Reference laser

Fig. 61. Schematics of pressure-induced and applied-potential-induced BLM deformations. Application of hydrostatic pressure (by lowering a piston into the aqueous solution bathing the cis side of the BLM) displaces the BLM from position 1 to position 2. The displacement involves both translational (lateral) motion (Ft) and curvature increase (Fc). As indicated, deformation of the BLM is accompanied by a change in its torus (Plateau-Gibbs border). 2R and 2Rm represent the diameters of the aperture of the pinhole in the Tefzel film and that of the membrane (excluding the torus). The object laser beam, incident upon the trans side of the BLM and reflected by it at 45° at a shortened wavelength produces concentric optical interference fringes with the reference laser beam. Ag/AgCl electrodes, placed in the cis and trans sides of the BLM, allow for continuous electrical measurements [413]...

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. 

Finally we have compared our reference -stabilized He-Ne laser with that at the "Institut National de Mdtrologie" which had been previously compared with the standard He-Ne lasers of the "Bureau International des Poids et Mesures". As a result, the frequency of our reference laser relative to the lasers of the BIPM is known with a precision better than 10-11. 

This ideal FM spectrum can be Fourier transformed into the frequency domain to give a spectrum of equally spaced modes with a Bessel function amplitude distribution. These equally spaced modes can be used for comparing optical frequencies by heterodyning a reference laser, unknown laser and FM laser on a nonlinear detector. Three beats can be observed ie the beats between the reference laser and one of the modes of the FM laser, the beats between the unknown laser and one of the modes of the FM laser and the mode spacing of the FM laser. The separation between the reference and unknown laser can hence be deduced. 

A conceptually even simpler approach uses just one optical parametric oscillator, pumped by a dye laser or diode laser at 4f and oscillating at the two frequencies f and 3f. The signal frequency f is enforced by injection locking with light from the 3.39 pm reference laser. The pump frequency is adjusted so that the idler frequency agrees with the third harmonic of the reference laser. The seventh harmonic is then generated by simply summing idler and pump frequency. 

A laser whose frequency is unknown can be compared to a reference laser by heterodyne methods to high precision. Beat frequency measurements up to 2.5 THz in the visible spectrum have already been made. An alternative to simple heterodyne schemes is harmonic mixing by use of synthesis chains. 

The close relationship between the field of laser spectroscopy of atoms and molecules and the techniques used for laser fiequency stabilisation in precision length metrology might be worth underlining. Developments in laser spectroscopy for pure atomic physics research, such as various techniques of eliminating the Doppler effect (such as saturation absorption), have been instramental in the evolution of the frequency-stabilised reference laser systems used today in length metrology. 

A Fourier transform spectrometer is also a scanning wavemeter. It transfers the absolute frequency calibration of a reference laser to the frequencies of all lines in the FT spectrum. The I2, Te2, Br2, and H20 line atlases, with absolute accuracy on the order of 0.001cm-1, are measured by FT spectroscopy relative to the more accurately known frequency of the He-Ne laser. 

Non-zero covariance values in V, between experimental results from Q, come from experiments that are related. For instance, some contributions are common to some experiments performed with similar set-ups. An example is the set of hydrogen spectroscopy experiments performed at the Laboratoire Kastler Brossel in Paris [3, A2-A6 in Table XI, p. 49] the transitions frequencies measured there between the 2S level and other levels are correlated, as they used the same reference laser, the same line shape analysis method, similar estimates of the Stark effect contribution to the final transition frequencies, etc. Thus, any deviation of one of the measured frequencies from its central measured value implies a correlated deviation of any of its related measured frequencies. Corresponding non-zero, non-diagonal elements in the covariance matrix V quantify such correlations. 

Fig. 9.51 Laser output as a function of absorbed pump power (quasi-CW) of the 62-mm (undoped YAG, 0.25 % EriYAG, and 0.5 % Er YAG) composite ceramic rod and the 45-mm (0.5 % Er YAG) single-crystalline reference laser rod, with slope efficiencies being calculated from the dashed lines. Reproduced with permission from [319]. Copyright 2010, Cambridge Univtrsity Press...

The operation of FTIR spectrometers has been described in detail elsewhere, (see, for example. Refs. [4, 64]), as have the advantages of these over dispersive instruments [4, 5, 64]. Briefly, the heart of an FTIR spectrometer is the Michaelson interferometer (MI) (Fig. 6). The infrared beam leaves the source, S, and is incident on a beam-splitter, B. Fifty percent of the light is transmitted to a moving mirror, MM, and 50% to a fixed mirror, FM. On reflection, these rays recombine and interfere at the beam-splitter before reaching the detector, D, via the window, W, and reflective working electrode, WE, of the spectroelectrochemical cell. The system also includes a reference laser, RL, which follows the same path through the interferometer, after which it is intercepted and directed at the laser detector, LD. 

RL, reference laser S, infrared source W, cell window WE, working electrode. 

In each spectrometer both CO2 reference lasers are frequency modulated at a 1 kHz rate using piezoelectric drivers on the end mirrors and are then servoed to the line center of the saturated fluorescence signals obtained from the external low-pressure CO2 cells. The FIR detectors and lock-in amplifier detect at the modulation rate hence, the derivatives of the absorptions are recorded. The depth of the frequency modulation of CO2 laser I can be increased up to 7 MHz to enhance the FIR frequency modulation, thereby increasing the sensitivity for the broader lines. 

This extremely high stability can be transferred to tunable lasers by a special frequency-offset locking technique [221]. Its basic principle is illustrated in Fig. 2.20. A reference laser is frequency stabilized onto the Lamb dip of a molecular transition at coq. The output from a second, more powerful laser at the frequency (D is mixed in detector D1 with the output from the reference laser at the frequency coq- An electronic device compares the difference frequency coq — co with the frequency co of a stable but tunable RF oscillator, and controls the piezo P2 such that a>o — CO = co dt all times. The frequency co of the powerful laser is therefore always locked to the offset frequency co = coo — co which can be controlled by tuning the RF frequency co. ... 

Height relative to reference (laser, infrared or ultrasonic sensor)... 

In Eq. (1) above the frequency of the RF/microwave synthesizer is predetermined by the operator or computer program, the I.F. frequency is very accurately measured (and averaged if so desired) even in the presence of appreciable frequency modulation (which may be necessary in order to line-center lock either or both lasers) thus the absolute accuracy of the TDL output frequency, vtdl will, to a very large degree, depend on the absolute accuracy, resettablllty and long term stability of the reference lasers(s). The most accurate results obtained to date were achieved with the use of COj reference lasers these will be briefly summarized in the next section. For detailed description of techniques and results the readers are referred to the references cited, which were either recently published or are about to be published. 

In principle at least, CO isotope lasers can most conveniently serve as reference lasers in the 4.9 to 8.0 pm wavelength domain. In terms of spectral purity, sealed-off operation ) a d abundance of readily available lasing transitions CO isotope lasers are at least as good as their COi counterparts. Lamb-dip stabilization of CO lasers was also accomplished 3) nearly 15 years ago. However, the resettability of the Lamb-dip stabilization method is at least 100 times less accurate than the 4.3 pm fluorescence stabilization of CO2 lasers. The absolute accuracy of presently available CO laser transition frequencies is also only good to within about one or two MHz. If one MHz or so accuracy is not sufficient, a direct comparison of a CO reference laser line with an appropriately selected frequency doubled line-center stabilized CO2 laser transition is always possible and was so demonstrated several years ago. ... 

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