Gain profile

Usually, mainly Doppler broadening determines the gain profile of a particular laser transition. Indeed, due to the different configurations achievable with gas lasers (namely, a large cavity length), the laser line can be narrower than the Doppler linewidth. Different experimental realizations of single-mode lasers are detailed elsewhere (Demtroder, 2(X)3). 

The essential characteristic of dye lasers is their broad homogeneous gain profile. 

In semiconductor lasers, the emission wavelength is essentially determined by the band gap of the material, which governs the gain profile. Nowadays, by choosing the proper semiconductor system, a very wide spectral region can be covered by these lasers (0.37-5 /u.m), as can be observed in Figure 2.15. 

Tunable coherent light sources can be realized in several ways. One possibility is to make use of lasers that offer a large spectral gain profile. In this case, wavelength-selecting elements inside the laser resonator restrict the laser oscillation to a narrow spectral interval and the laser wavelength may be continuously tuned across the gain profile. Examples of this type of tunable laser are the dye lasers were treated in the previous section. 

Another possibility for laser wavelength tuning is based on the shift of the energy levels in the active medium by external perturbations, which can cause a corresponding spectral shift in the gain profile and, therefore, in the laser wavelength. For instance, this shift may be caused by a temperature variation, as in the aforementioned case of semiconductor lasers. 

In general, two types of tunable solid state lasers have been developed those based on color centers in alkali halide crystals, and those based on transition metal ions (3d) in a crystalhne host. In both cases, the tunabihty rehes on the large spectral gain profile provided by the active center. 

The width of the gain profile in a CO2 laser is given as 66 MHz (close to the Doppler width of the emission band of the gas). If the eigenfrequency of the laser resonator is tuned to the center of the laser gain profile, what is the maximum length of resonator for which the laser can oscillate in a single mode ... 

The frequency of a single-mode laser inside the spectral gain profile of its active medium is mainly determined by the eigenfrequency of the active laser cavity mode. Therefore any instability of resonator parameters, such as variation of cavity length, mirror vibrations or thermal drifts of the refractive index will show up as frequency fluctuations and drifts of the laser line. 

Figure 7.15 Variation of computed and measured radial gain profiles [69].

Fig. 9. Operation of a gas laser in several axial cavity modes spaced by (e/2 Z) Hz (off-axis modes are not shown in the figure). The three cavity modes near the peak of the gain profile are above threshold for oscillation6 )...

Fig. 18. Comparison of undulator and optical klystron al, a2 Spontaneous emission bl, b2 laser induced electron bunch lengthening cl, c2 gain profiles at X = 4880 A and X = 5145 A respectively. Measurements as a function of undulator gap.

If several modes are simultaneously absorbed, the factor N in (1.22a-1.22b) stands for the ratio of all coupled modes to those absorbed. If all modes have equal frequency spacing, their number N gives the ratio of the spectral width of the homogeneous gain profile to the width of the absorption profile. 

In order to detect the intensity change of one mode in the presence of many others, the laser output has to be dispersed by a monochromator or an interferometer. The absorbing molecules may have many absorption lines within the broadband gain profile of a multimode dye laser. Those laser modes that overlap with absorption lines are attenuated or are even completely quenched. This results in spectral holes in the output spectrum of the laser and allows the sensitive simultaneous recording of the whoie absorption spectrum within the laser bandwidth, if the laser output is photographically recorded behind a spectrograph or if an optical multichannel analyzer (Vol. 1, Sect. 4.5) is used. 

A detailed consideration [11-17] shows that the time evolution of the laser intensity in a specific mode q a)) with frequency (d after the start of the pump pulse depends on the gain profile of the laser medium, the absorption a o)) of the intracavity sample, and the mean mode lifetime fm- If the broad gain profile with the spectral width Acpg and the center frequency coq can be approximated by the parabolic function... 

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). 

Although most experiments have so far been performed with dye lasers, the color-center lasers or the newly developed vibronic solid-state lasers such as the Tiisapphire laser, with broad spectral-gain profiles (Vol. 1, Sect. 5.7.3) are equally well suited for intracavity spectroscopy in the near infrared. An example is the spectroscopy of rovibronic transitions between higher electronic states of the H3 molecule with a color-center laser [24]. The combination of Fourier spectroscopy with ICLAS allows improved spectral resolution, while the sensitivity can also be enhanced [25, 34, 35]. 

The power P co) depends on the spectral gain profile G a>) and on the absorption profile a (co) of the intracavity sample, which is generally Doppler broadened. The Lamb peaks therefore sit on a broad background (Fig. 2.16a). With the center frequency a>i of the gain profile and an absorption Lamb dip at coo we obtain. 

In a small interval around coq we may approximate the gain profile G(co — coi) and the unsaturated absorption profile a (co) by a quadratic function of co, yielding for (2.40) the approximation... 

Fig. 2.17 Lamb peak at the slope of the Doppler-broadened gain profile and the first three derivatives, illustrating the suppression of the Doppler background...

These derivatives are exhibited in Fig. 2.17, which illustrates that the broad background disappears for the higher derivatives. If the absorptive medium is the same as the gain medium, the Lamb peak appears at the center of the gain profile (Fig. 2.16b, c). 

The steep zero crossing of the third derivative of narrow Lamb dips gives a good reference for accurate stabilization of the laser frequency onto an atomic or molecular transition. Either the Lamb dip in the gain profile of the laser transition or Lamb dips of absorption lines of an intracavity sample can be used. 

Without frequency-selective elements inside the laser resonator, the laser generally oscillates simultaneously on many resonator modes within the spectral gain profile of the active medium (Vol. 1, Sect. 5.3). In this multimode operation no definite phase relations exist between the different oscillating modes, and the laser output equals the sum intensities L of all oscillating modes, which are more... 

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