Heterodyne detection,

Heterodyne spectrometers achieve extremely high spectral resolution of about 10 to 10 cm in relatively narrow spectral intervals. The technique of heterodyning in the infrared resembles that used in heterodyne radio receivers. Radiation from an infrared source is superimposed by a beamsplitter with radiation from a local oscillator, a laser. The combined signals are then mixed in a nonlinear detector. The superimposed electric field at the detector is 

At the output of the detector, a signal appears with the beat frequency (the intermediate frequency, or IF), Am = in addition to the constant intensities 

Is = E and lo = E. The IF can be amplified using radio frequency (RF) techniques. The radio frequency circuits following the detector produce a time averaged signal proportional to the power in the oscillating term in Eq. (5.9.2), 

Phase information is no longer present in the output, and the recorded signal, S, is linearly proportional to the source intensity. Since each source frequency, t)s, is associated with an intensity, a spectrum, I ms), is produced by scanning the beat frequencies (difference between signal and local oscillator frequencies), or by using several fixed channels to detect all beat frequencies simultaneously. 

While the basic process is common to all heterodyne systems, differences exist between radio and infrared heterodyning. In radio receivers the local oscillator frequency is variable, permitting tuning of the receiver over a wide range, while the IF filters are set at a fixed frequency. In the infrared heterodyne spectrometer the typical local oscillator, a gas laser, operates at a fixed frequency. However, a small portion of the spectrum around each laser frequency can be reached with a radio frequency filter bank covering the intermediate frequencies. A source intensity. 

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Figure Al.6,8 shows the experimental results of Scherer et al of excitation of I2 using pairs of phase locked pulses. By the use of heterodyne detection, those authors were able to measure just the mterference contribution to the total excited-state fluorescence (i.e. the difference in excited-state population from the two units of population which would be prepared if there were no interference). The basic qualitative dependence on time delay and phase is the same as that predicted by the hannonic model significant interference is observed only at multiples of the excited-state vibrational frequency, and the relative phase of the two pulses detennines whether that interference is constructive or destructive.

In heterodyne detected. s + 1 wave mixing, phase infonnation is retained and one can take a fidl measure of... 

A connnon teclmique used to enliance the signal-to-noise ratio for weak modes is to inject a local oscillator field polarized parallel to the RIKE field at the detector. This local oscillator field is derived from the probe laser and will add coherently to the RIKE field [96]. The relative phase of the local oscillator and the RIKE field is an important parameter in describing the optical heterodyne detected (OHD)-RIKES spectrum. If the local oscillator at the detector is in phase with the probe wave, the heterodyne mtensity is proportional to... 

Tokmakoff A, Lang M J, Larson D S and Fleming G R 1997 Intrinsic optical heterodyne detection of a two-dimensional fifth order Raman response Chem. Phys. Lett. 272 48-54... 

F. R. Arams, E.W. Sard, B.J. Peyton, and F.P. Pace, Infrared Heterodyne Detection with... 

Diffractive Optics-Based Four-Wave Mixing with Heterodyne Detection... 

FIGURE 1.9 Schematic representation of the excitation, prohe, signal, and reference beams used for heterodyne detection in transient phase grating experiments. 

FIG U RE 1.10 Schematic representation of the experimental setnp for diffractive optics-hased fonr-wave mixing with heterodyne detection. (From Ogilvie, J. P., Plazanet, M., Dadusc, G., and Miller, R. J. D. 2002. J. Phys. Chem. 109 10460-67. With permission)... 

Dadusc, G., Ogilvie, J. R, Schulenberg, R, Marvet, U., and Miller, R. J. D. 2001. Diffractive optics-based heterodyne-detected four-wave mixing signals of protein motion From protein quakes to ligand escape for myoglobin. Proc. Nat. Acad. Sci. USA 98 6110-6115. 

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. 

Walther, M., Raicu, V., Ogilvie, J. R, Phillips, R., Kluger, R., and MiUer, R. J. D. 2005. Determination of the Pe-CO bond energy in myoglobin using heterodyne-detected transient thermal phase grating spectroscopy. J. Phys. Chem. B 109 20605-11. 

Heterodyne detection is widely used to improve the SNR of optical measurements. The additional advantage of heterodyne detection for CARS measurements is that it allows direct extraction of either real or imaginary parts of the susceptibility tensor (Vinergoni et al. 2004 Evans et al. 2004). Being introduced for CARS spectroscopy about 30 years ago (Eesley et al. 1978), heterodyne detection was for a long... 

Juma, M., Korterik, J. R, Otto, C., and Offerhaus, H. L. 2007. Shot noise limited heterodyne detection of CARS signals. Opt. Express 15 15207-13. 

Before melting and for some time after only the band at 625 cm of the AA [C4CiIm]+ cation was observed in the 600-630 cm i region. Gradually 603 cm i band due to the GA conformer became stronger. After about 10 min the AA/GA intensity ratio became constant. The interpretation [50] is that the rotational isomers do not interconvert momentarily at the molecular level. Most probably it involves a conversion of a larger local structure as a whole. The existence of such local structures of different rotamers has been found by optical heterodyne-detected Raman-induced Kerr-effect spectroscopy (OHD-RIKES) [82], Coherent anti-Stokes Raman scattering (CARS) [83],... 

This would give the noise power for a continuous wave (c.w.) microscope such as the transmission microscope described in 2.2. However, for a pulsed instrument with heterodyne detection the bandwidth is defined in the intermediate frequency (i.f.) stage, and the i.f. bandwidth A/ maybe used in (3.5). 

If vibration is applied both through the cantilever tip (at frequency oscillating force at the difference frequency cot — cos, very much like a heterodyne radio receiver. This technique is known as heterodyne force microscopy (HFM Cuberes et al. 2000). Once again, the tip-surface force non-linearity plays a critical role. The low-frequency beating oscillation carries information on the phase of the original high-frequency oscillations. 

In this contribution we present a study of ultrafast dynamics in liquid water employing heterodyne-detected TG and EPS techniques. Heterodyne detection allows us to separate the genuine photon echo signal that contains information on water dynamics, from thermal effects. The analysis of the experimental EPS data that includes thermal effects yields a 700-fs... 

Fig.l. (a) Experimental TG signal (solid line) and amplitudes of its additive components chromophore response (open circles) and solvent response (open squares) as found from the analysis of heterodyne-detected TG data. Inset the phase of the TG signal, (b) Experimental EPS data for the fixed delays to (empty circles) and t23 (solid circles), and the theoretical simulations (lines). Inset the excitation pulse spectra (shaded contour) and the absorption spectrum of the OH-stretch vibration of HDO molecules in D2O (dashed line). 

Combining TG experiment with heterodyne detection enabled us to obtain amplitudes and phases of the transient nonlinear polarizations. At short delays the response is mainly determined by the HDO molecules (Fig.la, open circles). However, at long delays the characteristics of the response change drastically it narrows in time, its phase is shifted by 7i(Fig.la, inset), and its spectrum becomes identical to the spectrum of the probe pulse. 

Therefore, the TG signal should originate from instantaneous nonlinearity, and for this reason, can not be related to HDO. This makes us conclude that the TG signal at long delays results from the grating written in the solvent, i.e. D2O. The analysis of heterodyne detected TG signal at different delay times yields the dynamics of the amplitudes of the on-resonant (HDO) and off-resonant (D2O) contributions to the total signal (Fig.la). 

To model the experimental data we used a global-fit procedure to simulate EPS, integrated TG, heterodyne-detected TG, and the linear absorption spectrum simultaneously. The pulse shape and phase were explicitly taken into account, which is of paramount importance for the adequate description of the experimental data. We applied a stochastic modulation model with a bi-exponential frequency fluctuation correlation function of the following form ... 

The quality of the fit is excellent as can be judged from Fig. 1(b). The following parameters of the frequency correlation function (Fig.lb, solid line) were obtained in the simulations 1/Afast 2 130 fs, Afas, = 90 cm 1, l/Asiow = 700 100 fs, Asiow = 65 cm 1. These results are in very good agreement with our previous findings from heterodyne-detected two-pulse photon echo experiments [19]. 

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