Problems

Problem 8.1 Short Questions on Lasers.

(a) A ring laser is composed of four identical mirrors, each with power reflectance $R=0.99$. Light traverses the amplifier once per round trip. Neglecting other losses, what is the minimum one-pass power gain $G$ at threshold?

(b) Give the frequency spacing of adjacent longitudinal modes in a linear cavity whose optical length is $nL=300$ mm.

(c) One mirror in a two-mirror cavity has complex amplitude reflectance $r=|r|e^{i\phi}$. Explain how $|r|$ changes the lasing threshold and how $\phi$ changes the longitudinal resonance condition.

Problem 8.2 A helium–neon laser has a rectangular gain band 1.0 GHz wide, centered near 633 nm, and an air-filled linear cavity 30 cm long. Estimate how many longitudinal resonances fall inside the band. Explain why an exact count also requires knowing how the cavity resonances align with the gain-band edges.

Problem 8.3 A pulsed laser produces approximately flat-top pulses of 10 $\mu$J energy and 1 ns duration. The pulse repetition frequency is 10 kHz. Give the peak power of the pulses and the average output power of the laser.