Consider a He-Ne laser oscillating at the wavelength of = 632.8 nm with a Dopple

Question

Consider a He-Ne laser oscillating at the wavelength of = 632.8 nm with a Doppler-broadened gain linewidth of g = 1.7×109 Hz. (The gain linewidth is the width of the Gaussian distribution of the gain of the laser medium. For gas lasers it is usually determined by Doppler broadening.) Assume that the laser operates with a resonator of length L = 50 cm. Calculate the number of modes in which the laser can emit laser light. Hint: calculate the number of standing waves for the given resonator that fall within the gain linewidth.

Explanation / Answer

Operating wavelength = o = 632.8nm =632.8 × 10-9 m

Length of the tube = L = 50cm = 0.5m

Let n be the mode number corresponding to o, then

n = L/(1/2 * o) = 0.5m / (1/2 * 632.8 × 10-9 m)

n = 1264222.2

However n must be an integer so 1264222 and 1264223 would be two possible modes that are within the spectrum

The n1 and n2 values corresponding to the shortest 1 and longest 2 wavelengths are

Delta = = 1.7×109 Hz =  1.72 × 10-16 m

n1 = L / [1/2(o - (1/2 *Delta ))] = 0.5 / 1/2(632.8 × 10-9 - (1/2 *1.76 × 10-12 m))] =  1580280.3

n2 = L / [1/2(o + (1/2 *Delta ))] = 0.5 / 1/2(632.8 × 10-9 + (1/2 *1.76 × 10-12 m))] =  1580275.9

Thus n values are: 1580275, 1580276, 1580277, 11580278, 1580279, 1580280 There are about six modes.

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