Spectroscopy heterodyne

Heterodyne spectroscopy uses two cw lasers with the frequencies coi and 0)2 (Ao) = 0)1 — 0)2 o)j, 0)2), which are stabilized onto two molecular transitions sharing a common level (Fig. 12.22). Measurements of the difference frequency of the two lasers then immediately yields the level splitting AE = El — E2 = hAo) of the molecular levels 1) and 2). 

For sufficiently low difference frequencies (Av = Ao)f2n 10 Hz) fast photodiodes or photomultipliers can be used for detecting Ao). The two laser beams are superimposed onto the active area of the detector. The output signal S of the photodetector is proportional to the incident intensity, averaged over the time constant r of the detector. For Aco In lx o)= (oji - -0)2) 12 

The accuracy of stabilizing the two lasers onto molecular transitions increases with decreasing linewidth. Therefore, the narrow Lamb dips of Doppler-broadened molecular transitions measured with saturation spectroscopy (Sect. 7.2) are well suited [12.76]. This was proved by Bridges and 

Chang [12.77] who stabilized two CO2 lasers onto the Lamb dips of different rotational lines within the vibrational transitions (00° 1) (10°0) at 10.4 xm 

Ezekiel and coworkers [12.78] used the reduction of the Doppler width in a collimated molecular beam (Sect. 9.1) for accurate heterodyne spectroscopy. The beams of two argon lasers intersect the collimated beam of I2 molecules perpendicularly. The laser-induced fluorescence is utilized to stabilize the laser onto the centers of two hfs components of a visible rotational transition. The difference frequency of the two lasers then yields the hfs splittings. 

The accuracy of stabilizing the two lasers onto molecular transitions increases with decreasing linewidth. Therefore, the narrow Lamb dips of Doppler-broadened molecular transitions measured with saturation spectroscopy (Sect.7.2) are well suited [12.70]. This was proved by Bridges and Chang [12.71] who stabilized two CO2 lasers onto the Lamb dips of different rotational lines within the vibrational transitions (00° 1) — (10°0) at 10.4 nm and (00° 1) - (02° 0) at 9.4 fim. The superimposed beams of the two lasers were focussed into a GaAs crystal where the difference frequency was generated. 

Instead of two different lasers a single laser can be employed when its output is amplitude-modulated at the variable frequency f. Besides the carrier frequency Uq two tunable sidebands appear. If the carrier frequency Uq is stabilized onto a selected molecular line, the sidebands can be tuned across other molecular transitions (sideband spectroscopy [12.73,74]. The experimental expenditure is smaller since only one laser has to be stabilized. The sideband tuning can be achieved with acousto-optical modulators at relatively small RF powers. The difference frequency Aw is, however, restricted to achievable modulation frequencies (Aw 2jrf ,a3j). 

In most of the methods discussed so far in high-resolution laser spectroscopy, the laser frequency was tuned across the molecular absorption spectrum and the frequency separation of different lines was determined either by interpolation between frequency marks provided from a long F.P.I., or by absolute wavelength measurements, using one of the methods explained in Sect.4.4. For many problems in spectroscopy, however, it is important to know accurately the splittings of closely separated lines rather than their absolute wavelengths. Examples are the hfs, Zeeman, or Stark splittings. 

Up to now the heterodyne technique is the most accurate method to determine such line splittings. Its accuracy is comparable with the optical-rf double-resonance method but its application range is more general. Two independent lasers are stabilized onto the line centers of two different molecular transitions (Fig.10.48). The output of the two lasers is superimposed on a nonlinear detector, such as a photomultiplier in the visible range or a semiconductor diode in the infrared. 

If both transitions share a common level, the difference frequency immediately gives the separation of the two other levels. We illustrate this technique by several examples. 

The range of difference frequencies which is experimentally accessible can be enlarged by mixing these frequencies further with harmonics of a microwave generator. The difference frequency of this second mixing is then directly counted [10.66]. 

This technique has been applied for example to study infrared line profiles in the planetary atmospheres. For further applications and more details see [10.69,70]. 

Up to now the hyperfine transition in the ground state of the Cs-atom at 9.192 GHz represents the accepted frequency standard. An alternative to the cesium atomic fountain is the dark resonance of Cs atoms in a cell when a coherent dark state of the hyperfine levels is realized where the optical transition is excited by a frequency modulated laser with a modulation frequency which matches the hyperfine splitting in the Cs ground state. This modulation frequency can be used for the stabilization of the microwave which modulates the laser output. Since the dark resonance is very narrow, the uncertainty of the stable frequency is small. 

Heterodyne spectroscopy uses two cw lasers with the frequencies coi and C02 (Aco = coi — C02 1, which are stabilized onto two molecular transitions sharing 

---

A number of mixing experiments have therefore been used to generate both pulses and CW THz radiation. Among these, diode-based mixers used as upconvertors (that is, heterodyne spectroscopy m reverse ) have been the workliorse FIR instruments. Two such teclmiques have produced the bulk of the spectroscopic results ... 

Hamm P, Lim M, DeGrado WF, Hochstrasser RM. Two dimensional self-heterodyned spectroscopy of vibrational transitions of a small globular peptide. J Chem Phys 2000 112 1907-1916. 

Heterodyne spectroscopy can be used to measure the diffusion coefficient of a macromolecule and thereby the radius of the particle. This is done by either measuring the time constant zq in Fi(q, t) or the half-width at half maximum (oq of the spectrum where... 

The literature [61,63-82] r rs to QELS by many differoit names, some of which are spediic methods of implemratation. The.se include dynamic light scattering, laser scattering, laser Doppler velocimeby, intensity fluctuation spectroscopy, photon correlation spectroscopy (PCS), light beating spectroscopy and homo- and heterodyne spectroscopy. Most of the techniques discussed here are based on PCS. 

The autocorrelation function C(t) is the product of the intensity at a given time and a delayed value of the intensity averaged as a function of delay time (r). For monodisperse particle systems in homodyne detection mode (heterodyne spectroscopy allows detection of light at much lower intensities than homodyne), C(t) is a single decaying exponential defined as ... 

Fig. 7.28 Heterodyne spectroscopy with two lasers, stabilized onto two molecular transitions. The difference frequency, generated in a nonlinear crystal, is either measured or a second downconversion is used by mixing with a microwave...

Correlation spectroscopy is based on the correlation between the measured frequency spectrum S(co) of the photodetector output and the frequency spectrum I((jo) of the incident light intensity. This light may be the direct radiation of a laser or the light scattered by moving particles, such as molecules, dust particles, or microbes (homodyne spectroscopy). In many cases the direct laser light and the scattered light are superimposed on the photodetector, and the beat spectrum of the coherent superposition is detected (heterodyne spectroscopy) [12.81,12.82]. 

H.D. Riccius, K.D. Siemsen Point-contact diodes. Appl. Phys. A 35, 67 (1984) H. Rosser Heterodyne spectroscopy for submillimeter and far-infrared wavelengths. Infrared Phys. 32, 385 (1991)... 

H. Rosser Heterodyne spectroscopy for submillimeter and far-infrared wavelengths. Infrared Phys. 32, 385 (1991)... 

---