Off-resonance frequency

In our tip-enhanced near-field CARS microscopy, two mode-locked pulsed lasers (pulse duration 5ps, spectral width 4cm ) were used for excitation of CARS polarization [21]. The sample was a DNA network nanostructure of poly(dA-dT)-poly(dA-dT) [24]. The frequency difference of the two excitation lasers (cOi — CO2) was set at 1337 cm, corresponding to the ring stretching mode of diazole. After the on-resonant imaging, CO2 was changed such that the frequency difference corresponded to none of the Raman-active vibration of the sample ( off-resonant ). The CARS images at the on- and off- resonant frequencies are illustrated in Figure 2.8a and b, respectively. 

A spontaneous Raman spectra is shown in Figure 2.8d in which the on- and off-resonant frequencies are indicated. The DNA bundles are observed at the resonant frequency, as shown in Figure 2.8a, while they cannot be seen at the off-resonant frequency in Figure 2.8b. This indicates that the observed contrast is dominated by the vibrationally resonant CARS signals. Figure 2.8c shows a cross-section of Figure 2.8a denoted by two solid arrows, which were acquired with a 5 nm step. The FWHM of... 

Fig. 10. Sequence for the assessment of magnetization transfer (MT) effects. Images recorded without (a) and with MT prepulses (b) have to be subtracted. In the presented example a standard gradient-echo sequence is used for MT imaging. The MT prepulse is Gaussian-shaped with a flip angle of 600° and 1.5 kHz off-resonance frequency.

FIGURE 10.13 CARS images of the DNA network, (a) TE-CARS image at on-resonant frequency (1337 cm ). (h) TE-CARS image at the off-resonant frequency (1278 cm ). (c) One-dimensional line profiles of the row indicated hy the solid arrows. The scanned area is 1000 nm x 800 nm. The numher of photons counted in 100 ms was recorded for one pixel. The acquisition time was -12 minutes for the image. The average powers of the (0 and tOj beams were 45 pW and 23 pW at the 800 kHz repetition rate. 

It often happens that there is at least one signal too close to the signal to be irradiated to allow for the setting of the two off-resonance frequencies in the optimal position. In fact, if another signal is close to one of the two off-resonance frequencies, in the difference spectrum this signal appears as strongly positive. 

Let us continue with the simple toy model. In the base ( 0) 1)), the quantum state given as column vector [C(0) C(l)] for which C(0) = 1 and C(l) = 0 corresponds to the ground state 11,0) -> (1 0). Off-resonance frequencies co set the system in a linear superposition state once an interaction operator is switched on normalization leads to amplitudes proportional to [cos /t sin /t] the parameter > can reflect coupling between base states and probed system. 

If the phase-sensitive detectors are adjusted to give a phase angle (Eq. 3.8) ( — 4>r ) = 0, the real part of the FT spectrum corresponds to pure absorption at the pulse frequency, but off-resonance lines display phase angles proportional to their off-resonance frequency as a consequence of limited rf power and nonzero pulse width (Eq. 2.55). However, acquisition of data as complex numbers from the two phase-sensitive detectors and subsequent processing with a complex Fourier transform permit us to obtain a spectrum that represents a pure absorption mode. 

We have already observed phase modulation in the acquisition of data in a ID spectrum, where finite rf power results in off-resonance magnetizations giving rise to a phase error proportional to the off-resonance frequency (see Eq. 2.55), and similar effects occur in the t2 dimension of 2D spectra. Here our interest is in modulation that arises in the f, dimension. A simple example (but with no utility as a 2D pulse sequence) is 90°, t2, which resembles a ID experiment in which... 

Fig. 16.11 Tip-enhanced CARS images of the DNA network obtained at (a) on-resonant frequency (1,337 cm ) and (b) off-resonant frequency (1,278 cm- ), (c) Cross-sectional line profiles at the position indicated by the solid arrows. The scaimed area is 1,000 nm x 800 nm (Reprinted from [106], Copyright 2004, with permission from American Physical Society)...

For large off-resonance frequencies, the angle 9 in (7.2.5) is small enough so that the second 90° pulse in the sequence of Fig. 7.2.4 can be discarded. Off-resonance spin locking can also be seen as a low-power alternative to spin locking, so that the technique may be used in medical applications [Fai 1]. 

One of the most significant implications of the result is that an absorption spectrum measured with intense white light may be significantly different from the spectrum that would be observed using tunable monochromatic radiation. In particular, there should be a decrease in the apparent width of many lines in any absorption spectrum measured with broadband radiation. This is because, for any sample transition of frequency coq, photons of appreciably off-resonant frequency (oiq + fi) can be cooperatively absorbed and result in the excitation of two separate molecules, provided selection rules permit. In fact the Lorentzian linewidth of the concerted absorption process is readily shown to be approximately 0.64 x the ordinary absorption linewidth, if the probe radiation is assumed to be of nearly constant intensity in the frequency region of interest. Nonetheless, the observed linewidth would not be reduced to quite this extent, because of the additional and invariably stronger response associated with normal single-photon absorption. 

Here, n and k are the real and imaginary parts of the complex index of refraction. The approximation in Eq. 5 is based on n > k, which is true for lower chromophore concentrations or for off-resonant frequencies. In this limit, the refractive index is mainly determined by the real part and the absorption by the imaginary part of Thus far, only the response from the chromophores has been considered, but usually the host polymer contributes to the susceptibility, too. Assuming that the host material does not have any significant absorption in the considered spectral region, the change in the refractive index can be modeled by a constant background index from the polymer backbone. 

Our measurements on manually cleaved thick (50-150 pm) crystals [118] showed a stronger damping with higher repetition rates of the laser system, i.e. higher heat load but lower peak intensities. No damping was observed at off-resonant frequencies, e.g. at 750 mn. Therefore, the damping is clearly related to the heat load absorbed by the crystal, an indica-... 

It should be noted that the parameters are dependent on co according to Eqs. (18) and (19), so spectrometer frequency is a variable that can be utilized. As shown in Fig. 1, the off-resonance parameters are also dependent on the off-resonance frequency, which can be another useful variable. 

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