Optical Parametric Generation (OPG) is a non-linear optical effect that is a result of the interaction between a strong optical field, called the pump, at a frequency ω3 with
the electrons in a non-centrosymmetric crystalline material. This interaction yields a pair of optical fields at frequencies ω2 and ω1 such that
ω3 =ω2+ω1 (3.29)
to the higher and lower frequency waves respectively. Generated beam frequencyw 2 Non-linear crystal Incident beam frequencyw 3 Generated beam frequencyw 1
Figure 3.3: Optical Parametric Generation
The pump wave is incident upon the non-linear crystal. Via the second order susceptibility
χ(2) the signal and idler waves are generated.
OPG can be described as a photon splitting process - the pump photon of energy E splits into two lower frequency photons the energies of which sum to the energy of the pump photon. When coupled with phasematching techniques described earlier, the OPG process forms the basis of an optical parametric amplifier (OPA). A single round trip wave does not provide any useful or significant output power. To produce signifi- cant continuous wave output powers it is necessary for at least one of the three waves to be resonant in an optical cavity surrounding the non-linear crystal. To understand this process in more detail we need to consider the propagation of the pump, signal and idler through the non-linear material, in terms of a three-wave mixing process. The majority of parametric devices are operated within an oscillator configuration, as in a conventional laser, by enclosing the non-linear gain medium within an optical cavity to provide feedback at generated waves. This type of configuration is known as an optical parametric oscillator (OPO). The amplification of the parametric waves to macroscopic levels is achieved by successive passes through the non-linear crystal and coherent output can be extracted from the oscillator. For a qualitative description of the working principle of the OPO we must consider the most basic setup of an OPO as shown schematically in Figure 3.4.
A laser beam at the pump source at an optical frequency ωp is sent through the
Pump
Signal Wave
Gain Medium
Mirror
Mirror
Idler Wave
Figure 3.4: Generic Optical Parametric Oscillator
OPG is initiated within a cavity whereby there is feedback at the generated waves and the parametric waves are amplified with output obtained at the output mirror of the cavity.
The non-linear crystal is selected for providing significant second order dielectric susceptibility χ(2) which enables a three wave mixing process. As a result the pump
wave travelling through the crystal provides gain for the signal and idler waves. The output waves satisfy the energy conservation law
ωp =ωs+ωi (3.30)
The gain provided by the pump wave for the signal and idler waves means that weak signal and idler waves travelling through the crystal are amplified whilst the pump power depletes. An initial signal and idler intensity is present due to vacuum fluctuations within the nonlinear crystal. As a result it is only necessary to provide the pump laser beam from an external source. By placing the non-linear crystal inside a resonator for the signal wave the signal is fed back into the crystal where it is further amplified through power transfer from the pump wave.
The Manley-Rowe relations in Equation 3.20 show that power is transferred between the propagating waves as they travel through the non-linear medium. The gain increases with the intensity of the pump wave, and as a consequence, there is a minimum pump intensity at which the amplification of the signal wave in the crystal compensates for the round trip losses in the resonator (due to mirror transmission,
absorption and scattering). At this threshold pump intensity, optical parametric oscillation sets in i.e a periodically oscillating signal wave is generated from an initially random field fluctuation. At the same time a significant portion of the pump power is converted into signal and idler power. This transfer of power from the pump wave to the generated waves reduces the pump intensity inside the non-linear crystal and thus the signal gain. In close analogy to the case of laser oscillation this effect is called ‘gain saturation’. This leads to to steady state operation of the OPO where the signal power generated in the crystal exactly balances the resonator losses for the signal wave. The frequencies of the two generated waves are not fixed but can be tuned over wide wavelength ranges. This frequency tunable down-conversion of the pump laser in the OPO is caused by the non-linear interaction of the three waves via the χ(2) susceptibility. This process can be highly efficient, with the vast majority of
the pump laser radiation converted to the two lower frequency beams.
While Equation 3.30 states that the sum-frequency of a signal and idler wave pair is equal to the pump frequency, it does not determine which of all possible signal-idler frequency pairs will actually be generated. In steady-state operation, the signal and idler frequency pair that is generated has a minimum threshold pump intensity (in analogy to a laser with spectrally broadened gain). Thus, the generated frequencies, and with them the ratio of the signal and idler frequencies are determined by the frequency dependence of the parametric gain in the crystal and by the frequency dependence of the resonator losses. In general, the parametric gain in the crystal provides only a coarse selection of the frequency ranges of the signal and idler wave, whereas the exact frequencies are given by the frequency selectivity of the OPO resonator. Therefore an OPO tends to operate at signal idler frequencies for which the wavevector mismatch, ∆k, is minimum. By changing the refractive indices for the three waves, for example by changing the crystal temperature or the direction of the beams through the crystal, this condition can be fulfilled for different frequency combinations, allowing, within certain limits, the output frequencies of an OPO to be coarsely tuned.