Biomedical Engineering Reference
In-Depth Information
in which
d
x
'. It should be noted that the ellipse folds into a straight line, producing
linear light if (1) E
x
6¼
d ¼ d
y
'-
0 and E
y
¼
0, or (2) E
y
6¼
0 and E
x
¼
0, or (3)
d ¼
m
p
in which m is a
positive or negative integer. The light becomes circular if e
x
¼
e
y
and
d ¼
(2m
þ
1)
p
/2, since
E
x
and E
y
would then have equal amplitudes and be in phase quadrature.
The polarization properties of light become particularly important for anisotropic media in
which the physical properties are dependent on direction (i.e., E
x
is different from E
y
and thus
values e
x
,e
y
,and
will vary along the propagation path, as depicted with a birefringent crys-
tal, polarization preserving optical fiber, or aligned tissue fibers such as collagen).
d
EXAMPLE PROBLEM 17.2
Consider a general solution to the wave equation represented as a plane electromagnetic wave
(in SI units) given by the expressions
*10
14
(t
E
x
¼
0,
E
z
¼
0,
E
y
¼
2 cos
½
2
p
x
=
c
Þþp=
2
For the equations shown, determine the frequency (f), wavelength (
l
), direction of motion (x, y, or z),
amplitude (A), initial phase angle (
f
), and polarization of the wave (linear, circular, elliptical).
Solution
The general form of a plane electromagnetic wave can be expressed as E
¼
A cos(kx
o
t
þ f
),
3*10
8
meters/second. The preceding equation can
where k
¼
2
p
/
l
,
l ¼
c/f,
o ¼
2
p
f, and c
¼
*10
14
t-(2
*10
14
x/c)
therefore be written in general form as E
y
¼
2 cos[2
p
p
þ p
/2]. Thus, compar-
1*10
14
Hertz,
3*10
6
ing the two equations yields the values f
¼
l ¼
¼
3 micrometers, motion is in
the positive x direction, A
¼
2 Volts/meter,
f ¼ p
/2, and since E
x
¼
E
z
¼
0, the wave must be
linearly polarized in the
y
direction.
17.1.3 Absorption, Scattering, and Luminescence
Having discussed polarization, attention will now be focused on the optical properties of
light that describe the changes in the light as it passes through biological media. The optical
properties of the light are defined in terms of the absorption, scattering, and anisotropy of
X
Ex
Z
Z=Zo
Hy
Y
FIGURE 17.3
Polarization propagation of an
E
wave.
