Fabry-Perot cavity length

Figure 12.17. (a) Diode laser band structure. (1) In thermal equilibrium. (2) Under forward bias and high carrier injection. Ec, v, and f are the conduction band, valence band, and Fermi energies respectively, (b) Fabry-Perot cavity configuration fora GaAs diode laser. Typical cavity length is 300//m and width 10/tm. d is the depletion layer. 

Enhancement of the Hght-matter interaction in a microscopic optical cavity is achieved because Hght trapped in the cavity has longer effective interaction time with absorbers. For short laser pulses, cavity length exceeding CTp allows avoidance of the interference between the pulses incident and reflected from the mirrors. Spectral selectivity of planar Fabry-Perot cavities can be used to achieve the localization at the resonant wavelength of the cavity. 

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... 

He-Ne laser. The frequency of the shifted infrared beam is locked to this reference Fabry-Perot cavity whose length is fixed. By changing the acousto-optic modulation frequency, which is provided by a computer-controlled frequency synthesizer, we can therefore precisely control the dye laser frequency over a range of 250 MHz centered at any desired frequency. 

These quantities characterize a Fabry-Perot cavity, or a laser cavity. I is the cavity spacing, and 21 is the round-trip path length. The free spectral range is the wavenumber interval between successive longitudinal cavity modes. 

Rcav is the effective cavity volume that is occupied by the electric field. The electric field in a Fabry-Perot cavity operating in TMqo mode is largely confined to a cylindrical element of radius (Al/2 r)i and length L equal to the mirror spacing (Section 2.1). The term cEqE equates to the power density term P in the Karplus and Schwinger equation. The power broadening contribution in that equation therefore becomes for a Fabry-Perot cavity... 

The first concave mirror in Figure 20 is not essential, but in many experiments the energy density is increased by placing the experimental cell in a spherical concentric Fabry-Perot cavity. The windows of the experimental cell must be tilted at the Brewster angle to reduce the losses in the cavity. The length of this cavity is piezoelectrically locked on the Laser frequency, to maximize the signal transmitted throug it. 

The structure of a FBG Fabry-Perot cavity sensor is shown in Fig. 10.4(a), which consists of two identical FBGs separated by a short cavity with a length of L. If the reflectivity of the two FBGs, Rg X is small, the reflection spectrum of the FBG Fabry-Perot cavity sensor, RgcW, is approximately given by ... 

A typical interferometric gravitational-wave detector, shown schematically in Fig. 7, is basically a Michelson interferometer with Fabry-Perot cavities (up to 4 km long) in each arm. These cavities increase the change in the optical path difference produced by arty change in the length of the arms by a factor eqtral to the ntrmber of times the bearrrs traverse the cavities. To reduce serrsitivity to fluctuatiorrs... 

The second solution is the use of Fabry-Perot cavities, where the laser spots from aU reflections coincide. A Fabry-Perot cavity consists of two plane mirrors at distance L. The power transmitted by the cavity is maximum at the resonance, when kL = nit, where is the wave vector. In this case, the power trapping in the cavity replaces the many round-trips of the laser beam. The phase of the light leaving from the cavity depends on the cavity length. If the cavity is working at resonance, the passage of a gravitational wave produces a phase shift near the resonance. The resonance characteristics of the Fabry-Perot cavity are described by the finesse F, which is related to the reflectivities ri, ri of the mirrors ... 

The VIRGO project is a French/Italian collaboration using a 3-km arm length detector close to Pisa, Italy. The Michelson interferometer is equipped with Fabry-Perot cavities. The seismic attenuation system is the combination of an inverted pendulum for preisolation and a five-stage pendulum cascade (superattemator). The arrangement allows for an extension of the sensitivity band down to 4 Hz. The interferometer is actually under constmction and is expected to be operative in 2002. 

The TAMA300 project is a Japanese interferometer with 300-m arm length and Fabry-Perot cavities. The detector began operating in 1999 with a sensitivity of 3 X 10 and has recently set an upper limit of 0.59 hr on the rate of coalescence of close binary neutron stars. 

Fig. 11 Geometry of interferometers and basic components. 1 Mach-Zehnder d interaction distance of light and sensing region. 2 Young M microscope objective, / length of the sensing window, d distance between the parallel channels, L lens, Z distance between the CCD camera and the end face of the interferometer. 3 Fabry-Perot G parallel mirrors, d distance between mirrors or the medium filling the cavity, L lens...

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 ... 

Aside from the active material a feedback mechanism is essential to complete a laser structure. In a simple case, a Fabry-Perot resonator may be utilized for this purpose by placing the organic material between two parallel mirrors. Here, standing electromagnetic waves are formed with wavelengths determined by the cavity length I and the effective refractive index neg- of the waveguide,... 

The effect of admitting an absorbing gaseous sample into a Fabry-Perot, or any resonant cavity, is to lower its Q by an amount proportional to the absorption coefficient a defined as the power attenuation per unit length traversed. Thus the incident power Pq is reduced to P ... 

A Fabry-Perot (FP) interferometer can be used in an optical sensing system to pass a specific part of the spectrum, functioning like a monochromator. An FP structure is the most suitable for passband optical filters. A Fabry-Perot optical filter consists of two parallel mirrors with a resonance cavity in the middle (Fig. 2). The equation 7u = 2nd shows its operation principle, where n is the refractive index of the cavity medium, d the cavity length, X the incident wavelength, and q the interference order q = 1,2,3,...). 

Cavity-based laser, a true laser, where the active medium is bound within a cavity of length L, has optical feedback such as mirrors for a linear Fabry-Perot case [97], a ring for whispering gallery mode of operation [120], or distributed feedback-type cavities [121]. In this type of laser the SE beam travels many times inside the resonator within the time dmation Tq determined by the laser Q-factor [97], which is given by the formula [122] ... 

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