Abstract
We created a computational model to investigate the characteristics of label-free molecular detection by stimulated emission, which is the fundamental process of stimulated emission microscopy proposed and experimentally demonstrated by Min et al. In our model the molecule is considered to be a two-state quantum system with finite number of vibrational states. The laser excitations are modelled as zero order Gaussian beams. The field-molecule interaction is considered to be an electric dipole interaction. Based on these assumptions we constructed a Liouville-von Neumann master equation for the reduced density operator. The numerical solution of the master equation determines the expectation value of additional photons produced by stimulated emission. Based on this model algorithms are proposed to evaluate relative excitations. Linear dependence in concentration and quadratic dependence in space resolution were obtained at weak excitations. Time delay dependent relative excitation can be evaluated by taking into account only a single vibrational mode. However, to calculate the spectrum of relative excitation two entangled vibrational modes are necessary. An algorithm is proposed that overcomes the problem of computational complexity and enables to evaluate the spectrum on a high-end computer. High correlation between calculated and measured data of time delay and frequency dependent relative excitation, confirm the validity of the proposed model.
Highlights
Observation of biomolecules is usually done by fluorescent microscopy, and in most cases the detected molecules have to be labelled by binding a large fluorescent chromophore molecule
We have examined the case when the lifetime of vibrational state is in the same order as the width of the pulse used for excitation and the lifetime of excited state
The Rabi frequencies are determined by the light intensities and the transition probabilities, the measured value depends on the two laser pulses following each other, and the response of the system depends on the multiplication of the pulse intensities at weak excitation. This quadratic behavior in the space domain is well known from other nonlinear techniques like two photon or stimulated emission depletion (STED) microscopy [8, 9]
Summary
Observation of biomolecules (detected molecules) is usually done by fluorescent microscopy, and in most cases the detected molecules have to be labelled by binding a large fluorescent chromophore molecule. The number of molecules in the focal volume is small, a high-frequency, phase-sensitive detection technique was implemented by modulating the excitation signal They measured the stimulated emission with and without excitation multiple times and amplified the difference. In order to understand the dominant physical processes during label-free detection and in the same time to insure a balance between the necessary computational requirements and accuracy, we modelled the interaction of matter and the electromagnetic field in the focus area. Using density matrix formalism we simulated the time evolution of the master equation that contains both the electronic and the vibrational processes [6] Capturing both the electronic and vibrational modes of a molecule in our model, we could determine the quantitative behavior of detection of a molecule by stimulated emission. Additional to calculate the measured data the model enables us to asses the role of parameter dependence as well as the role of effects of individual vibrational modes
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