3.1 Modulation of light fields

Laser interferometers typically use three different types of light fields: the laser with a frequency of, for example, f ≈ 2.8 ⋅ 1014 Hz, radio frequency (RF) sidebands used for interferometer control with frequencies (offset to the laser frequency) of f ≈ 1 ⋅ 106 to 150 ⋅ 106 Hz, and the signal sidebands at frequencies of 1 to 10,000 Hz3. As these modulations usually have as their origin a change in optical path length, they are often phase modulations of the laser frequency, the RF sidebands are utilised for optical readout purposes, while the signal sidebands carry the signal to be measured (the gravitational-wave signal plus noise created in the interferometer).

Figure 15View Image shows a time domain representation of an electromagnetic wave of frequency ω 0, whose amplitude or phase is modulated at a frequency Ω. One can easily see some characteristics of these two types of modulation, for example, that amplitude modulation leaves the zero crossing of the wave unchanged whereas with phase modulation the maximum and minimum amplitude of the wave remains the same. In the frequency domain in which a modulated field is expanded into several unmodulated field components, the interpretation of modulation becomes even easier: any sinusoidal modulation of amplitude or phase generates new field components, which are shifted in frequency with respect to the initial field. Basically, light power is shifted from one frequency component, the carrier, to several others, the sidebands. The relative amplitudes and phases of these sidebands differ for different types of modulation and different modulation strengths. This section demonstrates how to compute the sideband components for amplitude, phase and frequency modulation.

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