Time-dependent electric fields spectroscopy

In dielectric spectroscopy the polarization response P(t) of a dipolar material is monitored, which is subject to a time-dependent electric field (Maxwell field), E t). For a linear and isotropic dielectric one can write (e.g., Ref. 34) ... 

Transient terahertz spectroscopy Time-resolved terahertz (THz) spectroscopy (TRTS) has been used to measure the transient photoconductivity of injected electrons in dye-sensitised titanium oxide with subpicosecond time resolution (Beard et al, 2002 Turner et al, 2002). Terahertz probes cover the far-infrared (10-600 cm or 0.3-20 THz) region of the spectrum and measure frequency-dependent photoconductivity. The sample is excited by an ultrafast optical pulse to initiate electron injection and subsequently probed with a THz pulse. In many THz detection schemes, the time-dependent electric field 6 f) of the THz probe pulse is measured by free-space electro-optic sampling (Beard et al, 2002). Both the amplitude and the phase of the electric field can be determined, from which the complex conductivity of the injected electrons can be obtained. Fitting the complex conductivity allows the determination of carrier concentration and mobility. The time evolution of these quantities can be determined by varying the delay time between the optical pump and THz probe pulses. The advantage of this technique is that it provides detailed information on the dynamics of the injected electrons in the semiconductor and complements the time-resolved fluorescence and transient absorption techniques, which often focus on the dynamics of the adsorbates. A similar technique, time-resolved microwave conductivity, has been used to study injection kinetics in dye-sensitised nanocrystalline thin films (Fessenden and Kamat, 1995). However, its time resolution is limited to longer than 1 ns. 

Common dielectric spectroscopy assumes linear response between the applied, time-dependent electric field E o)t) and the resulting electrical displacement D o)t + S), a condition that is fulfilled for weak fields, typically far below 1 V/pm. At... 

In its broadest sense, spectroscopy is concerned with interactions between light and matter. Since light consists of electromagnetic waves, this chapter begins with classical and quantum mechanical treatments of molecules subjected to static (time-independent) electric fields. Our discussion identifies the molecular properties that control interactions with electric fields the electric multipole moments and the electric polarizability. Time-dependent electromagnetic waves are then described classically using vector and scalar potentials for the associated electric and magnetic fields E and B, and the classical Hamiltonian is obtained for a molecule in the presence of these potentials. Quantum mechanical time-dependent perturbation theory is finally used to extract probabilities of transitions between molecular states. This powerful formalism not only covers the full array of multipole interactions that can cause spectroscopic transitions, but also reveals the hierarchies of multiphoton transitions that can occur. This chapter thus establishes a framework for multiphoton spectroscopies (e.g., Raman spectroscopy and coherent anti-Stokes Raman spectroscopy, which are discussed in Chapters 10 and 11) as well as for the one-photon spectroscopies that are described in most of this book. 

Before delving into the Raman spectroscopy of intermolecular modes, it is useful to discuss the IR spectroscopy of these modes briefly. Consider a liquid composed of N molecules, each containing n atoms. The energy of interaction of a liquid with an external electric field E is given by —M E, where M is the collective dipole moment of the liquid. The dipole moment depends on the coordinates of the molecules (qi, q2, - - - fl3nN) in a complicated manner, and these coordinates evolve in time in an equally complicated manner. It is customary to describe the time dependence of... 

Its first use is perhaps the simulation of electronic dynamics like atoms and molecules in strong electric fields for example [211-214]. This is also an approach to electronic spectroscopy, calculating the electronic response to applied time-dependent potentials. The time-dependant electronic susceptibility is indeed the time-dependent reponse to a Dirac like perturbation. 

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