Application of the two-mode squeezed coherent state representation in deriving generalized optical Collins formula

We propose a new two-mode squeezed coherent state representation |z₁, z₂〉_g which is characteristic of the correlation between the squeezing and the displacement. Based on it and using the technique of integration within an ordered product of operators we obtain a generalized two-mode Fresnel operator (GTFO), which is an image of the mapping from (z₁, z₂) to in |z₁, z₂〉_g representation. The matrix element of GTFO in the coordinate representation leads to a generalized two-dimensional Collins formula (Huygens-Fresnel integration transformation describing optical diffraction) in entangled form.     

Spectral shift of partially coherent flattened multi-Gaussian beams with a hole passing through ABCD optical systems

Based on flattened multi-Gaussian beam model and partially coherent theory, the expression for cross-spectral density of partially coherent flattened multi-Gaussian beam with a hole was given. The analytical expression for on-axis spectrum of partially coherent flattened multi-Gaussian beam with a hole passing through a paraxial ABCD optical system was derived. The spectral shifts of the partially coherent flattened multi-Gaussian beam with a hole propagating in free space and passing through the lens have been analyzed. The effects of the beam profile, spatial coherence parameter and the system parameters on the relative spectral shift have been discussed. Our results show that the inner radius of flattened multi-Gaussian beam with a hole determines its relative spectral shift in near field and its outer radius determines that in far field. For the flattened multi-Gaussian beam with a hole passing through a lens, the on-axis relative spectral shift changes sharply near the focal plane with the increase in Fresnel number and the spatial coherence parameter.     

Propagation of super-Lorentzian beams through a paraxial ABCD optical system

Based on the Collins integral, analytical propagation formulae of super-Lorentzian (SL) SL₀₁, SL₁₀, and SL₁₁ beams passing through a paraxial ABCD optical system are derived by means of the convolution theorem of the Fourier transform. The propagation properties of the SL₀₁ and SL₁₁ beams in free space are graphically illustrated with numerical examples. The power in the bucket of the SL₀₁ and SL₁₁ beams has been also examined in the far-field plane. This research is useful to the applications of super-Lorentzian beams.     

Approximate analytical representation of Wigner distribution function for Gaussian beams passing through ABCD optical systems with hard aperture

Based on the treatment that a rectangular function can be expanded as an approximate sum of complex Gaussian functions with finite numbers, the analytical expression of the Wigner distribution function for a Gaussian beam passing through a paraxial ABCD optical system with hard-edged aperture is obtained. By numerical simulation, it is shown that the effect of the aperture on the Wigner distribution function is prominent. By comparing the analytical results with the numerical integral results, it is shown that this method of expanding hard-edged aperture into Gaussian functions with finite numbers is proper and ascendant. This method could be extended to study the Wigner distribution functions of other light beams passing through a paraxial ABCD optical system with hard-edged aperture.     

Propagation of a four-petal Gaussian vortex beam through a paraxial ABCD optical system

Based on the Collins diffraction integral formula, an analytical expression of a general four-petal Gaussian vortex beam passing through a paraxial ABCD optical system is derived by means of the mathematical technique. As a numerical example, the normalized intensity distribution of a four-petal Gaussian vortex beam propagating in free space is graphically demonstrated. The influences of beam order and topological charge on the normalized intensity distribution are discussed in detail. This research is useful to the optical trapping, optical communications, and beam splitting techniques, etc.     

The approximate ABCD matrix for a parabolic lens of revolution and its application in calculating the coupling efficiency

Using ray optics, we present an explicit formulation of the ABCD matrix for reflection and refraction of light beams at a parabolic interface separating media of different refractive indices under paraxial approximation. Based on the formulated ABCD matrix for refraction by a parabolic lens tip, we present a simple theoretical investigation of the coupling efficiency between a laser diode and a single-mode fiber with a parabolic lens formed on the fiber tip. The results show that this technique is effective and will be of benefit to designing suitable microlenses applying the laser-coupling technique.     

Matrix formulation of axis-symmetric laser beams through a paraxial ABCD system containing hard-edged apertures: A comparative study

A matrix formulation is presented, which enables us to study the propagation of axis-symmetric beams through a paraxial optical ABCD system containing hard-edged aperture. Numerical calculation results of super-Gaussian beams passing through a multi-aperture-lens system are given to illustrate the advantage of the method. A comparison of the matrix formulation, complex Gaussian expansion and direct numerical integration of the Collins formula is made, where the propagation of apertured Laguerre-Gaussian beams is chosen as an illustrative example. It is shown that the matrix formulation provides satisfactory results in both Fraunhofer and Fresnel regions, and reduces the computational time greatly in comparison with the direct integration. However, this method is suited only to axis-symmetric optical beams and systems. By using the complex Gaussian expansion discrepancies exist in the near zone closer to the aperture, but usually its computational efficiency is higher than the matrix formulation.     

A new finite-dimensional pair coherent state studied by virtue of the entangled state representation and its statistical behavior

In this paper we construct a new type of finite-dimensional pair coherent states |ξ, q〉 as realizations of SU(2) Lie algebra. Using the technique of integration within an ordered product of operator, the nonorthogonality and completeness properties of the state |ξ, q〉 are investigated. Based on the Wigner operator in the entangled state |τ〉 representation, the Wigner function of |ξ, q〉 is obtained. The properties of |ξ, q〉 are discussed in terms of the negativity of its Wigner function. The tomogram of |ξ, q〉 is calculated with the aid of the Radon transform between the Wigner operator and the projection operator of the entangled state |η, κ₁, κ₂〉. In addition, using the entangled state |τ〉 representation of |ξ, q〉 to show that the states |ξ, q〉 are just a set of energy eigenstates of time-independent two coupled oscillators.     

Observation of the 5pΠu Rydberg state of Li2

Some weak, collisionally induced transitions in ⁷Li₂ have been recorded by Fourier transform spectrometry in the near infrared, following excitation of the 5d¹Π_g state by optical-optical double resonance. They have been assigned as transitions to the 1 ¹Δ_g state from levels v=0 and 1 of a new ungerade Rydberg state, 5p¹Π_u. Quantum defect considerations indicate that the principal quantum number for this new state is 5, and that the assignment to 5p is compatible with a Rydberg series of which the lowest members would be the B¹Π_u and C¹Π_u states.     

Effect of sintering atmosphere on the electrical and optical properties of (ZnO)1−x(MnO2)x NTCR ceramics

Nominal composition of (ZnO)_1−x(MnO₂)_x (0.005≤x≤0.2) ceramics have been prepared by the standard solid-state reaction method in three different sintering atmospheres: Ar, air, and reductive atmosphere. The effect of sintering atmosphere on the electron spin resonance (ESR), negative temperature coefficient of resistivity (NTCR), and photoluminescence (PL) properties of (ZnO)_1−x(MnO₂)_x ceramics has been investigated in detail. The results demonstrate that the sintering atmosphere has significant effects on the ESR signals of (ZnO)_1−x(MnO₂)_x; the NTCR of the samples sintered in air is larger than those sintering in Ar and reductive atmosphere; the deep-level PL related to oxygen vacancy increases when sintered in the reductive atmosphere.     

Vibrational spectroscopy of trans and cis deuterated formic acid (HCOOD): Anharmonic calculations and experiments in argon and neon matrices

The absorption spectra of trans and cis conformers of deuterated formic acid (HCOOD) isolated in argon and neon matrices are analyzed in the mid-infrared and near-infrared spectral regions (7900-450 cm⁻¹). Vibrational excitation by narrow-band IR radiation is used to convert the lower-energy trans conformer to the higher-energy cis form. A large number of overtone and combination bands are identified. The results of anharmonic vibrational calculations (CC-VSCF) for both conformers are reported and compared to the experimental spectra.     

Influence of the redox state of QA on phycobilisome mobility in the cyanobacterium Synechocystis sp. strain PCC 6803

In a unicellular cyanobacterium, the mobile fraction of phycobilisome (PBS) was found to be maximum at a particular redox value of Q_A (i.e., 0.52). An upward or downward shift in the redox value leads to a decrease in this mobile fraction of PBS. Furthermore, the regulatory effect of the redox state of Q_A on PBS mobility was found to be independent of the effect exerted by the plastoquinone pool. These findings indicate for the first time that PBS mobility is regulated by the Q_A redox state in cyanobacteria. A possible working mechanism underlying this control is discussed.     

Theoretical research on optical properties and quantum efficiency of Ga1−xAlxN photocathodes

In order to design the optimal component structure of transmission-mode (t-mode) Ga_1−xAl_xN photocathode, the optical properties and quantum efficiency of Ga_1−xAl_xN photocathodes are simulated. Based on thin film principle, optical model of t-mode Ga_1−xAl_xN photocathodes is built. And the quantum efficiency formula is put forward. Results show that Ga_1−xAl_xN photocathodes can satisfy the need of detectors with “solar blind” property when the Al component is bigger than 0.375. There is an optimal thickness of Ga_1−xAl_xN layer to get highest quantum efficiency, and the optimal thickness is 0.3 μm. There is close relation between absorptivity and quantum efficiency, which is in good agreement with the “three-step” model. This work gives a reference for the experimental research on the Ga_1−xAl_xN photocathodes.     

function for the squeezed atomic coherent state in entangled state representation and some of its applications

Based on the Einstein, Podolsky, and Rosen (EPR) entangled state representation, this paper introduces the wave function for the squeezed atomic coherent state (SACS), which turns out to be just proportional to a single-variable ordinary Hermite polynomial of order 2j. As important applications of the wave function, the Wigner function of the SACS and its marginal distribution are obtained and the eigenproblems of some Hamiltonians for the generalized angular momentum system are solved.     

Spectroscopic and theoretical evidence for the photoinduced twisted intramolecular charge transfer state formation in N,N-dimethylaminonaphthyl-(acrylo)-nitrile

The phenomenon of excited state twisted intramolecular charge transfer (TICT) process in N,N-dimethylaminonaphthyl-(acrylo)-nitrile (DMANAN) has been reported on the basis of steady-state absorption and fluorescence spectroscopy in combination with quantum chemical calculations. The absorption and fluorescence characteristics of DMANAN in solvents of different polarity reveal the presence of a single species in the ground state which forms the intramolecular charge transfer state upon photoexcitation. The observed dual fluorescence is assigned to a high-energy emission from the locally excited or the Franck-Condon state and the red-shifted emission from the charge transfer (CT) state. In polar protic solvents, hydrogen-bonding interaction on CT emission has been established from the linear dependency of the position of the low-energy emission maxima on hydrogen-bonding parameter (α). The experimental findings have been correlated with the theoretical results based on TICT model obtained at density functional theory (DFT) level. The theoretical potential energy surface for the first excited state along both the donor and acceptor twist coordinates in the gas phase obtained by time dependent density functional theory (TDDFT) method and in polar solvent by time dependent density functional theory-polarized continuum model (TDDFT-PCM) method predicts well the experimental spectral properties.     

Microstructure, optical and static recording properties of AgOx film, and near-field simulation of sub-wavelength aperture based on the AgOx marks’ formation

Structures, spectra and surface topographies of as-deposited and annealed AgO_x films have been investigated by an X-ray diffractometer, a spectrophotometer and an atomic force microscopy (AFM). X-ray diffraction and spectrum results show that the as-deposited AgO_x films with high oxygen ratios (x≥0.5) are in amorphous states and Ag crystalline particles will separate out after annealed. AFM results show that the film surface will become much rougher and film thickness will increase greatly after annealed due to the decomposition of AgO_x with release of oxygen. Static recording results show that two microstructures of the recording marks can be produced: one is the bubble mark at a low recording power and the other is the rupture bubble with an ablated aperture (hole) in the center at a high recording power. Based on the formation of rupture bubble marks, the near-field optical distribution of a focused Gaussian laser beam through a sub-wavelength aperture (200 nm in diameter) has been simulated using finite-difference-time-domain (FDTD) method. Results show that the spot size can be greatly squeezed with still highly transmitted intensity, which may lead to the super-resolution readout.     

Luminescent properties of KGd1−x(WO4)2:Eux and KGd1−x(WO4)2−y(MoO4)y:Eux phosphors in UV-VUV regions

KGd_1−x(WO₄)_2−y(MoO₄)_y:Eu³⁺_x(0.1?x?0.75, y=0 and 0.2) phosphors are synthesized through traditional solid-state reaction and their luminescent properties in ultraviolet (UV) and vacuum ultraviolet (VUV) regions are investigated. Under 147 nm excitation, these phosphors show characteristic red emission with good color purity. In order to improve their emission intensity, the MoO₄²⁻ (20 wt%) is introduced into the anion of KGd_1−x(WO₄):Eu³⁺_x. The Mo⁶⁺ and Eu³⁺ co-doped KGd(WO₄)₂ phosphors show higher emission intensity in comparison with the singly Eu³⁺-doped KGd(WO₄)₂ in VUV region. The chromaticity coordination of KGd_0.45(WO₄):Eu³⁺_0.55 is (x=0.669, y=0.331), while that of KGd_0.45(WO₄)_1.8(MoO₄)_0.2:Eu³⁺_0.55 is (x=0.666, y=0.334) in VUV region.     

Ab Initio Study of the Charge-Transfer Complex of Xenon and Dicarbon

Correlated ab initio calculations with large basis sets are reported for C₂Xe. The complex has a linear structure and a considerable dipole moment due to charge transfer from xenon to dicarbon. The CXe interatomic potential is rather flat so that the predicted CXe distance remains uncertain even at the highest level employed (268 pm at BCCD(T)/VQZ+d-aug(C)). The calculations recover most of the observed red shift in the CC stretching wavenumber upon complexation and thus support the reported identification of C₂Xe in a xenon matrix. The properties of the C₂Xe complex are compared with those of the analogous charge-transfer complex F₂CCXe.