Tellurite And Fluorotellurite Glasses For Active And Passive

2. Literature review; MDO 43
The second-order non-linearity is a result of anharmonicity of electron motion. The
induced polarisation, P, in a material by an incident electromagnetic field, E, can be
described by the n th order non-linear susceptibility, χn.
2 3
P = ε ( χ E + χ E + χ E + .....)
(2.10)
0
1
2
3
where ε0 is the dielectric permeability [45]. Due to a lack of symmetry, glasses normally
have χ2 = 0. The glass structure can however be treated, inducing structural changes
which cause second-order non-linear effects.
Efficient second harmonic generation (SHG) requires χ2 > 0, and phase matching
between the fundamental (incident) wave, and the generated second harmonic (SH). The
intensity of the SH, I2ϖ, is given by equation (2.11).
I
⎡ ⎛ l∆δ
⎞⎤
⎢sin⎜
⎟
2
⎥
⎝ ⎠
⎢
⎢
⎣
∆δ
2
⎥
⎥
⎦
2
2 2
2
2ϖ
= l χ ⎢ ⎥
2
Iϖ
(2.11)
where l is the path length, ∆δ the phase mismatch, and Iϖ the fundamental intensity [45].
SHG has been shown in Ge-doped silica optical fibres, after exposure to a 20 kW Nd-
YAG laser. This SHG was thought to be due to formation of a dipole colour centre
grating in the fibre core. Some models have suggested that an alternating χ2 forms by
defects aligning with the DC field produced by χ3 effects. There is some contention if χ2