Open resonator

Such a resonator can be realized with an open cavity consisting of two plane or curved mirrors, as represented in Figure 2.7 linear cavity). Details of the stability conditions for different types of open resonators can be found elsewhere (Siegman, 1986). Other more sophisticated configurations, such as those of ring cavity lasers (Demtroder, 2003) and microlasers (Kasap, 2001) are also used. 

Another approach to MMW spectrometers is based on the Orotron This device, called after the Russian words for an open resonator and a reflection grating, was a semiconfocal Fabry-Perot cavity (Figure 5.1) with the plane mirror having a reflection grating ruled upon it. The cavity, with 0 lO, produced a spectral bandwidth without frequency locking 10-15 kHz and output power was 3-10 mW over 90-150 GHz. 

Values of the dielectric loss of CVD diamond have been measured over the past 3 years as a suitable material grade for dielectric window applications was being developed [5]. For open resonant cavity measurements, samples are usually required to be of at least 30 mm in diameter and of thickness in excess of 0.87 mm depending on the measurement frequency and the accuracy required. For recent CVD diamond, values of tan 5 below 10 have been achieved. A specific example is a window 100 mm in diameter and 1.6 mm thick which exhibited a tan 8 value of 0.6 ( 0.2) 10 . This is the lowest value so far reported for CVD diamond and would enable the material to be used as output windows in Gyrotron tubes of powers in excess of 2 MW as discussed in 2.4. 

Eradat-Oskouvei, N., et al. 1997. Laser properties of luminescent conducting polymers in open resonators. Proc SPIE 3148 352. 

Henry, C. H. (1986). Theory of spontaneous emission noise in open resonators and its application to lasers and optical amplifiars, J. Lightwave Technol. LT-4, 288-297. 

The function of the optical resonator is the selective feedback of radiation emitted from the excited molecules of the active medium. Above a certain pump threshold this feedback converts the laser amplifier into a laser oscillator. When the resonator is able to store the EM energy of induced emission within a few resonator modes, the spectral energy density p(v) may become very large. This enhances the induced emission into these modes since, according to (2.22), the induced emission rate already exceeds the spontaneous rate for p(v) > hv. In Sect. 5.1.3 we shall see that this concentration of induced emission into a small number of modes can be achieved with open resonators, which act as spatially selective and frequency-selective optical filters. 

These open resonators are, in principle, the same as the Fabry-Perot interferometers discussed in Chap. 4 we shall see that several relations derived in Sect. 4.2 apply here. However, there is an essential difference with regard to the geometrical dimensions. While in a common FPI the distance between both mirrors is small compared with their diameter, the relation is generally reversed for laser resonators. The mirror diameter 2a is small compared with the mirror separation d. This implies that diffraction losses of the wave, which... 

Fig. 5.4. Walk-off losses of inclined rays and reflection losses in an open resonator...

The mode configurations of open resonators can be obtained by an iterative procedure using the Kirchhoff-Fresnel diffraction theory [5.17]. Concerning the diffraction losses, the resonator with two plane square mirrors can be replaced by the equivalent arrangement of apertures with size 2a) and a distance d between successive apertures (Fig. 5.7). When an incident plane wave is traveling into the -direction, its amplitude distribution is successively altered by diffraction, from a constant amplitude to the final stationary distribution An(x,y). The spatial distribution An(x,y) in the plane of the nth aperture is determined by the distribution An- (x, y) across the previous aperture. 

Because the arrangement of successive apertures is equivalent to the plane-mirror resonator, the solutions of this integral equation also represent the stationary modes of the open resonator. The diffraction-dependent phase shifts 0 for the modes are determined by the condition of resonance, which requires that the mirror separation d equals an integer multiple of A/2. 

Fig. 5.13a-e. Some examples of commonly used open resonators... 

The stationary field configurations of open resonators, discussed in the previous sections, have an eigenfrequency spectrum that can be directly derived... 

G. Koppelniann Multiple beam interference and natural modes in open resonators. Progress in Optics 1 (North-Holland, Amsterdam 1969) pp. 1-66... 

In Sect. 2.1 we have seen that any stationary field configuration in a closed cavity (called a mode) can be composed of plane waves. Because of diffraction, plane waves cannot give stationary fields in open resonators, since the diffraction losses depend on the coordinates (x, y) and increase from the z-axis of the resonator towards its edges. This imphes that the distribution A x,y), which is independent of X and y for a plane wave, will be altered with each round-trip for a wave traveling back and forth between the mirrors of an open resonator until it approaches... 

Open resonator Dielectric (large) Dielectric 15-100 GHz Position sensitive... 

When the carbenium ion can be stabilized in a manner other than with a bridging bromine, the preference for anti addition diminishes. For example, cis- and frans-l-phenyl-propene give only 73% and 83% products from anti addition, respectively, while the remaining products are from syn addition (Eqs. 10.17 and 10.18). Here, there is an equilibrium between two forms of the carbenium ion a cyclic bromonium ion and an open, resonance stabilized benzyl cation. Syn addition and anti addition products can arise from the open form due to bond rotation, but only anti addition products can arise from the cyclic form. 

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