Laser phase

A. D. Bandrauk, E.-W. S. Sedik, and C. F. Matta, Effect of absolute laser phase on reaction paths in laser-induced chemical reactions, J. Chem. Phys. 121, 7764 (2004). 

Figure 12.18. The lower portion of the figure shows diode laser phase-modulation fluorescence lifetime...

It is possible to design multipath control schemes in which the laser phase cancels out of the interference term. One possibility is a diamond path configuration, co + 0)2 vs 0)2 + o), with a resonance near o) contributing a phase to the first path and a resonance near 0)2 contributing a phase to the second path. As before, the total probability is the square of the sum of the amplitudes for each path, but here the phases of the two laser beams appear in both paths and cancel in the cross term. In this case the control parameters are the laser frequencies, which determine the detuning from the resonances. This technique was used by Daniel Elliott and coworkers to control the differential cross sections for the ionization of Ba and NO. 

Thus far we have dealt with the idealized case of isolated molecules that are neither -subject to external collisions nor display spontaneous emission. Further, we have V assumed that the molecule is initially in a pure state (i.e., described by a wave function) and that the externally imposed electric field is coherent, that is, that the " j field is described by a well-defined function of time [e.g., Eq. (1.35)]. Under these. circumstances the molecule is in a pure state before and after laser excitation and S remains so throughout its evolution. However, if the molecule is initially in a mixed4> state (e.g., due to prior collisional relaxation), or if the incident radiation field is notlf fully coherent (e.g., due to random fluctuations of the laser phase or of the laser amplitude), or if collisions cause the loss of quantum phase after excitation, then J phase information is degraded, interference phenomena are muted, and laser controi. is jeopardized. < f... 

For example, consider Eq. (3.19) corresponding to control of photodissociation of) an initial two-level supeiposition state that is excited to the continuum. If there arer sufficiently strong external perturbations, or excessive jitter in the laser phase, thefij-this results in a complete average over 2, and Eq. (3.19) becomes f ... 

Since partial laser phase coherence affects both the direct terms as well as the cross terms, the extent of control is dependent on the laser properties through the relative magnitudes of ( l( ulg) (c02g))l and (l i-(w ) 2)> =1,2. To expose the dependence on the coherence of the pump field denote the terms ckc jF u>jk)dq kj)(E) by a ]- and consider the ratio of the k / j term in Eq. (5.44) to the associated diagonal terms. That is, consider the contrast ratio ... 

A more complex analysis of the effect of laser phase diffusion has been appli fS the case of one-photon vs. three-photon absoiption (i.e., simultaneous absorption 3a)j and third-harmonic generation frqnt>t coi laser. As discussed in Section 3.3.2, current experiments vary the relative ph of two laser beams by passing co3 and co, through a gas. If the laser frequcnc somewhat unstable, then the relative phase of the two beams will acquire a fhtct y ing phase that is a source of phase loss in the system. The phase fluctuations q ... 

For cw lasers, laser decoherence appears via the jitter and drift of the laser phase in the field E(z,t) [e.g., Eq. (3.16)] with a concomitant reduction in control (see Section 5.3). However, suitable design of the control scenario can result in a method that is immune to the effects of laser jitter. In particular, to do so we rely upon the way in which the laser phase enters into control scenarios. 

The role of the laser phase in controlling molecular dynamics was clear in the examples shown in Chapter 3, For example, in the one- vs. three-photon scenario the relative laser phase (3 — 3c/>,) enters directly into the interference term [see, e.g., Eq. (3.53)], as does the relative phase ((frl — (j>2) in the bichromatic control scenario [Eq. (3.19)]. These residts embody two useful general rules about the contribution of the laser phase to coherent control scenarios. The first is that the interference term contains the difference between the laser phase imparted to the molecule by one route, and that imparted to the molecule by an alternate route. Second, the phase imparted to the state Em) by a light field of the form ... 

The ratio Rqq, depends on a number of laboratory control parameters including f he relative laser intensities x, relative laser phase, and the ratio of e+1 and e via t. ... 

Figure 6.3 Contours of equal Na(3p) yield. Ordinate is the relative laser phase and abscissa y is the field intensity ratio x. Here for X0 = 623.367 nm, X+ = 603.491 nm, X = 644.596nm,. and t] = 1. (From Fig. 1, Ref. [206].) V...

This control scenario is not limited to the specific frequency scheme discusi above. Essentially all that is required is that two or more resonantly enhaw photodissociation routes interfere and that the cumulative laser phases of the routes be independent of laser jitter. As one sample extension, consider the ci... 

Figure 6.8 Dependence of the real part of n(a>) on F2/l in N2 (in the superposition state described in the text) for different values of relative laser phase dtp. Here dtp = —njl (solid), dtp = 0 and n (dashed), and dtp = n/2 (dot-dash). (From Fig. 1, Ref. [213], where dtp was i " denoted S.)...

In addition to the loss of the 62 phase dependence, when the laser-phase matrix is time independent, the dependence on the phases of the other lasers is also lost as well. This is because the time-independent exp[— (0O 1 + + 1)] term factors out... 

Numerical results using this technique were obtained [471] for the pump-dump photodissociation of Na2 to optimize the production of either Na(3s) + Na(3p) or Na(3s) + Na(4s). In this case optimal control often required pulses that were fairly heavily structured in laser phase and frequency. A more detailed study [471] indicated that this structure was necessary for the dissociation pulses, but not necessary for the excitation pulse. Further, as is often the case with OCT, pulses with very different structures were found to achieve similar control objectives in different ways. 

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. 

The laser phase Doppler particle analyzer (PDPA) simultaneously measures particle velocity, size and flux and may be considered an extension of laser Doppler velocimetry (LDV). It is particularly useful for... 

Hishida, K. and Maeda, M., Application of laser/phase Doppler anemometry to dispersed two-phase flow. Part. Part. Syst. Charact., 7, 152-159 (1990)... 

An overview of frequency-domain detection techniques is given in [88]. Frequency-domain techniques compare the phase shift and the modulation degree of the fluorescence with the modulated excitation. Modulation of the excitation is achieved either by actively modulating the light of a continuous laser or by using pulsed lasers of high repetition rate. With pulsed lasers, phase and modulation can be measured at the fundamental repetition frequency or at its harmonics. 

Flash photo-CIDNP spectra have been obtained in the authors laboratory using a dye laser (Phase-R 2100B), which delivers visible light flashes of 0.5 ys duration and 1 - 3 J energy, in conjunction with the 360 MHz spectrometer (15). 

Fig. 9.81 Laser phase modulation and gating time sequence for obtaining subnatural linewidths under cw excitation [1307]...

---