Frequency Modulation

According to the frequency modulation technique the continuous narrow band laser frequency $\omega_L$ is modulated at the much smaller modulation frequency $f$, which turns $\omega_L$ periodically from $\omega_L$ to $\Delta\omega_L$. When laser is turned through the absorption spectrum, the difference $I(\omega_L)-I(\omega_L+\Delta\omega_L)$ is detected with a phase-sensitive detector (lock-in amplifier) tuned to the frequency $f$. If the modulation sweep $\Delta\omega_L$ is small, the first term of the Taylor expansion

$$I(\omega_L+\Delta\omega_L)-I(\omega_L) \simeq \frac{dI}{d\omega}\Delta\omega_L$$ (79)

is dominant. It is seen that this term is proportional to to the first derivative of the absorption spectrum. When $I_0$ is independent on $\omega$ we obtain from eq. (77)

$$\frac{d k(\omega)}{d\omega} = -\frac{1}{I_0l}\frac{d I(\omega)}{d\omega}.$$ (80)

Thus, the absorption signal in the technique is proportional to the derivative of the absorption spectrum. The advantage of the spectroscopy with a frequency modulation of the laser is great restriction of the frequency response of the detection system due to the phase-sensitive detection to the narrow frequency interval centered at the modulation frequency $f$. Therefore, low-frequency background noise due to fluctuation of the laser intensity, or other experimental conditions is essentially reduced.

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