Wavelet-Transform Spectrum for Quantum Optical States

In the context of quantum mechanics we employ the technique of integration within an ordered product of operators to recast the classical wavelet transform to a squeezing-displacing transform between the mother wavelet vector and the state vector to be transformed. In this way we propose the wavelet-transform spectrum for quantum optical states. For some typical states we obtain numerical results which imply that the spectrum can be used to recognize a variety of quantum optical states, and the inverse wavelet transform has the possibility to play a role in quantum state engineering.     

Relation between Fresnel transform of input light field and the two-parameter Radon transform of Wigner function of the field

This paper proves a new theorem on the relationship between optical field Wigner function's two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ( x') propagates through an optical [ D( -B) ( -C) A] system, the energy density of the output field is equal to the Radon transform of the Wigner function of the input field, where the Radon transform parameters are D,B. It prove this theorem in both spatial-domain and frequency-domain, in the latter case the Radon transform parameters are A,C.     

Atom waveguide and 1D optical lattice using a two-color evanescent light field around an optical micro/nano-fiber

We propose a two-color scheme of atom waveguides and one-dimensional （1D） optical lattices using evanescent wave fields of different transverse modes around an optical micro/nano-fiber. The atom guide potential can be produced when the optical fiber carries a red-detuned light with TE01 mode and a blue-detuned light with HEll mode, and the 1D optical lattice potential can be produced when the red-detuned light is transformed to the superposition of the TE01 mode and HE11 mode. The two trapping potentials can be transformed to each other for accurately controlling mode transformation for the red-detuned light. This might provide a new approach to realize flexible transition between the guiding and trapping states of atoms.     

Atom waveguide and 1D optical lattice using a two-color evanescent light field around an optical micro/nano-fiber

We propose a two-color scheme of atom waveguides and one-dimensional(1D)optical lattices using evanes- cent wave fields of different transverse modes around an optical micro/nano-fiber.The atom guide poten- tial can be produced when the optical fiber carries a red-detuned light with TE_(01)mode and a blue-detuned light with HE_(11)mode,and the 1D optical lattice potential can be produced when the red-detuned light is transformed to the superposition of the TE_(01)mode and HE_(11)mode.The two trapping potentials can be transformed to each other for accurately controlling mode transformation for the red-detuned light.This might provide a new approach to realize flexible transition between the guiding and trapping states of atoms.     

The Design of Lens Imaging System byMeans of Fractional Fourier Transform

The relation between the 2nd fractional Fourier transform and the imaging process of an optical system is discussed. By changing the coordinate scales of the input plane in respect to the magnification of the optical imaging system, the fractional Fourier transform can be a powerful tool in designing specific imaging system. The Gaussian imaging formula of single lens is obtained by using the tool. Finally the procedures are generalized for designing a double-lens imaging system through an example.     

Optical wavelet-fractional squeezing combinatorial transform

By virtue of the method of integration within ordered product(IWOP)of operators we find the normally ordered form of the optical wavelet-fractional squeezing combinatorial transform(WFrST)operator.The way we successfully combine them to realize the integration transform kernel of WFr ST is making full use of the completeness relation of Dirac’s ket–bra representation.The WFr ST can play role in analyzing and recognizing quantum states,for instance,we apply this new transform to identify the vacuum state,the single-particle state,and their superposition state.     

Optical Wavelet Packet Transform

We employ optical wavelet packet transform (OWPT) to propose an opto-electronic system based on volume holography to select the best bases of image banks for image compression, because of the superior processing ability to optical wavelet transform and the potentiality in new application fields. The simulation results show that the best bases chosen are the same as the bases selected by discrete wavelet packet transform (DWPT).Because DWPT is time consuming, especially when the volume of image bank is very large, processing time can be greatly shortened by OWPT.     

Optical performance, structure and thermal stability of Al（lwt.-%Si）//Zr and Al（pure）//Zr multilayers designed for the 17-19 nm range

We report on the optical performance, structure and thermal stability of periodic multilayer films con- taining Zr and Al（lwt.-%Si） or Al（pure） layers designed for the use as extreme ultraviolet （EUV） high reflective mirrors in the range of 1~19 am. The comparison of A1/Zr （Al（lwt.-%Si）/Zr and Al（pure）/Zr） multilayers fabricated by direct-current magnetron sputtering shows that the optical and structural per- formances of two systems have much difference because of Si doped in A1. From the results of grazing incidence X-ray reflection （GIXR）, X-ray diffraction （XRD）, and EUV, the Si can disfavor the crystalliza- tion of AI and smooth the interface, consequently increase the reflectance of EUV in the Al（lwt.-%Si）/Zr systems. For the thermal stability of two systems, the first significant structural changes appear at 250 ~C. The interlayers are transformed from symmetrical to asymmetrical, where the Zr-on-A1 interlayers are thicker than Al-on-Zr interlayers. At 295 ~C for Al（pure）/Zr and 298 ~C for Al（lwt.-%Si）/Zr, the interfaces consist of amorphous Al-Zr alloy transform to polycrystalline Al-Zr alloy which can decrease the surface roughness and smooth the interfaces. Above 300 ~C, the interdiffusion becomes larger, which can enlarge the differences between Zr-on-Al and Al-on-Zr interlayers. Based on the analyses, the Si doped in Al cannot only influence the optical and structural performances of Al/Zr systems, but also impact the reaction temperatures in the annealing process.     

A compact interferometer insensitive to scanning speed variations

A compact moving optical-wedge interferometer (CMOWI) is presented. This device consists of a moving optical wedge (MOW), a fixed optical wedge (FOW), a fixed compensating plate, and a beam-splitting cube. The optical path difference (OPD) is calculated and analyzed. The factor between the OPD and the displacement of the MOW is less than 1 if the refractive index and wedge angle of the MOW and FOW are chosen properly. Therefore, the CMOWI is insensitive to scanning speed variations compared with the traditional Michelson interferometer. The CMOWI is compact, small-sized, and suitable for low-resolution Fourier transform spectroscopy.     

Fractional Fourier transform for partially coherent beam in spatial-frequency domain

By using Fourier transform and the tensor analysis method, the fractional Fourier transform (FRT) in the spatial-frequency domain for partially coherent beams is derived. Based on the FRT in the spatial-frequency domain, an analytical transform formula is derived for a partially coherent twisted anisotropic Gaussian－Schell model (GSM) beam passing through the FRT system. The connections between the FRT formula and the generalized diffraction integral formulae for partially coherent beams through an aligned optical system and a misaligned optical system in the spatial-frequency domain are discussed, separately. By using the derived formula, the intensity distribution of partially coherent twisted anisotropic GSM beams in the FRT plane are studied in detail. The formula derived provide a convenient tool for analysing and calculating the FRTs of the partially coherent beams in spatial-frequency domain.     

Invariant Joint Transform CorrelatorⅠ: Mapping Filter

l.IntroductionAVanderLugtcomp1exlnatchingspatialcorreIator[1jandajointtransformcorrela-tor[z~ejaret``omaJorkindsofcorrelators,however,theyaresensitivetoscalingandro-tationvariance.Thisdisadvantageisaseverelimitationforthemtobeusedinpracticalapplications-Invariantprocessingwiththeclassicalopticalcorre1atorwithproPertiesotherthanPOsitiondemandsthatthepropertyisrepresentedasashift.WithaIog-POlarmafrping[="j,thesizeandorientationw'il1beexpressedasshiftparameters,orratherrotationascyc1icshift.…     

Quantum Mechanics Version of Wavelet Transform Studied by Virtue of IWOP Technique

Using the technique of integral within an ordered product (IWOP) of operators we show that the wavelet transform can be recasted to a matrix element of squeezing-displacing operator between the mother wavelet state vector and the state vector to be transformed in the context of quantum mechanics. In this way many quantum optical states' wavelet transform can be easily derived.     

基于变形分数傅里叶变换的六重密钥图像加密

提出一种利用变形分数傅里叶变换和双随机相位编码对图像加密的方法.对要加密的图像分别进行两次变形分数傅里叶变换和两次随机相位函数调制,使加密图像的密钥由原来两重增加到六重.利用全息元件,可以用光学系统实现这种加密和解密变换.计算机模拟结果表明,只有当六重密钥都完全正确时,才能准确地重建原图像,这种六重密钥加密方法提高了图像信息的安全保密性.     

基于傅里叶变换的光纤探头光谱特性校正方法的研究

针对光纤自身对光谱的非线性衰减的影响，提出了一种基于傅里叶变换的光谱校正方法。首先对是否经过光纤的两种情况下光电倍增管的输出电流进行傅里叶变换，得到光谱频域中的校正函数，然后通过傅里叶逆变换得到光谱域中的校正函数。为实现测试，建立一个光电检测系统，在可见光范围内进行测试。分别对是否带有光纤的两种情况下数据进行采集，使用该校正方法可以使光线的衰减得到较好的修正，误差小于1．54％。实验结果表明，该方法对特定的光纤传导系统的光谱非线性衰减有较好的校正效果。     

Image encryption based on gyrator transform and two-step phase-shifting interferometry

A novel optical image encryption method is proposed, based on gyrator transform and phase-shifting interferometry. The input two-dimensional image to be encrypted is gyrator transformed two times, and two random phase masks are placed at the input plane and the output plane of the first gyrator transform. Two-step phase-shifting interferometry is used to record the digital holograms of the input image encrypted by use of double-random phase encoding technique in gyrator transform domain. The rotation angles of gyrator transform, the random phase mask in the gyrator plane and the arbitrary phase shift used for recording form the keys for decryption of the input image. Numerical simulations are presented to verify its validity and efficiency.     

The measurement of motion trajectories by speckle photography

We present a method for studying the lateral motion of a body with a rough surface. A speckle photograph of the moving body is recorded in addition to a still photograph of the same body. The total photograph is then optically Fourier transformed and recorded. Yet another optical Fourier transform yields a display of the motion path (‘trajectory’) of the moving body.     

Transformation of radiation upon its interaction with overtaking inhomogeneity in a medium with dispersion

The parametric Doppler effect is analyzed and simulated numerically in the case in which a wave or a pulse of optical radiation interacts with an inhomogeneity overtaking it in a medium with frequency dispersion. It is shown that, as the velocity of the inhomogeneity motion approaches the speed of light in vacuum, the frequency of the transformed radiation increases unboundedly but the efficiency of the transform decreases up to the zero value.     

一种新型光学模式转换器

提出了一种梯度折射率分布介质为基质的单体光学模式转换器,可以将两正交截面内瑞利长度相同、光腰重合的厄米-高斯光束转换为拉盖尔-高斯光束.这种转换器具有一体化且只有两个反射面的特点,因此易于调整、光能反射损耗小;对于两正交截面内瑞利长度不同、光腰不重合的厄米-高斯光束,提出了一种可调节其瑞利长度和光腰位置的光腰调节器,将光腰调节器与单体光学模式转换器组合使用,也可以将这种厄米-高斯光束转换为拉盖尔-高斯光束.     

Millimeter-wave pulse generation based on pulse reshaping using superstructure fiber Bragg grating

A novel optical approach is proposed to generate millimeter wave (MMW) pulse signal based on the pulse reshaping of superstructure fiber Bragg grating (SSFBG). In our scheme, one input pico-second Gaussian pulse is transformed into n Gaussian pulses by the SSFBG reshaping firstly, and then the pulse train is replicated to form a required frequency modulation MMW optical pulse envelope by the linear chirped fiber Bragg grating (LCFBG) or other highly dispersive element. The high-speed photodetector (PD) and band-pass filter can transform the MMW optical pulse into an MMW pulse signal ultimately. Depending on this scheme, MMW signals with frequency up to 10 GHz can be easily generated by the completed fiber components.