Abstract
A compact correlation-function expression for time-resolved stimulated Raman signals, generated by combining a spectrally narrow (picosecond) with a broad (femtosecond) pulse, is derived using a closed time path loop diagrammatic technique that represents forward and backward time evolution of the vibrational wave function. We show that even though the external spectral and temporal parameters of the pulses may be independently controlled, the effective temporal and spectral resolution of the experiment may not exceed the fundamental bandwidth limitation.
Highlights
Stimulated Raman spectroscopy (SRS) has found powerful applications in biomedical imaging.1,2 Closely related coherent Raman spectroscopy has been proposed for remote sensing.3,4 Pulse shaping techniques have been used for manipulating these signals.5–7 Impulsive stimulated Raman scattering uses femtosecond pulses to measure simultaneously molecular vibrations over a broad bandwidth.8–10 It has been argued that by using a combination of a femtosecond and a picosecond pulse it is possible to achieve both high spectral and temporal resolution that exceed the fundamental transform limit
This was denoted “circumventing Heisenberg.”11,12 Experiments on deuterated chloroform13 and other systems11 show how the phase of the Raman-like features changes with a time resolution (< 50 fs) while the spectral resolution is less than 30 cm−1
We show that when the temporal and the spectral resolution are properly defined, their product may not violate the transform limit
Summary
Stimulated Raman spectroscopy (SRS) has found powerful applications in biomedical imaging.1,2 Closely related coherent Raman spectroscopy (coherent anti-Stokes Raman spectroscopy) has been proposed for remote sensing.3,4 Pulse shaping techniques have been used for manipulating these signals.5–7 Impulsive stimulated Raman scattering uses femtosecond pulses to measure simultaneously molecular vibrations over a broad bandwidth.8–10 It has been argued that by using a combination of a femtosecond and a picosecond pulse it is possible to achieve both high spectral and temporal resolution that exceed the fundamental transform limit. Equation (4) for the time-dependent polarization is to be contrasted with the phenomenological expression used in the simulations of Ref. 14, where ωca(t)(t − T ) replaces the integral over the changing vibrational frequency. Some insight into the effective time resolution of these measurements can be obtained by considering a model system of a single vibrational mode whose frequency changes according to ωca(t) =
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