# Spectral coherence, Part I: Passive-resonator linewidth, fundamental laser linewidth, and Schawlow-Townes approximation

Pollnau, M.; Eichhorn, Marc

##### Abstract:
The degree of spectral coherence characterizes the spectral purity of light. It can be equivalently expressed in the time domain by the decay time τ or the quality factor Q of the light-emitting oscillator, the coherence time τ $^{coh}$ or length l$^{coh}$ of emitted light or, via Fourier transformation to the frequency domain, the linewidth Δν of emitted light. We quantify these parameters for the reference situation of a passive Fabry-Pérot resonator. We investigate its spectral line shapes, mode profiles, and Airy distributions and verify that the sum of all mode profiles generates the corresponding Airy distribution. The Fabry-Pérot resonator is described, as an oscillator, by its Lorentzian linewidth and finesse and, as a scanning spectrometer, by its Airy linewidth and finesse. Furthermore, stimulated and spontaneous emission are analyzed semi-classically by employing Maxwell′s equations and the law of energy conservation. Investigation of emission by atoms inside a Fabry-Pérot resonator, the Lorentz oscillator model, the Kramers-Kronig relations, the amplitude-phase diagram, and the summation of quantized electric fields consistently suggests that stimulated and spontaneous emission of light occur with a phase 90° in lead of the incident field. ... mehr

 Zugehörige Institution(en) am KIT Institut für Regelungs- und Steuerungssysteme (IRS) Publikationstyp Zeitschriftenaufsatz Publikationsmonat/-jahr 08.2020 Sprache Englisch Identifikator ISSN: 0079-6727, 1873-1627 KITopen-ID: 1000122140 Erschienen in Progress in quantum electronics Verlag Elsevier Band 72 Seiten Art.-Nr.: 100255 Schlagwörter Spectral coherence; Optical resonance; Fabry-Pérot resonator; Resonator linewidth; Finesse; Lasers; Laser theory; Laser resonators; Laser linewidth; Schawlow-Townes equation Nachgewiesen in DimensionsWeb of ScienceScopus
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