Two-dimensional Optical Beam Research Articles

Tunable giant two-dimensional optical beam shift from a tilted linear polarizer

We demonstrate an intriguing giant optical beam shift in a tilted polarizer system analogous to the Imbert-Fedorov shift in partial reflection around the Brewster's angle of incidence. We explain this giant shift using a generalized theoretical treatment for beam shift in a tilted uniaxial anisotropic material incorporating the three-dimensional orientation of its optic axis in the laboratory frame. A regulated control and tunability of both the magnitude and direction of the shifts are demonstrated further by wisely tuning the input polarization and the corresponding orientation angles. These findings open up the possibility of precise micron-level beam steering using a simple linear polarizer.

Static volumetric three-dimensional display based on an electric-field-controlled two-dimensional optical beam scanner.

Using the quadratic electro-optic effect and the gradient of the composition ratio m [Nb/(Ta+Nb) in mol. %] in a potassium tantalate niobate crystal, we have designed an electric-field-controlled two-dimensional optical beam scanner with a wide wavelength range and fast response. This scanner is used to realize a volumetric display based on a two-frequency, two-step upconversion technique that is used to address the imaging volume. Use of appropriately designed imaging optics and custom-designed software to convert 2D renderings of volumetric images into control signals for the scanner along with appropriate infrared laser source selection allows efficient single-color image generation with a large viewing zone, without flicker and with natural depth cues. The resulting system has the potential to increase image resolution to nearly 61.5×109 with high scanning frequency and to expand to display three-color imagery.

Stable dissipative optical vortex clusters by inhomogeneous effective diffusion.

We numerically show the generation of robust vortex clusters embedded in a two-dimensional beam propagating in a dissipative medium described by the generic cubic-quintic complex Ginzburg-Landau equation with an inhomogeneous effective diffusion term, which is asymmetrical in the two transverse directions and periodically modulated in the longitudinal direction. We show the generation of stable optical vortex clusters for different values of the winding number (topological charge) of the input optical beam. We have found that the number of individual vortex solitons that form the robust vortex cluster is equal to the winding number of the input beam. We have obtained the relationships between the amplitudes and oscillation periods of the inhomogeneous effective diffusion and the cubic gain and diffusion (viscosity) parameters, which depict the regions of existence and stability of vortex clusters. The obtained results offer a method to form robust vortex clusters embedded in two-dimensional optical beams, and we envisage potential applications in the area of structured light.

Resonant diffraction gratings for spatial differentiation of optical beams

Diffraction of a two-dimensional optical beam from a resonant diffraction grating is considered. It is shown that at certain resonance parameters the diffraction grating allows for spatial differentiation and integration of the incident beam. The parameters of the diffraction grating for spatial differentiation of optical beams in the transmission geometry are calculated. It is shown that the differentiating diffraction grating allows the conversion of the two-dimensional beam into the two-dimensional Hermite – Gaussian mode. The presented results of numerical modelling are in good agreement with the proposed theoretical description. The use of the considered resonant diffraction gratings is promising for solving the problems of all-optical data processing.

On-chip silicon optical phased array for two-dimensional beam steering

A 16-element optical phased array integrated on chip is presented for achieving two-dimensional (2D) optical beam steering. The device is fabricated on the silicon-on-insulator platform with a 250 nm silicon device layer. Steering is achieved via a combination of wavelength tuning and thermo-optic phase shifting with a switching power of P(π)=20 mW per channel. Using a silicon waveguide grating with a polycrystalline silicon overlay enables narrow far field beam widths while mitigating the precise etching needed for conventional shallow etch gratings. Using this system, 2D steering across a 20°×15° field of view is achieved with a sidelobe level better than 10 dB and with beam widths of 1.2°×0.5°.

Soliton Aided Propagation and Routing of Vortex Beams in Nonlocal Media

Two-dimensional optical vortex beams can propagate stably and undergo bending in nonlocal media with the aid of a spatial soliton, the latter preventing their destabilization and breakup. By colaunching a suitable pair of collinear soliton and vortex beams in nematic liquid crystals, we conduct a series of numerical experiments to demonstrate that the vortex beam can be made to propagate in the nematicon waveguide and follow its trajectory, even in the cases of refraction and total internal reflection at a dielectric interface. Modulation theory supports these findings and provides an excellent theoretical framework.

Two-Dimensional Optical Beam Steering With InP-Based Photonic Integrated Circuits

Two-dimensional optical beam steering using an InP photonic integrated circuit has been demonstrated. Lateral beam steering controlled by a 1-D phased array has been made easier through on-chip interferometer monitors. Longitudinal beam steering controlled by the input wavelength has demonstrated an efficiency of 0.14 °/nm. Very fast beam steering (>107 °/s) in both dimensions has been demonstrated as well. As the latest development, a widely tunable sampled-grating distributed Bragg reflector laser has been monolithically integrated and 2-D beam steering has been demonstrated with this on-chip tunable laser source.

High speed two-dimensional optical beam position detector

Disclosed is the design of a high speed two-dimensional optical beam position detector which outputs the X and Y displacement and total intensity linearly. The experimental detector measures the displacement from DC to 123 MHz and the intensity of an optical spot in a similar way as a conventional quadrant photodiode detector. The design uses four discrete photodiodes and simple dedicated optics for the position decomposition which enables higher spatial accuracy and faster electronic processing than conventional detectors. Measurements of the frequency response and the spatial sensitivity demonstrate high suitability for atomic force microscopy, scanning probe data storage applications, and wideband wavefront sensing. The operation principle allows for position measurements up to 20 GHz and more in bandwidth.

On the fabrication of three-dimensional silicon-on-insulator based optical phased array for agile and large angle laser beam steering systems

In this article, the authors present and discuss the fabrication of three-dimensional (3D) optical phased array (OPA) devices for large angle, two-dimensional optical beam steering. Fabrication of a single layer (one-dimensional) OPA prototype for one-dimensional beam steering on silicon nanomembrane is presented. The authors present different approaches, such as nanoimprint lithography, optical lithography, and self-aligned patterning of multibonded silicon-on-insulator wafers, for the realization of 3D OPA devices in particular and 3D photonic circuits in general. At the end, the authors discuss the challenges and potential solutions.

Electric field control of a two-dimensional higher order diffraction optical beam splitter based on a cubic K0.99Li0.01Ta0.63Nb0.37O3 single crystal

An electric field controlled two-dimensional higher order diffraction optical beam splitter has been realized based on a photorefractive higher order diffraction grating. In experiments, the splitter was produced by wave coupling (632.8 nm, 532.0 nm) at a small incident angle with a potassium lithium tantalate niobate single crystal. In the process of splitting, the incident beam of different wavelengths (632.8 nm, 532.0 nm) could be split into multi-output beams by the splitter. The influence of an externally applied electric field was studied and results show that the intensity of higher order diffraction could be controlled by the electric field. The polarization properties of higher order diffraction were discussed. An electric field controlled five–three optical beam splitter was investigated theoretically.

Two-dimensional higher-diffraction-order optical beam splitter based on phenanthrenequinone-doped poly(methyl methacrylate) photopolymer

A two-dimensional optical beam splitter has been realized that uses the higher diffraction orders of a refractive-index grating. Gratings were recorded experimentally with light from a semiconductor laser incident at a small angle on phenanthrenequinone-doped poly(methyl methacrylate) photopolymer. The incident signal beam, which was made up of three different wavelengths (632.8, 532.0, and 488.0 nm), was split by the grating into multiple output beams with nearly equal size and separation. Results are given for when the sample grating was placed behind, in front of, and in the focal plane of a Fourier lens. The properties of higher-order-diffraction images have been discussed. The discussion shows that a two-dimensional higher-diffraction-order optical beam splitter provides a practical method for splitting a signal beam.

Guiding and Nanofocusing of Two-Dimensional Optical Beam for Nanooptical Integrated Circuits

Guiding and Nanofocusing of Two-Dimensional Optical Beam for Nanooptical Integrated Circuits

Two-dimensional optical beam deflector operated by wavelength tuning

A new method based on an optical delay line structure is proposed for two-dimensional raster optical beam steering. For one-dimensional beam steering, the laser beam to be deflected is split into N co-directional sub-beams of equal intensity with the aid of a plane-parallel plate. These sub-beams experience a relative time delay, which translates into a phase difference, thus forming a phased array. When the laser wavelength is tuned, the relative phase varies and the far-field interference footprint can be steered across a receive plane. By employing two plane-parallel plates in series, the described scheme can be extended to produce a two-dimensional N x N array of sub-beams, allowing two-dimensional beam steering via wavelength tuning. In this case, wavelength tuning over a larger range leads to a linear deflection which repeats itself in a raster-like fashion. One direction of deflection repeats itself multiple times as wavelength is scanned over larger range, that is, a raster effect. In this paper, the principle is theoretically derived and formulated, and the preliminary experimental results with four sub-beams are presented.

Space-multiplexed optical scanner.

A low-loss two-dimensional optical beam scanner that is capable of delivering large (e.g., > 10 degrees) angular scans along the elevation as well as the azimuthal direction is presented. The proposed scanner is based on a space-switched parallel-serial architecture that employs a coarse-scanner module and a fine-scanner module that produce an ultrahigh scan space-fill factor, e.g., 900 x 900 distinguishable beams in a 10 degrees (elevation) x 10 degrees (azimuth) scan space. The experimentally demonstrated one-dimensional version of the proposed scanner has a supercontinuous scan, 100 distinguishable beam spots in a 2.29 degrees total scan range, and 1.5-dB optical insertion loss.

Wigner distribution and fractional Fourier transform for two-dimensional symmetric optical beams.

A useful relationship between the fractional Fourier transform power spectra of a two-dimensional symmetric optical beam, on the one hand, and its Wigner distribution, on the other, is established. This relationship allows a significant simplification of the standard procedure for the reconstruction of the Wigner distribution from the field intensity distributions in the fractional Fourier domains. The Wigner distribution of a symmetric optical beam is analyzed, both in the coherent and in the partially coherent case.

Crosstalk and interconnection distance considerations for board-to-board optical interconnects using 2-D VCSEL and microlens array

We describe the design and experimental characterization of a substrate-mode optical backplane using 0.5-, 0.75- and 1-mm spacing two-dimensional (2-D) optical beam arrays. The system uses arrays of multiplexed holograms to implement free space board-to-board interconnects, and employs 250-/spl mu/m pitch 2-D vertical-cavity surface-emitting lasers (VCSEL) and microlens array as a transmitter to provide 0.5- to 1-mm spacing 2-D beam array, operating at 850 nm. By comparing the optical beam properties at the detector plane including the spot size and power uniformity of the optical beam array, as well as signal-to-noise ratio (SNR), the maximum interconnect distances are justified. Furthermore, we point out the improvement of the throughput that can be achieved by 2D crosstalk analysis within the same design concept. The results of crosstalk analysis obtained here can be used for application to the standard five-board free-space optical backplane system.

Three-element fiber-type optical phased array antenna with high-speed two-dimensional optical beam steering

A fiber-type optical phased array antenna is proposed as a new configuration of phased array antennas operating in the optical frequency domain. The proposed antenna consists of fibers that connect an optical beamforming network consisting of integrated optical waveguides to an array antenna consisting of microlenses as the element antenna. High-speed two-dimensional optical beam steering can be achieved by reducing the relative phase fluctuation between element antennas and the generation of the grating lobe. In an experiment on the three-element fiber-type optical phased array antenna, three 1 × 2 variable power dividers and four variable phase shifters are integrated on a LiNbO3 substrate as the optical beamforming network, and graded-index-fiber (GIF) lenses are used as the antenna elements. These components are connected through polarization-maintaining fibers (PMF). The 3-dB bandwidth of the integrated variable phase shifter is from dc to 924 MHz, and the optical beam steering range of the three-element array is 0.2°; they are arranged in a triangle. The parameters of the GIF lens are optimized and it is estimated that at the maximum gain coefficient a grating lobe level of –14.5 dB and a gain coefficient of 0.815 can be obtained. © 1999 Scripta Technica, Electron Comm Jpn Pt 1, 82(8): 42–51, 1999

Self-trapping of one-dimensional and two-dimensional optical beams and induced waveguides in photorefractive KNbO_3

We demonstrate self-trapping of one-dimensional and two-dimensional optical beams in a photorefractive KNbO(3) crystal. We study the waveguides induced by the self-trapped beams for prospective applications of tunable nonlinear frequency conversion in soliton-induced waveguides.

Self-trapping of two-dimensional optical beams and light-induced waveguiding in photorefractive InP at telecommunication wavelengths

We demonstrated an experimental observation of self-trapping and self-deflection of a two-dimensional optical beam by the photorefractive effect at telecommunication wavelengths under an applied dc field. Self-trapping is effective for an intensity range related to the intensity-temperature resonance known for two-wave mixing in InP:Fe. The photorefractive index change giving rise to the trapping is measured at 10−4, while the photorefractive space-charge field is measured at about 50 kV/cm, ten times higher than the applied field. We show experimentally that this index change creates a waveguide that can be used to guide a second beam at 1.55 μm.

Variational analysis of nonlinear channel waveguides

The dynamics of a two-dimensional optical beam propagating in a nonlinear channel waveguide is investigated by means of a variational technique. Through this analysis, one can determine the eigenmodes (self-trapped modes) of the structure. Their stability has also been checked numerically.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>