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72 2 Extremely Short-External-Cavity Laser Diode 3.0
Thermal expansion coefficient (10 -6 /K) 30 Al Au l/2 (GaAs)

2.5
25
2.0
20
1.5
1.0
15
0.5
10

-0.5
3 4
0 5 Si N InP SiO2 GaAs Si 0mm
0 5 10 15 20 25 30
2
10
Young’s modulus 10 (N/m )
Fig. 2.49. Contour map of an MC deflection, with Young’s modulus E and thermal
expansion coefficient α as parameters

N 0 q 1

N , d 1 q 2
1
N , d 2 q 3
2
N , d 3
3
Fig. 2.50. Reflection and transmission of a plane wave in a two-layer film structure

angle for the j th layer film are denoted by N j ,d j ,θ j , respectively. The phase
shift in the j th film is
2π
β j = d j N j cos θ j . (2.35)
λ
The coefficients r ij and t ij associated with the reflection and transmission
at the i and j interfaces are given by the Fresnel formula. The formula for
r ijk and t ijk for the j th film sandwiched by the i th and k th films, are given
as follows [2.31]:

r ij + r jk e −i2β j
r ijk = , (2.36)
1+ r ij r jk e −i2β j
t ij t jk e −i2β j
t ijk = . (2.37)
1+ r ij r jk e −i2β j