Bandwidth transform-limited

Ultrafast time-resolved resonance Raman (TR ) spectroscopy experiments need to consider the relationship of the laser pulse bandwidth to its temporal pulse width since the bandwidth of the laser should not be broader than the bandwidth of the Raman bands of interest. The change in energy versus the change in time Heisenberg uncertainty principle relationship can be applied to ultrafast laser pulses and the relationship between the spectral and temporal widths of ultrafast transform-limited Gaussian laser pulse can be expressed as... 

Fig. 6.2. Illustration of the frequency-time dependences of pump and Stokes pulses in three different CRS excitation pulse schemes and their corresponding spectral resolution of Raman shifts. A Using a pair of transform-limited femtosecond pulses of broad spectral and narrow temporal widths results in a broad bandwidth of Raman shifts that exceeds the line width of a single Raman resonance. B Using transform-limited picosecond pulses of broad temporal and narrow spectral width readily provides high spectral resolution matching the Raman resonance line width to be probed. Selection of a Raman resonance shifted by AQr is achieved by tuning the frequency of one of the laser beams by the same amount. C Spectral focusing of a pair of identically linear chirped pump and Stokes femtosecond pulses results in a narrow instantaneous frequency difference in the CRS process, thus also providing narrow-bandwidth CRS excitation. Selection of a Raman resonance shifted by AQr is achieved by adjusting the time delay At between the pulses. Shifted pulses in (B) and (C) are depicted hatched...

As shown in Fig. 6.2B, this can be directly achieved by using transform-limited pump and Stokes pulses, of which the spectral bandwidth matches the Raman resonance line width to be probed [37]. The temporal width of the pulses is typically 5ps, corresponding to a spectral width of 2.9cm. A frequency-resolved CRS spectrum is obtained by tuning the wavelength of... 

Experiments were performed using a visible optical parametric amplifier based on noncollinear phase-matching in /3-barium borate, followed by a pulse compressor using chirped dielectric mirrors. This optical source provides ultrabroadband pulses, with bandwidth extending from 500 to 720 nm, compressed to an almost transform-limited duration of 5-6 fs. The pump-... 

The c.w. dye laser can also be passively mode-locked and two different arrangements have been used. The first employed two free flowing dye streams, one for the laser dye and the other for the absorber (see Fig. 4) [18, 19]. In the alternative arrangement, the saturable absorber dye flows in a narrow channel of variable thickness (0.2—0.5mm) and in contact with a 100% broadband reflectivity mirror. With an absorber thickness of 0.5 mm, output pulses of 1 ps duration have been obtained [20]. Pulses as short as 0.3ps were produced when the DODCI cell length was shortened to 0.2 mm. The subpicosecond pulses produced in this arrangement were transform-limited in bandwidth. 

Frequently, femtosecond pulses are used in such electronically resonant spectroscopy. Such pulses usually have near-transform limited bandwidths and can spectrally embrace a fair range of vibrational coherences. Thus, even when a single central colour is chosen to define the femtosecond exciting pulse, actually a broad band of colours is available to provide a range for both co j and C02- Instead of preparing single well-defined vibrational coherences using sharply... 

The NO2 dissociation rate was measured by a two-color picosecond pump-probe method in which the product NO was monitored by LIF. Of particular significance in this study is that the NO2 density of states at the dissociation limit of 25,130.6 cm is relatively well established from an extrapolation of experimentally determined densities at an energy of 18,500 cm . This density (for cold samples where the rotations do not contribute significant densities) is 0.3 states per cm , (Miyawaki et al., 1993) which leads to a minimum rate constant l/h p( ) = 1 x 10 sec . The experimentally measured rate increases from 0 to 1.6 x 10 sec at the dissociation limit. It is interesting that the subpicosecond laser pulses with their transform limited resolution of about 20 cm do not excite individual NO2 resonance states (see section 8.3, p. 284) but, instead, prepare a superposition of those states that are optically accessible within the laser bandwidth. It is thought that all resonance states in this bandwidth are... 

Transform limited pulses of a duration of 9 ns with a very stable center frequency were generated as follows A tunable single mode dye laser with a bandwidth of 2 MHz was pulsed with the help of an acousto-optical modulator. For the fluorescence lifetime experiments pulses of 9 ns FWHM and a separation of 1 ps were used. The laser pulses were focused onto a pinhole with a diameter of 5 pm and illuminated about 100 pm of the sample crystal. A set of lenses imaged the emerging fluorescence onto a fast photomultiplier. Optical cutoff filters removed scattered laser light from fluorescence. Recording times up to 1200 s were necessary to obtain reliable statistics for the fluorescence decay curves. The laser had to be stabilized onto a fixed frequency during the full measurement time. 

TABLE II Autocorrelation Widths and Spectral Bandwidths for Several Transform-Limited Pulse Shapes... 

An intense coherent tunable Fourier-transform-limited narrow-band all-solid-state vacuum-ultraviolet (VUV) laser system has been developed by Merkt and coworkers [573]. Its bandwidth is less than 100MHz and the tuning range covers a wide spectral interval around 120,000 cm (15 eV). At a repetition rate of 20 Hz the output reaches 10 photons per pulse, which corresponds to an energy of 0.25 nJ per pulse, a peak power of 25 mW for a pulse length of 10 ns, and an average power of 5 nW. For these short VUV wavelengths of around A = 80 nm this is remarkable and is sufficient for many experiments in the VUV. 

Another promising approach to controlling processes such as chemical reactions is presented by Brumer cind Shapiro [59], using the coherence of lasers by applying nanosecond lasers with close to transform-limited bandwidth. 

Table 2.2. Autocorrelation width and spectral bandwidth for different transform-limited pulses taken from [183]. At and Ata are the FWHMs of I(t) and G (t) respectively. Au is the FWHM of the measurable frequency spectrum.

Over-the past decade, not only have pulse durations decreased from 10 to 10" s but there has been a dramatic increase in the tunability of lasers, such that tunable coherent radiation can now span the VUV to the very long wavelength laser radar. Femtosecond spectroscopy, like most advances, has begun in the visible region and considerable research and development is necessary to expand this present spectral range around 600 nm (4). However, it is also the case that for many problems in photo dynamics, for which the state selectivity or the nature of the optically prepared initial state is of paramount importance, the spectral line-width (Av) of the pulse must remain narrow. Thus the transform-limited bandwidth relationships (AvA K) govern the temporal properties of the laser pulse and, for example, a 5 ns pulse of 0.01 cm" linewidth prepares a different ensemble than a 300 fs pulse of 26 cm linewidth at the same wavelength. 

As an example of a pulse combination that can stimulate a band of Raman frequencies, we design a pulse that sweeps the beat frequency linearly from Q to. To do this, we will split a transform-limited pulse of bandwidth... 

As an example of this method, we present a simulation of this technique using experimentally realistic values (/). We assume that the laser source is an ultrabroadband titanium-sapphire laser producing transform-limited pulses of uniform power spectral density between 700-1000 nm. The bandwidth from 800-1000 nm is reserved for stimulating CARS, while the bandwidth from 700-800 nm is used as the reference pulse. In this simulation, we desire to simulate the measurement of the relative amounts of DNA (deoxyribonucleic acid) which has a resonance at 1094 cm" and RNA (ribonucleic acid) which has a resonance at 1101 cm A hypothetical Raman spectrum was created which has Lorentzian resonances at both frequencies. A pulse is designed such that... 

If the pulse is transform limited [40] its spectrum and time profile are directly connected by a Fourier transformation. Hence the spectrum bandwidth is inversely proportional time duration Aw oc For a pulse of 100 fs duration, 100 x 10 s, we get a bandwidth of about 30 THz, equivalent to lOOcm. This specteum width is often large enough to include some intramolecular vibration modes. 

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