336
A. L. Chakraborty and A. Roy
electron-hole pair recombination events that gives rise to a synchronous intensity
modulation (IM) of the laser. The overall effect is that the high-frequency sinusoidal
modulation of the injection current results in simultaneous and synchronous WM
and IM that have a phase difference between them. The WM is of primary interest
because this makes it possible to scan and modulate the laser’s emission wavelength.
Unfortunately, it is not possible to eliminate the concomitant IM that introduces
significant levels of distortion in the signals of interest. This aspect is discussed later.
The simplicity of current tuning makes injection current modulated semiconductor
lasers very attractive for WMS applications.
The instantaneous emission frequency is given by,
ν(t) = ¯
ν + νcos(ω m t)
(13)
where ¯
ν is the slowly-varying emission frequency and ν is the FM amplitude. The
instantaneous laser intensity is written as, [6],
I (t) = I ( ¯
ν) + I 1 cos(ω m t + ψ 1 ) + I 2 cos(2ω m t + ψ 2 )
(14)
where I is the dc intensity that increases with the dc value of the injection current,
I 1 and I 2 are the 1st order (linear) and 2nd order (nonlinear) IM amplitudes
respectively, ψ 1 and ψ 2 are the phase differences between the FM and the 1st and
2nd order IM components respectively. The relatively strengths of I 1 and I 2
depends on the extent of nonlinearity of the laser. Higher order IM terms are usually
insignificant. The phase differences however depend on the type of laser and the
modulation frequency f m . These are obtained from DC and AC characterization of
the laser as explained later. Finally the relative transmission can be written as [4],
τ [ν(t)] =
I t
I (t)
= exp[−α( ¯
ν + ν cos ω m t)]
(15)
The absorbance α(ν) for a single absorbing species is given by,
α(ν) =
j
S j (T ) · P · x · φ j (ν) · L
(16)
where S j (T ) [cm
2 atm
−1 ] is the line-strength of the jth rotational-vibrational transition
at temperature T, P [atm] is the total pressure, x is the mole fraction of the target
species (only a single absorbing species assumed here), φ j (ν) [cm] is the transition
line shape and L [cm] is the optical path length. The interaction of the WM of the laser
with the gas absorption line is equivalent to a periodic modulation of the absorption
line about the wavelength values as the low-frequency current ramp slowly varies
the laser’s emission wavelength across the absorption line shape. Equation 15 can be
viewed as equivalent to spectral modulation of a nonlinear transfer characteristic. The
response to sinusoidal WM is therefore not sinusoidal and varies considerably across
the gas line shape even for constant input modulation amplitude. This is depicted in
A. L. Chakraborty and A. Roy
electron-hole pair recombination events that gives rise to a synchronous intensity
modulation (IM) of the laser. The overall effect is that the high-frequency sinusoidal
modulation of the injection current results in simultaneous and synchronous WM
and IM that have a phase difference between them. The WM is of primary interest
because this makes it possible to scan and modulate the laser’s emission wavelength.
Unfortunately, it is not possible to eliminate the concomitant IM that introduces
significant levels of distortion in the signals of interest. This aspect is discussed later.
The simplicity of current tuning makes injection current modulated semiconductor
lasers very attractive for WMS applications.
The instantaneous emission frequency is given by,
ν(t) = ¯
ν + νcos(ω m t)
(13)
where ¯
ν is the slowly-varying emission frequency and ν is the FM amplitude. The
instantaneous laser intensity is written as, [6],
I (t) = I ( ¯
ν) + I 1 cos(ω m t + ψ 1 ) + I 2 cos(2ω m t + ψ 2 )
(14)
where I is the dc intensity that increases with the dc value of the injection current,
I 1 and I 2 are the 1st order (linear) and 2nd order (nonlinear) IM amplitudes
respectively, ψ 1 and ψ 2 are the phase differences between the FM and the 1st and
2nd order IM components respectively. The relatively strengths of I 1 and I 2
depends on the extent of nonlinearity of the laser. Higher order IM terms are usually
insignificant. The phase differences however depend on the type of laser and the
modulation frequency f m . These are obtained from DC and AC characterization of
the laser as explained later. Finally the relative transmission can be written as [4],
τ [ν(t)] =
I t
I (t)
= exp[−α( ¯
ν + ν cos ω m t)]
(15)
The absorbance α(ν) for a single absorbing species is given by,
α(ν) =
j
S j (T ) · P · x · φ j (ν) · L
(16)
where S j (T ) [cm
2 atm
−1 ] is the line-strength of the jth rotational-vibrational transition
at temperature T, P [atm] is the total pressure, x is the mole fraction of the target
species (only a single absorbing species assumed here), φ j (ν) [cm] is the transition
line shape and L [cm] is the optical path length. The interaction of the WM of the laser
with the gas absorption line is equivalent to a periodic modulation of the absorption
line about the wavelength values as the low-frequency current ramp slowly varies
the laser’s emission wavelength across the absorption line shape. Equation 15 can be
viewed as equivalent to spectral modulation of a nonlinear transfer characteristic. The
response to sinusoidal WM is therefore not sinusoidal and varies considerably across
the gas line shape even for constant input modulation amplitude. This is depicted in