Sinusoidal phase modulation

Periodic spectral phase-modulation functions have been used in numerous experiments and theoretical studies on coherent control of atoms [75-79] and molecules [24, 25, 42, 68, 73, 80-85]. Applying a sinusoidal phase-modulation function of the form... 

Figure 6.10 Ultrafast efficient switching in the five-state system via SPODS based on multipulse sequences from sinusoidal phase modulation (PL). The shaped laser pulse shown in (a) results from complete forward design of the control field. Frame (b) shows die induced bare state population dynamics. After preparation of the resonant subsystem in a state of maximum electronic coherence by the pre-pulse, the optical phase jump of = —7r/2 shifts die main pulse in-phase with the induced charge oscillation. Therefore, the interaction energy is minimized, resulting in the selective population of the lower dressed state /), as seen in the dressed state population dynamics in (d) around t = —50 fs. Due to the efficient energy splitting of the dressed states, induced in the resonant subsystem by the main pulse, the lower dressed state is shifted into resonance widi die lower target state 3) (see frame (c) around t = 0). As a result, 100% of the population is transferred nonadiabatically to this particular target state, which is selectively populated by the end of the pulse.

Fig. 25. Interferograms recorded using (a) amplitude modulation (b) sinusoidal phase modulation, vibration amplitude 30 jum and (c) sinusoidal phase modulation, vibration amplitude 100 /um. The corresponding spectra are shown for comparison. All data were to taken from Ref. 56)...

To master this complexity, more flexible pulse shapes in terms of both temporal amplimde and phase were used in experiment as well as in theory. A sinusoidal phase modulation (p a>) = A sin[r(ft>—laser spectrum, yielding a highly flexible and controllable multi-pulse sequence [51,69], adjustable by the phase parameters A for the amplitude of the subpulses, T for the temporal separation of the subpulses, and (p conflolling the relative temporal phases between adjacent subpulses. 

In Chapter 20 we saw how photoacoustic (PA) spectra could be measured with a step-scan interferometer no matter whether the PA signal was demodulated with a lock-in amplifier or by digital signal processing (DSP). For DSP, a Fourier transform (FT) has the same function as the lock-in amplifier. Manning et al. [14] showed that the same approach is feasible in DIRLD spectrometry with a step-scan FT-IR spectrometer but without a PEM. Consider the case where the detector signal contains components caused by simultaneous sinusoidal phase modulation at frequency /pm, and sample modulation at frequency fs. The phase- and sample-modulated components of the signal can be demodulated either with a... 

In a second kind of infrared ellipsometer a dynamic retarder, consisting of a photoelastic modulator (PEM), replaces the static one. The PEM produces a sinusoidal phase shift of approximately 40 kHz and supplies the detector exit with signals of the ground frequency and the second harmonic. From these two frequencies and two settings of the polarizer and PEM the ellipsometric spectra are determined [4.316]. This ellipsometer system is mainly used for rapid and relative measurements. 

Phase-modulation fluorometry The sample is excited by a sinusoidally modulated light at high frequency. The fluorescence response, which is the convolution product (Eq. 6.9) of the pulse response by the sinusoidal excitation function, is sinusoidally... 

Phase-modulation immunoassay measurements are made with sinusoidally modulated light. Since the emission is a forced response to the excitation, the emitted light has the same periodicity as the excitation. Due to the time lag between absorption and emission, the emission is delayed in comparison with the excitation. The time delay between the zero crossing of one period of the excitation and of the emission is measured as the phase angle (Figure 14.11). The emission is also demodulated, due to a decrease in the alternating current (AC) component of the AC to direct current (DC) ratio. 

Figure 14.11. Diagram of phase-modulation fluorometry with sinusoidally modulated excitation, with demodulated and delayed, or phase-shifted emission. (From Ref. 31 with permission.)...

In the following, we describe two prominent types of spectral phase modulation, each of which plays an important role in coherent control. Both types, namely sinusoidal (Section 6.2.1) and quadratic (Section 6.2.2) spectral phase modulation, are relevant for the experiments and simulations presented in this contribution. We provide analytic expressions for the modulated laser fields in the time domain and briefly discuss the main characteristics of both classes of pulse shapes. 

Figure 6.3 Shaped femtosecond laser pulses from sinusoidal spectral phase modulation of an 800 nm, 20 fs FWHM input pulse. The left column shows the modulated pulses in the frequency domain, decomposed into spectral amplitude (gray line and background) and modulation...

In order to produce surface-relief electro-optic gratings, Munakata et compared two fabrication methods of SRG inscription. In the first, the SRG was produced with an interference pattern of cw laser, with relatively modest intensities. The gratings so recorded were photo- and thermally erasable, and efficient writing was polarization dependent. In the second method, a phase mask was employed to provide the periodic intensity modulation of a pulsed laser, the 3rd-order harmonic (at 355 nm) of a Nd YAG laser. The SRG was produced with a single laser pulse, allowing a very short fabrication time (less than Is). The direshold for ablation was 500 mj/(em pulse), and the amplitude of the SRG increased with pulse energy. A depth of up to 300 rim could be achieved, leading to a smooth but not sinusoidal surface modulation. 

In phase-modulation fluorometry, the sample is excited by a sinusoidally modulated light at high frequency. The fluorescence response, which is the convolution product (Eq. (7.6)) of the d-pulse response by the sinusoidal excitation function, is sinusoidally modulated at the same frequency but delayed in phase and partially demodulated with respect to the excitation. The phase shift and the modulation ratio M (equal to m/mo), that is the ratio of the modulation depth m (AC/DC ratio) of the fluorescence and the modulation depth of the excitation mg, characterize the harmonic response of the system. These parameters are measured as a function of the modulation frequency. No deconvolution is necessary because the data are directly analyzed in the frequency domain. 

In practice, a sinusoidal motion of the oscillating mirror is to be preferred to the square-wave motion, and in most applications, the sinusoidal motion is used. The effects of phase modulation are the same in this case, the only difference being that the modulation factor in Eqs. (4.11) to (4.13) will be the first Bessel function 7l(2 i (ro) instead of sin(25i [Pg.116]

The theory of spinodal decomposition was first examined by Cahn [164]. It predicts the exponential growth of sinusoidal composition modulations at a fixed wavelength A. The size of each phase may be given by A written as [165],... 

In a phase-modulation fluorometer, the sample is illuminated with sinusoidally modulated light which is intensity-modulated with a circular modulation frequency (i> (Hgure... 

Phase modulation is often used to create additional frequencies to a monochromatic laser beam of frequency m. To do this, the fixed voltage V applied to the crystal is replaced by a sinusoidally varying voltage of frequency /. The phase-modulated output signal will now contain sidebands to the primary output with frequency co, a) f,co 2f... (Figure 9.10b). 

Figure 9.10 An electro-optic phase modulator (a) schematic of experimental arrangement (b) output power for a sinusoidally varying voltage...

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