FM spectroscopy is a sophisticated heterodyne technique used to improve the sensitivity in laser spectroscopy.
FM spectroscopy records the phase shift imposed on a probe laser by a molecular or atomic line instead of its very weak absorption signal. The dispersive nature of the line-shapes acquired by FM spectroscopy with a linear slope and a zero-crossing on resonance makes them ideal to act as a lock signal for the frequency stabilization of lasers.
Role of Electro-Optic Modulator in FM Spectroscopy
The FM signal is generated in the standard Doppler-Free Saturation Absorption Spectroscopy (SAS) with counter-propagating beams through external frequency modulation of the probe laser by an electro-optic modulator, which generates sidebands in the laser spectrum with definite relative phases (+/- 90° relating to the carrier) (Figure 1). Beat signals that are detectable by a photodetector are absent as this modulation is pure phase modulation.
Figure 1. An electro-optic modulator is used to frequency modulate the probe laser externally to generate FM-signal in standard Doppler-Free SAS with counter-propagating beams.
All interferences between carrier and sidebands are canceled irrespective of several frequency elements in the spectrum. Even so, a phase shift is imposed between sidebands and carrier by an atomic or molecular transition because of its different refractive index on the blue and red side of the line. This causes a beat note and interferences at the modulation frequency f0.
Figure 2. Credit ESO in use
The comparison of the photodetector signal and the local oscillator (f0) at the right relative phase can generate the FM signal (i.e. the dispersive line-shape), which can be utilized as a locking signal for frequency stabilization of lasers. Generally, a modulation frequency f0 selected is well outside the laser noise and natural linewidth. The practical limitation is typically the functional bandwidth of the photodetector and RF circuit. The typical range of modulation frequencies is 10-100MHz.
Although a modulation index of roughly 1 rad (about 255 in each sideband) is selected for optimum signal/noise ratio, much weaker modulation < 0.1% is sufficient due to proportional variation of the beat signal to the geometric average of the intensities in carrier and sideband sqrt(I0*I1).
Variations of FM Spectroscopy
Two-Tone FM Spectroscopy (TTFM)
TTFM is advantageous in case of applying the FM principle to GHz broad lines, i.e., Doppler- or pressure-broadened. TTFM eliminates the use of a GHz photodetector. When the laser is modulated with two slightly different frequencies in the GHz range outside the linewidth, a Double-Resonance electro-optic modulator, for instance, can be used to observe a beat signal at the different frequency using a standard photodetector of lower bandwidth. The beat signal can then be used in the mixing process.
Modulation Transfer (MT) Spectroscopy
MT spectroscopy involves the separation of the counter-propagating pump and probe beams prior to the vapor cell and frequency modulation of only the pump beam by an electro-optic modulator. Within the natural atomic linewidth, it is possible to transfer this modulation in a four-wave mixing process (chi(3)) onto the weak probe beam, which then transmits a phase-sensitive amplitude modulated signal that can be recorded by a photodetector.
The configuration of MT spectroscopy is intricate when compared to standard FM spectroscopy. However, it provides well-defined signals of only the closed transitions free from any Doppler background. This means well defined zero-crossings without offset. It is essential for the electro-optic modulator have the modulation frequency f0 close to the natural linewidth. Qubig provides electro-optic modulator models with widely tunable resonance frequencies for MT spectroscopy for optimized MT signal.
This information has been sourced, reviewed and adapted from materials provided by Qubig GmbH.
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