Depth of modulation

The measuring technique consists of exciting the sample with sinusoidally modulated light and determining either the depth of modulation or the phase shift of the fluorescent emissions. 

Fig. 7. The applied voltage to the modulator (upper trace) and the optical signal from the modulator (lower trace). The horizontal time scale is 0.5 nsec per major division. The peak applied voltage was 64 V, and the peak in the optical signal corresponds to a 1% depth of modulation. [From Phelan el al. (1981).]...

The usual measure of the depth of modulation (sharpness) of interference fringes is a visibility in an interference pattern defined as... 

In this case the intensity exhibits additional cosine and sine modulations, and at the minima the intensity is different from zero, indicating that the maximum depth of modulation of 100% is not possible for two fields of different frequencies and/or initial phases. Moreover, for large differences between the frequencies of the fields (A/coo 1) the cos (k,tR- + Scfi) and sin (koR A 8( )j terms rapidly oscillate with R and average to zero that washes out the interference pattern. In terms of which-way information has been transferred, a detector located in the point P and adjusted to measure a particular frequency or phase could distinguish the frequency or the phase of the two fields. Clearly, one could tell which way the detected held came to the point P. Thus, whether which-way information is available depends on the intensities as well as frequencies and phases of the interfering fields. Maximum possible which-way information results in the lack of the interference pattern, and vice versa, the lack of which-way information results in maximum interference pattern. 

An alternative way to detect an internal state of the two atom system is to observe an interference pattern of the fluorescence field emitted in the direction R, not necessary perpendicular to the interatomic axis. The usual measure of the depth of modulation of the interference fringes is a visibility defined as... 

In the frequeney domain, the sample is exeited with modulated light (D). The amplitude and the phase are measured at a single frequeney or at a small number of frequeneies. Different modulation frequeneies ean be obtained by ehanging the exeitation frequeney or by using different harmonies of a pulsed exeitation waveform. The effieieney of the modulation teehnique depends on a number of techni-eal details, espeeially the depth of modulation of the exeitation light and the way the deteetor signal is demodulated. Only for exeitation with short pulses of high repetition rate and ideal demodulation a near-ideal effieieney is obtained. 

Modulation index (m) or depth of modulation affects the overall energy transfer into the implant. At a given rf signal amplitude, less energy is transferred into the implanted device when 100% modulation is used m = 1) as compared to 10% modulation (m = 0.053). However, retrieval of 100% modulated signal is much easier than retrieval of a 10% modulated signal. 

The depth of modulation is determined by the ratio of the thickness of the laser material to the grain size of the ceramics [287, 289-291]. Analytical expressions for eigen polarizations and phase delays in grains of thermally loaded Nd YAG ceramic rods have been established [287]. It was suggested that the depolarization of radiation in polycrystalline ceramics led to beam modulation with a characteristic size of the order of the ceramic grain size. Therefore, increasing the ratio of rod... 

The 1.9 psec modulation is thus understood as originating from a modulation of the dipole density at a single transition and not from an interference of atomic radiators working on different transitions. All our results are accounted for except the depth of modulation. Vfe believe this is due to jitter in the temporal delay we mechanically introduce. 

Fig. 1. Schematic of the photorefractive process. Note the phase shift, (j), between the incident intensity grating and the resulting photorefractive grating in the material. Depending upon the trapping depth and depth of modulation of the intensity of light incident on the material, the phase shift can vary between 0 and ti/2. The absence of this phase shift indicates that mechanisms of photoinduced refractive index change other than photorefraction are involved. Many photorefractive applications require phase shifts approaching jt/2.

For camera tubes, two important parameters to consider are modulation depth and lag. Modulation depth is determined by the spot diameter of the electron beam and by the thickness of the photoconductive layer. Lag is governed by the process of recharging the photoconductive layer. This is accomplished by the electron beam. The speed of the process is limited by the capacitance of the photoconductive layer and the differential resistance of the electron beam. The photoconductive layer is essentially capacitive in nature as the layer thickness increases, the capacitance decreases. As the capacitance is reduced, response time for recharging is improved, but due to additional hght dispersion, depth of modulation decreases. 

The theory therefore predicts an intensity modulation of 100 per cent in this geometry when the excitation pulse is sufficiently short. For pulses which do not satisfy the condition Ul o it is found that the depth of modulation is reduced and that there is a phase shift in the modulation term. The reason for this can be easily visualized on the classical model, for the Larmor precession during a long excitation pulse causes the dipoles to be distributed through an angle w At in the plane perpendicular to B, rather like a fan. In the limit that Wj At > 1, the dipoles are isotropically distributed in this plane and no modulation is observed. 

The time-independent terms in equations (15.51a,b,c) describe Hanle effect signals excited by the unmodulated component of the incident radiation density, equation (15.47), while the time-dependent terms in equation (15.51a) describe the phase shift and depth of modulation which is expected when a system having a damping constant F is periodically excited (Problem 15.10). Since this is a population effect these terms are independent of the applied magnetic field. 

In experiments involving transient excitation the depth of modulation will only be significant when the excitation pulse length At satisfies the condition (u2 < >2) 1 The... 

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