Cavity resonance mode

Figure 2.8 A schematic diagram of the gain spectral profile, G(v), of a laser transition (solid line), together with the axial resonator modes (dotted line) of a cavity in which the frequency separation between adjacent modes is A v. (a) Multimode and (b) single-mode operation. The frequencies of those modes for which the gain exceeds the losses have been marked.

Considering that only reflection losses due to the mirrors of the cavity cause the decrease of the energy stored in the resonator modes, determine the expression for the mean lifetime of a photon in the resonator as a function of the reflectivities of the mirrors, R and R2. 

The 328 nm light is then coupled into a linear enhancement cavity placed inside the vacuum system. The metastable ions will ultimately be focused through the centre of the resonant mode of the cavity where they will interact with the light. The waist size of the fundamental mode of the cavity is around 100 /rm, chosen to make the transit-time broadening roughly equal to the natural width of the transition. A cavity is a convenient way of providing the counter-propagating beams required for the Doppler-free excitation of the two-photon transition,... 

The term c/2D gives the frequency separation between consecutive modes and is approximately 300 MHz for a mirror separation D of 50 cm. The shape of the cavity resonance is Lorentzian, and its full width at half height (Avc) is typically 1 MHz at a frequency vc of 10 GHz. The quality factor, Q, which is equal to vc/Avc, is approximately 104, which is high. 

Lasers have three primary components (Fig. 4) 1) an active medium that amplifies incident electromotive waves 2) an energy pump that selectively pumps energy into the active medium to populate selected levels and to achieve population inversion and 3) an optical resonator, or cavity, composed of two opposite mirrors a set distance apart that store part of induced emission concentrated in a few resonator modes. A population inversion must be produced in the laser medium, deviating from the Boltzman distribution thus, the induced emission rate exceeds the absorption rate, and an electromotive wave passing through the active medium is amplified rather than attenuated. The optical resonator causes selective feedback of radiation emitted from the excited species in the active medium. Above a pump threshold, feedback converts the laser ampler to an oscillator, resulting in emission in several modes. 

The situation changes drastically if the field mode is allowed to interact with some detector placed inside the cavity. Following other findings [188,189] we demonstrate the effect in the framework of a simplified model, when a harmonic oscillator tuned to the frequency of the resonant mode is placed at the point of maximum of the amplitude mode function v /mn(x,y L ) in the 3D rectangular cavity. 

While ANi describes the total spontaneous emission rate. A N refers to that part of it that remains in the cavity and contributes to the photon density q. A is related to the spontaneous emission coefficient A in a more complicated fashion which involves consideration of the resonator modes and the bandwidth of the transition. This will not be discussed in detail here. 2 25> The term Sq describes the output with the coupling coefficient... 

The experimental arrangement of the Yale experiment is shown in Fig. 3. A Na positron source of about 15 mCi is placed inside a microwave cavity resonant in the TMno mode at 2.323 GHz and filled with N2 gas to a pressure between 0.25 and 3 atm. Eight Nal(Tl) detectors count in coincidence 0.5 MeV annihilation y rays emitted at 180°. The magnetic field of about 8 kG is varied across the resonance line as indicated in Fig. 4. The signal is the increase in Ps(2y) rate, and the linewidth is determined principally by the lifetime of the M=0 triplet state. 

As has been pointed out above, a laser basically consists of an active material and a resonator. The latter enables the build-up of certain resonant modes and essentially determines the lasing characteristics. In most conventional devices, the optical feedback is provided by an external cavity with two end mirrors forming the resonator. With the advent of polymers as active materials, various new feedback structures were invented. Initially, a microcavity resonator device of the type shown schematically in Fig. 6.13 a was employed [48]. 

This mirror translation mechanism has to be made with some care in order to step the cavity resonant frequency 500 KHz as explained before. Considering the dominant mode, the resonant frequency was given as... 

The CRDS technique uses the same principle as intra-cavity spectroscopy, namely increasing the effective absorption path length. The difference is that in CRDS the absorption coefficient is determined from a time measurement, i.e., the decay time of the ringing cavity , while in intra-cavity spectroscopy the gain competition between different resonator modes is used as the enhancement factor. 

If several resonator modes within the bandwidth of the laser pulse are excited, beat signals are superimposed onto the exponential decay curve. These beats are due to interference between the different modes with differing frequencies. They depend on the relative phases between the excited resonator modes. Since these phase differences vary from pulse to pulse when the cavity is excited by a train of input pulses, averaging over many excitation pulses smears out the interference pattern, and again a pure exponential decay curve is obtained. 

If the modulator is placed inside the laser resonator with the mirror separation d and the mode frequencies = vo m cjld (m = 0,1,2,...), the sidebands coincide with resonator mode frequencies if the modulation frequency / equals the mode separation Av = cjld. The sidebands can then reach the oscillation threshold and participate in the laser oscillation. Since they pass the intracavity modulator they are also modulated and new sidebands y = vq i 2/ are generated. This continues until all modes inside the gain profile participate in the laser oscillation. There is, however, an important difference from normal multimode operation the modes do not oscillate independently, but are phase-coupled by the modulator. At a certain time the amplitudes of all modes have their maximum at the location of the modulator and this situation is repeated after each cavity round-trip time T = 2d c (Fig. 6.8c). We will discuss this in more detail The modulator has the time-dependent transmission... 

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