Mode competition

D. Zardi and G. Seminara. Chaotic mode competition in the shape oscillations of pulsating bubbles. J. Fluid Mech., 286 257-276, 1995. 

Intracavity enhancement, relative to conventional single pass absorption spectroscopy, is due to mode competition and to threshold effects. A simple calculation of the latter for a single mode laser, starting with... 

The effect of mode competition, which is generally the dominant effect, is more subtle since, to a first approximation, a cw dye laser has only one mode. Theories of IDLS which account for mode competition have been put forward by Hansch, Schlawlow, and Toschek (HST) and by Brunner and Paul (BP). HST start with a realistic set of laser rate equations but use substantial approximations to solve them. BP use an approximate and very empirical set of rate equations which they solve analytically. Each theory yields a prediction for the dependence of enhance-m it on pumping power P relative to the threshold pumping power... 

Direct spectroscopic measurements of absorptions could provide substantial and much-needed complimentary information on the properties of BLMs. Difficulties of spectroscopic techniques lie in the extreme thinness of the BLM absorbances of relatively few molecules need to be determined. We have overcome this difficulty by Intracavity Laser Absorption Spectroscopic (ICLAS) measurements. Absorbances in ICLAS are determined as intracavity optical losses (2JI). Sensitivity enhancements originate in the multipass, threshold and mode competition effects. Enhancement factor as high as 106 has be en reported for species whose absorbances are narrow compared to spectral profile of the laser ( 10). The enhancement factor for broad-band absorbers, used in our work, is much smaller. Thus, for BLM-incorporated chlorophyll-a, we observed an enhancement factor of 10 and reported sensitivities for absorbances in the order of lO- (24). 

TABLE 20.6-5 Effects of Dual-Mode Competition on C02-CH4 Separation ... 

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The first exponential factor describes the spectral narrowing of the gain profile with increasing time t due to saturation and laser mode competition, and the second factor can be recognized as the Beer-Lambert absorption law for the transmitted laser power in the th mode with the effective absorption length Leff = ct. In practice, effective absorption lengths up to 70,000 km have been realized [15]. The spectral width of the laser output becomes narrower with increasing time, but the absorption dips become more pronounced (Fig. 1.15). 

Comparison of the differences between pure and mixed compment cases for the penmealnlities of each component calculated in the standard fashion and in the thennodynamically normalized Esshkm (P ) is revealing. The difference between the pure and mixed gas cases for the P columns of each conqxment corresponds to the apparent total depression in flux resulting fnmi both true dual-mode competition effects and nonideal gas-phase effects. The differences between the pure and mixed gas cases for die P cohimns are free of complications arising from nonideal gas-phase efli. Therefore, the differences b ween these columns are manifestations of the rather small competition efliect due to dual-mode sorption under these conditions. 

In fact, such single-mode operation without further frequency-selecting elements in the laser resonator can be observed only in a few exceptional cases because there are several phenomena, such as spatial hole burning, frequency jitter, or time-dependent gain fluctuations, that interfere with the pure case of mode competition discussed above. These effects, which will be discussed below, prevent the unperturbed growth of one definite mode, introduce time-dependent coupling phenomena between the different modes, and cause in many cases a frequency spectrum of the laser which consists of a random superposition of many modes that fluctuate in time. 

In the case of a purely inhomogeneous gain profile, the different laser modes do not share the same molecules for their amplification, and no mode competition occurs. Therefore all laser modes within that part of the gain profile, which is above the threshold, can oscillate simultaneously. The laser... 

The intensity I(t) of a cw laser is not completely constant, but shows periodic and random fluctuations and also, in general, long-term drifts. The reasons for these fluctuations are manifold and may, for example, be due to an insufficiently filtered power supply, which results in a ripple on the discharge current of the gas laser and a corresponding intensity modulation. Other noise sources are instabilities of the gas discharge, dust particles diffusing through the laser beam inside the resonator, and vibrations of the resonator mirrors. In multimode lasers, internal effects, such as mode competition, also contribute to noise. In cw dye lasers, density fluctuations in the dye jet stream and air bubbles are the main cause of intensity fluctuations. 

Here the net gain is 0.94 x 1.1 = 1.03 without mode competition. The two adjacent resonator modes reach the threshold. Therefore three longitudinal modes can oscillate. 

In the absorption measurements described above an external laser beam was used. A great increase in sensitivity can be achieved if the sample is placed inside the laser cavity [9.49,50]. This is due to the mode competition in a multi-mode laser. The principle of intra-cavity absorption measurements is given in Fig. 9.4. 

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