Cavttatton (Influence of Free Gas Content) 
1 oo? Vii et) 
1A 
favient = 
describes the propagation of optical monochromatic radiation, where 
Vtdbdetes. Sle ee 
~— 
and W(x) is the complex amplitude. 
Physically, the wave amplitude will vary as 
Re \w(x)e =e ny 
If the operations on V(x, t) are linear and only the long time average 
is required, then the physical quantity is the real part of the final 
expression. Thus, for our application, the wave equation can be 
transformed to the Helmoltz equation 
lege athe Ee eclonladen aur00 (2A) 
27 w : 
where the wave number k =—>— =-@-. Here we have applied the 
restriction that the radiation is essentially monochromatic. The so- 
lution of equation (2A) can be written in integral form with G(£é :x) 
the appropriate Green's function, 
— 
where w(é) = g(&) | onthe surface s, and 
SCS ay ee ord, Ey 
with i and j unit normal vectors. 
S isa plane perpendicular to the Z axis and its outer normal is in 
the direction of negative Z. The Green's function for this case is 
ikr 
cree a). e 
d 4 mr 
where PS hf Ze +|&- -x | 2 : 
1149 
