Homogeneously broadened line

To achieve the instability of homogeneous broadened line lasers, a satisfaction of much more difficult conditions is required large gain and the so-called bad-cavity properties. This special regime for damping constants and mode intensity is fulfilled in the far-infrared lasers [36]. In 1985 Weiss et al. [37,38] experimentally found a period doubling route to chaos in the NH3 laser. Further experimental investigation of chaotic dynamics in such lasers was reported later [39]. 

For example, a homogeneously broadened line with a half width of Av =5 cm (fwhm) can be related in the low temperature limit to the lifetime of the corresponding vibrational state by... 

Both this fluorescence line narrowing and hole burning spectroscopy are conceptually trivial. Still, they can provide very useful information on the homogeneously broadened lines as illustrated in Fig. 18.11. What makes life less simple and more interesting is that other dynamical effects can express themselves in this... 

Fig. 3.4.1 Homogeneously and inhomogeneously broadened lines, (a) Echo train generated by repeated refocussing of the FID (CPMG method, cf. Fig 2.2.10(b)). (b) The Fourier transform of the slowly decaying echo envelope is the homogeneously broadened line, (c) The Fourier transform of the fast decaying echo is the inhomogeneously broadened line.

Fig. 14. Schematic of selective excitation and ID exchange spectroscopy, (a) Typical pulse sequence with a soft selective pulse centered at pulsation a>s with a frequency dispersion AcoP <3C Aoj much smaller than the typical linewidth. After an evolution time te smaller or of the order of the spin-lattice relaxation time, a reading sequence of hard pulses that covers uniformly the whole broad line is applied, (b) Effect of a selective excitation on a homogeneously broaden line, (c) Selective frequency labeling of an inhomogeneously broaden line at the irradiation pulsation cos of the first soft pulse. For a soft n pulse, the magnetizations of all the spins that can exchange energy at this pulsation are reversed. By following the difference spectra between the spectra acquired at different evolution times te and the fully relaxed spectrum AS(te) — S(t -> oo) — S(te), limits or evaluation of the correlation time tc of the motion can be achieved.

How about some other examples of homogeneously broadened lines The application of high radio frequency power to a transition not only causes saturation (if is sufficiently long) but also causes power broadening for the entire system. When a strongly coupled system, coupled by dipolar interactions, permits spin diffusion and the establishment of a common spin temperature, the attempt to burn a hole in the line will also result in a collapse of the entire line. Dipolar interactions, spin diffusion, and spin temperatures are discussed later in this chapter, as well as in III.C.l. and in IV.D. 

Since the absorption profile a(co) of a homogeneously broadened line is Lorentzian, see (3.36b), the induced absorption probability of a monochromatic wave with frequency o) follows a Lorentzian line profile B[2p(co) L co — coo). We can therefore introduce a frequency-dependent spectral saturation parameter 5 for the transition E E2,... 

However, in reality it often happens that the different atoms A are placed at nonequivalent lattice points with nonequal electric fields. This is particularly true in amorphous solids or in supercooled liquids such as glass, which have no regular lattice structure. For such cases, the line centers co j of the homogeneously broadened lines for the different atoms Aj are placed at different frequencies. The total emission or absorption forms an inhomogeneously broadened line profile, which is... 

The intensity of ESR absorption relates to spin concentration, and spin susceptibility can also be measured using standard sample of known spin susceptibility. The g tensor depends upon the paramagnetic species present and its value is the fimction of the spin environment. For free electrons g = 2.00232. The linewidth peak to peak (A//pp) depends on the relaxation time. Homogeneously broadened lines have Lorentzian shapes, whereas inhomogeneously broadened lines have Gaussian shapes. In practice, a combination of both occurs. Normally the ratio of low field to high field is unity, but it can be greater. 

In Sect.2.8, we saw that a sufficiently strong radiation field can significantly change the population densities and N2 of an atomic system by induced absorption and emission. This saturation of the population densities also causes additional line broadening. The spectral line profiles of such partially saturated transitions are different for homogeneously and for in-homogeneously broadened lines [3.19]. We treat first the homogeneous case. 

Fig.3.19a-c. Saturation by a monochromatic standing wave, (a) Population distribution n(v ) for 03 coq. (b) Absorption coefficient a(o3) of an in-homogeneously broadened line, as obtained when tuning the frequency U3 of the standing wave across the line profile, (c) Saturation of a homogeneous absorption profile... 

We have discussed gain saturation in detail for a homogeneously-broadened line since simple explicit expressions can be obtained for the gain coefficient and the intensity of laser radiation. Unfortunately this is not possible in the case of inhomogeneous broadening which we examine in the following section. 

In the small-signal limit we see that equation (13.30) reduces to equation (11.7) as expected. Comparing equations (13.19) and (13.30) we find that the gain of a Doppler-broadened transition saturates more slowly than that of a homogeneously-broadened line. This is a consequence of the fact that in the inhomogeneous case only a small fraction of the total number of atoms are on speaking terms with radiation of angular frequency u. 

From Fig.13.7 we see that even at the lowest input signal of 7 8 yW there is clear evidence of gain saturation. For a homogeneously-broadened line we have from equation (13,19)... 

Fig.13.7. Laser amplifier gain as a function of input signal intensity. , experimental results obtained on the 3-51 pm line of Xe. Solid plot is of the theoretical prediction, equation (13.35), for a homogeneously-broadened line. (After Bridges (1963).)...

A laser with a homogeneously-broadened line is operated in a cavity in which one mirror is perfectly reflecting while the other has an output transmission of t. The total round trip loss of the cavity is therefore given by 6 = t + 6 where 6 represents the unavoidable fractional cavity losses. Plot the laser output power for several different values of 6 as a function of the mirror transmission t and show that the mirror transmission for maximum output power is given by... 

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