Laser resonators

For a laser output power of 3 mW at A = 633 nm, the rate of emitted photons is f n = lO s. In this example (he total pump rate has to be F = (1.5 + 1) X 10 s = 2.5 X 10 s , where the fluorescence emitted in all directions represents a larger loss than the mirror transmission. 

In Sect. 2.1 it was shown that in a closed cavity a radiation field exists with a spectral energy density p(v) that is determined by the temperature T of the cavity walls and by the eigenfrequencies of the cavity modes. In the optical region, where the wavelength A is small compared with the dimension L of the cavity, we obtained the Planck distribution (2.13) at thermal equilibrium for p(v). The number of modes per unit volume, 

In order to achieve a concentration of the radiation energy into a small number of modes, the resonator should exhibit a strong feedback for these modes but large losses for all other modes. This would allow an intense radiation field to be built up in the modes with low losses but would prevent the system from reaching the oscillation threshold in the modes with high losses. 

Assume that the fcth resonator mode with the loss factor Pk contains the radiation energy Wk. The energy loss per second in this mode is then 

Under stationary conditions the energy in this mode will build up to a stationary value where the losses equal the energy input. If the energy input is switched off at t = 0, the energy will decrease exponentially since integration of (5.17) yields 

This differential equation system couples the two unknown functions AN t) and p(f) the equations are non-linear because they both contain the term pAN. Analytical solutions 

Clearly, this confirms mathematically the hand-waving arguments used in the description of a four-level laser system, namely that, in a four-level laser, population inversion is produced as soon as pumping commences. 

The actual resonator constitutes the total volume bounded by the two (or more) reflective mirror surfaces. However, other factors affect the resonator volume, e.g. like the size and shape of the active medium and other elements in the beam path, and may have to be included in any theoretical treatment. In a simple two-mirror optical resonator, a line through its centre and perpendicular to the mirror 

For optimum performance of a laser it is essential that any intemaT losses, i.e. unwanted losses other than the desired output coupling loss, are minimized. The following important factors contribute to losses within the optical resonator of a laser  

Let us denote the initial intensity of the light wave at point 1 as 7i. Then, after passage through the active medium, at point 2, it is amplified to an intensity of h = GJ, where Ga is for amplifier gain, which is given by 

When we define the quality factor Qk of the th cavity mode as 2n times the ratio of energy stored in the mode to the energy loss per oscillation period 

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Sensitivity can be improved by factors of 10 using intracavity absorption, placing an absorber inside a laser resonator cavity and detecting dips in the laser emission spectmm. The enhancement results from both the increased effective path length, and selective quenching of laser modes that suffer losses by being in resonance with an absorption feature. 

Fig. X Principle of laser resonance ionization of "Tc based on three different modes, (a), (b) and (c) [12]...

Fan, X. White, I. M. Zhu, H. Suter, J. D. Oveys, H., Overview of novel integrated optical ring resonator bio/chemical sensors, Proc. SPIE (Laser Resonators and Beam Control X) 2007, 6452, 64520M.1 64520M.20... 

Since one of the most investigated systems for the incorporation of laser resonators is the Forster-transfer couple Alq3 DCM [188, 189], we will discuss this as a representative example for low molecular glass lasers. 

One class of laser resonators is based on circular structures like spheres, disks, and rings. In these structures, the optical modes form closed circular loops and... 

Figure 3.25. Laser resonators applicable to molecular glasses A = microdroplet, B = microdisk, C = ring laser, D = vertical cavity distributed bragg laser, E = distributed feedback laser, F = random laser.

One final type of laser resonator, which is also applicable for molecular glasses, should be mentioned The random laser, based on coherent backscat-tering in an amplifying medium [212, 213]. In these structures, strongly scattering nanoparticles like Ti02 colloids are randomly dispersed in the amorphous films leading to self-contained optical paths and thus to the localization of optical modes. Since disordered structures are much easier to produce than ordered... 

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. 

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 ... 

It should be noted, however, that the Q factors of open microcavities do not characterise directly the threshold gain values of the corresponding semiconductor lasers. To overcome this difficulty a new lasing eigenvalue problem (LEP) was introduced recently (Smotrova, 2004). The LEP enables one to quantify accurately the lasing frequencies, thresholds, and near- and far-field patterns separately for various WG modes in semiconductor laser resonators. However, the threshold of a lasing mode depends on other... 

Boriskina, S.V., Benson, T.M., Sewell, P., and Nosich, A.I., 2003, Highly efficient design of spectraUy engineered WG-mode laser resonators. Opt Quantum Electron. 35 545-559. 

Advanced electro-optical methods (e.g., laser resonance absorption) capable of measuring average concentrations over long distances still requite extensive research and field testing to demonstrate their practical application to ozone monitoring. Because electro-optical methods have not yet been widely used, they are not discussed further here. 

The next section, which is the most extensive, deals with the various kinds of spectroscopic experiments which have been done or can be done with lasers as external light sources, where external means that the probe under investigation is placed outside the laser resonator. Together with a brief description of the experiments and a summary of the results, there is a discussion of the main qualities of the laser which made these special investigations possible. 

Section IV explains a new approach to high resolution spectroscopy based on various kinds of saturation effects. Some of the experiments are performed inside the laser resonator, which implies the presence of coupling phenomena between the absorbing molecules under investigation and the laser oscillation itself. These feedback effects can be used for high-precision frequency stabilization and to measure frequency shifts and line profiles with an accuracy never... 

The wavelength of a laser line, however, is determined by two factors the fluorescence profile of the corresponding transition in the laser medium and the eigenfrequencies of the laser resonator modes. At normal multimode operation of a laser, where many axial and transverse modes participate in laser oscillation, these eigenfrequencies cover the whole spontaneous line profile nearly uniformly. 

With special techniques it is possible to stabilize the laser frequency down to some 10 sec" 38,39) and promising experiments with the infrared line X = 3.39p of the He-Ne laser indicatethat a stability of 10 cycles/sec or better may be obtained when using the saturated absorption of molecules inside the laser resonator as the stabilizing element (see Section IV.3). 

Let us consider a laser oscillating at a single frequency (single-mode operation) and gas molecules inside the laser resonator which have absorption transitions at this frequency. Some of the molecules will be pumped by the laser-light into an excited state. If the relaxation processes (spontaneous emission and collisional relaxation) are slower than the excitation rate, the ground state will be partly depleted and the absorption therefore decreases with increasing laser intensity. 

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