Homodyne beating

Equations 5.446 and 5.450 are applicable in the so-called homodyne method (or self-beating method), where only scattered light is received by the detector. In some cases, it is also desirable to capture by the detector a part of the incident beam that has not undergone the scattering process. This method is called heterodyne (or method of the local oscillator) and sometimes provides information that is not accessible by the homodyne method. It can be shown that if the intensity of the scattered beam is much lower than that of the detected nonscattered (incident) beam, the detector measures the autocorrelation function of the electrical held of the scattered light, dehned as... 

We will illustrate homodyne spectroscopy (self-beating spectroscopy) with some examples. 

Vol. 1, Sect. 5.6). Its intensity profile /(homodyne spectroscopy. The different fi equency contributions inside the line profile I (co) interfere, giving rise to beat signals at many different frequencies coi - cok < Aco [929]. If a photodetector is irradiated by the attenuated laser beam, the frequency distribution of the photocurrent (7.68) can be measured with an electronic spectrum analyzer. This yields, according to the discussion above, the spectral profile of the incident light. In the case of narrow spectral linewidths this correlation technique represents the most accurate measurement for line profiles [940]. 

The excitation rate of free carriers in a semiconductor depends upon the rate of absorption of photons, which is a measure of the intensity of the absorbed radiation. Because the intensity is proportional to the square of the electric field vector, a photoconductor or a photovoltaic detector is a square law detector. Therefore, an alternative to the conventional way of viewing photoexcitation is that the semiconductor acts as a mixer element, beating the electric field vector against itself in a homodyne manner. Thus if two coherent sources of radiation having different frequencies (wavelengths) are superimposed upon a semiconductor, mixing action will occur. The resultant intensity will contain the four terms shown below ... 

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]. 

The electric field autocorrelation function can be obtained in a heterodyne system, in which the scattered light is mixed with unscattered light from the laser source, thus obtaining a beat frequency. The characteristic exponential decay rate for the heterodyne correlation function is q DI2 that is, one-half the decay rate of the homodyne autocorrelation function. Sometimes there will be a partial heterodyne character to the autocorrelation function if unwanted stray light from the incident laser mixes with the scattered light, termed accidental heterodyning [16]. 

Self beating can be described as the result of comparing the signals from pairs of particles within the sample against each other. The homodyned signals are represented by FI and F2. The self beating frequencies can be considered as interference. 

Practically, a measurement may be neither self-beating nor homodyne. A careful judgement is then needed to apply the correct equations to resolve the dynamic information from the ACF. If the instmment efficiency coefficient (P) is known, Eq. 5.35 can be used to extract the field ACF from a scattering signal with an arbitrary ratio, where a is the intercept of the normalized intensity ACF, i.e., G Vt(0)/A = 1+a [94],... 

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