Wavelength Modulation Spectroscopy
335
4.1 Simultaneous Modulation of Intensity and Frequency
A typical WMS experimental setup is shown in Fig. 7a. The only additions to the
setup used in direct detection is a high-frequency signal generator and a lock-in
amplifier. In WMS, a high-frequency sinusoid (tens of kHz) is superimposed on the
low frequency ramp signal (few Hz) and this doubly-modulated current waveform is
injected into the laser. The injection current i(t) may be written as,
i(t) = i 0 + i cos(ω m t)
(12)
where i(t) is the instantaneous value of the current, i 0 is the slowly varying value of
the bias current, and i is the amplitude of the sinusoidal current modulation and ω m
is the angular frequency of modulation (rad s
−1 ). The component i 0 varies much more
slowly than the modulation component and it’s time-dependence has therefore been
suppressed to simplify the expression. The current ramp slowly sweeps the emission
wavelength across the gas line as before, while the sinusoidal component introduces
additional wavelength modulation (WM) about the slowly-varying wavelength. This
is illustrated in Fig. 7a that shows the sinusoidal WM being applied about two very
different points A and B on the gas line. The current modulation introduces timevarying electron and hole concentrations in the active region of the pn junction diode,
which produces a time-varying refractive index. This effect gives rise to the WM.
The current also causes heating of the active region that also modulates the laser
cavity length and therefore of the oscillating frequency. The time-varying electron
and hole concentrations in the active region also naturally leads to time-varying
Fig. 7 a A typical WMS experimental setup and illustration of the process of spectral modulation.
b The variation of the first three Fourier components (H 1 , H 2 , H 3 ) with m showing that H 1 is the
dominant component. c The variation of the peak value of (H 1 , H 2 , H 3 ) with m. Note the slow
variation of H 1 and H 2 about m = 2.0 and m = 2.2 respectively
335
4.1 Simultaneous Modulation of Intensity and Frequency
A typical WMS experimental setup is shown in Fig. 7a. The only additions to the
setup used in direct detection is a high-frequency signal generator and a lock-in
amplifier. In WMS, a high-frequency sinusoid (tens of kHz) is superimposed on the
low frequency ramp signal (few Hz) and this doubly-modulated current waveform is
injected into the laser. The injection current i(t) may be written as,
i(t) = i 0 + i cos(ω m t)
(12)
where i(t) is the instantaneous value of the current, i 0 is the slowly varying value of
the bias current, and i is the amplitude of the sinusoidal current modulation and ω m
is the angular frequency of modulation (rad s
−1 ). The component i 0 varies much more
slowly than the modulation component and it’s time-dependence has therefore been
suppressed to simplify the expression. The current ramp slowly sweeps the emission
wavelength across the gas line as before, while the sinusoidal component introduces
additional wavelength modulation (WM) about the slowly-varying wavelength. This
is illustrated in Fig. 7a that shows the sinusoidal WM being applied about two very
different points A and B on the gas line. The current modulation introduces timevarying electron and hole concentrations in the active region of the pn junction diode,
which produces a time-varying refractive index. This effect gives rise to the WM.
The current also causes heating of the active region that also modulates the laser
cavity length and therefore of the oscillating frequency. The time-varying electron
and hole concentrations in the active region also naturally leads to time-varying
Fig. 7 a A typical WMS experimental setup and illustration of the process of spectral modulation.
b The variation of the first three Fourier components (H 1 , H 2 , H 3 ) with m showing that H 1 is the
dominant component. c The variation of the peak value of (H 1 , H 2 , H 3 ) with m. Note the slow
variation of H 1 and H 2 about m = 2.0 and m = 2.2 respectively