Reflectivity finesse

When the reflectivity of the two end faces is low (e.g., 4% from an air-glass interface), the multiplex reflections in the cavity have negligible contribution to the optical interference. Under this circumstance, the FP cavity is commonly referred to as the low-finesse cavity and the signal can be modeled using a two-beam interference model, given by5,6 ... 

To sweep the dye laser its beam is split and the secondary beam is driven into an acousto-optic device. The frequency-shifted beam is reflected back into the acousto-optic crystal so that one of the emerging beams is shifted twice. This beam then enters a reference Fabry-Perot cavity (indicated as FPR in Fig. 2) of very high finesse, whose length is locked to an I2 - stabilized... 

In Fabry-Perot etalons, the cavity encloses air, a gas, or vacuum, while for interference filters transparent dielectric layers are used. The real length of the interfering beam is N times the length of the cavity, due to multiple reflection. /V, the so-called finesse, is determined by the reflectivity p of the mirrors N = K , /pl( - p). Therefore, the resolving power, as above, equals the length of the interfering beam in units of the wavelength ... 

In a reflection mode spectrometer of high finesse or quality factor Q, the reflected power when matched on resonance is many decibels below the incident power, which reduces the noise floor by many decibels with respect to a transmission mode resonator. When the ESR sample is resonant, the residual resonator mismatch changes, which causes the reflected power to change, and a small signal on a low background is presented to the detector. In order for the signal to be detected, however, it must be discriminated from the radiation incident on the resonator, just as in a conventional reflection mode ESR spectrometer. 

One simple method for varying the coupling is to construct the resonator from two polarizers. We can show (Tudisco, 1988) that the finesse of such a resonator is proportional to cos, where is the relative orientation of the two polarizers. This device is the quasioptical analog of the cavity coupling scheme of Lebedev (1990). There are several limitations to this scheme as pointed out by the author, namely, the radiation must be linearly polarized, which complicates transmit-receive duplexing in a reflection mode spectrometer on resonance, the power minimum occurs in transmission, which precludes using the device in a reflection mode spectrometer if we wish to work with low background levels. 

At each mirror, the reflected or transmitted wave is multiplied by a factor of r, or t- respectively. If the resonator has a large finesse, there will be many reflections and transmissions. A simple case where r, = rj = r and = t2 = t is shown in Fig. 12b. Each reflected wave picks up an amplitude coefficient r and each transmitted wave picks up a coefficient t. The individual waves are called partial waves. It is the sum of all of the partial waves shown in Fig. 12b that gives the resonator its characteristic... 

EBIT as shown in Fig. 2. The trapped Si + ions will lie at the laser beam waist within the enhancement cavity, and to keep the finesse of the cavity as high as possible it is necessary for the high reflectivity mirrors to lie within the EBIT vacnnm chamber. The Ti sapphire laser will be locked to the high finesse cavity nsing the rf sideband locking techniqne [33]. Fast frequency fluctuations will be corrected using an acousto-optic modulator in a double-pass configuration, whilst the slower branch of the servo loop will use a piezo-mounted mirror in the laser cavity. 

The relation between the overlap of the spontaneous emission spectrum and the cavity length is illustrated in Fig. 1.8, which shows the optical mode density of a short and a long cavity. Both cavities have the same mirror reflectivities and finesse. The natural emission spectrum of the active region is shown in Fig. 1.8(c). The best overlap between the resonant optical mode and the active region emission spectrum is obtained for the shortest cavity. Thus a cavity length of 2/2 provides the largest enhancement. 

Total finesses of the order of 50 can be obtained routinely for A./200 plates with R = 98%. Higher reflectivities only lower the transmission without appreciably increasing the finesse because other factors become dominant. 

The primary efficacy endpoint of FINESSE is the composite of all-cause mortality and post-MI complications within 90 days of randomization. Complications included in the endpoint are resuscitated ventricular fibrillation occurring >48 hours after randomization, rehospitalization or emergency department visit for congestive heart failure, and cardiogenic shock. This composite endpoint was chosen to reflect the physiological hypothesis that combination medical therapy prior to PCI will result in earlier and improved reperfusion, leading to improved myocardial salvage and, hence, decreased infarct size-dependent complications. 

The small amount of radiation that leaks out of the cavity is measured with an appropriate detector. The decay lifetime is affected by the presence of an absorbing species within the cavity. The high finesse, resulting from extremely well fabricated high reflective coatings on the cavity mirrors, translates into an effective path length of tens of meters. If a molecular beam expansion is performed within the cavity, the direct absorption by molecular clusters can be observed. Considerable attention has been paid to the theory associated with the use of both pulsed and cw lasers. This method, while still in its infancy, promises to be another useftil tool in the characterization of hydrogen-bonded neutral molecular clusters. 

A pair of low-reflectivity etalons (finesse of 1.8) reduces the BRF oscillating bandwidth to that of a single longitudinal cavity mode, the thin etalon of 7.5 cm FSR or -mm physical thickness, and the thick etalon of 0.33-cm FSR and 10-mm physical thickness. Two etalons of low finesse give less loss for the selected mode than a single high-finesse etalon, due to a more complete overlap of the interfering beams (less walk-off loss). In Fig. I la the thin-etalon transmission functions for the three central orders are shown as solid lines, and the products of the BRF and thin etalon functions (the composite filter) for several more orders are shown as dashed. The... 

Since we have assumed an ideal plane-parallel plate with a perfect surface quality, the finesse (4.53a) is determined only by the reflectivity R of the surfaces. In practice, however, deviations of the surfaces from an ideal plane and slight inclinations of the two surfaces cause imperfect superposition of the interfering waves. This results in a decrease and a broadening of the transmission maxima, which decreases the total finesse. If, for instance, a reflecting surface deviates by the amount X/q from an ideal plane, the finesse cannot be larger than q. One can define the total finesse F of an interferometer by... 

A plane, nearly parallel plate has a diameter D = 5 cm, a thickness d = 1 cm, and a wedge angle of 0.2". The two reflecting surfaces have the reflectivity R = 95%. The surfaces are flat to within A./50, which means that no point of the surface deviates from an ideal plane by more than A./50. The different contributions to the finesse are ... 

Wedge finesse with a wedge angle of 0.2" the optical path between the two reflecting surfaces changes by about 0.1A.(A, = 0.5p,m) across the diameter of the plate. For a monochromatic incident wave this causes imperfect interference and broadens the maxima corresponding to a finesse of about 20. 

This illustrates that high-quality optical surfaces are necessary to obtain a high total finesse [4.32]. It makes no sense to increase the reflectivity without a corresponding increase of the surface finesse. In our example the imperfect parallelism was the main cause for the low finesse. Decreasing the wedge angle to 0.1" increases the wedge finesse to 40 and the total finesse to 27.7. 

A much larger finesse can be achieved using spherical mirrors, because the demand for parallelism is dropped. With suflSciently accurate alignment and high reflectivities, values of F > 50 000 are possible (Sect 4.2.8). 

The total finesse of a confocal FPI is therefore mainly determined by the reflectivity R of the mirrors. For R = 0.99, a finesse F = n R/( — R) 300 can be achieved, which is much higher than that obtainable with a plane FPI, where other factors decrease F. With the mirror separation r = d = 3 cm, the free spectral range is 3 = 2.5 GHz and the spectral resolution is Au = 7.5 MHz at the finesse F = 300. This is sufficient to measure the natural linewidth of many optical transitions. With modem high-reflection coatings, values of F = 0.9995 can be obtained and confocal FPI with a finesse F > 10" have been realized [4.41]. 

A higher finesse F caused larger reflectivities of the reflecting films not only decreases the bandwidth but also increases the contrast factor. With R — 0.98 F = 4R/(l — R) = 9.8 x 10, which means that the intensity at the transmission minimum is only about 10 of the peak transmission. 

Because of imperfections of the alignment and deviations from ideal planes, the effective finesse is lower than the reflectivity finesse. With a value of = 50, which can be achieved, we obtain for nd I cm... 

A confocal FPI shall be used as optical spectrum analyzer, with a free spectral range of 3 GHz. Calculate the mirror separation d and the finesse that is necessary to resolve spectral features in the laser output within 10 MHz. What is the minimum reflectivity R of the mirrors, if the surface finesse is 500 ... 

Since the laser resonator is a Fabry-Perot interferometer, the spectral distribution of the transmitted intensity follows the Airy formula (4.57). According to (4.53b), the halfwidth Avr of the resonances, expressed in terms of the free spectral range 5y, is Avr = Sy/F. If diffraction losses can be neglected, the finesse F is mainly determined by the reflectivity R of the mirrors, therefore the halfwidth of the resonance becomes... 

Fig. 5.37a,b. Mode selection with a Fox-Smith selector (a) experimental setup (b) maximum reflectivity and inverted finesse /F of the Michelson-type reflector as a function of the reflectivity Rbs of the beam splitter for R2 = Rs= 0.99 and Abs = 0.5%... 

Figure 5.37b exhibits the reflectance / max for 0 = 2m7r and the additional losses of the laser resonator introduced by the Fox-Smith cavity as a function of the beam splitter reflectance / bs- Tho finesse F of the selecting device is also plotted for R2 = R3 = 0.99 and Abs = 0.5%. The spectral width Av of the reflectivity maxima is determined by... 

Figure 4.39 Finesse of a Fabry-Perot interferometer as a function of the mirror reflectivity R...

---