A unique design method of two cascaded diffractive optical elements (DOEs) with different sizes of effective phase region to modulate broadband beam is presented with consideration of single production material and low relief height on DOE. The iterative algorithm to calculate the relief heights on these DOEs is introduced at first. Where after, a broadband beam at wavelength from 500nm to 600nm propagates through the designed DOEs and is focused on the target plane in the simulation part. The shaping results demonstrate the excellent shaping ability of this unique design method. The shaping system proposed in this paper is significant for nonmonochromatic light modulation and has many applications such as graphic encryption, three-dimensional color display and multi wavelength division multiplexing.
A two-dimensional anisotropic annular photonic crystal structure is presented to obtain an absolute photonic band gap.
This structure is composed of circular air holes and dielectric rods in a triangular lattice. Uniaxial crystal is introduced to
photonic crystal with extraordinary axis parallel to the extension direction of rods. The role of each dielectric and
geometric parameter is investigated and a mid-gap ratio above 35% is realized by the parameter optimization. Large gap
favors the structure with negative uniaxial veins and positive uniaxial rods. As the air-hole radius scales up, the
dielectric-rods radius to sustain the maximum band gap scales down. The positive uniaxial material Tellurium is used to
achieve a large polarization-insensitivity gap.
The far-field focusing properties of two dimensional photonic crystals based flat lens with rod-type honeycomb
lattice are investigated using finite difference time domain (FDTD) method. The results match the wave-beam negative
refraction law with relative refractive index of -1. But, the image qualities are limited by low transmission at large
incident angles. To improve the image qualities, the effects of interface on the far-field image in a two-dimensional
honeycomb photonic crystal are investigated. It is found that the image qualities can be improved by modifying the
radius of rod near the surface of photonic crystals slab.
It is believed that combining the techniques of smoothing by spectral dispersion (SSD) in the time domain and diffractive optical elements (DOE) in the space domain can improve beam uniform illumination. Adding another SSD unit to the combined system in different grating direction can disturb the incidence wave front more confused, thus the number of speckle patterns in the target plane is increased. The intensity in the target plane becomes smoother after a period of accumulation. However, the wave front distortion is limited by the dimension number of grating directions and the intensity distribution in each direction. In this paper we introduce the air turbulence and study its influence on the wavefront. The disturbance on wave front acts as an infinite aggregate in the number of direction dimension and intensity dimension because of the property of turbulence. The numerical calculation indicates that introducing disturbance by air turbulence on amplitude and phase of the light beam that incident to DOE can smooth the distribution on target plane after a period of accumulation.
A design of multi-step diffractive optical element (MDOE) is developed for the high power laser output smoothing. A hybrid algorithm is presented which inserts a quasi-optimum process in every iterative loop. This method of MDOE design saves the computing time tremendously. The top profile error (TPE) is about 8.4%, which looks inferior to what we have gotten in the earlier years with using continues profile design, but very easy in manufacture to match the design data. Now this MDOE with 16 steps on the surface of K9 glass can be realized with four masks' etching facility. The maximum etching error of the depth is 10-80nm, which is receivable with tolerance analyze in our design. The MDOE has 70mm diameter, and uniform illumination area is an Φ600μm spot. With using expanding 1.064 μm beam, the smoothing pattern in focus plane is measured. The result shows that the TPE is about 19%. It is believable that with the influence by the interaction of second hot electron and time domain smoothing this result is acceptable.
Indirect-drive Inertial Confinement Fusion(ICF) system has two requests: first, it requires incident beam to focus on a small spot with very low circular side-lobe around the edge of the hole; second, when it continue to transmit onto the wall of cavity, it requires uniform illumination. A two-step iteration algorithm aiming at two positions of this system is proposed to match these two requests with using Pure Phase Plate (PPE). Our results show that the circular side-lobe near the target hole has been depressed to about 10-11 W/cm2, and the beam has small top modulation on the target wall.
Focus shaping with highly focused cylindrical vector beam is an interesting and important topic in both applied optics and physical optics. In this paper, we describe optimization algorithms to design diffractive optical elements for various beam shaping applications. "Optical bubbles" with desired size and numbers for trapping particles and flat-top focusing with low side-lobe to improved micro printing are proposed. Ultra small focus spot with long depth of focus without energy split to extend the region around the image plane is also presented.
The existence and stability properties of three-component vector solitons are studied. Linear stability analysis and numerical simulations show that when the power of vortex component is below a threshold, the fundamental component is stable, and the vortex components break up into dipole solitons; the dipole solitons originating from the vector solitons with total zero topological charges are very unique. While if the power of vortex components is higher than that threshold, all soliton components are unstable and break up into independent fundamental solitons. The instability of solitons with total zero topological charges is largely suppressed comparing to that of solitons with total nonzero topological charges.
The internal oscillation of spatial optical solitons in a cubic-quintic nonlinear medium is investigated systemically in their stability parameter region. Both internal oscillations of fundamental soliton and localized optical vortex soliton are determined. Internal modes with and without angular dependence are found. Our results show that internal oscillations exist only when the power of the soliton exceeds a threshold value. We also simulate the dynamics of soliton perturbed by internal modes. Numerical results show that internal oscillations induced by these modes are very robust. Some novel and interesting phenomena are discovered during the propagation process. Evolution of the perturbed state visually appears that the spatial soliton is uniformly (unevenly) breathing or rotating around the propagating axis periodically, the periods approximately equal to that of the internal oscillations.
One-dimensional magneto-optical (MO) photonic crystals display enhanced MO effect due to the localization of light, it can be used to fabricate small-size optical isolator with only tens of micros which can enlarge the integration of system. A transfer matrix method (TMM) that is suitable for solving the problems of the propagation of polarized light in anisotropic media at an arbitrary incidence angle, is described detailedly in this paper. Using this method, we discussed two types of reflection-mode "sandwich structure" of MOMF isolator, and found that the structure with thicker MO layer has advantages in working stability and fabrication.
In this paper, design of diffractive optical element (DOE) for optical bubble creating and controlling with radially polarized incident beam focused by a high numerical aperture (NA) aplanatic lens is proposed and its application in optical trapping is discussed. We use a DOE to modify the phase of the incident radial polarization beam to form different kinds of optical bubbles. Optimization algorithms are used to design the DOE to adjust the bubble size and depth to meet the requirements. The results show that the size of the bubble is inversely proportional to its depth. Owing to the overlapping of the field strengths around the focus, the bubble tends to merge into flattop distribution as it is getting smaller and smaller. With a fixed DOE design, bubbles with smaller size and larger depth can be generally obtained with higher NA, owing to a more confined field strength distribution from the strong longitudinal field component.
This paper describes a fast simulation annealing algorithm for the optimum design and applies to beam shaping by diffractive optical elements. The algorithm introduced the corresponding utilities function, and used Tsallis statistic for optimum design. The simulated results show that to converge the incident energy into the desired region with the same mean square error, our method only cost 1% percent of time that needed by the traditional SA. This algorithm brings forward a new and fast method for the design of Diffractive Optical Elements, and potentially for other optimization problems.
KEYWORDS: Wave propagation, Diffractive optical elements, Solids, Dielectric polarization, Beam propagation method, Interfaces, Optical storage, 3D optical data storage, Data storage, Near field optics
In solid immersion lens (SIL) system, both propagating waves and evanescent waves contribute to the total field strength with different properties. By using diffractive optical element to modify the cylindrical vector incident beam, we study how the field strength changes when propagating (evanescent) waves are balanced against each other and the evanescent (propagating) waves dominate the field strength. The simulation results show that for radially polarized incident beam, the rate of slope of axial field strength v.s transverse field strength by evanescent waves contribution is greater than that by propagating waves contribution. With general cylindrical vector incident beams, increasing (the rotation angle of polarization from the radial direction) will also make the axial field strength decrease while the variation of the transverse field strength is small. These methods can be used to control the aspect ratio of three dimensions storage dot, which may find applications in near field optical data storage system.
We present a vector angular spectrum approach by using self-iterative algorithms for beam shaping. It is rigorous and still valid to sub-wavelength feature size. The approach bases on scalar angular spectrum theory and modifies by keeping the variation of the beam's polarization. The comparison of this approach with Fraunhofer diffraction integrals by using different self-iterative algorithms to design the diffractive optical elements for beam shaping shows the former one is more efficient. Design example in the near field for beam shaping with sub-wavelength minimum feature is also presented.
Beam shaping theory is naturally one of the inverse problems and it is unable to get a unique minimum resolution. In the case of high demands to target beam quality such as uniform illumination, or the complex style of incident beams, one still needs to improve the classical design algorithm to satisfy fabrications and applications.
In this paper, new iteration algorithm based on phase mixture algorithm (PMA) and input-output (IO) algorithm is presented. By using random phase mixture factor instead of fixed phase mixture factor in PMA and random feedback factor in IO algorithm, and introducing a selection rule in each loop of the iteration, the degree of freedom of the iteration is increased and better target beam quality is obtained. A continuous diffractive optical element (DOE) for uniform illumination of annular Gaussian incident beam with diameter 240 mm is shown as a design example. Comparison of iteration results between the new algorithm and classical PMA or IO shows that the new algorithm provided better target beam quality and thinner DOE phase thickness. The design result of new algorithm only has 2.25% top profiled error (TPE) with a phase thickness of about 8 π while the best simulated result of PMA and IO algorithm has 3.42% TPE with a phase thickness of 12.4 π.
Laguerre-Gaussian (LG) mode carries a well-defined orbit angular momentum. We design a fork-like grating to produce the superposition of two LG modes. It is useful in the high-dimensional quantum communication.
The transfer matrix method and the block-iterative frequency-domain method are used to calculate the point defect of 2D photonic crystals. The transmission and dispersin curves are analyzed and discuss the mechanism of increasing Q value using point defect photonic crystal as laser resonant microcavity.
To get two-dimensional (2-D) complete bandgap, a square lattice with complex crystal cell and a rectangular lattice with dielectric cylinders in air were investigated using plane wave expansion method. Their band structures were found to be different from those of an exact square lattice and they both can be implemented 2D compelte bandgaps. The rectangular lattice has compete 2D bandgaps when the ratio of the two bases is chosen properly.
The phase distribution design process of the pure phase element (PPE) used for quasi-annular beam shaping is introduced in this paper. A new optimization algorithm named Quasi-Gradient Descent (Quasi-GD) algorithm has been developed and used here to meet such design requirement. With a more restrictive sampling mode named precise sampling in the optimization, the simulated result shows that the uniformity of energy distribution on the focal plane is invariant with different sampling intervals and the true beam shaping effect is achieved.
KEYWORDS: Diffractive optical elements, Diffraction gratings, Personal protective equipment, Etching, Diffraction, Ion beams, Chemical elements, Beam shaping, High power lasers, Modulation
An integrated DOE is designed for beam combination and shaping. The DOE is double-faced carved. One is transmission blazed grating to convert four declined incident incoherent beams to parallel beams, the other is continuous profile relief for shaping. The simulated intensity focal-plane profile has little modulation in the main lobe and high diffraction efficiency.
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