The effect of field modulation on a simple resonance line shape

Abstract

AbstractThe Lorentzian line shape is the most basic line shape found in field swept continuous wave electron paramagnetic resonance (CW EPR). CW EPR employs Zeeman field modulation for detection purposes. The absorption signal at the first harmonic of modulation is the standard CW EPR signal. Under weak modulation conditions the first harmonic in‐phase absorption signal is equivalent to the derivative of the unmodulated Lorentzian line shape. When the field modulation amplitude is appreciable, the distorted first harmonic absorption line shape can still be expressed by a simple analytic formula, as long as the modulation frequency is sufficiently low. We state this often‐overlooked formula for the first harmonic signal, and exhibit its extension to arbitrary harmonics. Certain commonly used properties of the weak modulation (derivative Lorentzian) spectrum, such as the peak‐to‐peak height dependence on microwave power, are also stated in a form that fully takes account of the modulation amplitude. These analytic expressions are compared to numerical simulations of a version of the Bloch equation that contains modulation explicitly. A simple experimental example of overmodulation is also provided to show how the analytic formulas quantitatively account for the effects of modulation amplitude. The impact of modulation on the interpretation of EPR spectra is important given the frequent use of overmodulation when sample concentrations are low, such as in biological EPR studies. The simple analytic formulas demonstrated here are limited by the same physical considerations that limit applicability of the Lorentzian line shape. However, because the Lorentzian line shape is often appealed to in the interpretation of EPR spectra, its simple extension to the regime of appreciable modulation offers valuable insight. For example, the observation that the doubly integrated intensity of the first harmonic absorption spectrum has microwave power dependence that is insensitive to modulation amplitude is demonstrated explicitly. In contrast, the standard formula for the microwave power dependence of the first harmonic peak‐to‐peak absorption height is modified in a nontrivial way when the modulation amplitude is included. © 2004 Wiley Periodicals, Inc. Concepts Magn Reson Part A 23A: 38–48, 2004