Polarization of a photon beam

The different basis systems will be illustrated for two examples, linear polarization along the x-direction and right circular polarization. According to equ. (8.4) the electric field vector is represented as 

In the discussion of light polarization so far the Cartesian basis and spherical basis have been considered. Because the linear polarization might be tilted with respect to the (ex, e -basis, a third basis system has to be introduced against which such a tilted polarization state can be measured via its non-vanishing components. This coordinate system is called (e e and its axes are rotated by +45° with respect to the previous ones. This leads to a third representation of the arbitrary vector b  

An arbitrary polarization P of a photon beam can then be represented in either basis system in the helicity formulation by 

One then derives for the Stokes parameters of the photon beam with individual wavelets (j) in the helicity basis (superscript h)  

The polarization properties are often discussed for different definitions of the Stokes parameters. For the optical convention used in Parts A and B, one has 

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Figure 7.3 A schematic of a two-beam photon-force measurement system. Obj objective lens (lOOx oil immersion, N.A. 1.4), PBS polarization beam splitter, FI color filter for eliminating red illumination laser beam, F2 color filter for eliminating green illumination laser...

A photonic realization of qubit can be obtained through the polarization state of a photon or usingthe continuous phase and amplitude of a many-photon laser beam [5,48]. At first, the difficulty in achieving significant photon-photon interactions necessary for multi-qubit operations can be seen as a drawback of this proposal. However, it was demonstrated that scalable QC is possible using only linear optical circuits and single-photon sources and detectors [16]. The method (known as the KLM scheme for Knill, Laflamme and Milburn) [49] uses quantum interference with auxiliary photons at a beam splitter as the source of interactions, and has... 

To illustrate some of these principles the angular momentum of a photon will be examined [56]. Suppose a beam of circularly polarized light falls on a perfectly black absorbing surface, which not only heats up (E = hv) but also acquires a torque, on account of the angular momentum it absorbs. Circular polarization means that the probability of an elementary observation 0(P ) = The ratio of energy/torque = w(= 2m/), the angular frequency of... 

Figure 1.15 Tilted collision frame at the sample. The photon beam direction defines the z-axis the x- and y-axes are aligned with the major (a) and minor (b) axes of the polarization ellipse which lies in the plane perpendicular to the direction of the photon beam. X is the tilt angle between the x-axis and the plane of the storage ring. The direction of the emitted electron is described by the polar and azimuthal angles 0 and measured in the tilted...

Figure 1.17 An experimental set-up for electron spectrometry with synchrotron radiation which is well suited to angle-resolved measurements. A double-sector analyser and a monitor analyser are placed in a plane perpendicular to the direction of the photon beam and view the source volume Q. The double-sector analyser can be rotated around the direction of the photon beam thus changing the angle between the setting of the analyser and the electric field vector of linearly polarized incident photons. In this way an angle-dependent intensity as described by equ. (1.55a) can be recorded. The monitor analyser is at a fixed position in space and is used to provide a reference signal against which the signals from the rotatable analyser can be normalized. For all three analysers the trajectories of accepted electrons are indicated by the black areas which go from the source volume Q to the respective channeltron detectors. Reprinted from Nucl. Instr. Meth., A260, Derenbach et al, 258 (1987) with kind permission of Elsevier Science—NL, Sara Burgerhartstraat 25, 1055 KV Amsterdam, The Netherlands.

Fig. 5 (a) The contact potential difference (CPD) measured between the gold-coated monolayer of polyalanine and a gold substrate as a function of temperature, (b-d) The photoelectron spectra that were measured at 297 K, 264 K, and 250 K, respectively. The signal intensity is plotted vs the photoejected electrons kinetic energy. The photon energy used is 5 eV. Separate spectra are shown for a clockwise circularly polarized (+ red curve) photon beam and a counterclockwise circularly polarized (— blue curve) photon beam, (c) The photoelectron spectrum at 264 K, where the CPD is zero (see a). Here the spectrum does not depend on laser polarization and does not exhibit a broad resonance. PHYSICAL REVIEW B 68, 115418 (2003). Copy right permission granted. 

The experimental apparatus is depicted in Fig. 3 and is described in detail elsewhere [14]. It consists of a molecular beam scattering chamber, pulsed frequency-doubled dye laser, double fresnel rhomb polarization rotator, fibre bundles to coUect fluorescence from excited states, and time-gated photon counting and boxcar averaging equipment. 

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