Generation of near-field hexagonal array illumination with a phase grating

Phase-locking dynamics of a 2D VCSEL hexagonal array with an integrated Talbot cavity

In this paper, phase-locking dynamics of 2D VCSEL hexagonal array with an integrated Talbot cavity are numerically investigated based on rate equations aiming at achieving high brightness output. The processes of wavelength synchronization and phase locking under different fill factors ff and fractional Talbot cavity lengths L were addressed comprehensively. Different supermodes of phase-locked VCSEL array were then analyzed from both near-field and far-field pattern, and proved to be well matched with the results of coupled-mode theory. With appropriate configuration the Talbot-VCSEL system can operate in a full in-phase mode eventually, which is beneficial for determining the parameter interval corresponding to the most expected single narrow-lobe far-field pattern. Furthermore, the simulation results also indicate that, considering the parametric interactions the distribution of optical feedback from the fractional Talbot cavity should be consistent as much as possible to facilitate the realization of phase-locked state. Our study could provide a theoretical support to obtain the full in-phase coupled VCSEL array with high performance.

Influence of the photonic nanojet of microspheres on microsphere imaging

The imaging properties of BaTiO₃ glass (BTG) microspheres in the diameter range of 5-50 µm which are fully immersed in a polydimethylsiloxane layer are experimentally studied. Our experimental results show that for both Blu-ray disc samples and the single-layer hexagonally close-packed microsphere array samples, with the increase of the diameter of BTG microspheres, the range of focal image positions (RFIP) increases linearly. When the diameter of BTG microspheres increases from 5 to 50 μm, the RFIP changes from 4 to 25 μm. For the microsphere array samples, Talbot effect is observed, and both the position of Talbot images and the Talbot distance depend on the diameter of BTG microspheres. Numerical simulations indicate that the length of the photonic nanojet changes from 2.9 to 7.1 μm when the BTG microsphere size increases from 5 to 50 μm, and the calculated RFIP is between 6 and 24 μm. The calculated RFIPs match well with the experimental ones. Our researches reveal that the RFIP depends on the length of the photonic nanojet of the BTG microsphere.

Fresnel diffraction of fractal grating and self-imaging effect

Based on the self-similarity property of fractal, two types of fractal gratings are produced according to the production and addition operations of multiple periodic gratings. Fresnel diffractions of fractal grating are analyzed theoretically, and the general mathematic expressions of the diffraction intensity distributions of fractal grating are deduced. The gray-scale patterns of the 2D diffraction distributions of fractal grating are provided through numerical calculations. The diffraction patterns take on the periodicity along the longitude and transverse directions. The 1D diffraction distribution at some certain distances shows the same structure as the fractal grating. This indicates that the self-image of fractal grating is really formed in the Fresnel diffraction region. The experimental measurement of the diffraction intensity distribution of fractal grating with different fractal dimensions and different fractal levels is performed, and the self-images of fractal grating are obtained successfully in experiments. The conclusions of this paper are helpful for the development of the application of fractal grating.

Reciprocal vector theory for diffractive self-imaging

A reciprocal vector theory for analysis of the Talbot effect of periodic objects is proposed. Using this method we deduce a general condition for determining the Talbot distance. Talbot distances of some typical arrays (a rectangular array, a centered-square array, and a hexagonal array) are derived from this condition. Further, the fractional Talbot effect of a one-dimensional grating, a square array, a centered-square array, and a hexagonal array is analyzed and some simple analytical expressions for calculation of the complex amplitude distribution at any fractional Talbot plane are deduced. Based on these formulas, we design some Talbot array illuminators with a high compression ratio. Finally, some computer-simulated results consistent with the theoretical analysis are given.

Tunable two-dimensional hexagonal phase array in domain-engineered Z-cut lithium niobate crystal

An optical phase array with tunable phase step is demonstrated. The phase array consists of a two-dimensional hexagonal lattice of inverted ferroelectric domains fabricated on a Z-cut lithium niobate substrate. The electro-optically tunable phase step is obtained by the application of an external electric field along the z axis of the crystal via transparent electrodes. Theoretical analysis and experimental results are presented, showing that a tunable and flexible adaptive optical illuminator device can be realized by combining the electro-optic tunability with the Talbot effect. Generation of a multiplicity of light patterns is shown.

Optimized condition for etching fused-silica phase gratings with inductively coupled plasma technology

Polymer deposition is a serious problem associated with the etching of fused silica by use of inductively coupled plasma (ICP) technology, and it usually prevents further etching. We report an optimized etching condition under which no polymer deposition will occur for etching fused silica with ICP technology. Under the optimized etching condition, surfaces of the fabricated fused silica gratings are smooth and clean. Etch rate of fused silica is relatively high, and it demonstrates a linear relation between etched depth and working time. Results of the diffraction of gratings fabricated under the optimized etching condition match theoretical results well.

Circular Dammann grating

A circular Dammann grating that can produce circular equal intensities at various orders in the far field is described. A set of parameters such as order, circular number, uniformity, and diffraction efficiency has been defined to describe the novel diffractive phase elements. Numerical solutions of binary-phase (0, pi) circular Dammann gratings are given. The results of experiments with a four-order circular Dammann grating made by a lithographic technique are presented. This novel diffractive optical element should be highly interesting in a wide variety of practical applications.

Multifunctional double-layered diffractive optical element

We propose a novel multifunctional double-layered diffractive optical element (DOE) based on the fractional Talbot effect. This DOE consists of two layers: one is the encoding layer, in which multiple sub-DOEs, i.e., multiple optical functions, are encoded; the other is the decoding layer, which is a properly designed Talbot illuminator. This DOE can perform each of the multiple optical functions one by one by shifting the encoding layer. Experimental results demonstrate that this method is efficient. This device should be highly interesting for integrated optics, optical interconnection, secure optical storage, and dynamic optical fiber communications.