Frequency-resolved nonlinear turbulent energy transfer into zonal flows in strongly heated L-mode plasmas in the HL-2A tokamak.

The absolute rate of nonlinear energy transfer among broadband turbulence, low-frequency zonal flows (ZFs) and geodesic acoustic modes (GAMs) was measured for the first time in fusion-grade plasmas using two independent methods across a range of heating powers. The results show that turbulent kinetic energy from intermediate frequencies (20-80 kHz) was transferred into ZFs and GAMs, as well as into fluctuations at higher frequencies (>80 kHz). As the heating power was increased, the energy transfer from turbulence into GAMs and the GAM amplitudes increased, peaked and then decreased, while the energy transfer into the ZFs and the ZFs themselves increased monotonically with heating power. Thus there exists a competition between ZFs and GAMs for the transfer of turbulent energy, and the transfer into ZFs becomes dominant as the heating power is increased. The poloidal-radial Reynolds stress and the mean radial electric field profiles were also measured at different heating powers and found to be consistent with the energy transfer measurement. The results suggest that ZFs play an important role in the low-to-high (L-H) plasma confinement transition.

Dual-negative refraction in photonic crystals with hexagonal lattices.

We present a dual-negative refraction effect based on the overlapping bands in a two-dimensional triangular photonic crystal formed by holographic lithography. Under certain conditions, one incident plane wave launched into this photonic crystal can be dispersed into two negative refracted waves at the same frequency and the same perpendicular polarization state with different phase velocities and group velocities. We find that this dual-negative refraction behavior can be easily manipulated by adjusting the incident angle, the frequency of incident wave and the filling ratio of the PhC. This special effect can be applied to realize wave-front division and optical interference in optical holography. Based on this effect, a double focusing imaging phenomenon has been achieved by the PhC slab. These unique features may show great impacts on both fundamental physics and optical device applications.

Anomalous refractive effects in honeycomb lattice photonic crystals formed by holographic lithography.

We have investigated for the first time the anomalous refractive effects of a photonic crystal (PhC) formed by holographic lithography (HL) with triangular rods arranged in a honeycomb lattice in air. Possibilities of left-handed negative refraction and superlens are discussed for the case of TM2 band with the index contrast n = 3.4:1. In contrast to the conventional honeycomb PhC made of regular rods in air, the HL PhCs show left-handed negative refraction over a wider and higher frequency range with high transmissivity (>90%), and the effective indices quite close to -1 for a wide range of incident angles with a larger all-angle left-handed negative refraction (AALNR) frequency range (Deltaomega/omega approximately 14.8%). Calculations and FDTD simulations demonstrate the high-performance negative refraction properties can happen in the holographic structures for a wide filling ratio and can be modulated by changing the filling ratio easily.

Wavefront reconstruction and three-dimensional shape measurement by two-step dc-term-suppressed phase-shifted intensities.

A wavefront reconstruction and three-dimensional (3-D) shape measurement method by a two-step phase-shifting algorithm with arbitrary phase shift in (0,pi) is proposed. In this method, only two phase-shifted intensities, with the removal of the dc term by an averaging technique in spatial domain or low-pass filter operation in the frequency domain, are needed, and the other additional measurements are no longer required. The simulation for an irregular wavefront has shown the feasibility, and the optical experiment for a 3-D face mask in the case of a sinusoidal fringe projection system has illustrated the validity of the proposed method.

Improvement of transmission properties through two-bend resonance by holographic design for a two-dimensional photonic crystal waveguide.

We have investigated the transmission properties of a photonic crystal waveguide (PCW) formed by holographic lithography for the first time with a two-dimensional (2D) triangular holographic photonic crystal (PhC) including a line defect with two 60 masculine bends. Calculations have shown that for this PCW high transmission (>90%) through sharp corners can be obtained in a wide frequency range from 0.298 to 0.310 (omega alpha/2pi c) with the relative band gap of 4% when the dielectric contrast is 7.6:1. As far as we know, this result should be the widest frequency range with high transmission (>90%) in the waveguide of similar 2D triangular PhCs ever reported. We have also found that the specific holographic designs of PhC have strong influence on the resonance between the two waveguide bends, and thus this fact can be used as an effective means to improve the transmission property of 2D holographic PCW. In addition to the simplicity and low cost of holographic fabrication of PhCs, these features may reveal the possibly better guiding ability of holographic PCW than the conventional waveguide and the promising potential of the former in the application of photonic integrated circuits.

Security enhancement of double-random phase encryption by amplitude modulation.

Conventional double-random phase encoding is vulnerable to a chosen or known plaintext attack owing to the linearity of the system. We introduce a technique to break down this linearity with an undercover amplitude modulation in the encryption scheme. As an additional key, this operation can significantly enhance the security of the system. A series of computer simulations have shown the effectiveness of this method and its resistance against the known plaintext attack. The design and parameter choice of the amplitude modulator is also discussed.

Simple direct extraction of unknown phase shift and wavefront reconstruction in generalized phase-shifting interferometry: algorithm and experiments.

An algorithm to extract the arbitrary unknown phase shift and then reconstruct the complex object wave in generalized phase-shifting interferometry (GPSI) without the iteration process and measurement of object wave intensity is proposed. This method can be used for GPSI of any frame number >or=2. Both computer simulations with smooth and diffusing object surfaces and optical experiments have verified the effectiveness of this method over a wide range of phase shifts with very satisfactory results.

Large complete bandgaps in a two-dimensional square photonic crystal with isolated single-atom dielectric rods in air.

It is well known that the square lattice of isolated single-atom dielectric rods in air does not give rise to complete bandgaps even when asymmetry is introduced to lift some degeneracy. However, in this paper, a new kind of two-dimensional square photonic crystal with isolated single-atom dielectric rods in air formed by holographic lithography is proposed, and the relation between their photonic bandgap properties and their specific holographic design are systematically analyzed. In addition to the large complete relative bandgap, namely 9.68% gap/midgap ratio for the dielectric constant contrast of 13.6:1, this structure has very large tolerance on the system parameters and fabrication conditions. This fact can greatly relax the experimental requirements. This work may demonstrate the unique feature and advantages of photonic crystals made by the holographic method and provide a guideline for their design and fabrication.

Negative refractions in two-dimensional photonic crystals formed by holographic lithography.

We present a study on negative refractions in the four lowest bands of two-dimensional (2D) square lattices formed by holographic lithography (HL) and compare these features with those of a lattice of the same kind but with regular dielectric columns. The plane wave calculations and FDTD simulations have shown that in some bands or for some interfaces the negative refraction can only happen in holographic structures, and generally the rightness of holographic structures and regular structures of the same kind may be different.

Fast blind extraction of arbitrary unknown phase shifts by an iterative tangent approach in generalized phase-shifting interferometry.

A novel fast convergent algorithm to extract arbitrary unknown phase shifts in generalized phase-shifting interferometry (PSI) is proposed and verified by a series of computer simulations. In this algorithm an error function is introduced and then the unknown phase shifts are found by an iterative tangent approach. In combination with the statistical method, this algorithm can give the most exact results in the fewest iteration steps. It can be used for generalized PSI of arbitrary frames for both smooth and diffusing objects and can usually reach the exact phase shifts with only four or five iterations for three- or four-frame PSI.

Two-step phase-shifting interferometry and its application in image encryption.

Conventional phase-shifting interferometry (PSI) needs at least three interferograms. A novel algorithm of two-step PSI, with an arbitrary known phase step, by which a complex object field can be reconstructed with only two interferograms is proposed. This algorithm is then applied to an information security system based on double random-phase encoding in the Fresnel domain. The feasibility of this method and its robustness against occlusion and additional noise attacks are verified by computer simulations. This approach can considerably improve the efficiency of data transmission and is very suitable for Internet use.

Holographic design and band gap evolution of photonic crystals formed with five-beam symmetric umbrella configuration.

We propose a holographic design of five-beam symmetric umbrella configuration, where there are a central beam and four ambient beams symmetrically scattered around the central one with the same apex angle, for fabrication of three-dimensional photonic crystals with tetragonal or cubic symmetries, and systematically analyzed the band gap properties of resultant photonic crystals when the apex angle is continuously increased. Our calculations reveal that large complete photonic band gaps exist in a wide range of apex angle for a relatively low refractive index contrast. Specifically, the face-centered cubic structure with a relative band gap of 25.1% for epsilon = 11.9 can be obtained with this recording geometry conveniently where all the beams are incident from the same half-space. These results will provide us with more understanding of this important recording geometry and give guidelines to its use in experiments.

Generalized phase-shifting interferometry with arbitrary unknown phase steps for diffraction objects.

A general method of extracting the arbitrary unknown and unequal phase steps in phase-shift interferometry from interferograms recorded on the diffraction field of an object and then reconstructing the object wave front digitally with our derived formulas is proposed. The phase steps are first calculated based on the statistical nature of the diffraction field and are further improved by an iterative approach. This method is simple, highly accurate, and usable for any frame number N (N > or = 3) and for both smooth and diffusing objects, as is verified by a series of computer simulations.

Larger bandgaps of two-dimensional triangular photonic crystals fabricated by holographic lithography can be realized by recording geometry design.

The photonic band gap (PBG) properties of two classes of two-dimensional (2-D) triangular lattice fabricated by holographic lithography are investigated numerically. The effect of intensity threshold on the filling ratio and then the shape of "atoms", and the corresponding photonic gap are comprehensively studied. Our results show that the recording geometry for a given 2-D triangular lattice is not unique, and this fact gives us more freedom in choosing proper recording geometry to obtain larger bandgap.

Phase-shifting with computer-generated holograms written on a spatial light modulator.

We propose a new computer-controlled phase-shifting method based on computer-generated holograms (CGHs) displayed on a spatial light modulator (SLM). In this method the accurate phase shifts required in phase-shifting digital holography or interferometry are induced by a suitable transformation of the encoding patterns of the CGH displayed on a SLM. Both the theoretical analysis and the experimental results demonstrate the feasibility of this approach. We also discuss possible applications of this method in the field of interferometric null testing of aspheres.

Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps.

A new approach to reconstructing the object wave front in phase-shifting interferometry with arbitrary unknown phase steps is proposed. With this method the actual phase steps are first determined from measured intensities with an algorithm based on the statistic property of the object phase distribution in the recording plane. Then the original object field is calculated digitally with a derived formula. This method is simple, accurate, and capable of retrieving the original object field, including its amplitude and phase distributions simultaneously, with arbitrary and unequal phase steps in a three- or four-frame method. The effectiveness and correctness of this approach are verified by a series of computer simulations for both smooth and diffusing surfaces.

Interference of four umbrellalike beams by a diffractive beam splitter for fabrication of two-dimensional square and trigonal lattices.

A simple optical interference method for fabricating two-dimensional square and trigonal lattices is demonstrated. A general formula for the interference contrast formed by two arbitrary polarized elliptical waves is deduced, the relation between wave vectors of incident light and the resultant pattern is analyzed, and polarization optimization of all beams to ensure uniform contrast is given.

Formation of three-dimensional periodic microstructures by interference of four noncoplanar beams.

A newly reported method of making three-dimensional microstructures or photonic crystals by holographic lithography has some obvious advantages over other techniques with the same purpose. A systematic and comprehensive analysis of interference of four noncoplanar beams (IFNB) is provided. It shows that all 14 Bravais lattices can be formed by means of IFNB and gives explicit relationships between each lattice and the corresponding recording geometry. The concept of pattern contrast is extended to the case of IFNB, and it is indicated that a uniform contrast for each interference term can be obtained by properly choosing the beam ratio and polarization. A calculation algorithm is then developed to optimize the direction of polarization of each beam to ensure maximum uniform contrast. These results, verified by computer simulations, may lay a theoretical foundation for fabrication of photonic crystals with the approach of IFNB.

All fourteen Bravais lattices can be formed by interference of four noncoplanar beams.

The interference of four noncoplanar beams (IFNB) is analyzed. It is shown that all 14 Bravais lattices can be formed by a holographic method of IFNB. The relationship among the three basis vectors of the lattice that are to be produced, the required wavelength, and the geometric arrangement of the four beams is derived. This analysis may lay the foundation for fabrication of three-dimensional photonic crystals by holographic lithography.

One-step recording of a dot-array color hologram with a reference beam encoding plate.

A novel method of making a dot-array color hologram in one step with a prefabricated reference beam encoding plate (RBEP) is proposed. This RBEP can produce three sets of dot-array reference beams simultaneously, which are spatially separated on the recording plane and overlap three digital images that correspond, respectively, to the three primary color images of a color object at the same time. Therefore only one exposure is needed for recording the color hologram. Both the theoretical analysis and experimental results that confirm the feasibility of this approach are given.