Integrated Optics - Applied Optics Fundamentals and Device Applications - page 247

Optical phase retardation [42]

2 π

λ

l

Γ = ( n E ( ) − n E ( )) (5.22)

1 2

0

where
Γ = Ed/V , l = crystal thickness in the direction of the applied field
n 1 ( E ), n 2 ( E ) are the field dependent indices of refraction

The voltage length for a phase shift V π L is

d
n r

V L π = (5.23)

3

This is an important parameter as it incorporates the degree of overlap
between the optic and electrical fields and must be minimized for low volt-
age operation.
Another property of LiNbO 3 which may be exploited for some devices is
the photorefractive effect (a permanent change in the refractive index profile
caused by the transmitted optical flux). Optical power levels must be limited to
prevent refractive index changes. The effect can be alleviated to a certain degree
via the use of longer wavelengths, or it can be exploited in device applications.
Integrated optic lenses and reflectors can be fabricated through control of the
refractive index. The effect is controllable in LiNbO 3 crystals as a function of
the impurity levels present [43]. The field spatial change will be of the form

1
ε

d
d

n
z

⎡
⎢

⎤
⎥

E = k l z α ( ) + eD d t (5.24)

where
ε is the permittivity
k is the photovoltaic coefficient
α is the absorption coefficient
l ( z ) is the intensity of incident light
D is the diffusion coefficient
e is the charge of an electron
d n /d z is the concentration gradient of free carriers

The first term relates to the ionization of impurities present in the LiNbO 3 ,
while the second term describes the current induced by the diffusion of free
carriers. Whether the photorefractive effect is a detriment depends on the
device application and design.