Slowdown of group velocity of light by means of phase coupling in photorefractive two-wave mixing

We show theoretically that the group velocity of light can be slowed down by means of phase coupling in the photorefractive two-wave mixing process. It is shown that the group velocity of light propagating in a photorefractive material could be significantly reduced because of a steep variation of the phase-coupling coefficient with respect to the angular frequency difference between two coupling beams in a two-wave mixing process. The results for the case of a photorefractive Bi12SiO20 crystal are presented and discussed in detail.     

Three interfering beams in laser Doppler velocimetry for particle position and microflow velocity profile measurements

It is proposed to use three interfering and coplanar laser beams to form the probe volume of laser Doppler systems. This allows us to obtain, for each particle crossing this probe volume, a Doppler signal whose frequency amplitude spectrum exhibits two characteristic peaks. Electromagnetic calculations and experimental validations clearly demonstrate that we can estimate simultaneously, from the analysis of these two frequency peaks, the particle position along the optical axis and one velocity component. This technique is expected to have great potentialities for velocity profile measurements in microfluidic or boundary layer flows, as well as for the sizing of spherical particles.     

Dynamic evolution of dissipative holographic solitons in photorefractive materials via two-wave mixing with a moving grating

The dynamic evolution and stability of bright dissipative holographic solitons supported by photorefractive materials via two-wave mixing with a moving grating are investigated numerically. Results show that these solitons are stable relative to small perturbations. The state of such solitons can be easily controlled by adjusting some system parameters, such as the linear loss of the crystal and the frequency detuning between the pump beam and the self-trapping beam. Potential amplification in optical switches, repeaters or splitters is discussed.     

Optical manipulation of multiple stable states in photorefractive four-wave mixing

Abstract

We propose an approach to manipulate the convergence in multiple solutions of phase conjugate reflectivity in photorefractive four-wave mixing. Although a method forcibly adding a π-phase shift to an incident beam has been already proposed to control the reflectivity, some restrictions have been required in the boundary conditions for the successful operation. Here, we control the reflectivity with the boundary conditions in which the phase shift operation is ineffective by itself. In our method, the phase shift operation is combined with the procedure of turning an incident beam on and off. With a numerical analysis of four-wave mixing, we show that our new approach brings drastic change in the spatial distribution of the index grating and leads the phase conjugate reflectivity which was not manipulated previously.     

Cross-polarized photorefractive four-wave mixing with extraordinary writing beams and an ordinary reading beam

In parallel-polarized photorefractive four-wave mixing the phase-matching condition can be achieved automatically if the pump beams are allowed to propagate in directions opposite to each other. However, in cross-polarized photorefractive four-wave mixing, the incident angles of the beams should be adjusted to maintain the phase-matching condition. We analyze the phase-matching properties of cross-polarized four-wave mixing with extraordinary writing beams and an ordinary reading beam and obtain the phase-conjugate reflectivity in consideration of phase mismatching. We also perform an experiment in which a phase-conjugate beam is generated in cross-polarized four-wave mixing and confirm the analyses.     

Optical Doppler velocimetry at various retinal vessel depths by variation of the source coherence length

We report on what we believe is a novel approach to measuring the velocity of red blood cells (RBC's) at different depths of retinal vessels by use of low-coherence sources. The technique, variable coherence optical Doppler velocimetry (VCODV), performs Doppler shift measurements through autodyne mixing between the light scattered by the RBC's and by the vessel front wall (reference). Only the light from RBC's moving at a depth less than half the coherence length (CL) mixes efficiently with the reference. Measurements of the Doppler shifts from RBC's with sources of four different CL's in a 152-mum vein of a volunteer confirmed the feasibility of VCODV. This approach has the potential to monitor in vivo retinal RBC velocity gradient at the vessel wall and the velocity profile within the blood vessel in the condition of symmetric blood flow profiles.     

One-dimensional description of cylindrically symmetric laser beams: application to bessel-type nondiffracting beams

We introduce a new representation of coherent laser beams that are usually described in circular cylindrical coordinates. This representation is based on the decomposition of a laser beam of a given azimuthal order into beams exhibiting Cartesian symmetry. These beams, which we call constituent waves, diffract along only one of their transverse dimensions and propagate noncollinearly with the propagation axis. A cylindrically symmetric laser beam is then considered a coherent superposition of constituent waves and is represented by an integral over an angular variable. Such a representation allows for the introduction of the propagation factor M2, defined in terms of one-dimensional root-mean-square (rms) quantities, in the treatment of two-dimensional beams. The representation naturally leads to the definition of a new rms parameter that we call the quality factor Q. It is shown that the quality factor defines in quantitative terms the nondiffracting character of a laser beam. The representation is first applied to characterize Laguerre-Gauss beams in terms of these one-dimensional rms parameters. This analysis reveals an asymptotic link between Laguerre-Gauss beams and one-dimensional Hermite-Gauss beams in the limit of high azimuthal orders. The representation is also applied to Bessel-Gauss beams and demonstrates the geometrical and one-dimensional characters of the Bessel-Gauss beams that propagate in a nondiffracting regime. By using two separate rms parameters, Q and M2, our approach gives an alternative way to describe laser beam propagation that is especially well suited to characterize Bessel-type nondiffracting beams.     

Glass-fiber self-mixing intra-arterial laser Doppler velocimetry: signal stability and feedback analysis

We have developed a blood velocimeter based on the principle of self-mixing in a semiconductor laser diode through an optical fiber. The intensity of the light is modulated by feedback from moving scattering particles that contain the Doppler-shift frequency. Upon feedback the characteristics of the laser diode change. The threshold current decreases, and an instable region may become present above the new threshold. The amplitude of the Doppler signal turns out to be related to the difference in intensity between situations with and without feedback. This amplitude is highest just above feedback. The suppression of reflection from the glass-fiber facets is of paramount importance in the obtaining of a higher signal-to-noise ratio. Using an optical stabilization of the feedback, we optimized the performance of the laser-fiber system and the Doppler modulation depth and clarified its behavior with a suitable physical model. We also investigated the effect of the finite coherence length of the laser. We tested the efficiency of the self-mixing velocimeter in vivo with the optical glass fiber inserted in the artery with endoscopic catheters, both in upstream and in downstream blood flow conditions. For the latter we used a special side-reflecting device solution for the fiber facet to allow downstream measurements.     

Measurement uncertainty and temporal resolution of Doppler global velocimetry using laser frequency modulation

A Doppler global velocimetry (DGV) measurement technique with a sinusoidal laser frequency modulation is presented for measuring velocity fields in fluid flows. A cesium absorption cell is used for the conversion of the Doppler shift frequency into a change in light intensity, which can be measured by a fiber coupled avalanche photo diode array. Because of a harmonic analysis of the detector element signals, no errors due to detector offset drifts occur and no reference detector array is necessary for measuring the scattered light power. Hence, large errors such as image misalignment errors and beam split errors are eliminated. Furthermore, the measurement system is also capable of achieving high measurement rates up to the modulation frequency (100 kHz) and thus opens new perspectives to multiple point investigations of instationary flows, e.g., for turbulence analysis. A fundamental measurement uncertainty analysis based on the theory of Cramér and Rao is given and validated by experimental results. The current relation between time resolution and measurement uncertainty, as well as further optimization strategies, are discussed.     

Diffraction field of tightly focused laser beams and its influence to laser accelerator

In this paper, we have studied the dynamic characteristics of relativistic electron injected into stationary intense vacuum laser fields. We found the dynamic trajectories can basically be classified as three categories, namely Inelastic Scattering (IS), Capture and Acceleration Scenario (CAS) and Penetrate into Axial Region and Move (PARM) trajectory. The physical mechanism as to the three kinds of electrons have been examined. In particular, the PARM trajectory which we presented in this paper is different from the CAS and IS trajectory which we had already found in our previous work. We will show the PARM stems from the strong diffraction effect of a tightly focused laser field. In addition, the initial condition for the three kinds of electrons to emerge were detailed investigated. It has been found that there are four factors which chiefly decide the appearance of the three kinds of dynamics trajectories, namely the laser beam width w₀ and intensity a₀, the electrons incident angle θ and initial transversal momentum p_ti. The implication of the PARM electrons to the planned vacuum laser accelerators is illustrated.     

Analysis of molecular dynamics of colloidal particles in transported dilute samples by self-mixing laser Doppler velocimetry

Colloidal particles in a liquid medium are transported with constant velocity, and dynamic light scattering experiments are performed on the samples by self-mixing laser Doppler velocimetry. The power spectrum of the modulated wave induced by the motion of the colloidal particles cannot be described by the well-known formula for flowing Brownian motion systems, i.e., a combination of Doppler shift, diffusion, and translation. Rather, the power spectrum was found to be described by the q-Gaussian distribution function. The molecular mechanism resulting in this anomalous line shape of the power spectrum is attributed to the anomalous molecular dynamics of colloidal particles in transported dilute samples, which satisfy a nonlinear Langevin equation.     

Optical superresolution of focused partially spatially coherent laser beams

We report design theories of a diffractive superresolution element (DSE) to implement optical superresolution of focused partially spatially coherent laser beams. The design problem of the DSE can be transformed into a problem of linear programming to obtain a globally optimal solution. By using the design theories, some fundamental limits of optical superresolution of focused partially spatially coherent laser beams are proposed, and several design examples are provided. As expected, both the fundamental limits and the design examples show that worse spatial coherence will cause worse superresolution performance. The design theories provide a design approach with partially coherent beams and may be useful for other design problems under partially coherent illumination.     

Analysis and simulations of two-wave mixing in photopolymer holographic recording media

Abstract

The process of two-wave mixing in photopolymer recording materials was investigated theoretically. The diffraction grating already forms during exposition and it may influence the original interference field distribution through diffraction of waves on the refractive index modulation. In order to show this, Kogelnik's coupled wave theory was extended to demonstrate the possibility of energy transfer from one recording wave to the other. The energy transfer and the intensity distribution during the recording process were systematically analysed depending on the boundary conditions. As a next step, the first harmonic model of the transmission grating recording, based on a simple material model, was implemented and solved. The ratio of the input intensities was found to be a crucial parameter and thus extensive simulations for various ratios of intensities were carried out. Modelling implies that the interference field and the refractive index grating just coincide for equal intensities. For intensities differing from unity they do not overlap themselves during the recording process. It has also turned out that the diffraction efficiency of the recorded grating drops against the case where the effects of two-wave mixing are not considered. The results of our analysis and simulation help give a better understanding of the physics of the recording process and proper adjustment of recording parameters in such applications as optical holography and holographic memories.     

Indentation of functionally graded beams and its application to low-velocity impact response

The problem of contact between a rigid cylindrical indenter and a functionally graded (FG) beam is studied. The elastic modulus of the material varies in an exponential fashion across the thickness of the beam. For the sake of comparison indentation of a homogeneous beam is also considered. In the case of FG beams indentation of both soft and hard sides of the beam are studied. Results are presented for contact force–contact length relations and contact stresses in the three types of beams. Maximum normal strains and stresses and maximum transverse shear stresses are plotted as a function of strain energy (work done by the indenter) in the beam. The results are extended to low-velocity impact problems. It is seen that for a given impact energy in low-velocity impacts, the maximum stresses and strains are significantly lower in FG beams when the impact occurs on the softer side of the beam.     

Two-dimensional wavelet transform and application to holographic particle velocimetry

The goal of holographic particle velocimetry is to infer fluid velocity patterns from images reconstructed from doubly exposed holograms of fluid volumes seeded with small particles. The advantages offered by in-line holography in this context usually make it the method of choice, but seeding densities sufficient to achieve high spatial resolution in the sampling of the velocity fields cause serious degradation, through speckle, of the signal-to-noise ratio in the reconstructed images. The in-line method also leads to a great depth of field in paraxial viewing of reconstructed images, making it essentially impossible to estimate particle depth with useful accuracy. We present here an analysis showing that these limitations can be circumvented by variably scaled correlation, or wavelet transformation. The shift variables of the wavelet transform are provided automatically by the optical correlation methodology. The variable scaling of the wavelet transform derives, in this case, directly from the need to accommodate varying particle depths. To provide such scaling, we use a special optical system incorporating prescribed variability in spacings and focal length of lenses to scan through the range of particle depths.

Calculation shows, among other benefits, improvement by approximately two orders of magnitude in depth resolution. A much higher signal-to-noise ratio together with faster data extraction and processing should be attainable.

     

Optical levitation and translation of a microscopic particle by use of multiple beams generated by vertical-cavity surface-emitting laser array sources

An optical levitation and translation method for a microscopic particle by use of the resultant force induced by multiple light beams is studied. We show dependence of the radiation pressure force on the illuminating distribution by numerical calculation, and we find that the strongest axial force is obtained by a specific spacing period of illuminating beams. Extending the optical manipulation technique by means of vertical-cavity surface-emitting laser (VCSEL) array sources [Appl. Opt. 40, 5430 (2001)], we are the first, to our knowledge, to demonstrate levitation of a particle and its translation while levitated by using a VCSEL array. The vertical position of the target particle can be controlled in a range of a few tens of micrometers with an accuracy of 2 microm or less. The analytical and experimental results suggest that use of multiple beams is an effective method to levitate a particle with low total illumination power. Some issues on the manipulation method that uses multiple beams are discussed.