A general non-complex analytical expression for the nth Fourier component of a wavelength-modulated Lorentzian lineshape function

A general, analytical expression for the nth Fourier component of a wavelen gth-modulated Lorentzian lineshape function in terms of a normalized detuni ng and a normalized modulation amplitude is derived. The expression is cast in a purely real form and is therefore easier to use than the normally use d expression, which is given in terms of various combinations (sums, square roots, and powers) of complex expressions and their complex conjugates. An alytical expressions for the nine first Fourier components (n = 0,...,8), c learly showing their dependence on normalized detuning and modulation ampli tude, are explicitly given. Simplified expressions for the even harmonics o f the Fourier components on resonance, at which they take their maximum val ue, solely given in terms of the normalized modulation amplitude, are also explicitly given. It is shown that previously published, numerically calcul ated conditions for maximization of higher-order Fourier components are inc orrect. The normalized modulation amplitudes that maximize the four lowest even harmonics of the Fourier components, i.e. for n = 2, 4, 6, and 8, are 2.20, 4.12, 6.08, and 8.06, respectively. (C) 2000 Elsevier Science Ltd. Al l rights reserved.