Fabry-Perot frequency

At 10Hz in a typical Nd-YAG laser 1000Hz/- /Hz, and the typical finesse asymmetry is of the order of one percent. In order to detect a gw signal the laser frequency noise has to be lowered by six orders of magnitudes (compared to the noise of a free running laser), and the two arms made as identical as possible. In order to achieve this complex frequency stabilization methods are employed in all interferometric detectors, and in order to insure the perfect symmetry of the interferometer, all pairs of Virgo optical components are coated during the same run (both Fabry-Perot input mirrors then both end mirrors are coated simultaneously). 

Let us consider an optical system with two modes at the frequencies oo and 2oo interacting through a nonlinear crystal with second-order susceptibility placed within a Fabry-Perot interferometer. In a general case, both modes are damped and driven with external phase-locked driving fields. The input external fields have the frequencies (0/, and 2(0/,. The classical equations describing second-harmonic generation are [104,105] ... 

Let us consider a quantum optical system with two interacting modes at the frequencies coi and ff>2 = respectively, interacting by way of a nonlinear crystal with second-order susceptibility. Moreover, let us assume that the nonlinear crystal is placed within a Fabry-Perot interferometer. Both modes are damped via a reservoir. The fundamental mode is driven by an external field with the frequency (0/ and amplitude F. The Hamiltonian for our system is given by [169,178] ... 

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. 

The joint gate function is centered around the frequency wo and the time to and acts as a filter on the bare signal /. As an example we shall consider the case when the spectral gate is given by the Fabri-Perot etalon [16] and the time gate is exponential,... 

KF-IO3 Hz. Since conventional spectrometers (e.g., a grating spectrometer or a Fabry-Perot interferometer) are not capable of resolving such small frequency shifts, it is necessary to rely on beating techniques to obtain the information contained in the scattered spectrum. 

Fabry-Perot fringes 1.3 GHz apart provide the frequency scale (from ref. 21). 

Laser spectroscopy of the 1S-2S transition has been performed by Mills and coworkers at Bell Laboratories (Chu, Mills and Hall, 1984 Fee et al, 1993a, b) following the first excitation of this transition by Chu and Mills (1982). Apart from various technicalities, the main difference between the 1984 and 1993 measurements was that in the latter a pulse created from a tuned 486 nm continuous-wave laser with a Fabry-Perot power build-up cavity, was used to excite the transition by two-photon Doppler-free absorption, followed by photoionization from the 2S level using an intense pulsed YAG laser doubled to 532 nm. Chu, Mills and Hall (1984), however, employed an intense pulsed 486 nm laser to photoionize the positronium directly by three-photon absorption from the ground state in tuning through the resonance. For reasons outlined by Fee et al. (1993b), it was hoped that the use of a continuous-wave laser to excite the transition would lead to a more accurate determination of the frequency interval than the value 1233 607 218.9 10.7 MHz obtained in the pulsed 486 nm laser experiment (after correction by Danzmann, Fee and Chu, 1989, and adjustment consequent on a recalibration of the Te2 reference line by McIntyre and Hansch, 1986). 

Moreover, in recent years broad band lasers have appeared which lack any frequency modal structure, at the same time retaining such common properties of lasers as directivity and spatial coherence of the light beam at sufficiently high spectral power density. The advantages of such a laser consist of fairly well defined statistical properties and a low noise level. In particular, the authors of [245] report on a tunable modeless direct current laser with a generation contour width of 12 GHz, and with a spectral power density of 50 /xW/MHz. The constructive interference which produces mode structure in a Fabry-Perot-type resonator is eliminated by phase shift, introduced by an acoustic modulator inserted into the resonator. 

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/... 

Figure 8 Frequency interval between the fundamental mode and the first transverse mode of the Fabry-Perot etalon, measured as a function of the orientation of the plane of incidence of the auxiliary He-Ne laser. Similar behaviour has been observed for the dye laser radiation... 

If we have a two-level sample we expect to see a series of resonances separated by half the inverse of the repetition rate of the laser as the carrier frequency is scanned. If a second transition is within the bandwidth of the laser then this too will give rise to a series of resonances. The resulting spectrum is rather like that obtained from a Fabry-Perot interferometer with overlapping orders. However, in the mode-locked case the modes are precisely equally spaced in frequency. 

The frequency distribution of the scattered light is analyzed with a Fabry-Perot interferometer. A detailed discussion of this instrument is given in Ref. 12,13, and 15. For the present chapter, it is most important... 

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... 

---