Nonlinear computer-generated holograms

Abstract

We propose a novel technique for arbitrary wavefront shaping in quadratic nonlinear crystals by introducing the concept of computer-generated holograms (CGHs) into the nonlinear optical regime. We demonstrate the method experimentally showing a conversion of a fundamental Gaussian beam pump light into the first three Hermite-Gaussian beams at the second harmonic in a stoichiometric lithium tantalate nonlinear crystal, and we characterize its efficiency dependence on the fundamental power and the crystal temperature. Nonlinear CGHs open new possibilities in the fields of nonlinear beam shaping, mode conversion, and beam steering.

Fabrication of Pattern Poled Lithium Niobate Film and its Nonlinear Optical Applications

“…Furthermore, we can effectively tailor nonlinear wavefronts with designed ferroelectric domain through computer-generation holograms (CGH) [18][19][20]. Also, suitable domain structure could be flexibly introduced into LN for spontaneous parametric downconversion [21].…”

Nonlinear Optical Holography

“…The concept of CGH was recently extended by us into the nonlinear optical regime. In this case, the second-order nonlinear coefficient of a crystal is modulated, so that when a fundamental light beam passes through it, a wavefront with the chosen amplitude and phase is obtained in the second harmonic.Specifically, nonlinear CGH were recently used to convert a fundamental Gaussian beam into high order Hermite-Gauss or Laguerre-Gauss beam at the second harmonic [1][2][3][4]. In addition, the nonlinear process enables to all-optically control the properties of the generated beam.…”

“…Specifically, nonlinear CGH were recently used to convert a fundamental Gaussian beam into high order Hermite-Gauss or Laguerre-Gauss beam at the second harmonic [1][2][3][4]. In addition, the nonlinear process enables to all-optically control the properties of the generated beam.…”

“…This continuous coding scheme was implemented by us in electric-field poled stoichiometric LiTaO 3 (SLT) crystal. The crystal was then used to convert a fundamental Gaussian beam into Hermite-Gauss HG 01 and HG 02 beams at the second harmonic [1].…”

Spectral and temporal holograms with nonlinear optics

“…In an article by Lee [4], a general and accurate method for the design of a binary CGH was developed. In essence, given the complex representation of the Fourier transform of the object wave to be recorded, ux; y Ax; y expiφx; y, the binary CGH transmission is prescribed by tx; y signfcos2πf c x φx; y − cosπqx; yg; (1) where f c , the carrier frequency, is the periodic grating frequency upon which the information is modulated using the object wave's phase φx; y and amplitude Ax; y, where by setting sin πqx; y Ax; y the object wave is obtained in the first diffraction order.Recent advances in CGH research incorporated nonlinear optics; in this so-called "nonlinear CGH," the quadratic nonlinear coefficient is modulated, thereby allowing us to convert a fundamental Gaussian beam into a second-harmonic beam with a desired wavefront [5,6]. In this Letter we further extend nonlinear CGHs from the spatial domain to the spectral domain, arbitrarily shaping the spectrum of the generated pulse, and, owing to the Fourier transform relation between the spectrum of a pulse and its temporal shape, this also enables one to shape the nonlinearly generated pulse in time.…”