Laser linewidth

Laser linewidth is the spectral linewidth of a laser beam. Two of the most distinctive characteristics of laser emission are spatial coherence and spectral coherence. While spatial coherence is related to the beam divergence of the laser, spectral coherence is evaluated by measuring the linewidth of laser radiation. The first human-made coherent light source was a maser. The acronym MASER stands for "Microwave Amplification by Stimulated Emission of Radiation". More precisely, it was the ammonia maser operating at 12.5 mm wavelength that was demonstrated by Gordon, Zeiger, and Townes in 1954. One year later the same authors derived theoretically the linewidth of their device by making the reasonable approximations that their ammonia maser Notably, their derivation was entirely semi-classical, describing the ammonia molecules as quantum emitters and assuming classical electromagnetic fields (but no quantized fields or quantum fluctuations), resulting in the half-width-at-half-maximum (HWHM) maser linewidth denoted here by an asterisk and converted to the full-width-at-half-maximum (FWHM) linewidth . is the Boltzmann constant, is the temperature, is the output power, and and are the HWHM and FWHM linewidths of the underlying passive microwave resonator, respectively. In 1958, two years before Maiman demonstrated the laser (initially called an "optical maser"), Schawlow and Townes transferred the maser linewidth to the optical regime by replacing the thermal energy by the photon energy , where is the Planck constant and is the frequency of laser light, thereby approximating that iv. one photon is coupled into the lasing mode by spontaneous emission during the photon-decay time , resulting in the original Schawlow–Townes approximation of the laser linewidth: Also the transfer from the microwave to the optical regime was entirely semi-classical, without assuming quantized fields or quantum fluctuations. Consequently, the original Schawlow–Townes equation is entirely based on semi-classical physics and is a four-fold approximation of a more general laser linewidth, which will be derived in the following.