Wavelength Modulation Spectroscopy
323
history, can also be measured and correlated to specific phases of growth. Such measurements allow for rapid, non-invasive, non-destructive antimicrobial susceptibility
testing (AST) [35], which is acknowledged to be an important clinical aspect [36, 37].
2 Spectroscopic Basis of TDLS
It is necessary to review some basic theoretical aspects of molecular spectroscopy
that assume great significance in WMS. The discussion is not exhaustive and the
interested reader is referred to authoritative texts [38, 39] that discuss these aspects
in greater detail.
2.1 Absorption of Light by Molecules
In a classical framework, the interaction of the molecule with an electromagnetic
wave is viewed as being analogous to a spring-mass system driven by an external
force. The flexible inter-atomic bonds bend and stretch along different axes at any
non-zero temperature. The bonds behave as simple harmonic oscillators when excited
by an electromagnetic waves and absorb energy from it. The absorption spectrum
corresponds to the resonance condition for a given mode of vibration. Energy is
efficiently transferred to the molecule if the wave’s frequency is within a narrow range
of the resonance frequency of these modes. The molecule then makes a transition from
a lower energy state to a higher energy state. Specifically, the infrared spectrum of a
molecule results from energy transitions within the molecule’s rotational-vibrational
energy levels. The infrared spectrum is considered as the spectral signature of the
molecule due to the characteristic position of the spectral lines that are unique to that
molecule. This specificity of infrared spectra is used in detection and quantification
of gases using laser spectroscopy.
In reality, molecular vibrations are distinctly anharmonic because real molecular
bonds do not obey Hooke’s law. The anharmonicity is pronounced for large vibration
amplitudes (approximately greater than 10% of the bond length). Figure 1 shows the
oscillating dipole, the potential energy variation and a typical line spectrum of a
diatomic molecule (CO in this case). Figure 1a shows the asymmetric stretching in
response to the driving electric field. Unlike a harmonic oscillator, the expression for
the potential energy is much more complicated and the spacing of the energy levels
reduces with energy. The potential energy curve shown in Fig. 1b of a diatomic
molecule is given by the purely empirical Morse function, E = D eq [1 − e
a(r−r eq )
]
2 ,
where, a is a constant for a molecule and D eq is the dissociation energy of the
molecule. When this expression is used to solve the Schrodinger equation, the allowed
quantized energy levels are given by,
323
history, can also be measured and correlated to specific phases of growth. Such measurements allow for rapid, non-invasive, non-destructive antimicrobial susceptibility
testing (AST) [35], which is acknowledged to be an important clinical aspect [36, 37].
2 Spectroscopic Basis of TDLS
It is necessary to review some basic theoretical aspects of molecular spectroscopy
that assume great significance in WMS. The discussion is not exhaustive and the
interested reader is referred to authoritative texts [38, 39] that discuss these aspects
in greater detail.
2.1 Absorption of Light by Molecules
In a classical framework, the interaction of the molecule with an electromagnetic
wave is viewed as being analogous to a spring-mass system driven by an external
force. The flexible inter-atomic bonds bend and stretch along different axes at any
non-zero temperature. The bonds behave as simple harmonic oscillators when excited
by an electromagnetic waves and absorb energy from it. The absorption spectrum
corresponds to the resonance condition for a given mode of vibration. Energy is
efficiently transferred to the molecule if the wave’s frequency is within a narrow range
of the resonance frequency of these modes. The molecule then makes a transition from
a lower energy state to a higher energy state. Specifically, the infrared spectrum of a
molecule results from energy transitions within the molecule’s rotational-vibrational
energy levels. The infrared spectrum is considered as the spectral signature of the
molecule due to the characteristic position of the spectral lines that are unique to that
molecule. This specificity of infrared spectra is used in detection and quantification
of gases using laser spectroscopy.
In reality, molecular vibrations are distinctly anharmonic because real molecular
bonds do not obey Hooke’s law. The anharmonicity is pronounced for large vibration
amplitudes (approximately greater than 10% of the bond length). Figure 1 shows the
oscillating dipole, the potential energy variation and a typical line spectrum of a
diatomic molecule (CO in this case). Figure 1a shows the asymmetric stretching in
response to the driving electric field. Unlike a harmonic oscillator, the expression for
the potential energy is much more complicated and the spacing of the energy levels
reduces with energy. The potential energy curve shown in Fig. 1b of a diatomic
molecule is given by the purely empirical Morse function, E = D eq [1 − e
a(r−r eq )
]
2 ,
where, a is a constant for a molecule and D eq is the dissociation energy of the
molecule. When this expression is used to solve the Schrodinger equation, the allowed
quantized energy levels are given by,