Spectroscopy heterodyne-polarization

In most detection schemes of saturation or polarization spectroscopy the intensity fluctuations of the probe laser represent the major contribution to the noise. Generally, the noise power spectrum PNoise(/) shows a frequency-dependence, where the spectral power density decreases with increasing frequency (e.g., l//-noise). It is therefore advantageous for a high S/N ratio to detect the signal S behind a lock-in amplifier at high frequencies /. 

This is the basic idea of heterodyne polarization spectroscopy [275, 276], where the pump wave at the frequency cop passes through an acousto-optical modulator, driven at the modulation frequency /, which generates sidebands at co = cop 2nf (Fig. 2.47). The sideband at coi = cop-h 2nf is sent as a pump beam through the sample cell, while the probe beam at frequency cop is split off the laser beam in front of the modulator. Otherwise the setup is similar to that of Fig. 2.22. 

The signal intensity transmitted by the analyzer P3 is described by (2.50). However, the quantity x = 2(co — a)Q — 27tf)/y now differs from (2.48) by the frequency shift /, and the amplitude of the polarization signal is modulated at the difference frequency / between pump and probe beam. The signal can therefore be detected 

The signal intensity transmitted by the analyser P3 is described by (7.41). However, the quantity x = 2(o)-Wo-2irf)/Tf now differs from (7.39) 

---

Fig. 2.47 (a) Experimental arrangement of heterodyne polarization spectroscopy (b) section of the Na2 polarization spectrum showing the hyperfine splitting of the R(24) rotational line of the spin-forbidden transition Eg Flu [276]... 

Levenson, M. D., and Eesley, G. L. 1979. Polarization selective optical heterodyne detection for dramatically improved sensitivity in laser spectroscopy. Appl. Phys. 19 1-17. Librizzi, R, Viapianni, C., Abbruzzetti, S., and Cordone, L. 2002. Residual water modulates the dynamics of the protein and of the external matrix in trehalose-coated MbCO An infrared and flash-photolysis study. J. Chem. Phys. 116 1193-1200. 

The description of pump-probe signals presented in the preceding section can be immediately generalized to heterodyne-detected transient grating spectroscopy as well as to other four-wave mixing techniques. Heterodyne detection involves mixing the scattered field with an additional heterodyne field 4(r). The signal in the ks direction can then be written in terms of the polarization Ts(t) as... 

M.D. Levenson, G.L. Eesley, Polarization selective optical heterodyne detection for dramatically improved sensitivity in laser spectroscopy. Appl. Phys. 19, 1 (1979)... 

Besides various detection mechanisms (e.g. stimulated emission or ionization), there exist moreover numerous possible detection schemes. For example, we may either directly detect the emitted polarization (oc PP, so-called homodyne detection), thus measuring the decay of the electronic coherence via the photon-echo effect, or we may employ a heterodyne detection scheme (oc EP ), thus monitoring the time evolution of the electronic populations In the ground and excited electronic states via resonance Raman and stimulated emission processes. Furthermore, one may use polarization-sensitive detection techniques (transient birefringence and dichroism spectroscopy ), employ frequency-integrated (see, e.g. Ref. 53) or dispersed (see, e.g. Ref. 54) detection of the emission, and use laser fields with definite phase relation. On top of that, there are modern coherent multi-pulse techniques, which combine several of the above mentioned options. For example, phase-locked heterodyne-detected four-pulse photon-echo experiments make it possible to monitor all three time evolutions inherent to the third-order polarization, namely, the electronic coherence decay induced by the pump field, the djmamics of the system occurring after the preparation by the pump, and the electronic coherence decay induced by the probe field. For a theoretical survey of the various spectroscopic detection schemes, see Ref. 10. 

To summarize, the EOM-PMA considerably facilitates the computation of various optical signals and 2D spectra. With shght alterations, the EOM-PMA can also be applied to compute nonlinear responses in the infrared (IR). The three-pulse EOM-PMA can be extended to calculate the A-pulse-induced nonhnear polarization [51], which opens the way for the interpretation of fifth-order spectroscopies, such as heterodyned 3D IR [52], transient 2D IR [53, 54], polarizability response spectroscopy [55], resonant-pump third-order Raman-probe spectroscopy [56], femtosecond stimulated Raman scattering [57], four-six-wave-mixing interference spectroscopy [58], or (higher than fifth order) multiple quantum coherence spectroscopy [59]. 

H. Watanabe, S. Yamaguchi, S. Sen, A. Morita, and T. Tahara,/. Chem. Phys., 132, 144701 (2010). Half-Hydration At the Air/Water Interface Revealed by Heterodyne-Detected Electronic Sum Frequency Generation Spectroscopy, Polarization Second Harmonic Generation, and Molecular Dynamics Simulation. 

Kostiuk, T., Mumma, M. J., Espenak, E, Deming, D., Jennings, D. E., Maguire, W., Zipoy, D. (1983). Measurements of shatospheric ethane in the Jovian South Polar Region from infrared heterodyne spectroscopy of the vg band near 12 ixm. 

---