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Unformatted text preview: rj 2 = 0.9, thus the ﬁnesseinvoking
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
righthanded 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 selfconsistency 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 selfconsistent 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 < 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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 Fall '11
 KirkW.Madison
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