Beat Note

If two laser beams with different optical frequencies are superimposed on a photodetector measuring the optical intensity, a beat note – i.e., a signal with the difference of the optical frequencies – can usually be observed, if some conditions are met:

• The spatial distributions of the two light fields must overlap and must not be orthogonal. (For example, there may be no beat note if a laser beam with TEM₀₀ and TEM₀₁ modes excited hits a detector.) Somewhat clipping the beams, or even just some non-uniformity of the detector surface, can solve this problem.
• The polarization states also must not be orthogonal.
• The optical frequency difference must be within the bandwidth of the detector.
• Obviously, the wavelengths must be within the range where the photodetector is sensitive.

Figure 1: Superposition of two optical oscillations with a frequency difference of 25 THz. The bottom two curves show the electric field strengths of the isolated oscillations, and the top curve the additive superposition. A sufficiently fast intensity detector would record an oscillation of the power with the difference frequency.

As a fast photodetector can have a bandwidth of tens of gigahertz (or even higher), optical frequency differences of this order of magnitude can be measured e.g. by analyzing the photodetector output with an electronic frequency counter or an electronic spectrum analyzer. An important application of this is in frequency metrology. For example, the frequency of some laser can be measured by recording a beat note between that laser and a close-by optical signal with known optical frequency. Such measurements are greatly facilitated by an optical frequency comb which can cover a wide range of well-defined optical frequencies, so that a sufficiently nearby reference frequency for a beat measurement can be found for any frequency in this large range.

The linewidth of a beat note of two free-running lasers with uncorrelated laser noise is larger than the linewidth of each laser separately. However, the beat linewidth can be smaller if the phase noise of both lasers is at least partially correlated. In an extreme case, one of the lasers may be phase-stabilized so as to obtain a constant beat frequency, as defined e.g. by some electronic oscillator. The linewidth of the beat note, measured against a clock in synchronism with the electronic oscillator, can then be exactly zero, if the phase difference exhibits only small stationary fluctuations.

Optical beat notes are essential for the technique of optical heterodyne detection.

See also: frequency metrology, optical frequency, photodetectors, optical heterodyne detection, Spotlight article 2008-07-26, Spotlight article 2009-07-29
and other articles in the category optical metrology

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