PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

2.2.3.2 Symmetric Laue case
For an infinite incident plane wave, the α and β wave functions combine at the exit surface in
accordance with the boundary conditions to generate a forward transmitted and a diffracted wave in
vacuum. In order to simplify the relevant expressions without losing generality, we restrict
ourselves to the symmetric Laue case in a parallel-faced crystal slab and a full reflection (χ O = χ H ).
The amplitudes of the emergent waves can then be written as
it(1
y)
V
t S
2
y t
2
T(y, t) O
(y, t) e cos y 1 i sin y 1
2
S
y 1
S
(38a)
and
R(y, t) (y, t) ie
V
H
i t(1 y) 2Zf
y
S
t
S
2
sin y 1
2
y 1
, (38b)
t denoting the slab thickness and Z f being the distance of the incidence surface from the origin
measured along n i . As explained in Fig.5, the ψ O , wave emanates exactly along the incidence
direction, represented by y, whereas the ψ H wave exits at an angle corresponding to -y with the
exact Bragg condition. The associated intensities
I (y, t) 1 I (y, t) , (39a)
O
H
with
I (y, t)
t
y 1
2 2
sin y 1
S
H 2
; (39b)
are both symmetric about the centre of diffraction viz. y=0. The diffracted intensity exhibits
2 2 2 2
maxima equal to y 1 / ( t ) 1
2 2
m S m S
m
at angles y=y m satisfying the condition,
S
tan t y 1 / t y 1 / . The H and O intensities have been plotted in Fig.6 for
t=20.25Δ S . Both the intensities oscillate strongly, the oscillations becoming more rapid in the
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