Introduction to Laser Physics

Introduction to Laser Physics – Study Notes

1. What Is a Laser?

2. Fundamental Concepts

2.1. Atomic Energy Levels

• Ground state (E₁) – lowest energy level, most atoms occupy this at thermal equilibrium.
• Excited state (E₂) – higher energy level; population can be created by pumping.

2.2. Spontaneous vs. Stimulated Emission

2.3. Population Inversion

• Condition: N₂ > N₁ (more atoms in excited state than ground state).
• Required for net gain because stimulated emission must out‑balance absorption.

2.4. Gain Medium

• Material that provides the active transition (e.g., ruby crystal, Nd:YAG, semiconductor quantum wells, gas mixtures).
• Characterized by gain coefficient g(ν), which depends on wavelength, pump power, and temperature.

3. Laser Cavity (Resonator)

3.1. Longitudinal Modes

• Integer number q of half‑wavelengths fits into cavity: q·λ/2 = L.
• Frequency of mode q: ν_q = q·(c/2L).

3.2. Transverse Modes

• Spatial field distribution described by Hermite‑Gaussian (TEMₘₙ) or Laguerre‑Gaussian patterns.
• Fundamental mode TEM₀₀ gives the smallest divergence.

4. Rate‑Equation Model (Simplified)

For a two‑level system:

[ \frac{dN_2}{dt}=R_{\text{pump}} - \frac{N_2}{\tau} - B_{21}, \rho(\nu), (N_2 - N_1) ]

[ \frac{d\Phi}{dt}=B_{21}, \rho(\nu), (N_2 - N_1) - \frac{\Phi}{\tau_c} ]

• (R_{\text{pump}}) – pump rate (atoms s⁻¹).
• (τ) – spontaneous lifetime.
• (B_{21}) – Einstein coefficient for stimulated emission.
• (ρ(\nu)) – photon density in the cavity.
• (Φ)