4. [20 pts, Past exam prob.] Below is a QWP-biased Pockels cell modulator. LiNbO

Question

4. [20 pts, Past exam prob.] Below is a QWP-biased Pockels cell modulator. LiNbO3 was used as the Pockels crystal and the applied voltage was set to induce a phase shift of A. By accident, the QWP was replaced by a half-wave plate (the direction of optic axis was maintained). Find the relation between the phase shift Ao and the detected intensity Idet. Use the trigonometric identities if needed. The transmission axis of the analyzer (TA) is tilted from Eo by 90°. A+B A+ B sin A+ sin B2 sin cos A +B cos A -cos B2 sin A+B OA LiNbO3 Pockels cell Analyzer Ex Ex Ex Eo Detector Sy switched to a HWP

Explanation / Answer

Optical Parametric Model

The normalized measured intensity values for a single diffusing particle as a function of the axial piezo z-position controlling the separation of the two confining surfaces is depicted by the black scatter plot in Fig. 1d. In addition, the signal of the normalized background intensity is shown in blue. From the data, two critical aspects are immediately apparent: 1) The overall amplitude of the particle signal oscillations is roughly twice the amplitude of the background signal oscillations. 2) The particle intensity is less than the background intensity for most data points. These observations cannot be explained by the model often used for interpreting iSCAT intensity data in which the reflectivity of the glass surface is ignored.

Idet = |Eref + Ep| 2 = I0(|rref | 2 + |rp| 2 + 2|rref rp|cos),

where Idet is the detected intensity at the particle position and is the relative phase shift of the two interfering light fields from the reflective reference surface, Eref , and the particle, Ep. Eq. predicts a particle intensity varying about a mean value I0(|rp| 2 +|rref | 2 ), which is greater and not less than the background intensity I0|rref | 2 and contradicts observation 2). Concerning observation 1), the background signal oscillations are of similar magnitude as the particle signal oscillations. This indicates that the fields originating from the glass and the particle reflections are of similar magnitude, and thus the glass reflection cannot be neglected.

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