Electro Optical Characterisation of Short Wavelength Semiconductor ...

E i
−2 L
t 1 r1 r E 2 i e
−2 L
t 1 r E 2 i e
t 1 E i
Physics of Semiconductor Lasers
input mirror output mirror
L
−3 L
t 1 r1 r E 2 i e
− L
t 1 r E 2 i e
− L
t E 1 i e
−3 L
t 1t 2 r 1r E 2 i e
− L
t 1t E 2 i e
Figure 1.7: Fabry-Pérot resonator of length L. t and r are transmission and reflection
coefficients. Ei represents a plane wave, incident onto the input mirror [25].
Γ = α + i 2π
· (1.15)
λ
The cavity of a laser is amplifying. This fact needs to be considered.
Γ = (αi − g) + i 2πn
, (1.16)
λ
where αi represents the whole internal loss, and g is the gain of the cavity. Propagation of
light in matter of refractive index n = 1 leads to chromatic dispersion; thus λ.
Combining
n
Eqs. 1.14 and 1.16 yields
r1r2e (g−αi)2L −i2L
e 2πn
λ
!
= 1, (1.17)
which is representative for a wave covering a distance of 2L inside the cavity, returning to
the input mirror with the same amplitude and in phase. Equating the real and imaginary
parts of Eq. 1.17, two lasing conditions are obtained
r1r2e (g−αi)2L
cos 2L 2πn
!=
1 (1.18)
λ
sin 2L 2πn
!=
0 (1.19)
λ
z
11