Optical pulse train

Optical detectors can routinely measure only intensities (proportional to the square of the electric field), whether of optical pulses, CW beams or quasi-CW beams the latter signifying conditions where the pulse train has an interval between pulses which is much shorter than the response time of the detector. It is clear that experiments must be designed in such a way that pump-induced changes in the sample cause changes in the intensify of the probe pulse or beam. It may happen, for example, that the absorjDtion coefficient of the sample is affected by the pump pulse. In other words, due to the pump pulse the transparency of the sample becomes larger or smaller compared with the unperturbed sample. Let us stress that even when the optical density (OD) of the sample is large, let us say OD 1, and the pump-induced change is relatively weak, say 10 , it is the latter that carries positive infonnation. 

In this case the electric field would be repetitive with the round trip time. Therefore C(t) is a constant and its Fourier transform is a delta function centered as uc = 0. If it becomes possible to build a laser able to produce a stable pulse train of that kind, all the comb frequencies would become exact harmonics of the pulse repetition rate. Obviously, this would be an ideal situation for optical frequency metrology. 

These examples are instructive, but it is important to note that experimentally we neither rely on a strictly periodic electric field nor on the assumption of a chirp free pulse train. The strict periodicity of the spectrum as stated in Eqn. 7 and the possibility to resolve single modes are the only requirements that enable the fs laser system to achieve precise optical to radio frequency conversions. 

The spectral width of a pulse train emitted by a femtosecond laser can be significantly broadened in a single mode fiber [27]. This process that maintains the mode structure is described in the time domain by the optical Kerr effect or selfphase modulation. The first discussion is simplified by assuming an unchanging pulse-shape under propagation. After propagating the length l the intensity dependent refractive index n(t) = n0 + ri2/(f) leads to a self induced phase shift... 

The mode-locked pulse train is one of a range of ways of comparing optical frequencies. A second technique which we have been investigating is the use of a frequency modulated (FM) dye laser. This has similarities to the mode-locked laser in that we are using the precise nature of the mode spacing when intracavity modulation is applied. In the case of the FM laser phase modulation is applied and in the case of the mode-locked laser amplitude modulation is applied. 

In impulsive multidimensional (1VD) Raman spectroscopy a sample is excited by a train of N pairs of optical pulses, which prepare a wavepacket of quantum states. This wavepacket is probed by the scattering of the probe pulse. The electronically off-resonant pulses interact with the electronic polarizability, which depends parametrically on the vibrational coordinates (19), and the signal is related to the 2N + I order nonlinear response (18). Seventh-order three-dimensional (3D) coherent Raman scattering, technique has been proposed by Loring and Mukamel (20) and reported in Refs. 12 and 21. Fifth-order two-dimensional (2D) Raman spectroscopy, proposed later by Tanimura and Mukamel (22), had triggered extensive experimental (23-28) and theoretical (13,25,29-38) activity. Raman techniques have been reviewed recently (12,13) and will not be discussed here. 

Essentially, a small part of the laser pulse train that is ultimately used to trigger the photocathode is split off to create a synchronized laser probe pulse train. The probe line is equipped with different nonlinear optical devices that permit the tunability of the probe beam from the near UV to the NIR. Available probe sources include the laser fundamental (790 nm) and second harmonic (395 nm), a white-light continuum (470-750 nm) generated in a sapphire plate, and a continuously tunable Optical Parametric Amplifier (470-750 nm, 1000-1600 nm, and 240-375 nm by SHG), able to deliver light pulses shorter than 30 fs after compression. 

In the first reported measurements made with picosecond pulses, an optical beam splitter was used to pick off a portion of the pulse train and a variable optical delay path was introduced between the two beams [7]. The main beam was used to excite (pump) a dye sample, and the weak (probe) beam was used to monitor the recovery of dye transmission as a function of delay. Over the past two decades, this pump-probe method has been extended to a variety of measurement geometries and used to measure electronic polarization dephasing times as well as population lifetimes. 

Population inversion is often achieved by a multi-level atomic or molecular system in which the excitation process, called pumping, is accomplished by electrical means, by optical methods, or by chemical reactions. In some cases, the population inversion can be sustained to produce a continuous wave (CW) output beam that is continuous with respect to time. In other cases, the lasing action is self terminating, so that the laser is operated in a pulsed mode to produce a repetitive pulse train or a single-shot action. ... 

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