Cavity Fabry-Perot

An alternative approach to obtaining microwave spectroscopy is Fourier transfonn microwave (FTMW) spectroscopy in a molecular beam [10], This may be considered as the microwave analogue of Fourier transfonn NMR spectroscopy. The molecular beam passes into a Fabry-Perot cavity, where it is subjected to a short microwave pulse (of a few milliseconds duration). This creates a macroscopic polarization of the molecules. After the microwave pulse, the time-domain signal due to coherent emission by the polarized molecules is detected and Fourier transfonned to obtain the microwave spectmm. 

We have seen how the presence of shot noise dictates some key choices minimum laser power, beam and mirror diameter, necessity to use Fabry-Perot cavities in the arms. Other noise sources will fix other important optical parameters. 

Multicavity filters. Multicavity Fabry-Perot filters are used to make very narrow transmission filters. A simple Fabry-Perot cavity (see Ch. 2) consists of a halfwave layer surrounded by two reflectors of typically 10 layers each. Figure 4 shows three transmission profiles obtained with one, two or three cavity filters. The three cavity HL) 5HH(LH) 5) " 3 filter has a 1.2 nm bandwidth. It has 60 layers. Note that the three-peak top of the transmittance. Each cavity has to be well adapted to the following one if not the resulting transmittance can be very poor. Such cavities are broadly used in telecoms in between arrays of antennas for cell phones. 

Semiconductor laser diodes are widely used in CD players, DVDs, printers, telecommunication or laser pointers. In the structure, they are similar to LEDs but they have a resonant cavity where laser amplification takes place. A Fabry-Perot cavity is established by polishing the end facets of the junction diode (so that they act as mirrors) and also by roughening the side edges to prevent leakage of light from the sides of the device. This structure is known as a homojunction laser and is a very basic one. Contemporary laser diodes are manufactured as double heterojunction structures. 

Fabry-Perot cavity, 14 849, 850 Fabry-Perot etalons, 11 151, 152 Face-centered cube lattice, 8 114t Face-centered cubic (FCC) crystal structure in Ni-base alloys, 13 512 of spinel ferrites, 11 60 Facial makup, 7 846-847 Facial preparations, 7 842t Facial tridendate ligand, 7 578 Facihtated transport, 15 826-827 carrier, 15 845-846... 

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. 

To demonstrate the method an example of a slow-wave optical structure is modelled. Such structures consist of a cascade of directly coupled optical resonators in order to enhance the nonlinear effects. The structure used here was recently defined within Working Group 2 of the European Action COST Pll (http //w3.uniromal.it/energetica/slow waves.doc). One period of the structure consists of one-dimensional Fabry-Perot cavity placed between two distributed Bragg reflectors (DBR) and can be described by the sequence... 

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. 

Another recent notable technical advance has been the development of a pulsed Orotron source currently being used and tested in the 360 GHz system at Berlin. This electron-beam device (Smith Purcell free electron laser) has feedback via a high-Q Fabry-Perot cavity and thus features good frequency stability as well as pulse output powers at 360 GHz in the many tens of mW. 

An illustration of this fact comes from the nonlinear Schrodinger equation. This equation describes an electromagnetic wave in a nonlinear medium, where the dispersive effects of the wave in that medium are compensated for by a refocusing property of that nonlinear medium. The result is that this electromagnetic wave is a soliton. Suppose that we have a Fabry-Perot cavity of infinite extend in the x direction that is pumped with a laser [6,7]. The modes allowed in that cavity can be expanded in a Fourier series as follows ... 

There are two possible approaches towards making feasible devices. One approach is to develop device structures that need smaller coefficients to operate, e.g lossy Fabry-Perot cavities (8), the other approach is to trade-off some of the speed and low loss in current organics for larger responses, for instance by tuning into resonances. In this paper we will explore the latter route and show how this can be achieved in some materials whilst maintaining, at acceptable levels, the critical figures of merit relating the nonlinear refraction to linear loss and two photon absorption to nonlinear refraction. 

The light source is a home made CM ring LD 700 dyo laser, pumped by a Kr+ laser. In the range 730-780 nm (wavelength of the two-photon 2S-nD transitions for n 8 it provides a power of about 1W on single mode operation. The frequency stabilization is made by locking the laser to an external auxiliary Fabry-Perot cavity indicated FPA in Fig.2 the resulting... 

A Fabry-Perot cavity (shown in Fig.l) having its optical axis coincident with the metastable atomic beam provides a standing wave that induces the two-photon transitions- This cavity is locked to the laser frequency in order to increase the intensity of the standing wave to 50W in each propagation direction. 

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. 

The line position (relative to the frequency determined by the reference Fabry-Perot cavity) obtained from the fit is then investigated as a function of the light power (see Fig.6) extrapolation to zero light power gives the value corrected for light shifts. 

The absolute frequency position of the two-photon transition is measured by comparing the infrared dye laser wavelength with an I - stabilized He-Ne reference laser at 633 nm (see Fig.2). The hey of the wavelength comparison is a nonconfocal etalon Fabry-Perot cavity (indicated as FPE in Fig.2) kept under a vacuum better than 10-6 mbar. This optical cavity is built with two silver-coated mirrors, one flat and the other spherical (R = 60 cm), in optical adhesion to a zerodur rod. Its finesse is 60 at 633 nm and 100 at 778 nm. An auxiliary He-Ne laser as well as the dye laser are mode-matched and locked to this Fabry-Perot cavity. Simultaneously the beat frequency between the auxiliary and etalon He-Ne lasers is measured by a frequency counter. 

The frequencies at the red and infrared radiations inside the etalon Fabry-Perot cavity are determined by the resonant condition /10/... 

A schematic diagram of the spectrometer is shown in figure 10.16 its successfid operation depends critically upon the ability to achieve accurate timing for a sequence of several events. First, a short pulse of gas is produced from a pulsed-nozzle source, the gas travelling in a direction perpendicular to the axis of an evacuated Fabry Perot cavity, described later. This gas pulse lasts for about 1 ms, and the expansion in the cavity is in an essentially collision-free environment... 

The most important and unique part of a Fourier transform microwave spectrometer is the Fabry Perot cavity. A fairly complete description of the principles has been given by Balle and Flygare [14] and we here summarise the main aspects, with the aid of figure 10.19. We use the cavity built by Balle and Flygare as a typical example. It is formed by two parallel, spherical concave mirrors made from solid aluminium. The mirrors are 36 cm in diameter, have a radius of curvature (R) of 84 cm, and are situated... 

Figure 10.19. Geometry of a microwave Fabry-Perot cavity.

The electric dipole interaction of the standing wave electric field in a Fabry-Perot cavity with a two-level system has been treated theoretically by Campbell, Buxton,... 

The gaseous sample was produced by using argon as a carrier gas, passing over CuCl or CuBr powder exposed to pulses from an ArF excimer laser, and injected through a pulsed nozzle into the Fabry Perot cavity. In contrast to the earlier work on the rare earth oxides mentioned above, the nozzle expansion was injected along the axis of the microwave cavity, rather than with the perpendicular orientation illustrated... 

Figure 10.38. Laser ablation pulsed nozzle source, for gas injection parallel to the axis of the Fabry-Perot cavity, described by Walker and Gerry [92].

The first stage was the production of a pulsed free-jet molecular beam of helium containing 20% CO, which was then crossed with an electron beam to produce ionisation. The ions were produced close enough to the beam nozzle for cooling to occur downstream. Some 4 cm from the nozzle the beam entered a confocal Fabry-Perot cavity where it was exposed to millimetre wave radiation close to 120 GHz in frequency. Following microwave excitation, when on resonance, the beam was probed with a Nd YAG pumped dye laser beam with the frequency chosen to drive rovibronic components of the A 2 U-X 2 + band system. Figure 11.54 shows two recordings of a spin component of the lowest rotational transition the line shown in (a) is... 

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. 

A5. Amity, I., Fabry-Perot cavity for millimetre and sub-millimetre electron spin resonance spectrometers. Rev. Sci. Imtrum. 41, 1492-1494 (1970). 

The second kind of cavity which has been used is Fabry-Perot cavity [10]. These cavities are completely tunable and have the advantage that they are open, allowing far better access to the atoms than the closed cavity shown in Fig. 1. The improved access was critical for measurements of angular distributions of the electrons ejected in microwave ionization [11]. Their cylindrical symmetry is useful for measurements involving circularly polarized microwaves, but a closed cylindrically symmetric cavity is equally good [12]. 

---