Biophotonics_Concepts_to_Applications

4 :4 Excimer lasers generally contain a mixture of a noble gas (such as argon,

krypton, or xenon) and a reactive gas (such asfluorine or chlorine) and emit

in the UV range from 193 to 350 nm. Using Web resources,find the possible

pulse repetition rates and output powers for thefive excimer lasers listed in

Table5.1. Describe the uses of such lasers for eye surgery.

4 :5 Using Web resources,find some characteristics of alexandrite and Nd:YAG

lasers for removal of unwanted hair. Consider different physical and opera-

tional factors such as irradiance, wavelength, pulse duration, and spot size

diameter.

4 :6 An important parameter of a GaAs light source when coupling it to an optical

fiber is the value of its refractive index as a function of wavelength. For the

rangeλ= 0.89–4.1μm the refractive index is given by

n^2 ¼ 7 : 10 þ

3 : 78 k^2

k^2  0 : 2767

whereλis given in micrometers. Compare the refractive indices of GaAs at
810 and 900 nm. [Answer: n = 3.69 at 810 nm and 3.58 at 900 nm.]
4 :7 By differentiating the expression E = hc/λ, show why the full-width
half-maximum (FWHM) power spectral width of LEDs becomes wider at
longer wavelengths.
4 :8 A particular LED has a 5-ns injected carrier lifetime. When no modulation
current is applied to the device, the optical output power is 0.250 mW for a
specified dc bias. Assuming other factors that might affect the modulation
speed are negligible, show that the optical outputs at modulation frequencies
f of (a) 25 MHz is 197μW and (b) 150 MHz is 52μW.
4 :9 Consider a particular LED that has a 4.5-ns injected carrier lifetime. (a) Show
that the 3-dB optical bandwidth of this device is 61.2 MHz (b) Show that the
3-dB electrical bandwidth of this device is 43.3 MHz.
4 :10 A GaAs Fabry-Perot laser operating at 860 nm has a 550-μm length and a
refractive index n=3.7. Show that the frequency spacing and the wave-
length spacing are 73.7 GHz and 0.182 nm, respectively.
4 :11 In order for a mode to be supported in a lasing cavity, the condition N = 2L/λ
must be satisfied, where L is the cavity length,λis the wavelength of the
allowed mode, and N is an integer. Suppose a lasing cavity has 0.400-mm
length. Show that 1500 nm is not an allowed wavelength, but that 1498.13
and 1500.94 nm correspond to lasing modes.
4 :12 Assume that the cleaved mirror end faces of a GaAs laser are uncoated and
that the outside medium is air, which has a refractive index of 1.00. If the
refractive index of GaAs is 3.60, show that the reflectance for light incident
normal to the air-laser end face is 0.32. Recall the expression for reflectance
given in Eq. (2.35).
4 :13 A Nd:YAG laser can be pumped by a laser diode or by a lamp to several
different energy levels. One possibility is to use a wavelength of 808.7 nm to
raise the energy level to 1.534 eV. From there the excited state quickly drops

116 4 Fundamentals of Light Sources