equation. Solving the eikonal equation by the method of characteristics provides a mathematical derivation of ray tracing equations. So, the ray tracing system is folly based on the approximate high-frequency asymptotic methods. If the eikonal is complex, more strictly, the eikonal is real value at the rays and complex outside rays, we can derive the Gaussian beam. This article mainly concentrates on the theory of Gaussian beam. To classical ray tracing theory, the Gaussina beam method (GBM) has many advantages. First, rays are no longer required to stop at the exact position of the receivers; thus time-consuming two-point ray tracing can be avoided. Second, the GBM yields stable results in regions of the wavefield where the standard ray theory fails (e.g., caustics, shadows zones and critical distance). Third, unlike seismograms computed by conventional ray tracing techniques, the GBM synthetic data are less influenced by minor details in the model representation. Here, I realize kinematical and dynamical system, and based on this, realize the GBM. Also, I give some mathematical examples. From these examples, we can find the importance and feasibility of the ray tracing system. Besides, I've studied about the reflection coefficient of inhomogeneous S-electromagnetic wave at the interface of conductive media. Basing on the difference of directions of phase shift constant and attenuation constant when the electromagnetic wave propagates in conductive medium, and using the boundary conditions of electromagnetic wave at the interface of conductive media, we derive the reflection coefficient of inhomogeneous S-electromagnetic wave, and draw the curves of it. The curves show that the quasi total reflection will occur when the electromagnetic wave incident from the medium with greater conductivity to the medium with smaller conductivity. There are two peak, values at the points of the critical angles of phase shift constant and attenuation constant, and the reflection coefficient is smaller than 1. This conclusion is different from that of total reflection light obviously.

Biosensor with Total Internal reflection Imaging Ellipsometry

In order to monitor multiple protein reaction processes simultaneously, a biosensor based on imaging ellipsometry operated in the total internal reflection mode is proposed. It could be realised as an automatic analysis for protein interaction processes with real-time label-free method. Its principle and methodology as well as a demonstration for its applications are presented.

Nonpolarizing beam splitter designed by frustrated total internal reflection inside a glass cube

A method for the design of an all-dielectric nonpolarizing prism beam splitter utilizing the principle of frustrated total internal reflection is reported. The nonpolarizing condition for a prism beam splitter is discussed, and some single layer design examples are elaborated. The concept can be applied to a wide range of wavelengths and arbitrary transmittance values, and with the help of a computer design program examples of 400-700 nm, T-p = T-p = 0.5 +/- 0.01, with incident angles of 45 degrees and 62 degrees are given. In addition, the sensitivity and application of the design are also discussed. (c) 2006 Optical Society of America.

Design of high-efficiency diffraction gratings based on total internal reflection for pulse compressor

We present designs of high-efficiency compression grating based on total internal reflection (TIR) for picosecond pulse laser at 1053 nm. The setup is devised by directly etching gratings into the bottom side of a prism so that light can successfully enter (or exit) the compression grating. Dependence of the -1 order diffraction efficiencies on the constructive parameters is analyzed for TE- and TM-polarized incident light at Littrow angle by using Fourier modal method in order to obtain optimal grating structure. The electric field enhancement within the high-efficiency TIR gratings is regarded as another criterion to optimize the structure of the TIR gratings. With the criterion of high diffraction efficiency, low electric field enhancement and sufficient manufacturing latitude, TIR compression gratings with optimized constructive parameters are obtained for TE- and TM-polarized incident light, respectively. The grating for TE-polarized light exhibits diffraction efficiencies higher than 0.95 within 23 nm bandwidth and relatively low square of electric field enhancement ratio of 5.7. Regardless of the internal electric field enhancement, the grating for TM-polarized light provides diffraction efficiencies higher than 0.95 within 42 nm bandwidth. With compact structure, such TIR compression gratings made solely of fused silica should be of great interest for application to chirped pulse amplification (CPA) systems. (c) 2007 Elsevier B.V. All rights reserved.

Integrated folding 4x4 optical matrix switch with total internal reflection mirrors on SOI by anisotropic chemical etching

A folding rearrangeable nonblocking 4 x 4 optical matrix switch was designed and fabricated on silicon-on-insulator wafer. To compress chip size, switch elements (SEs) were interconnected by total internal reflection (TIR) mirrors instead of conventional S-bends. For obtaining smooth interfaces, potassium hydroxide anisotropic chemical etching of silicon was utilized to make the matrix switch for the first time. The device has a compact size of 20 x 1.6 mm(2) and a fast response of 7.5 mu s. The power consumption of each 2 x 2 SE and the average excess loss per mirror were 145 mW and -1.1 dB, respectively. Low path dependence of +/- 0.7 dB in total excess loss was obtained because of the symmetry of propagation paths in this novel matrix switch.

Novel folding large-scale optical switch matrix with total internal reflection mirrors on silicon-on-insulator by anisotropy chemical etching

A compact optical switch matrix was designed, in which light circuits were folded by total internal reflective (TIR) mirrors. Two key elements, 2 x 2 switch and TIR mirror, have been fabricated on silicon-on-insulator wafer by anisotropy chemical etching. The 2 x 2 switch showed very low power consumption of 140 mW and a very high speed of 8 +/- 1 mus. An improved design for the TIR mirror was developed, and the fabricated mirror with smooth and vertical reflective facet showed low excess loss of 0.7 +/- 0.3 dB at 1.55 mum.

SOI optical switch matrix integrated with spot size converter (SSC) and total internal reflection (TIR) mirrors

SOI (Silicon on Insulator) based photonic devices has attracted more and more attention in the recent years. Integration of SOI optical switch matrix with isolating grooves, total internal reflection (TIR) mirrors and spot size converter (SSC) was studied. A folding re-arrangeable non-blocking 4x4 optical switch matrix and a blocking 16x16 matrix with TIR mirrors and SSC were fabricated on SOI wafer. The performaces, including extinction ratio and the crosstalk, are better than before. The insertion loss and the polarization dependent loss (PDL) at 1.55 mu m increase slightly with longer device length, more bend and intersecting waveguides. The insertion losses decrease 2 similar to 3 dB when anti-reflection films are added in the ends of the devices. The rise and fall times of the devices are 2.1 mu s and 2.3 mu s, respectively.

Large positive and negative lateral displacements from total internal reflection configuration with a weakly absorbing dielectric film

It is theoretically shown that the simultaneously large positive and negative lateral displacements will appear when the resonant condition is satisfied for a TE-polarized light beam reflected from the total internal reflection configuration with a weakly absorbing dielectric film. Appearance of the enhanced negative lateral displacement is relative to the incidence angle, absorption of the thin Elm and its thickness. If we select an appropriate weakly absorbing dielectric film and its thickness, the simultaneously enhanced positive and negative lateral displacements will appear at different resonant angles. These phenomena may lead to convenient measurements and interesting applications in optical devices.

Total-internal-reflection fluorescence microscopy with W-shaped axicon mirrors

A scheme based on a W-shaped axicon mirror device for total-internal-reflection fluorescence microscopy (TIRFM) is presented. This approach combines the advantages of higher efficiency compared with traditional TIRFM, adjustable illumination area, and simple switching between wide-field and TIRF imaging modes. TIRF images obtained with this approach are free of shadow artifacts and of interference fringes. Example micrographs of fluorescently labeled polystyrene beads, of Convallaria majalis tissue, and of Propidium-iodide-labeled Chinese hamster ovary cells are shown, and the capabilities of the scheme are discussed. (C) 2010 Optical Society of America

Reflection and transmission of Gaussian beam from a uniaxial crystal slab

We investigate the characteristics of Gaussian beams reflected and transmitted from a uniaxial crystal slab with an arbitrary orientation of its optical axis. The formulas of the total electric and magnetic fields inside and outside the slab are derived by use of Maxwell's equations and by matching the boundary conditions at the interfaces. Numerical simulations are presented and the field values as well as the power densities are computed. Negative refractions are demonstrated when the beam is transmitted through a uniaxial crystal slab. Beam splitting of the reflected beam is observed and is explained by the resonant transmission for plane waves. Dependences of the lateral shift on the incident angle and beam width are discussed. Negative and positive lateral shifts are observed due to the spatial anisotropic properties.

Roles of equatorial waves and western boundary reflection in the seasonal circulation of the equatorial Indian Ocean

An ocean general circulation model (OGCM) is used to study the roles of equatorial waves and western boundary reflection in the seasonal circulation of the equatorial Indian Ocean. The western boundary reflection is defined as the total Kelvin waves leaving the western boundary, which include the reflection of the equatorial Rossby waves as well as the effects of alongshore winds, off-equatorial Rossby waves, and nonlinear processes near the western boundary. The evaluation of the reflection is based on a wave decomposition of the OGCM results and experiments with linear models. It is found that the alongshore winds along the east coast of Africa and the Rossby waves in the off-equatorial areas contribute significantly to the annual harmonics of the equatorial Kelvin waves at the western boundary. The semiannual harmonics of the Kelvin waves, on the other hand, originate primarily from a linear reflection of the equatorial Rossby waves. The dynamics of a dominant annual oscillation of sea level coexisting with the dominant semiannual oscillations of surface zonal currents in the central equatorial Indian Ocean are investigated. These sea level and zonal current patterns are found to be closely related to the linear reflections of the semiannual harmonics at the meridional boundaries. Because of the reflections, the second baroclinic mode resonates with the semiannual wind forcing; that is, the semiannual zonal currents carried by the reflected waves enhance the wind-forced currents at the central basin. Because of the different behavior of the zonal current and sea level during the reflections, the semiannual sea levels of the directly forced and reflected waves cancel each other significantly at the central basin. In the meantime, the annual harmonic of the sea level remains large, producing a dominant annual oscillation of sea level in the central equatorial Indian Ocean. The linear reflection causes the semiannual harmonics of the incoming and reflected sea levels to enhance each other at the meridional boundaries. In addition, the weak annual harmonics of sea level in the western basin, resulting from a combined effect of the western boundary reflection and the equatorial zonal wind forcing, facilitate the dominance by the semiannual harmonics near the western boundary despite the strong local wind forcing at the annual period. The Rossby waves are found to have a much larger contribution to the observed equatorial semiannual oscillations of surface zonal currents than the Kelvin waves. The westward progressive reversal of seasonal surface zonal currents along the equator in the observations is primarily due to the Rossby wave propagation.

Interferometric Measurement of Density in Nonstationary Shock Wave Reflection Flow and Comparison with CFD

We present density measurements from the application of interferometry and Fourier transform fringe analysis to the problem of nonstationary shock wave reflection over a semicircular cylinder and compare our experimental measurements to theoretical results from a CFD simulation of the same problem. The experimental results demonstrate our ability to resolve detailed structure in this complex shock wave reflection problem, allowing visualization of multiple shocks in the vicinity of the triple point, plus visualization of the shear layer and an associated vortical structure. Comparison between CFD and experiment show significant discrepancies with experiment producing a double Mach Reflection when CFD predicts a transitional Mach reflection.

The Mach reflection of a detonation based on soot track measurements

This paper presents a series of soot tracks formed by gaseous detonation waves diffracting around wedges with different wedge angles. These cellular structure patterns describe the Mach-reflection processes of a detonation and reveal some unique characteristics. They can be used to analyze the relationship between the trajectory angle of the triple point, wedge angle, and initial pressure in Mach reflection. Compared to the Mach-reflected one-dimensional shock wave in nonreactive air, all these unique characteristics for a Mach-reflected detonation should be attributed to the transverse-wave structure of the detonation front; meanwhile, the precursor shock wave and transverse wave influence the Mach-reflected detonation, respectively. The experimental results support the recently published numerical simulation of this complex phenomenon.

Wave Dynamic Processes in Cellular Detonation Reflection from Wedges

When the cell width of the incident detonation wave (IDW) is comparable to or larger than the Mach stem height, self-similarity will fail during IDW reflection from a wedge surface. In this paper, the detonation reflection from wedges is investigated for the wave dynamic processes occurring in the wave front, including transverse shock motion and detonation cell variations behind the Mach stem. A detailed reaction model is implemented to simulate two-dimensional cellular detonations in stoichiometric mixtures of H (2)/O (2) diluted by Argon. The numerical results show that the transverse waves, which cross the triple point trajectory of Mach reflection, travel along the Mach stem and reflect back from the wedge surface, control the size of the cells in the region swept by the Mach stem. It is the energy carried by these transverse waves that sustains the triple-wave-collision with a higher frequency within the over-driven Mach stem. In some cases, local wave dynamic processes and wave structures play a dominant role in determining the pattern of cellular record, leading to the fact that the cellular patterns after the Mach stem exhibit some peculiar modes.