Nonlinear Optical Holography

Abstract

Coding schemes for designing computer generated holograms can be implemented in nonlinear optics. Spatial modulation of the quadratic nonlinearity enables to arbitrarily shape the amplitude, phase and spectrum of the frequency converted beam. OCIS codes: (090.1760) Computer holography; (190.2620) Harmonic generation and mixingIn linear optics, holography is a used for storing and reconstructing both the amplitude and the phase of a wavefront from an illuminated object. Rather than using a real object, it was proposed in the mid-60s' of the previous century to compute and print the required pattern of the hologram. When a light beam is sent through such a computer generated hologram (CGH), the far-field diffracted wave-front has the desired amplitude and phase. 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. For example, the orbital angular momentum of (OAM) Laguerre-Gaussian beams can be controlled by the angular momentum of the pump beam and the nonlinear crystal, and follows a quasi-angular momentum conservation law, in a similar fashion to the well-known linear momentum conservation law of quasi phase matching (QPM) [2,5].Unlike its linear counterpart, a challenge that appears in the nonlinear CGH is the requirement for phasematching of the interacting waves. Moreover, the main method for modulating the nonlinear coefficient -electric field poling in ferroelectric crystals-is a planar method which enables to utilize only two out of the three available axes of the nonlinear crystal. Fortunately, there are several methods to overcome this limitation. If we limit the design to only one out of the two transverse axes, we can use the propagation axis (the crystallographic X axis) for quasi-phase-matching, while using only one of the transverse axes (the crystallographic Y axis) for imposing the amplitude and phase modulation. The 2D modulation of nonlinear coefficient is therefore