A Nd doped phosphate glass rod laser is 10 cm long. The refractive index of rod is 1.82. The lasing transition has a center wavelength of 1064 nm, a spectral linewidth of 0.12 THz with a Lorentzian lineshape function, and a fluorescence lifetime

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poshan reddy le 22 Mar 2016

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A Nd doped phosphate glass rod laser is 10 cm long. The refractive index of rod is 1.82. The lasing transition has a center wavelength of 1064 nm, a spectral linewidth of 0.12 THz with a Lorentzian lineshape function, and a fluorescence lifetime of 0.23 ms. If the excitation can provide population inversion density of 1019 cm‐3. (You should use math software to do the following questions.) (a) Please calculate the maximum gain at its central wavelength of 1064 nm. (b) Please express the emission central wavelength as frequency in terms of THz; (c) Please calculate the mode spacing of this laser cavity in terms of THz; (d) Please estimate the mode number q for this cavity at central wavelength 1064 nm; (e) Please plot the gain coefficient as a function of frequency with units of THz and center the frequency at central wavelength of 1064 nm with upper and lower bounds of one spectral linewidth. (f) Please plot the phase shift function as a function of frequency with units of THz and center the frequency at central wavelength of 1064 nm with upper and lower bounds of one spectral linewidth. (g) Plot as a function of frequency with units of THz and center the frequency at central wavelength of 1064 nm with upper and lower bounds of one spectral linewidth. (h) Solve frequency (in THz unit) in the equation for q’=q‐10, q5, q, q+5, q+10, where q is the result from (d). Compare these frequency values to 0 ( ) ( ) vv vv v      0 ( ) ( ) 2 vvc f v v v v      0 ( ) ' 22 vv cc v v q v nd      the results from the equation where the phase shift is not considered and explain the “mode pulling” effect. (i) Repeat (h) but increase the population inversion density to 1020 cm‐3. Is the mode pulling effect more serious?