Optical-phase conjugation in difference-frequency generation A. Andreoni, M. Bondani, F. Paleari Dept. Sciences, Univ. Insubria and Istituto Nazionale di Fisica della Materia, I.N.F.M. Como, Italy V. N. Mikhailov Photophysics of Holographic Processes Department, S.I.Vavilov State Optical Institute St. Petersburg, Russia

Space-dependent phase reversal E3 pump field (Nd SH) at 2w E1 seed field (Nd fund) at w E2 difference-freq. generated (DFG) field at w k1 E1 E2 optical axis y z a x NL crystal entrance face E3 k3 k2 Aim: E2 optical phase conjugate (OPC) of E1, being E1 strongly phase/amplitude modulated Outline: Theory of DFG in conditions of phase-mismatch, for seed and generated fields non-collinearly propagating (non-depleted plane-wave pump). Experiments showing that the pump-field wave-fronts behave as efficient phase-conjugating mirrors.

x E2 E1 a z k2 E3 k1 k3 y Interacting fields: AMP seed DFG Equations that describe the interaction: x E1 E2 O.A. a z k2 Error in phase-matching Coupling coefficient (type I) E3 k1 k3 y

Property of the equations: conservation law Boundary conditions Solutions

Properties of the solutions: Field amplitudes Direction of propagation of constant-phase surfaces Poynting vectors (energy propagation) Photon flux density of the DFG field E2 Increase in photon flux density of the seed field E1 due to AMP

Direction of Dk C k2-surface k1-surface Dk k2 k1 k1-k2 bisector k3 Continuity with the solution in PM Bondani et al.,Phys. Rev. A 66 (2002) C Conservation of photon flux densities k2-surface k1-surface Dk k2 k1 k1-k2 bisector k3

Theoretical conclusion (relevant to OPC experiment) On planes parallel to the E3 wavefronts, E2 OPC of E1 . In a regime of linear amplification and . If then: y z Mirror Diffusing plate Take and a plane mirror at exit face reflecting E2 back to .

Experimental setup Nd Seed/AMP l1 = 1053 nm Pump l3 = 526.5 nm Nd:YLF passive Q-switch ring oscillator; Nd:glass double-pass amplifier (Brillouin scattering phase-conjugating mirror) Frequency doubling KTP. Seed/AMP l1 = 1053 nm Pump l3 = 526.5 nm DFG l2 = 1053 nm PD2 Pump monitor F2 Nd:YLF source L6 Nd M3 PH2 M1 F3 L5 BS1 (wedged) CCD camera BBO DM L3 PH1 L2 F1 Long coherence length (>3m) Pulse duration  20 ns Energy per pulse  1 J at =526.5 nm PD1 Seed monitor L1 L4 M2 Diffusing Plate

efficiency: 10% per mm BBO I Cut for collinear SHG of Nd:YAG Fujian Castech Crystals Inc., China efficiency: 10% per mm VERYFIED Linear regime of Ampl./DFG. OPC of the co-propagating fields and beyond the crystal E1 E2

back-reflected by mirror and at same distance D (D = 51 cm, 291 cm) E1 Diffusing Plate CCD sensor BBO II Distance D BBO II The diffusing glass plate introduces a seed beam divergence of 0.5 deg and produces the intensity distribution Speckle pattern of measured at 6 cm from diffusing plate E1 Measurements of back-reflected by mirror and at same distance D (D = 51 cm, 291 cm) E1 E2

51 cm 291 cm Seed beam after removal of diffusing plate and in the absence of pump. Reflected DFG beam after back- propagation through diffusing plate.

THANKS TO CO-AUTHORS AND TO AUDIENCE Maria Bondani Fabio Paleari Paper in press: J. Opt. Soc. Am. B (Aug. 2003) Viktor N. Mikhailov