Understanding the characteristics of gain saturation for homogeneously broadened laser medium from the point of view of the bandwidth Geguo D College of Electronic Science and Technology, Shenzhen University, Shenzhen, 518060, PR China Abstract: It is very important to understand the characteristics of gain saturation for homogeneously broadened laser medium. Assuming a Lorentzian lineshape function with a linewidth of AvH. we have derived the analytical functions of the gain coefficient under three different conditions: 1)a small and 2)a large signal incident on the medium respectively, and 3)a small signal accompanied by a large signal simultaneously incident on the medium. We have found that the bandwidth Av of the gain coefficient is equal to the linewidth AVH for condition D)and 3)while it is Av= 1+In //, AvH for condition 2). Here, I, and I, are the intensity of the large signal and the saturation intensity at the center frequency Vo, respectively. The reasons are also presented for such results. For condition 2), gain saturation effect is strongly dependent on the frequency of the large signal the more the frequency deviates from the center frequency, the weaker the gain saturation effect. This results an increase of the bandwidth. For condition 3), the intensity of the large signal only changes the distribution of populations on the upper and lower energy levels. Hence, the shape of the gain coefficient does not change with the gain reduction of the small signal, thus its band width remains the same OCIS codes:(1403430)laser theory, 000 2060 Education 1. Introduction When populations between two energy levels of an atom are inverted, the medium can act as an amplifier. Therefore, as an optical signal passes through it, the signal intensity I grows more or less exponentially with distance along the length of the amplifier. However, when the signal intensity increases to a certain value, I, the population difference and hence the gain coefficient in the laser medium decreases. This behavior is often referred to as gain saturation. Where Is is the saturation intensity at center frequency vo Gain saturation is the primary mechanism that determines the power level at which a laser will oscillate. When a laser oscillator begins to oscillate, the oscillation amplitude grows first until the intensity inside the cavity is sufficient to saturate down the laser gain. The steady-state oscillation then occurs when the saturated laser gain becomes just equal to the total cavity losses, so that the net round-trip gain is exactly unity The saturation behavior is different for homogeneously and inhomogeneously broadened laser media. In this paper, we will analyze the characteristics of gain saturation for homogeneously broadened system from the point of view of the bandwidth The radiation emitted by the spontaneous transition from energy level 2 to level I in a medium is not strictly monochromatic(that is, of one frequency) but occupies a finite frequency bandwidth. The function describing the distribution of emitted intensity versus the frequency v is referred to as the lineshape function vvo)(of the transition 2-1)and its arbitrary scale factor is usually chosen so that the function is normalized according to