PHYS 408 HOMEWORK 9 SOLUTIONS

9 thus the nesse invoking parameter r r1 r2 09 the

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Unformatted text preview: |rj |2 = 0.9, thus the ﬁnesse-invoking parameter r = r1 r2 = 0.9. The ﬁnesse is F= ￿ π |r| = 29.8 1 − |r| (3) For F ￿ 1, which is the case here, the approximate spectral width is δν ≈ νF c = = 5.03 MHz F 2F d 2 (4) 2 Polarization Use the convention eikz corresponds to a wave propagating in the +z direction. Also, the top component of the Jones vector crossed into the second component of the Jones vector is proportional to the direction of wave propagation; this is consistent with the convention used in Saleh and Teich as well in lecture, for a travelling wave (single ￿ ). This may seem arbitrary, but k it’s as conventional as choosing the +z direction to the be default direction of wave propagation, along with the choice of a right-handed coordinate system, both of which are conventions chosen in many branches of physics. Regarding handedness, the convention chosen here is to consider a snapshot in time and see which direction the electric ﬁeld rotates, as seen from an observer looking at the wave approaching. Marking was lax on the Jones vectors, for the reason of Jones vector degeneracy (there is no unique Jones vector), and few people rigorously labeled their Jones vector components. Marking was more rigorous on the handedness/polarization, and components of marking included self-consistency of answer, explicit calculation of phase angle or some other system to determine handedness/polarization, and outright statement of conventions used. The most marks deducted occured in cases where the answers were not self-consistent and there was no statement of handedness convention and no explicit method of calculation for handedness was provided. 2.1 (a) The Jones vector and normalized Jones vector are ￿ J = Ax Ay = ieiπ/3 2i 1 1 ˆ ￿ J=√ 5 2e−iπ/3 (5) The phase diﬀerence is φ = −π /3, which is not linearly polarized (not 0 or π ) or circularly polarized (not ±π /2), and the components are of unequal magnitude, so it is elliptically polarized. Further, that φ &lt; 0 implies that – for an observer looking at the wave as it travels towards the observer – the electric ﬁeld vector rotates counter clockwise in an elliptical fas...
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