Estimate the efficiency of a GaAs laser operating well above threshold, given that n=3.6, and that the length of the laser cavity is 200 um. The loss coefficient is 800/m and the internal quantum efficiency is 0.8.
Answers
Answer:
%),
4.12 (0.5%), 4.15 (0.5%), 4.16 (0.5%)
1.15. Spectral widths
a) Suppose that the frequency spectrum of a radiation emitted from a source has a
central frequency ν₀ and a spectral width ∆ν. The spectrum of this radiation in
terms of wavelength will have a central wavelength λ₀ and a spectral width ∆λ.
Clearly, λ₀ = c/ν₀. Since ∆λ ≪ λ₀ and ∆ν ≪ ν₀, using λ = c/ν, show that the line
width ∆λ and hence the coherence length lc
are
c
2
0
0
0 λ
ν
ν
λ
∆λ = ∆ν = ∆
and
λ
λ
∆
= ∆ =
2
0
l c t
c
b) Calculate ∆λ for a lasing emission from a He-Ne laser that has λ₀ = 632.8 nm
and ∆ν ≈ 1.5 GHz.
Solution.
a)
2
ν ν
λ c
d
d
= −
c = λν
ν
λ
ν
λν
ν
λ
= − = − 2
d
d
The negative sign means that if λ increases by dλ then ν decreases by dν. The
spectral width, ∆λ or ∆ν are much smaller than the emission wavelength (or the
central wavelength, λ₀) or the emission frequency (or the central frequency),
respectively. The negative sign is omitted since ∆λ and ∆ν the intervals
Explanation: