Cavity loss

Lasing occurs whenever the gain arising from stimulated emission exceeds the cavity losses. Internal losses, a, result from absorption and scattering of light. The reflectivity, R, of the mirror facet must be <1 and this contributes a loss term of (1/L)ln(l/E), where Eis the cavity length. At threshold, the gain, is equal to losses and... 

Laser instabilities were experimentally investigated in many kinds of lasers (see an overview of early papers [14]), but the first experimental observation of the optical chaos was performed by Arecchi et al. [30] in 1982. They used a stabilized CO2 laser with modulated cavity loss = y(l + a cos fit) and by changing the frequency of modulation 2, they found a few period doubling oscillations of the output intensity, both numerically and experimentally. 

These values for the threshold current density are roughly consistent with calculated values. Depending on the cavity losses, theory predicts a practical lower limit of the threshold current density around 1 kA/cm2 [33,34], m line with the experimental experience. According to the band structure of the nitrides, a large threshold current density is inherent to this material system. 

We perform concrete calculations in the complex P-representation [Drummond 1980 McNeil 1983] in the frame of both probability distribution functions and stochastic equations for the complex c-number variables. We follow the standard procedures of quantum optics to eliminate the reservoir operators and to obtain a master equation for the density operator of the modes. The master equation is then transformed into a Fokker-Planck equation for the P-quasiprobability distribution function. In particular, for an ordinary NOPO and in the case of high cavity losses for the pump mode (73 7), if in the operational regime the pump depletion effects are involved, this approach yields... 

The symbol y appearing above is a damping constant responsible for the cavity loss. Thus, solving the master equation (36), we can determine the probabilities of finding the system in an arbitrary w-photon state. Of course, the evolution during single ultrashort, external pulse is determined by the operator tlK as before. 

All the experimental techniques described here involve the determination of the delay time between initiation of the pumping pulse and laser-pulse onset, or the coincidence of two such delay times belonging to different transitions. An analytical model has been presented by Chester et al. 116> to describe the delay re between flashlamp initiation and the start of the laser signal in the flash-photolysis HF chemical laser. The model has been used to predict the functional dependence of re on pressure, flashlamp intensity, optical-cavity losses, and the absolute magnitude of rc. However, the possible extension of this work to a detailed vibrational energy-partitioning study has not been demonstrated so far. 

To achieve lasing, N must surpass the required threshold population difference (Mh) by having the gain due to stimulated emission exceed the optical cavity losses. 

The optical cavity losses can be evaluated by first noting that absorption of the lasing wavelength is negligible due to the large Stokes shift discussed earlier. Thus, only the mirror losses contribute. Assuming that both mirrors are identical (symmetric cavity), the distributed cavity loss coefficient (a) can be written as... 

The effect of the sample is not only to increase the cavity loss function but also to broaden its frequency response. Both these cause a modification of the signal observed by an FM spectrometer and will be considered in more detail in Section 6.8. 

Next we may consider the sensitivity of the system to insertion of an analytical sample. This will act to increase the cavity loss, and so lower its Q (Equation 2.4). The optimum sensitivity will therefore occur when the derivative of the appropriate expression above with respect to k and to /Qc is a maximum. Choosing this appropriate expression is not, however, quite so straightforward as it may seem. For, with a reflection cavity we are observing not the signal inside the cavity, but that reflected from it. The most appropriate parameter to consider is therefore the derivative of the voltage reflection coefficient p with respect to... 

Fig. 3. IB CRLAS apparatus, nable infrared laser radiation U coupled into the ring-down cavity. The light transmitting the output mirror is focused into an InSb detector. The resulting signal is amplified, digitized, and sent to a PC where it is fit to a firsi order exponential, which is directly related to the total cavity loss per laser pass. The PC additionally controls the scanning of the dye laser. Base line losses are determined by scanning the laser with the expansion turned off and are then subtracted from the data, yielding the absolute sample absorbance, from which the carrier concentrations are extracted." ...

Round trip cavity losses at 6500 A First experiment ... 

The dye laser was fully optimized for these fundamental tuning curves, making the available input power be the limit to the output reached. With the weaker pump lines, the radius of the fold mirror (Ml of Fig. 10) was decreased to tighten the dye and matching pump focal areas and keep the gain well above the 2.5% s.f. cavity losses. (The 10-cm radius for the red dyes became 7.5 cm for the stilbenes, coumarins, and S9M, and 5.0 cm for IR140). The transmission of the output coupler was also optimized across the span of each dye (the breaks on several of the tuning curves are places where a different output coupler was... 

A simple all-fiber laser is shown schematically in Fig. 1. A pump laserprovides energy to the fiber amplifier. For the laser to exceed threshold and generate a coherent optical output, the amplifier must produce sufficient gain to overcome cavity losses, including the outpnt coupling loss. The absorbed pump power required to reach threshold is approximately... 

FIGURE 21 In the pump phase the timing diagram for the cavity-dumped case is identical to the Q-switched case. After switching the Pockels cell to enable lasing, the cavity loss now is very small since, for a cavity-dumped architecture, the reflectivity of both resonator mirrors is 100%. Once the power in the cavity has reached the maximum value, the Pockels cell is again switched and ejects the intracavity intensity from the laser in a pulse equal to the round-trip time of the resonator cavity. 

If an absorbing sample is introduced into the cavity such that the absorption follows Beer s law (Equation (6.2)) for a single pass of the laser pulse through the medium, then this absorption (proportional to the attenuation constant a) simply adds to the per-pass cavity loss, resulting in a shorter ring-down time. Equation (6.4) thus becomes... 

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