EE125Principles of Lasers
Prof.Cheng Wang
ShanghaiTech University
Homework1
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1.1If the laser have a continuous output power of1W when(a)λ=10µm,(b)λ=500nm and(c)ν=3000MHz,what is the population each second N that are transition from E2to E1?
1.2If levels1and2of Fig.1.2are separated by an energy E2−E1such that the corresponding frequency isν(the wavelength isλ),the carrier density of each level is N2and N1.Assume that the two level have the same degeneracy.
(a)Whenν=3000MHz,T=300K,calculate the ratio N2/N1.
(b)Whenλ=1µm,T=300K,calculate the ratio N2/N1.
(c)Whenλ=1µm,N2/N1=0.1,calculate T.
Figure1.2
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1.3A laser cavity consists of two mirrors with reflectivities R1=1and R2=0.5 while the internal loss per pass is L i=1%.Calculate the total logarithmic losses per pass.If the length of the active material is l=7.5cm and the transition cross section isσ=
2.8×10−19cm2,calculate then the threshold inversion.
1.4Consider a He-Ne laser,in order to make the coherence length equal to1km, what is the monochromaticity∆λ/λ0?(Hint:the output center wavelength of He-Ne laser isλ0=63
2.8nm)
1.5The beam from a ruby laser(λ∼=694nm)is sent to the moon after passing through a telescope of1m diameter.Calculate the approximate value of beam diameter on the moon assuming that the beam has perfect spatial coherence(the distance between earth and moon is approximately384,000km).
1.6The brightness of probably the brightest lamp so far available(PEK Labs type 107/109,excited by100W of electrical power)is about95W/(cm2·sr)in its most intense green line(λ=546nm).Compare this brightness with that of a1W Argon laser(λ=514.5nm),which can be assumed to be diffraction limited(Hint:β=1.22for plane wave).
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