Resonator losses

Ferrites aHowing for operation at frequencies well above 1 MH2 have also become available, eg, 3F4 and 4F1 (Table 6). Other newer industrial power ferrites are the Siemens-Matsushita N-series (28,97) the TDK PC-series (28,100), and the Thomson B-series (28,103). While moving to higher frequencies, the ferrites have been optimized for different loss contributions, eg, hysteresis losses, eddy current losses, and resonance losses. Loss levels are specified at 100°C because ambient temperature in power appHcations is about 60°C plus an increase caused by internal heat dissipation of about 40°C. 

The microresonator therefore can also be used as a sensitive absorption sensor. In both set-ups as refractive or absorption sensor, the ultimate sensitivity is determined by the slope of the resonance peak, which is related to the resonator losses. 

The ability to measure small index perturbations, (I/Ven. depends on the depth (i.e., the extinction ratio at resonance) and width of these resonances. The depth and width in turn depend on the relative values of the coupling coefficient t and the resonator loss a. Figure 9.16 shows typical ring resonator spectra calculated for two different loss values. The maximum extinction ratio is obtained at critical coupling when t = a, and the output intensity at resonance is exactly zero. The width of the resonances depends on the total round trip resonator loss, at, which is the product of waveguide losses within the ring (a) and coupling loss (t) at the coupler. 

If collisions become more frequent, the resonance lines widen and the resonance loss peak placed in the vicinity of x = 1 shifts to low frequencies.57 The effect of collisions on the loss curves is more emphasized for the Gross line... 

The computed absorption and loss factor are shown, respectively, in Figs. 31a and 31b Fig. 31c represents the low-frequency wing of the /r(v) curve characteristic for the non-resonance loss spectrum. Fig. 32 represents the frequency dependence of the dielectric constant s (v) and the Cole-Cole plot s"[s (v)]. The latter two graphs also agree with experiment. We see that our theory agrees reasonably well with the spectra observed by Bertie et al. [51]. Note the empirical formulas (72)-(74) by Hufford [20] could be applied for describing of the far IR ice loss spectrum (viz., at v < 100 cm-1), if the constant cfit in Eq. (72) is fitted properly (see Fig. 33). For T = 100 K cfit 17. 

The thermal loss decreases with increasing temperature and thus tends to make the system thermally unstable. This tendency is more pronounced if the size of the lumps is large, i.e. if the lattice spacing is large. It may be possible to give reasonably accurate estimates concerning this effect but lacking information about the behavior of the resonance loss, we cannot settle the major question of overall stability at the present time. 

With larger bodies of uranium, the size and distribution of the uranium-bearing particles disposed in a moderator affect the value of the reproduction factor K because the 35 resonance loss (absorption by increases with de-... 

A number of structural and electronic factors can interfere with the amide resonance (Figure 6.101). The reasons for the resonance loss can be structural (enforced twisting due to steric hindrance or due to cyclic restraints that lock the nitrogen lone pair out of alignment with the carbonyl) or electronic (pyramidaUzation at nitrogen due to rehybridization imposed by strain or electronegativity, i.e. Bent s rule). ... 

If the resonator losses are mainly due to the transmission T2 of the output mirror, the enhancement factor Q then becomes Q = l/y = l/T2 = q, which is equal to the enhancement of the previous detection method 1. 

An absorbing sample in a cell with L = 4 cm is placed within the laser resonator with a total resonator loss of 2 % per round trip and a transmission T = 0.5% of the output coupler. 

Fig. 6.3 Pump power Pp(t), resonator losses y t), inversion density AN(t), and laser output power Pl(0 for a Q-switched laser...

When the gain exceeds the total optical losses a due to mirror output coupling, scattering losses, and resonator losses, then net amplification and lasing is achieved. The threshold popnlation inversion is defined as the inversion reqnired for the gain to eqnal the losses ... 

Setting the saturated gain equal to the resonator losses (asumed small) as in Eq. (3), solving Eq. (6) for /e, and putting this into Eq. (4) gives the expected form for the output power (valid above threshold, when the expression in the last bracket is positive) ... 

The term hc/Xp)(l/x(p) is the pump power dissipated (by all spontaneous decay processes) per molecule in the upper laser Si. It is useful to estimate from Eq. (11) the minimum pump intensity needed to reach threshold in a dye laser. This will be when the pump power density absorbed by all ground-state molecules, N OpIp, balances against the power density dissipated by upper-state decays, N hc/Xp)( /x(p), to give that exdted-state fraction producing gain equal to the resonator losses. 

In short-pirlse dye lasers there is insufficient time for triplet-state buildnp and the resirlts above are itsable without correction. In flashlamp-pitmped dye lasers, not only are triplet terms significant, but often the full time-dependent rate eqirations are needed, reqitiring mtmer-ical integrations in modehng their behavior. In mode-locked dye lasers the resonator losses are dehberately time-dependent, requiring further discussion (see Section V). 

These experimental values measure the response of the (fye medium to changes in resonator loss, and as such represent the average over the active volume of the microscopic inversion variations in the cfye. A direct comparison with theoiy would thus involve a (numerical) integration of the plane-wave equations over the focal volume. 

An AM modulator in the laser resonator adjusts its loss periodically. The resonator loss is very high for some time, and light waves with certain phases during this period are attenuated no laser output develops. The inverse is true for the subsequent period of low resonator loss. The AM modulator period equals the cavity round trip time, i.e. Tam = 2.Llc = Tp. Because of this specific periodicity the AM modulator locks the modes to each other. AM modulation can be achieved using a Pockel cell or an AO modulator, similar to the devices shown in Figure 3.12. 

The loss factor y also depends on the frequency v because the resonator losses are strongly dependent on v. The frequency spectrum of the laser therefore depends on a number of parameters, which we discuss in more detail in Sect. 5.2. 

In the resonator of Fig. 5.14a the waves are coupled out of both sides of the resonator. The resultant high resonator losses are generally not tolerable and for practical applications the resonator configurations of Fig. 5.14b and Fig. 5.15 consisting of one large and one small mirror are better suited. Two types of nonsymmetric spherical unstable resonators are possible with gig2 > 1 => G > 1 (Fig. 5.15a) with the virtual beam waist outside the resonator and with ig2<0=>-G<—1 (Fig. 5.15b) where the focus lies inside the resonator. 

The threshold pump power depends on the size of the pump focus and on the resonator losses, and varies between 1 mW and several watts. The size of the pump focus should be adapted to the beam waist in the dye laser resonator (mode matching). If it is too small, less dye molecules are pumped and the maximum output power is smaller. If it is too large, the inversion for transverse modes exceeds threshold and the dye laser oscillates on several transverse modes. Under optimum conditions, pump efficiencies (dye laser output/pump power input) up to rj = 35% have been achieved, yielding dye output powers of 2 W for only 8 W pump power. 

In order to avoid laser waves propagating in both directions through the ring resonator, losses must be higher for one direction than for the other. This can be achieved with an optical diode [5.32]. This diode essentially consists of a birefringent crystal and a Faraday rotator (Fig. 5.18), which turns the bifringent rotation back to the input polarization for the wave incident in one direction but increases the rotation for the other direction. 

Calculate the necessary threshold inversion of a gas laser transition at X = 500 nm with the transition probability A(k = 5 x 10 s and a homogeneous linewidth Auhom = 20MHz. The active length is L = 20cm and the resonator losses per round-trip are 5%. 

A laser medium has a Doppler-broadened gain profile of halfwidth 2 GHz. The homogeneous width is 50 MHz, and the transition probability Aik = 1 X 10 s" Assume that one of the resonator modes (L = 40 cm) coincides with the center frequency vq of the gain profile. What is the threshold inversion for the central mode, and at which inversion does oscillation start on the two adjacent longitudinal modes if the resonator losses are 10% ... 

Estimate the optimum transmission of the laser output mirror if the unsaturated gain is 2 and the internal resonator losses are 10. 

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