Homodyne scheme

Hirose et al. [26] proposed a homodyne scheme to achieve the background-free detection of the fourth-order field. With pump irradiation in a transient grating configuration, the fourth-order field propagates in a direction different from that of the second-order field because of different phase match conditions. The fourth-order field is homodyned to make ffourth(td. 2 D) and spatially filtered from the second-order response hecond td, 2 D). 

The homodyne scheme is the most frequently utilized form of lightbeating spectroscopy. In the field of interfaces, however, the heterodyne detection scheme is most often applied. To give some examples of studies on interfaces that have been carried out during the last 15 years, we mention some papers that we believe to be representative. 

Fig. 7.7. Measured power spectrum of the photocurrent fluctuations (homodyne scheme) wavelength of the surface wave (bending mode) A = 11.1 pm, and the thickness of the film (/ij +2A ) —47.5 nm. The composition of the solution is the same as in Figs. 7.5 and 7.6.

In the simplest (homodyne) detection scheme one measures the time-integrated intensity of the field generated by the sample in a given direction ky ... 

In a homodyne detection scheme, such as in the stimulated photon echo experiments described in the next paragraph, the detector measures the t-integrated intensity of the square of the third-order polarization... 

First, let us show that the operational phase concepts can naturally be embedded in the general scheme of quantum estimation theory [66,67] as was done by Hradil, Zawisky, and others [68-71]. Let us consider the eight port homodyne detection scheme [63,72] with four output channels numbered by indices 3,4,5,6, where the actual values of intensities are registered in each run. Assume that these values fluctuate in accordance with some statistics. The mean intensities are modulated by a phase parameter 0... 

The squeezing mode experiments were carried out using the homodyne detection scheme with scattering angles within 20° of either the reflected beam ( q=60°) or the transmitted beam. A small region of 4° around either the transmitted or reflected beam was excluded because here a gradual, but not exactly reproducible, transition from homodyne to heterodyne detection is observed. 

In a homodyne detection scheme, the return beam is divided and additional phase shifts imposed by appropriate polarization optics (e.g., quarter- and half-wave plates), giving at least three phase shifts between them. Intensities at multiple detectors are combined to give phase (OPD) at nanometer resolution. 

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. 

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