Two-level

Linear Absorption & Beer-Lambert Law

Weak probe pulses and continuous-wave fields in a two-level absorber. Demonstrates Beer-Lambert attenuation, the role of spontaneous decay, and how increasing optical depth reshapes the transmitted pulse.

Linear Absorption — Beer–Lambert Law

Self-Induced Transparency & Optical Solitons

Strong resonant pulses whose area exceeds π can form area-conserving solitons via self-induced transparency (McCall–Hahn). 2π solitons propagate without loss; larger areas break up into multiple solitons. Odd-π inputs are unstable fixed points of the area theorem.

Self-Induced Transparency: Area Theorem and Solitons

Photon Echo & Coherence Time ($T_2$) Measurement

A π/2 pulse followed by a π pulse creates a photon echo at $t = +tau$ in an inhomogeneously broadened (Doppler-broadened) medium. The echo amplitude decays as $e^{-2tau/T_2}$, allowing the homogeneous coherence time $T_2$ to be measured even when the lineshape is dominated by inhomogeneous broadening.

Two-Level: Two-Pulse Photon Echo