Showing papers on "Parametric Image published in 1971"

Geometric Optics Theory of Parametric Image Upconversion

Abstract: This paper describes a general geometric optics theory of visible or near‐visible image formation in parametric upconversion. A formula is derived that relates the location of the image to the locations of the object and the pump. Aberrations are caused by the finite thickness of the nonlinear material; these aberrations vanish when both the pump waves and the object waves are parallel plane waves. The primary factor that limits the field of view of parametric image upconversion is the phase‐match condition.

The Magnification for Optical Parametric Image Conversion in Thin Nonlinear Materials

Abstract: T.he relation between the longitudinal, transverse and angular magnifications in optical parametric image conversion was presented. These obey relations quite similar to the Maxwell elongation and Smith-Helmholtz formulas in geometrical optics. The fundamental equation for analyses of spherical aberrations wftc s ac lso given. 1. IRtroduction The up-conversion of infrared li.ght to the visible by means of an optical. parametric process in a nonlinear crystal has been studied in detail by severa1 1nvestlgators. In the range of infrared wavelengths that can be upconverted for a given pump wavelength, Warneri) d.iscussed the directional characteristics and the required geometry for phase-matched up-conversion in terms of the orientations of the various wave vectors with respect to the crystalline axis. IMidwinter2) proposed a means of broad-band, high resolution and high eMciency image conversion and pointed out that an image up-converter competitive with existing scanning photodetectors (such as lnSb detectors) in the 1 to 10 ptm band can be built. Firester3> demonstrated that th.e effect of the pump beam divergence did not degrade the resolution but changed the transverse and longitudinai magnification of the image by a paraxial ray-tracing anaiysis. Also, he discussed the dependence on the system parameters of the converted image resolution, location and chromatic aberration in the case where the pump is at infinity by the Fourier transform theory‘〉, The factors that }.imit the resolution of the upconverted image, the efliciency of up-conversion and several characteristics of six nonliRear crystals were analyzed by Andrews5). However, the general questions of aberra{ions have not been considered6). The purpose of this paper is to show a fundament’al equation aRd the relation between the longitudinal, transverse and angular magnifications for optical parametric interaction in th.in nonlinear mate.rials. “S“ @”P’his investigatien was supported in part by a Resea.rch Gant from the Ilapanese Eclucational Ministry, No. 85070 of 1970. 一d ac Department of Electronic lt.ngineering, Hol〈1〈aiclo University, Sapporo, Japan. 28 Ichiro SAKURABA 2 2. Optical Parametric lmage Conversion in lnfinitesimally Thick Nonlinear Materials Image up-conversion is possible in materiais where the d.ielectyic susceptibility coefflcients which are frequency-dependent tensor elements, are sensitive to directions of the various optical fieid and propagation vectors with respect to crystal axes. The first order nonlinear.ity z(2) couples signai and pump waves and generates a nonligear polarizatlon Pi at the idler frequency fi Pt= Z(2) E.p E,s, (1) in the case of perfectly phase-matcked up-conversion ノアール==ノ~,十ノ~, (2) ki=kp十ks, (3) and E, and E, are the electric fields at pump frequency f. and signal frequeHcy f,, respectively, and k is the corresponding wave vector. For a crystal of a width zv the phase-matched up-coRversion takes place as long as7) iAkl = lkp Nr ks-kil .〈.= 2ni /tv (4) where for convenieRce it is assumed that dk is 一一“’一一“’一一一一一一;.;.;7fAk algng.thg directi.on of ki (see Fig. 1). This t’ polarization radiates a wave at a frequency ft ks/ Y / Which produces the upconverted imag6. θθ’ @/ th夏ll、羅lll糠よ鷲s濃e。盤謡塩l kp pump beam direction), and the angle e’ which Fig. 1 Schematic diagram of up-conver一 the idler wave make’s with the optic axis are sion geometry. related by3) ti’一 lf,,”e (s) where馬andλs are the optical. wave lengthes at freq.uencies/li, and/1,,, respectivel.y. Consider aR iRfinitesimal thickness of isotropic, perfectly phase-matched, Roniinear material that is perpendicular to a line connecting a point object and point-source pump. This thin plate is a distance x, from the pump of frequency f, and a distaRce x, from the object of frequency / as shown iR Figs. 2 and 3. The distance from O to the point of interaction Q is y. lt is assumed that the spherical wavefronts originating at points P and S intersect at point Q and they NONUNEAR kp, ’ MEDIUM ’