Complex Optical Field Research Articles

Digital coherent receiver for orbital angular momentum demultiplexing

We put forward a type of receiver for coherent detection of the photon orbital angular momentum (OAM). A coherent array receiver, consisting of multiple subapertures, with each subaperture coupled to a single-mode fiber, maps the complex optical field in the image plane. Using digital samplers connected to each array element, the local electrical signals resulting from the detection process can be measured coherently, moving the complexity of the full OAM measurement from the optical domain to the digital domain. By computer processing the coherent electrical patterns obtained, one can retrieve full information (amplitude and phase) of the different OAM components that constitute any incoming beam.

An ameliorated fast phase retrieval iterative algorithm based on the angular spectrum theory

For designing the light beam shaper in the optical transmitting antenna in inter-satellite optical communication system, the essential problem is, according to the input optical field and ideal output light field, to determine the shaper of phase distribution, in which its core is in phase recovery. Based on the traditional Gerchberg-Saxton (G-S) iterative algorithm, using the angular spectrum propagation theory, a kind of amplitude gradient addition iterative algorithm is proposed, and the detailed algorithm process and analysis are given. Compared with G-S algorithm, the new one using iterative process, constructs the light field amplitude feedback loop, and searches out the optimal iteration path using the gradient; their joint action accelerates the convergence process. Numerical simulation shows that the iterative error-drop speed caused by unit iterations in the new algorithm is 1.7 times that of the G-S algorithm, its convergence rate is obviously superior to the G-S algorithm; for different random initial phase, the new algorithm can effectively carry out iteration, show the advantages of the strong adaptability and the good convergent consistency. Amplitude gradient addition iterative algorithm gives a new effective way of recovering the complex optical field phase, and provides technical support for designing all kinds of diffraction optical element.

Optimal synthesis of double-phase computer generated holograms using a phase-only spatial light modulator with grating filter

We propose an optical system for synthesizing double-phase complex computer-generated holograms using a phase-only spatial light modulator and a phase grating filter. Two separated areas of the phase-only spatial light modulator are optically superposed by 4-f configuration with an optimally designed grating filter to synthesize arbitrary complex optical field distributions. The tolerances related to misalignment factors are analyzed, and the optimal synthesis method of double-phase computer-generated holograms is described.

Complex-optical-field lidar system for range and vector velocity measurement

A coherent lidar system based on the measurement of complex optical field is demonstrated for the first time. An electro-optic in-phase/quadrature (I/Q) modulator is used in the lidar transmitter to realize carrier-suppressed complex optical field modulation in which the positive and the negative optical sidebands can carry independent modulation waveforms. A fiber-optic 90° hybrid is used in the lidar receiver for coherent heterodyne detection and to recover the complex optical field. By loading a constant modulation frequency on the lower optical sideband and a wideband linear frequency chirp on the upper sideband, vector velocity and target distance can be measured independently. The wide modulation bandwidth of this lidar system also enabled unprecedented range resolution and the capability of measuring high velocity unambiguously.

Uncertainty-managed phase-shifting digital holography

Phase-shifting digital holography is a digital measurement technology of a complex optical field profile that uses focal plane array detectors without the loss of bandwidth. It has been known that the accuracy of phase-shifting digital holography is limited mainly by the phase tolerance of reference. In this Letter, it is revealed that the uncertainty in an expected signal is highly dependent on the phase of the signal itself, as well as the phase tolerance of the reference. Based on the uncertainty analysis, we propose a novel scheme of phase-shifting digital holography that exploits an uncertainty property to enhance the measurement accuracy even under significant reference phase tolerance.

Holographic generation of a class of nondiffracting fields with optimum efficiency

We discuss the accurate generation of complex optical fields using phase holograms that provide the optimum diffraction efficiency. In each considered case, the phase modulation of the employed hologram is identical to the phase of the desired optical field. We show that periodic and quasiperiodic nondiffracting optical fields, mathematically obtained through the superposition of multiple plane waves, can be generated with high fidelity using this approach.

Frequency-modulated continuous-wave lidar using I/Q modulator for simplified heterodyne detection

A frequency-modulated continuous-wave (FMCW) lidar is demonstrated with heterodyne detection. The lidar transmitter utilizes an electro-optic I/Q modulator for the first time to generate carrier-suppressed and frequency-shifted FM modulation. This eliminates the need for an acousto-optic frequency shifter commonly used in heterodyne lidar transmitters. It also allows the use of a much wider modulation bandwidth to improve the range resolution. The capability of complex optical field modulation of the I/Q modulator provides an additional degree of freedom compared with an intensity modulator, which will benefit future lidar applications.

Full-range, complex spatial light modulator for real-time holography

We demonstrate a full-range complex and transmissive spatial light modulator (SLM) for simultaneous and independent amplitude and phase modulation of an input wave field. Arbitrary scalar complex optical fields are generated by stacking a pixelated liquid crystal display operating in phase-only (2π) modulation with passive polarization-sensitive components. The principle is based on optical combining the light fields of two neighboring phase-only modulating pixels, which were made orthogonally polarized by a structured half-wave plate, then passing through a birefringent plate to laterally shift one of the beams collinear to the other, and finally bringing to interference by a linear polarizer. Complex modulation by the proposed SLM is experimentally verified in monochrome green operation.

3D reconstruction of the complex dielectric function of glass during femtosecond laser micro-fabrication

We report on a new technique to reconstruct the 3D dielectric function change in transparent dielectric materials and the application of the technique for on-line monitoring of refractive index modification in BK7 glass during direct femtosecond laser microfabrication. The complex optical field scattered from the modified region is measured using two-beam, single-shot interferogram and the distribution of the modified refractive index is reconstructed by numerically solving the inverse scattering problem in Born approximation. The optical configuration suggested is further development of digital holographic microscopy. It takes advantage of high spatial resolution and almost the same optical paths for both interfering beams, and allows ultrafast time resolution. © Springer Science+Business Media, LLC. 2011.

Motion analysis of complex optical flow field and feature extraction

Motion analysis of complex optical flow field and feature extraction

Diffractive and geometric optical systems characterization with the Fresnel Gaussian shape invariant

Full characterization of optical systems, diffractive and geometric, is possible by using the Fresnel Gaussian Shape Invariant (FGSI) previously reported in the literature. The complex amplitude distribution in the object plane is represented by a linear superposition of complex Gaussians wavelets and then propagated through the optical system by means of the referred Gaussian invariant. This allows ray tracing through the optical system and at the same time allows calculating with high precision the complex wave-amplitude distribution at any plane of observation. This method is similar to conventional ray tracing additionally preserving the undulatory behavior of the field distribution. That is, we are propagating a linear combination of Gaussian shaped wavelets; keeping always track of both, the ray trajectory, and the wave phase of the whole complex optical field. This technique can be applied in a wide spectral range where the Fresnel diffraction integral applies including visible, X-rays, acoustic waves, etc. We describe the technique and we include one-dimensional illustrative examples.

All-optical phase and amplitude regenerator for next-generation telecommunications systems

Fibre-optic communications systems have traditionally carried data using binary (on-off) encoding of the light amplitude. However, next-generation systems will use both the amplitude and phase of the optical carrier to achieve higher spectral efficiencies and thus higher overall data capacities(1,2). Although this approach requires highly complex transmitters and receivers, the increased capacity and many further practical benefits that accrue from a full knowledge of the amplitude and phase of the optical field(3) more than outweigh this additional hardware complexity and can greatly simplify optical network design. However, use of the complex optical field gives rise to a new dominant limitation to system performance-nonlinear phase noise(4,5). Developing a device to remove this noise is therefore of great technical importance. Here, we report the development of the first practical ('black-box') all-optical regenerator capable of removing both phase and amplitude noise from binary phase-encoded optical communications signals.

基于旋转相位调制的复杂光场相位恢复算法

基于旋转相位调制的复杂光场相位恢复算法

Phase retrieval of complex optical fields by binary amplitude modulation

A method to retrieve the complex optical fields from the intensity information recorded in only one plane is discussed. The wavefront to be reconstructed is modulated by using a random binary amplitude mask. Wavefronts with a rather large phase depth can be accurately retrieved by using several masks in combination with iterative Fresnel algorithms and without any prior information. The influences of the contrast of the mask and the dynamic range of the detector on the accuracy of the phase retrieval are analyzed.

Mapping of complex optical field patterns in multimode photonic crystal waveguides by near-field scanning optical microscopy

We use near-field scanning optical microscopy (NSOM) operating in collection mode to map the optical field distribution of continuous wave infrared light propagating along an air-bridged W3 silicon photonic crystal (PC) slab multimode waveguide in a subwavelength resolution. The detected near-field optical intensity distribution patterns show very different longitudinal propagation features and transverse field profiles at different wavelength ranges. We have analyzed the dispersion of the guided modes in the PC waveguide and the corresponding eigenfield profile for each guided mode by means of the three-dimensional plane-wave expansion simulations. It is found that the experimentally observed complex while interesting near-field pattern features can be well explained by the field profiles of the multiple waveguide modes and their superposition at different excitation wavelengths. The detection and analysis of this multimode PC slab waveguide via NSOM could help us to understand complex wave propagation behavior and to further design novel PC devices.

Optical implementation of iterative fractional Fourier transform algorithm

An optical implementation of iterative fractional Fourier transform algorithm is proposed and demonstrated. In the proposed implementation, the phase-shifting digital holography technique and the phase-type spatial light modulator are adopted for the measurement and the modulation of complex optical fields, respectively. With the devised iterative fractional Fourier transform system, we demonstrate two-dimensional intensity distribution synthesis in the fractional Fourier domain and three-dimensional intensity distribution synthesis simultaneously forming desired intensity distributions at several multi-focal planes.

Three-dimensional surface contouring of macroscopic objects by means of phase-difference images

We report a technique to determine the 3D contour of objects with dimensions of at least 4 orders of magnitude larger than the illumination optical wavelength. Our proposal is based on the numerical reconstruction of the optical wave field of digitally recorded holograms. The required modulo 2pi phase map in any contouring process is obtained by means of the direct subtraction of two phase-contrast images under different illumination angles to create a phase-difference image of a still object. Obtaining the phase-difference images is only possible by using the capability of numerical reconstruction of the complex optical field provided by digital holography. This unique characteristic leads us to a robust, reliable, and fast procedure that requires only two images. A theoretical analysis of the contouring system is shown, with verification by means of numerical and experimental results.

An elaborated model of fly small-target tracking

Flies have the capability to visually track small moving targets, even across cluttered backgrounds. Previous computational models, based on figure detection (FD) cells identified in the fly, have suggested how this may be accomplished at a neuronal level based on information about relative motion between the target and the background. We experimented with the use of this "small-field system model" for the tracking of small moving targets by a simulated fly in a cluttered environment and discovered some functional limitations. As a result of these experiments, we propose elaborations of the original small-field system model to support stronger effects of background motion on small-field responses, proper accounting for more complex optical flow fields, and more direct guidance toward the target. We show that the elaborated model achieves much better tracking performance than the original model in complex visual environments and discuss the biological implications of our elaborations. The elaborated model may help to explain recent electrophysiological data on FD cells that seem to contradict the original model.

Swept Coherent Optical Spectrum Analysis

Swept coherent optical spectrum analysis is becoming a viable method for subpicometer spectral characterization of optical communications signals. The performance of this technique depends on a number of factors that we have investigated both theoretically and experimentally. This includes the influence of signal linewidth, polarization, optical phase, intensity noise, and electrical filtering methods. These effects are discussed in detail and illustrated through spectral measurements on communications transmitters. We extend the heterodyne method to permit measurement of both spectral amplitude and phase of the spectral sidebands. The transformation of the complex optical field spectrum to the time domain waveform is demonstrated.

Three-dimensional optical measurement of instantaneous pressure

Local perturbations in material density induced in a material by a compressional wave give rise to local perturbations in refractive index. Accurate, high-resolution, three-dimensional, optical measurements of an instantaneous refractive index perturbation in a homogeneous, optically transparent medium may be obtained from measurements of scattered optical intensity alone. The method of generalized projections allows incorporation of optical intensity measurements into an iterative algorithm for computing the phase of the interrogating optical pulse as the solution of a fixed point equation. The complex optical field amplitude, computed in this manner, is unique up to a constant unit magnitude complex coefficient. The three-dimensional refractive index distribution may be computed via the Fourier slice reconstruction algorithm from the optical phase data under the assumption of weak optical scattering. The refractive index perturbation is related to local instantaneous pressure under a linear, small-displacement model for the mechanical wave. A numerical simulation of the measurement experiment, phase recovery, and reconstruction process for a plane piston ultrasound transducer with a semicircular aperture and center frequency of 1.5 MHz is described and corresponds very well with experiment. Experimental data obtained using an 810-nm laser source are used to reconstruct the three-dimensional pressure field from two elements of a 2.5-MHz linear array. Comparison with a measurement obtained via a 500-microm needle hydrophone shows excellent agreement.