| With the development of optoelectronic technology,semiconductor lasers are used in aerospace,material processing,military and medical fields widely.The narrow linewidth semiconductor lasers have become the core light source devices in the fields of long-distance space optical communication,high-sensitivity optical sensing and energy detection due to their narrow linewidth,low noise,high stability,high coherence and good dynamic single-mode performance.In these fields,extremely stringent requirements are put forward for the linewidth,phase noise and frequency noise of laser source.Therefore,the linewidth and phase-frequency noise characteristics of narrow linewidth semiconductor lasers are experimentally researched in this paper.And a method for calculating the linewidth of narrow linewidth semiconductor lasers based on β algorithm is proposed,the complete distribution characteristics of laser linewidth in its frequency domain are obtained.The generation mechanism and distribution characteristics of the linewidth of semiconductor lasers are analyzed theoretically,it is clarified that the spontaneous emission,cavity length,optical output power and optical loss of semiconductor lasers directly affect the laser linewidth.And the frequency noise spectral density of semiconductor lasers based on the Wiener-Khintchine theorem is introduced.The basic characteristics of 1/f noise and white noise in frequency noise are compared and analyzed,it is determined that the spontaneous emission,impurities and external oscillation of semiconductor lasers are all the influencing factors of phase-frequency noise.In the aspect of linewidth characterization,the basic principle of traditional linewidth measurement technology is introduced and analyzed.it is proved that they all have the disadvantages of the single expression form of linewidth.In order to obtain the complete distribution characteristics of a laser linewidth and frequency noise,a method for calculating the linewidth of narrow linewidth semiconductor lasers based on β algorithm is proposed in this paper.The method combines the theory of white noise and 1/f noise in frequency noise to induce different laser line shape to determine the laser linewidth.The basic principle of the β algorithm has been introduced at first,the relationship between frequency noise and laser linewidth in different frequency ranges are analyzed.Secondly,the frequency noise and the line shape are numerically simulated.The results show that 1/f noise in frequency noise leads to a Gaussian line shape,and the linewidth increases with the cut-off frequency,while the white noise leads to Lorentzian line shape,and the linewidth does not change with the cut-off frequency.Therefore,the linewidth of the laser is an integral of the frequency noise in the Gaussian line shape region.Experimentally,the optimal lasing spectrum has been measured by current tuning and temperature control of a narrow linewidth semiconductor laser.Under the same working conditions,the frequency noise spectral density is measured by the delay self-homodyne measurement system.The laser linewidth at full Fourier frequency has been successfully obtained,which is calculated by integrating the frequency noise spectral density using the β algorithm.Meanwhile,a delayed self-heterodyne measurement system with delay fiber of 50 km and central frequency of 140 MHz is constructed.The measured linewidth of a narrow semiconductor laser working under 110 mA inject current is about 1.8 kHz,which is consistent with the calculated result of the β algorithm,of which the frequency bandwidth is 2.8 kHz.The experimental results prove the accuracy of the β algorithm.In conclude,the complete distribution characteristics of frequency noise and laser linewidth at full frequency can be presented by the β algorithm,which is of great significance to research of narrow linewidth semiconductor lasers. |