Time and frequency gated

There are many systems of different complexity ranging from diatomics to biomolecules (the sodium dimer, oxazine dye molecules, the reaction center of purple bacteria, the photoactive yellow protein, etc.) for which coherent oscillatory responses have been observed in the time and frequency gated (TFG) spontaneous emission (SE) spectra (see, e.g., [1] and references therein). In most cases, these oscillations are characterized by a single well-defined vibrational frequency, It is therefore logical to anticipate that a single optically active mode is responsible for these features, so that the description in terms of few-electronic-states-single-vibrational-mode system Hamiltonian may be appropriate. 

Summarizing, it is demonstrated that the developed model correctly reproduces the general trends in various experimentally measured responses, which include cuts of time- and frequency-gated spectra at particular frequencies, peak-shifts of the fluorescence spectra, and integral signals. Moreover, the relative shapes and intensities of the spectral cuts at different frequencies are correctly reproduced. For a more complete and quantitative description of the experimental data, the theoretical model has to be augmented by including additional system and/or solvation modes. 

If the system under consideration possesses non-adiabatic electronic couplings within the excited-state vibronic manifold, the latter approach no longer is applicable. Recently, we have developed a simple model which allows for the explicit calculation of RF s for electronically nonadiabatic systems coupled to a heat bath [2]. The model is based on a phenomenological dissipation ansatz which describes the major bath-induced relaxation processes excited-state population decay, optical dephasing, and vibrational relaxation. The model has been applied for the calculation of the time and frequency gated spontaneous emission spectra for model nonadiabatic electron-transfer systems. The predictions of the model have been tested against more accurate calculations performed within the Redfield formalism [2]. It is natural, therefore, to extend this... 

V. Extension to Heterodyne-Detected Four-Wave Mixing Appendix A Time- and Frequency-Gated Autocorrelation Signals Appendix B The Signal and the Optical Polarization... 

APPENDIX A TIME- AND FREQUENCY-GATED AUTOCORRELATION SIGNALS... 

There exist two major approaches to the theoretical description of the time and frequency gated spontaneous emission (TFG SE). In the first approach, the TFG SE spectrum is defined as the rate of emission of photons of a certain frequency within a definite time interval. The influence of the measuring device is not taken into account in this formulation. Starting from this definition, one obtains an ideal (bare) TFG SE spectrum, which is not guaranteed to be positive, however. For instance, for certain parameters of the Brownian oscillator model, the spectrum can attain negative values. Moreover, the time and frequency resolutions of this ideal spectrum are not limited by the fundamental time-frequency uncertainty principle. This underlines the necessity to develop a more comprehensive theory, in which both a spectrometer and a time-gating device enter the description from the outset. 

To make the chapter self-contained and easy to read, we introduce the necessary definitions and starting equations in Section 9.2. Sections 9.3 and 9.4 describe the two-and three-pulse EOM-PMA, respectively. In Section 9.5, we discuss the time- and frequency-gated (TFG) spontaneous emission (SE) and optical two-dimensional (2D) three-pulse (3P) PE spectra for a model system, which accounts for strong electronic... 

S.2.2 TFG SE Spectra The ideal time- and frequency-resolved SE spectrum would be observed with perfect time and frequency resolution. In reality, one has to sacrifice either the former or the latter when measuring two-dimensional TFG SE spectra (an increase of the temporal resolution results in a decrease of the frequency resolution and vice versa). Once the ideal time- and frequency-resolved signal is known, one can calculate the real TFG spectrum for a given gate pulse and frequency... 

Potential or current step transients seem to be more appropriate for kinetic studies since the initial and boundary conditions of the experiment are better defined unlike linear scan or cyclic voltammetry where time and potential are convoluted. The time resolution of the EQCM is limited in this case by the measurement of the resonant frequency. There are different methods to measure the crystal resonance frequency. In the simplest approach, the Miller oscillator or similar circuit tuned to one of the crystal resonance frequencies may be used and the frequency can be measured directly with a frequency meter [18]. This simple experimental device can be easily built, but has a poor resolution which is inversely proportional to the measurement time for instance for an accuracy of 1 Hz, a gate time of 1 second is needed, and for 0.1 Hz the measurement lasts as long as 10 seconds minimum to achieve the same accuracy. An advantage of the Miller oscillator is that the crystal electrode is grounded and can be used as the working electrode with a hard ground potentiostat with no conflict between the high ac circuit and the dc electrochemical circuit. 

Both TCSPC and frequency-domain fluorimetry are limited in time resolution by the response of available detectors, typically >25 ps. For cases in which higher time resolution is needed, fluorescence up-conversion can be used (22). This technique uses short laser pulses (usually sub-picosecond) both to excite the sample and to resolve the fluorescence decay. Fluorescence collected from the sample is directed through a material with nonlinear optical properties. A portion of the laser pulse is used to gate the fluorescence by sum frequency generation. The fluorescence is up-converted to the sum frequency only when the gate pulse is present in the nonlinear material. The up-converted signal is detected. The resolution of the experiment therefore depends only on the laser pulse widths and not on the response time of the detectors. As a result, fluorescence can be resolved on the 100-fs time scale. For a recent application of fluorescence up-conversion to proteins, see Reference 23. 

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