Laser line shape and spectral density of frequency noise

Abstract

International audiencePublished experimental results show that single-mode laser light is characterized in the microwave range by a frequency noise which essentially includes a white part and a 1/f (flicker) part. We theoretically show that the spectral density (the line shape) which is compatible with these results is a Voigt profile whose Lorentzian part or homogeneous component is linked to the white noise and the Gaussian part to the 1/f noise. We measure semiconductor laser line profiles and verify that they can be fit with Voigt functions. It is also verified that the width of the Lorentzian part varies like 1/P where P is the laser power while the width of the Gaussian part is more of a constant. Finally, we theoretically show from first principles that laser line shapes are also described by Voigt functions where the Lorentzian part is the laser Airy function and the Gaussian part originates from population noise

Simple approach to the relation between laser frequency noise and laser line shape

“…However, the real noise spectrum of a laser is much more complicated and leads to a nonanalytical line shape that can be determined only numerically. Lasers are generally affected by flicker noise at low frequency, and this type of noise has been widely studied in the literature [14][15][16][17]. The major feature of this type of noise is to produce spectral broadening of the laser linewidth compared to the Schawlow-TownesHenry limit, but an exact expression of the line shape cannot be obtained, and different approximations have been proposed to describe this situation.…”

“…For example, Tourrenc [15] numerically showed the divergence of the linewidth with increasing observation time in the presence of 1=f -type noise, while Mercer [16] gave an analytical approximation for this diverging Gaussian linewidth. Stéphan et al [14] gave a different approximation of the 1=f -induced Gaussian contribution to the line shape, with a linewidth that does not contain any dependency on the observation time, and Godone et al [18,19] gave the rf spectra corresponding to phase noise spectral densities of arbitrary slopes. Finally, some publications also stated that the combined contribution of white noise Lorentzian line shape and 1=f -noise Gaussian line shape resulted in a Voigt profile for the optical line shape [14,16,20].…”

Experimental validation of a simple approximation to determine the linewidth of a laser from its frequency noise spectrum

“…The optical line shape, and thus the linewidth, may in principle be calculated from the frequency noise spectrum, while the reverse process is not possible. However, the exact determination of the linewidth from the frequency noise spectral density is not straightforward in most cases and involves a two-step numerical integration procedure [6][7][8][9], which we will briefly recapitulate at the beginning of Section 2.…”

Spectral control of diode lasers using external waveguide circuits

“…These perturbations cause amplitude and phase noise in the generated light wave. Owing to the wide range of statistical and spectral properties of the perturbations there are several different ways to characterize the resulting noise [29]. The most straightforward and standard way to quantify noise in lasers is to measure what is commonly called the FWHM spectral width of the optical power density, the laser bandwidth or laser linewidth.…”