Page 352 - Tunable Lasers Handbook

31 2 Norman P. Barnes

The spectral bandwidth of the parametric oscillator depends on the spectral
bandwidth of the pump laser as well as the spectral bandwidth of the interaction.
Consider the situation in a singly resonant oscillator where, in addition, only a
single resonant wavelength exists. If the pump laser consists of several wave-
lengths. each wavelength of the pump laser would mix with the single resonant
wavelength of the parametric oscillator. As a result, each pump wavelength of
the pump would produce a corresponding wavelength around the nonresonant
wavelength. If Ahl is the spectral bandwidth of the pump. the corresponding
spectral bandwidth of the nonresonant wavelength is given by

AI2 = Ah, .

If the singly resonant oscillator does not restrict itself to a single wavelength but
consists of a distribution of wavelengths with a spectral bandwidth of Ah3, then
each resonant wavelength would mix with each pump wavelength to produce a
corresponding wavelength around the nonresonant wavelength. In this case, the
spectral bandwidth of the nonresonant wavelength can be approximated as

For equal spectral bandwidths of the pump and the resonant wavelength, the
spectral bandwidth of the pump is weighted more heavily since the pump wave-
length is shorter.
The spectral bandwidth of the parametric oscillator can also depend on the
beam divergence of the pump. Heretofore, the phase mismatch has been
expanded using a single variable. However, this parameter can be expanded as a
function of two variables: for example, the wavelength and the propagation of
direction. For each direction of propagation there is a combination of the signal
and idler that minimizes the phase mismatch. Because a pump beam with finite
divergence can be decomposed into a distribution of plane waves, each having a
slightly different direction of propagation, a variety of wavelengths could result.
To estimate this effect, the phase mismatch can be expanded in a Taylor series of
two variables. Keeping terms only through first order and expanding around the
ideal phase-matching direction yields

dAk
Ak=--AA+-AO dAk
ah ae
where e is an angle in the optic plane of an uniaxial crystal. For a beam with a
divergence of A@, the corresponding spectral bandwidth becomes