Optical tweezers of programmable shape with transverse scattering forces

We propose a non-holographic method to create line traps of arbitrary shape in the sample plane. Setting the phase gradient along theses lines gives control over the transverse forces acting on the confined particles. Phase structures, displayed on a spatial light modulator, are optically processed by a spiral phase filter and imaged onto the object plane of a microscope objective. The resulting bright line structures can be used to trap microparticles. Additionally, they exert transverse scattering forces, which can be exploited for inducing orbital motions or for creating “attracting” or “repelling” points, respectively. We give theoretical and experimental evidence that these scattering forces are proportional to the curvature of the line tweezers.     

Necessity analyses of phase masks in joint fractional Fourier transform correlator

In this paper, the mathematical expressions and the particularities of the joint fractional Fourier transform correlator (JFRTC) are detailedly analyzed. In a JFRTC, the distance between the two fractional correlation peaks can be adjusted flexibly by shifting the fractional orders. However, the intensity of the fractional correlation peaks decreases rapidly as the first fractional order p₁ drops. The former property is very useful in a practical recognition system, but the latter one seriously reduces the recognition sensitivity of a JFRTC. For this reason, phase masks should be added at the input plane of the JFRTC to enhance the intensities of the fractional correlation peaks and effectively overcome the default. Compared with the existing JFRTC with single phase modulation, a JFRTC with double phase modulation is suggested to more flexibly improve the performance of a JFRTC.     

The filtering characteristics of simple grating optical low-pass filters

We studied the characteristics of a two-dimensional grating optical low-pass filter (GOLF) theoretically and experimentally. The modulation transfer function (MTF) of an optical system that consists of a lens and a GOLF is theoretically derived by taking all orders of diffracted beams into consideration. The MTFs of a two-phase chess-board-type GOLF and a three-phase GOLF were calculated for various phase differences and compared with that of a birefringent low-pass filter (BLF). The three-phase GOLF with nine center beams of equal strength removes most moiré fringes, but the resolution degradation is severe compared to the BLF. The two-phase GOLF with a phase difference of 180°, which is similar to the BLF in term of beam distribution, has a medium characteristic somewhere between those of the three-phase GOLF and the BLF. Samples of two GOLFs are made and experimented on by attaching them to a digital camera. The experimental result coincides with the theoretical development. Received: 31 October 2001 / Revised version: 4 March 2002 / Published online: 2 May 2002     

Correlator-aided alignment of phase key in encrypted holographic storage systems

An encrypted holographic scheme with a compact alignment system for a phase key is proposed. Alignment for a phase key is performed by a holographic correlator. A filter in the correlator system contains the phase information used for encryption. Thus, it can be used to check the authorization of the phase key. Owing to the shift-invariant property of the holographic correlator, the location of the correlation peak is highly related to the alignment of the phase key. Therefore, the phase key can be repositioned on the desired location by searching for the specific position of the correlation peak. With the help of the correlator, alignment of the phase key can be done in 1 min. Experimental results using a correlator system in support of our proposed idea are demonstrated as well.     

The modeling and the optimization of a grating optical low-pass filter

Through the one-dimensional analysis of the diffraction of a phase grating, we calculated the optical transfer function (OTF) of a phase grating. By a 0th-order approximation of the optical transfer function, we analyzed the feasibility of using it as a spatial frequency filter and obtained the structure of a grating for the optimum-filtering characteristics. The OTF of a phase grating as an optical low-pass filter is optimal when the incoming light is equally divided into three beams. The distance of those beams must be equal to the pixel size. The theoretical development was verified through an experiment. Received: 21 May 2001 / Revised version: 16 July 2001 / Published online: 15 October 2001     

Optical trap with spatially varying polarization: application in controlled orientation of birefringent microscopic particle(s)

We report the use of the interference of two orthogonally polarized beams for generation of an optical trap with spatially varying polarization. The spatial variation of polarization in the optical trap has been used for demonstration of simultaneous rotation or orientation of multiple microscopic birefringent particles. Other potential applications of an optical trap with spatially varying polarization are also discussed.This revised version was published online in August 2005 with a corrected cover date.     

Temporal filtering using time lenses for optical transmission systems

An optical signal processing scheme using time lenses in a 4-f configuration for optical communication systems is proposed. The first time-lens combined with a dispersive element such as an optical fiber produces the Fourier transform of the input signal and the second time lens combined with an optical fiber placed after the temporal filter produces the inverse Fourier transformation. Typically, in an optical signal processing scheme based on space/time-lens, the signal at the output is space/time-reversed because of the direct Fourier transformation after the spatial/temporal filter, which is undesirable for a practical optical communication system. Here, we propose a technique to implement both direct and inverse Fourier transformation using time lenses which has no spatial analogue. As a result, the bit sequence at the output is not time-reversed. Two applications of the proposed scheme, a demultiplexer for wavelength division multiplexing (WDM) systems and a higher-order dispersion compensator, have been discussed and numerically implemented.     

Generation of optical vortices with tunable intensity modulation

We analyze vortex properties of the optical beams generated by a spiral phase plate (SPP) which cannot modulate the phase of the incident beam range from 0 to 2π nicely, and find that the vortices have intensity modulation (IM) with central bright speckle. We construct an improved SPP to produce high quality optical vortices with definite IM. Theoretical analysis and real experiments show that this improved SPP can be used to produce optical vortices with configurable intensity modulation degree and without central bright spot.     

High-rate pulse-train generation by phase-only filtering of an electrooptic frequency comb: Analysis and optimization

We investigate the generation of high-rate optical pulse trains by spectral phase-only filtering of a frequency comb derived from an electrooptically phase-modulated continuous-wave laser. The technique is initially analyzed as a two-step filtering process. First, a fundamental pulse-train with repetition-rate equal to the modulation frequency is obtained by line-by-line phase-cancellation of the electrooptic frequency comb. Second, the temporal Talbot-effect is considered so that the output pulse repetition-rate is an integer multiple of the electrooptic modulation frequency. Nonidealities found in the fundamental train lead, in general, to multiplied trains with important degradations. We numerically analyze optimum modulation conditions for generation of output pulse trains with minimum peak-to-peak variations and/or maximum extinction level. On the other hand, a genetic algorithm is considered to numerically find optimum line-by-line phase-only filters that generate output multiplied trains with minimized degradations. Numerical simulations show that, in general, this second approach allows for improvement in the quality of the resultant multiplied trains, in terms of the uniformity degree and/or noise-level, compared with the pulse trains resulting from the Talbot-effect-based approach.     

Demonstration of a spatial-spectral holographic LIDAR range-Doppler processor

We present a new approach to laser interferometric Doppler and ranging (LIDAR) processing using spatial-spectral holography (SSH). In this approach, broadband optical signals from a random noise or frequency-modulated laser are transmitted and reflected off remote targets. The return signals interfere spatially and spectrally with a local copy of the original transmit signal in an SSH medium, resulting in spectral gratings that have a spectral period inversely proportional to the LIDAR target's range and a position proportional to the target's Doppler (or velocity). These gratings are subsequently read out by a slowly chirped source onto a parallel detector array, and the velocity and range of the targets are inferred. We present the theoretical framework that describes the function of the LIDAR processor, as well as proof-of-concept experimental results.     

Design of Super-resolution Filters with a Gaussian Beam in Optical Data Storage Systems

Super-resolution filters based on a Gaussian beam are proposed to reduce the focusing spot in optical data storage systems. Both of amplitude filters and pure-phase filters are designed respectively to gain the desired intensity distributions. Their performances are analysed and compared with those based on plane wave in detail. The energy utilizations are presented. The simulation results show that our designed super-resolution filters are favourable for use in optical data storage systems in terms of performance and energy utilization.     

The study of the nonlinear absorption in the nonlinear-imaging technique with phase object

The nonlinear absorption can produce a nonlinear image very similar with the one created by the nonlinear refraction when using the nonlinear-imaging technique with phase object to measure the third-order nonlinearity of materials, but the principles of them are different. The formation of the nonlinear absorption image is explained, and the condition that the highest sensitivity of the nonlinear absorption measurement can be reached is deduced. For the materials with both nonlinear absorption and refraction, we find a proper phase shift of the phase object where the effect of the nonlinear refraction to the measured signal can be eliminated. The nonlinear absorption and refraction are numerically simulated when the phase shift of phase object to be π/2 that is normally used. The qualitative tendency of the signal variation is presented.     

Design and application of three-zone annular filters

We design three-zone annular filters to be applied to optical storage system. The designed filters extend the depth of focus and realize transverse superresolution simultaneously, which will improve the performance of optical storage system greatly. And we propose two feasible schemes to improve imaging resolution of three-dimensional imaging system. One scheme depends on a complex filter formed by cascading of a three-zone phase filter and a three-zone amplitude filter. The complex filter converge the optimized transverse superresolution and the optimized axial superresolution of two different filters onto a single filter. It can improve the three-dimensional imaging performances greatly. Another scheme depends on a single three-zone complex filter. We propose a three-zone complex filter with phase shift 0.8π, which presents bigger design margin, better imaging quality and stronger three-dimensional superresolution capability.     

Binary polarization pupil filter: Theoretical analysis and experimental realization with a liquid crystal display

The Jones matrix formalism has been applied to evaluate the response of an optical system when a non-uniform polarizing pupil is introduced. With this formalism we analyze and experimentally demonstrate the properties of a binary polarization pupil filter having two regions with two orthogonal linear polarization orientations. We first study the case when no analyzer is placed behind the pupil filter, and both, the transversal and the axial behavior are described in terms of the intensity and the local state of polarization. Then it is shown how the response of the optical system can be easily changed through the orientation of an analyzer placed behind the pupil. We experimentally verified the theory using a twisted nematic liquid crystal display, which produces two orthogonal linear polarization states for two different addressed voltages.     

Optimization and limits of optical nonlinear measurements using imaging technique

We report on analytical calculations for a 4f coherent imaging system in presence of a phase object at the entry of the set-up. We give the results of the optimized parameters to be used in this system so as to increase the sensitivity of the measurement of the nonlinear refraction coefficient. Analytical and previously reported simulated image profiles are compared here. Our study also gives the limits of the nonlinear imaging technique with a phase object for relatively high nonlinear phase shifts.     

Propagation characteristics of laser beams with amplitude modulations and phase fluctuations in apertured fractional Fourier transforming system

The apertured fractional Fourier transforming system is introduced and applied to treat the propagation of Gaussian beams with amplitude modulations and phase fluctuations. Based on the treatment that a rectangular function can be expanded into an approximate sum of complex Gaussian functions with finite numbers, the analytical expressions for the mutual intensity distribution of laser beams with amplitude modulations and phase fluctuations passing through the apertured fractional Fourier transforming system are obtained. Some numerical simulations are illustrated for their propagation properties.     

Generation of Optical Vortex Using a Spiral Phase Plate Fabricated in Quartz by Direct Laser Writing and Inductively Coupled Plasma Etching

A simple, economical and reliable technique is proposed for fabricating a spiral phase plate （SPP） in a quartz substrate to generate optical vortex with a unit topological charge at the wavelengths of 632.8nm. The spiral phase plate is first formed in the photoresist by direct laser writing lithography and then transferred into the quartz substrate by inductively coupled plasma etching. The performance of the fabricated SPP is verified by using beam intensity distribution, which is in agreement with the theoretical calculation result. The interference measurement suggests that we have succeeded to generate optical vortex with a unit topological charge with the fabricated SPP.     

Characterization of optical and nonlinear properties of periodically-poled RbTiOAsO4 in the mid-infrared range via difference-frequency generation

Tunable mid-infrared coherent radiation (3.25- 3.7 μm) is generated by quasi-phase-matched difference frequency generation in a multi-grating periodically-poled RbTiOAsO₄ crystal. The spontaneous polarization and coercive field of flux-grown RbTiOAsO₄ are determined by polarization switching measurements. The nonlinear interaction enables us to explore the optical and nonlinear properties of this material in the mid-infrared range, where data is scarce. The measurements are used to derive a mid- infrared corrected dispersion equation for n_z in RbTiOAsO₄. This equation is in excellent agreement with previously published measurements of nonlinear interactions in periodically-poled RbTiOAsO₄. The measured wavelength and temperature bandwidths are ≈48 nm cm and ≈29 °C cm, respectively. A relatively high temperature tuning slope of the phase-matched idler wavelength, -1.27 nm/°C, is measured. This may be useful for realizing temperature-tuned nonlinear devices. Received: 30 March 2000 / Revised version: 9 May 2000 / Published online: 30 June 2000     

Unified approach to short optical pulse recording and spatial imaging with subwavelength resolution

We propose and numerically demonstrate a simple method for measuring waveforms of optical pulses that have spectral bandwidths much larger than the passband of the measuring system, thus enabling a kind of temporal superresolution. The technique is based on pulse intensity modulation that contains high-order harmonics. Parts of the pulse intensity spectrum that are shifted as a result of the modulation, are moved over (“umklapped”) to the center of the passband, transmitted and then recorded by an oscilloscope. The pulse intensity spectrum is restored by parts from the Fourier transform of a few oscillograms, measured after performing the temporal shifts between the pulse train and the modulation. A similar approach is applied for achieving subwavelength spatial resolution in far -field microscopy. The spatial modulation is performed by a diffraction grating. The method allows one to restore a subwavelength object in a single measurement.     

High dynamic range measurement of temporal shape and contrast of ultrashort UV pulses

This paper presents an experimental technique for measurement of the contrast ratio of ultrashort UV pulses. As a multiple-shot device based on the scheme of difference frequency generation this is, to our knowledge, the only cross correlator in the UV so far, which offers a dynamic range of 10⁷ and operates with input pulse energies as low as 5 μJ. By changing the cross correlator into single-shot mode, the temporal shape of the UV pulse can be measured. Received: 26 October 1998 / Revised version: 13 January 1998 / Published online: 28 April 1999