Biophotonics_Concepts_to_Applications

which defines a circle. Choosing the phase difference to beδ=+π/2 and using the
relationship cos (a+b) = (cos a)(cos b) + (sin a)(sin b) to expand Eq. (2.9), then
Eqs. (2.8) and (2.9) become

ExðÞ¼z;t exE 0 cosðxtkzÞð 2 :17aÞ

EyðÞ¼z;t eyE 0 sinðxtkzÞð 2 :17bÞ

In this case, the endpoint ofEwill trace out a circle at a given point in space, as
Fig.2.7illustrates. To see this, consider an observer located at some arbitrary point
zreftoward whom the wave is moving. For convenience, pick the reference point at
zref=π/k at t = 0. Then from Eq. (2.17a) it follows that

ExðÞ¼z;t exE 0 andEyðÞ¼z;t 0 ð 2 : 18 Þ

so thatElies along the negative x axis as Fig.2.7shows. At a later time, say at
t=π/2ω, the electricfield vector has rotated through 90° and now lies along the
positive y axis. Thus as the wave moves toward the observer with increasing time,
the resultant electricfield vectorErotates clockwise at an angular frequencyω.It
makes one complete rotation as the wave advances through one wavelength. Such a
light wave isright circularly polarized.

E

Ey

Ex

Ex

Ey

Phase difference

between Exand E

E

y

Ey

Ex

x

y

Ellipse traced

out by E in a

travelling wave

z

Direction

of wave

propagation

δ

Fig. 2.6 Elliptically polarized light results from the addition of two linearly polarized waves of
unequal amplitude having a nonzero phase differenceδbetween them

34 2 Basic Principles of Light