Lorentzian linewidths

Results of calculation of second moment line for analyzed systems were obtained by summation over 106 cells in lattice, they are presented in Table 2. The Lorentzian linewidth calculated from these M2 values... 

The spectral parameters were obtained by fitting the experimental EPR spectra using the WinSim package. In order to determine the hyperfine linewidth, the specific modulation amplitude of the CW detection mode had to be taken into account. To this end, the theoretical spectrum with optimized Lorentzian linewidth was used as a starting point. Then the theoretical spectrum with the same hyperfine parameters but a reduced Lorentzian linewidth was calculated and transformed taking into account the broadening due to the CW modulation technique. The reduced Lorentzian linewidth was varied until the best correlation between experimental and modulation-transformed theoretical spectrum was obtained. 

For transitions in the visible region, an excitation with f = 1 wUl arise from a transition dipole moment of magnitude 2.5 Debye. An oscillator strength of f = 1 is the order of magititude seen for an organic dye molecule. For a transition at 500 mn the radiative lifetime of such an excited state would be 4ns, leading to a Lorentzian linewidth of 40 MHz or 1.3 x 10 cm. These values are appropriate to measurements in vacuo and need to be scaled by the dielectric constant of the medium in which the chromophore is embedded, in order to correct for the actual field experienced by the chromophore. 

One of the most significant implications of the result is that an absorption spectrum measured with intense white light may be significantly different from the spectrum that would be observed using tunable monochromatic radiation. In particular, there should be a decrease in the apparent width of many lines in any absorption spectrum measured with broadband radiation. This is because, for any sample transition of frequency coq, photons of appreciably off-resonant frequency (oiq + fi) can be cooperatively absorbed and result in the excitation of two separate molecules, provided selection rules permit. In fact the Lorentzian linewidth of the concerted absorption process is readily shown to be approximately 0.64 x the ordinary absorption linewidth, if the probe radiation is assumed to be of nearly constant intensity in the frequency region of interest. Nonetheless, the observed linewidth would not be reduced to quite this extent, because of the additional and invariably stronger response associated with normal single-photon absorption. 

In Fig. 2 we show data taken with similar TJS lasers at three temperatures for AVjujjjjj as a function of inverse power. The characteristic linear dependence of the Lorentzian linewidth on inverse power is clearly evident. A representative value for the linewidth-differential power product for (GaAl)As lasers at room temperature is Avpyjjjj AP 100 MHz mW. As the temperature is reduced, a power-independent linewidth component becomes increasingly evident. This is observed to increase from about 2 MHz at 273 K to over 11 MHz at 77 Additional measurements on these TJS de-... 

The frequency noise power spectral density of a SL typically exhibits a 1/f dependence below 100 kHz and is flat from 1 MHz to well above 100 MHz. Relaxation oscillations will induce a pronounced peak in the spectrum above 1 GHz. The "white" spectral component represents the phase fluctuations that are responsible for the Lorentzian linewidth and its intensity is equal to IT times the Lorentzian FWHM.20 xhe 1/f component represents a random walk of the center frequency of the field. This phase noise is responsible for a slight Gaussian rounding at the peak of the laser field spectrum and results in a power independent component in the linewidth. Figure 3 shows typical frequency noise spectra for a TJS laser at two power levels. 

To begin with, the typical single mode output power of lead-salt diode lasers presently available is generally (much) less than 10 mw. Also, Qc, the "cold" cavity Q calculated for a "solitary" diode laser (the cavity of which is defined by two cleaved end facets) is generally much less than 10. In terms of the usually measured semiconductor laser parameters the full Lorentzian linewidth between half-maximum power points (FWHM) can be written as... 

This is more than just a mathematical artifice. This substitution is tantamount to replacing the energy E by E — ihs), so that the intermediate state 1 > exhibits the time dependence exp — iE t/h — st) and hence physically decays with lifetime l/2e. The constant e can be identified with y/4, where y is the Lorentzian linewidth (Chapter 8). Such linewidths are generally much smaller than level energies E , so that dropping s at the end of the integration yields good approximations to cf t) in Eq. 10.10. Next, we have... 

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