Basic Laser Physics Refresher

Use steady-state rate equations to show why an ideal two-level medium cannot sustain population inversion under continuous optical pumping.

Analyze the pumping and relaxation conditions required for inversion in a three-level laser medium.

Analyze the pumping and relaxation conditions required for inversion in a four-level laser medium.

Solve steady-state rate equations for the level populations of an ideal continuously pumped four-level medium.

Calculate the frequency-dependent small-signal net gain coefficient from level populations and absorption and emission cross sections.

Derive the saturation intensity of a gain transition under a specified lifetime and cross-section model.

Calculate the intensity evolution through a homogeneously broadened amplifier when gain saturation is significant.

Estimate the upper bound on optical efficiency from pump and laser photon energies and specified parasitic losses.

Calculate the intensity profile, spot size, and wavefront curvature of a fundamental Gaussian beam at a specified axial position.

Determine a Gaussian beam’s Rayleigh range and far-field divergence from its wavelength and waist.

Propagate a Gaussian beam through free space and thin lenses using the complex beam parameter and ABCD matrices.

Determine whether a two-mirror optical resonator is stable using its g parameters.

Calculate the waist location and mirror spot sizes of the fundamental Gaussian mode of a stable two-mirror resonator.

Derive the longitudinal resonance frequencies and free spectral range of an optical cavity.

Determine transverse-mode resonance frequencies for a stable resonator and identify the fundamental TEM00 mode.

Calculate cavity finesse, resonance linewidth, and photon lifetime from mirror and intracavity losses.

Derive the round-trip gain condition for laser threshold in a resonator with distributed and mirror losses.

Calculate the threshold inversion density for a specified gain medium and optical cavity.

Calculate the threshold pump rate of an ideal three-level or four-level laser from its rate equations.

Explain gain clamping above threshold using the coupled population and photon balance equations.

Calculate steady-state output power and slope efficiency as functions of pump rate above threshold.

Determine the output-coupler transmission that maximizes extracted power under a stated saturated-gain model.

Predict which cavity modes reach threshold from frequency-dependent gain and loss, and explain how homogeneous gain saturation produces mode competition.

Calculate the fundamental Schawlow–Townes-type laser linewidth from spontaneous-emission, intracavity-photon, and cavity-decay parameters.

Formulate coupled time-dependent rate equations for inversion and intracavity photon number in a single-mode laser.

Determine the relaxation-oscillation frequency and damping from linearized laser rate equations.

Explain how rapid modulation of cavity loss converts stored inversion into a Q-switched pulse.

Estimate the energy, duration, and peak power of an idealized Q-switched pulse from its initial inversion, output coupling, and cavity lifetime.

Show how fixed phase relationships among longitudinal modes produce a periodic train of short pulses.

Calculate a mode-locked laser’s pulse repetition rate and estimate its pulse duration from cavity length, locked bandwidth, and an assumed pulse shape.

Apply the time–bandwidth product to determine whether a pulse is transform limited and to identify the effect of chirp.

Compare active modulation and saturable absorption as mechanisms for establishing mode locking.

Trace the pumping, excitation-transfer, inversion, and emission processes in a helium–neon laser.

Apply four-level laser principles to analyze threshold and efficiency in an optically pumped Nd:YAG laser.

Explain population inversion and optical gain in a semiconductor diode laser using quasi-Fermi levels.

Infer the operating behavior of an unfamiliar laser architecture from its energy levels, gain bandwidth, pump scheme, and resonator.

Explain how second-order nonlinear polarization generates second-harmonic light and why phase matching controls coherent buildup.

Calculate coherence length and relative second-harmonic conversion efficiency from crystal length and phase mismatch.

Calculate the beam-quality factor M² from waist and divergence measurements and use it to predict real-beam propagation.

Select an appropriate detector for measuring continuous-wave power, pulse energy, or pulse waveform from given detector specifications.