Gain saturation

When the pump power of a laser is increased beyond its threshold value, laser oscillation will start at first at a frequency where the net gain, that is, the difference between total gain minus total losses, has a maximum. During the 

In the case of a homogeneous profile g(v —vo) all molecules in the upper level can contribute to stimulated emission at the laser frequency Ua with the probability Bikpgiva I d), see (5.8). Although the laser may oscillate only with a single frequency v, the whole homogeneous gain profile a(v) = ANa v) saturates until the inverted population difference AN has decreased to the threshold value AAthr (Fig- 5.23a). The saturated amplification coefficient asat(v) at the intracavity laser intensity / is, according to Sect. 3.6, 

In the case of inhomogeneous laser transitions, the whole line profile can be divided into homogeneously broadened subsections with the spectral width (for example, the natural linewidth or the pressure- or 

This implies that with increasing saturation more molecules from a larger spectral interval Ayv, can contribute to the amplification. The gain factor decreases by the factor 1/(1-f 5) because of a decrease of A A caused by saturation. It increases by the factor (1+5) / because of the increased homogeneous width. The combination of both phenomena gives (Sect. 7.2) 

In the case of inhomogeneous laser transitions, the whole line profile can be divided into homogeneously broadened subsections with the spectral width (for example, the natural linewidth or the pressure- or power-broadened linewidth). Only those molecules in the upper laser level that belong to the subgroup in the spectral interval vl centered at the laser frequency vl, can contribute 

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The gain-saturation intensity product, ( optical power density available for extraction from the laser discharge medium. 

Gain bandwidth Type, gain saturation Homogeneous saturation flux Decay lifetime (lower level) Inversion density Small signal gain coefficient Pump power density Output power density Laser size (diameter length) Excitation current/voltage Excitation current density Excitation power Output power Efficiency... 

The use of an extrinsic photoconductor with direct injection has the advantage that dc gain can enhance I and therefore g, but gain saturation due to sweepout will limit ac gain to 1/2 at frequencies near f [6.30]. The capacitance C of an extrinsic photoconductor can be an order of magnitude lower than for a photodiode, which will lead to a higher /. With an extrinsic photodetector, crosstalk problems must be considered for the detector thicknesses necessary to provide reasonable quantum efficiency, and even for the 3-5 pm window operating temperatures will tend to be below 50 K. 

Spatial hole burning Gain saturation by a singlefrequency standing wave Add proceeds primarAy... 

C. Spectral Condensation, Gain Saturation, and Laser Output Power... 

The interpretation of the saturation intensity result, Eq. (8), contains a snbtlety. In the conservative two-state system nnder discnssion, a molecule removed from the upper state by laser-stimulated emission at the rate aJe(hc/Xu) per molecule must appear in the lower state. There it itmnediately is subjected to a pump rate (per molecule) of a l j hcjX returning it to the upper state. Thus for stimulated emission to produce a reduction of the small-signal upper-state population by half, it must be at a transition rate per molecule equal to the sum of the spontaneous decay rate plus the return rate, yielding Eq. (8). This makes the saturation intensity a linear function of the pump intensity at high pump rates, the e bleaches, the small-signal gain saturates at the total inversion value AT,CTe, and the output power increases with pump rate solely through the h term in Eq. (9). 

Other phenomena that influence the modulation dy-nanucs of semiconductor lasers include the spontaneous emission, gain saturation, and the external electrical connections to the device. These effects normally manifest themselves as a suppression of the relaxation oscillations, which reduces the peak of the modulation response and also reduces the modulation bandwidth. 

Due to spectral gain saturation competition effects between different oseil-lating laser modes occur they may influence the amplitudes and frequencies of the laser modes. 

The total amplification /t//o has maxima for cp — lqn, which corresponds to the condition (5.53) for the eigenfrequencies of the resonator with the modification (5.57). For G(v) 1, the total amplification Ij/h becomes infinite for (j) = 2qn. This means that even an infinitesimally small input signal results in a finite output signal. Sueh an input is always provided, for instance, by the spontaneous emission of the excited atoms in the active medium. For G(v) = 1 the laser amplifier converts to a laser oscillator. This condition is equivalent to the threshold condition (5.7). Because of gain saturation (Sect. 5.3), the amplification remains finite and the total output power is determined by the pump power rather than by the gain. 

The different gain saturation of homogeneous and inhomogeneous transitions strongly affects the frequency spectrum of multimode lasers, as can be understood from the following arguments ... 

X 60 cm. The total volume of Nd laser glass for multiple beam lasers can be >10 cm . Important materials properties for these high-power lasers are the nonlinear refractive index which governs the deliverable focusable power to a fusion target, the gain coefficient with affects the overall efficiency, and the stimulated emission cross section which determines the gain saturation behavior (Weber, 1976). 

Desurvire E Sulhoff I.W., Zyskind J.L., Simpson J.R. Study of spectral dependence of gain saturation and effect of inhomogeneous broadening in erbium-doped aluminosilicate fibo" amplifiers. IEEE Photon. Technol. Lett. 1990 2 653-655... 

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