The electric field at the incident face for the two counter propagating beams can then be expressed as
(27.2)
(27.3)
where R is the reflectivity of the uncoated flat. For the weaker CW beam, , the coefficient of linear absorption and , the linear refractive index. However, for the stronger CCW beam, and , where is the effective nonlinear absorption coefficient and is the nonlinear index of refraction. The electric field of a pulsed Gaussian beam at the exit face of the sample (thickness = ) with a nonlinear absorption and nonlinear refractive index is
(27.4)
where is the incident electric field, , is the effective length of the sample, is the intensity incident on the beam splitter, is the intensity incident on the sample, is a constant (< 1) accounting for the reflection losses at the sample and lens surfaces while is another constant.
, the coefficient of linear absorption and 
, the linear refractive index. However, for the stronger CCW beam, 
and 
, where 
is the effective nonlinear absorption coefficient and 
is the nonlinear index of refraction. The electric field of a pulsed Gaussian beam at the exit face of the sample (thickness = 
) with a nonlinear absorption and nonlinear refractive index is 
is the incident electric field, 
, 
is the effective length of the sample, 
is the intensity incident on the beam splitter, 
is the intensity incident on the sample, 
is a constant (< 1) accounting for the reflection losses at the sample and lens surfaces while 
is another constant.