1. 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

2. 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.

3. 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

4. Property of the equations:
conservation law
Boundary conditions
Solutions

5. 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

6. 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

7. 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

8. 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 = 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

9. 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
E E2

10. 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

11. 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.

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