Laser Consider a laser with a simplified geometry shown in Fig. 5.1. A gain medium of length 1 = 10 cm is placed between

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Laser Consider A Laser With A Simplified Geometry Shown In Fig 5 1 A Gain Medium Of Length 1 10 Cm Is Placed Between 1 (242.99 KiB) Viewed 12 times

Laser Consider a laser with a simplified geometry shown in Fig. 5.1. A gain medium of length 1 = 10 cm is placed between two mirrors with reflectivities R1 and R2, spaced at length L = 15 cm. The frequency-dependent gain coefficient y of the medium (non-degenerate levels) is given by 7(v) = (n2 – nı)Sg,(v). (5.1) Here, n2 and nį are the populations (atoms per volume) in the upper and lower laser levels, respectively. S is the line strength, and g(v) the normalised line profile of the lasing transition. -n Et an2 R1 soon1 R2 1 = 10 cm output 38300spoopool 1 = 632.8 nm gain medium mirror L = 15 cm mirror Figure 5.1 Laser resonator with gain medium. 0 = (a) Name and state the condition for which the laser medium provides gain. Briefly state how it can be achieved. {3} (b) Without the medium (under vacuum), the resonator's finesse is F = 1000. Calculate the mode spacing Avfsr (free spectral range) and cavity decay time TR of the empty laser resonator. State your results with units. {4} (c) State the value of the mode spacing of the laser, assuming that the medium has a refractive index n = 1.2. Assume n=1 for the empty part. State your results with units. {2} (d) The medium is a gas of neon atoms with mass m = 20.2 amu at temperature T = 300 K. Calculate the line width Av (full width half maximum, FWHM) of the 1 = 632.8 nm lasing transition for a Doppler-broadened gain profile g(v) with standard deviation 1 ГkBT ĪV m (5.2) State your result with units.{4} (e) State how many cavity modes fall within the width (FWHM) of the gain profile. {2} (f) For lasing to occur, the minimal gain coefficient is 7th = (2B – In RįR2), (5.3) where B is a general loss coefficient to describe scattering and absorption at the various interfaces. The line strength of the medium is S = 4 x 10-6 m?s-1. For the case of B = 10-3, R1 = 1, and R2 = 0.994, calculate the minimal population difference n2 – ni that is required for lasing (with units). {6} Hint: The normalised Gaussian profile is given by 1 (v – vo)2 gv(v) = exp (5.4) V2πσ2 202 (g) Use the ideal gas law to state the minimal neon pressure that is required for lasing if none of the populations n2 and nį ever exceed the other by more than 50%.{4} c )