15.1 Basic Concepts and Formulae
711
Zone Plate
1
a
+
1
b
=
nλ
r 2
n
=
1
f n
(15.44)
where a and b are the distances of the object and image from the zone plate, r n is
the radius of the nth zone and f the focal distance.
Polarization
Let the x- and y-components of the electric vector be given by
E x = a 1 sin ωt
(15.45)
E y = a 2 sin(ωt + δ)
(15.46)
E 2
x
a 2
1
+
E 2
y
a 2
2
− 2
E x E y
a 1 a 2
cos δ = sin
2
δ
(15.47)
(i) Plane-polarized (linearly polarized) light:
If
δ = 2nπ where n = 0, 1, 2, . . . for which
E y =
a 1
a 2
E x
(15.48)
or
δ = (2n + 1)π, for which
E y = −
a 1
a 2
E x
(15.49)
In either case the electric field oscillates on a straight line.
(ii) Elliptically polarized light:
If δ = (n + ½)π, where n = 0, 1, 2, . . . and a 1 = a 2
E 2
x
a 2
1
+
E 2
y
a 2
2
= 1
(15.50)
If δ = π/2, 5π/2, 9π/2, . . . the tip of the electric vector rotates clockwise for
an observer towards whom light approaches, and the light is said to be left-handed
elliptically polarized.
If δ = 3π/2, 7π/2, 11π/2, . . . the ellipse is described in the counterclockwise
direction and the light is said to be right-handed elliptically polarized.
(iii) Circularly polarized light
If δ = (n + ½)π where n = 0, 1, 2, . . . and a 1 = a 2 = a
E
2
x + E
2
y = a
2
(15.51)
Right-handed and left-handed circularly polarized light are described as in case (ii).
711
Zone Plate
1
a
+
1
b
=
nλ
r 2
n
=
1
f n
(15.44)
where a and b are the distances of the object and image from the zone plate, r n is
the radius of the nth zone and f the focal distance.
Polarization
Let the x- and y-components of the electric vector be given by
E x = a 1 sin ωt
(15.45)
E y = a 2 sin(ωt + δ)
(15.46)
E 2
x
a 2
1
+
E 2
y
a 2
2
− 2
E x E y
a 1 a 2
cos δ = sin
2
δ
(15.47)
(i) Plane-polarized (linearly polarized) light:
If
δ = 2nπ where n = 0, 1, 2, . . . for which
E y =
a 1
a 2
E x
(15.48)
or
δ = (2n + 1)π, for which
E y = −
a 1
a 2
E x
(15.49)
In either case the electric field oscillates on a straight line.
(ii) Elliptically polarized light:
If δ = (n + ½)π, where n = 0, 1, 2, . . . and a 1 = a 2
E 2
x
a 2
1
+
E 2
y
a 2
2
= 1
(15.50)
If δ = π/2, 5π/2, 9π/2, . . . the tip of the electric vector rotates clockwise for
an observer towards whom light approaches, and the light is said to be left-handed
elliptically polarized.
If δ = 3π/2, 7π/2, 11π/2, . . . the ellipse is described in the counterclockwise
direction and the light is said to be right-handed elliptically polarized.
(iii) Circularly polarized light
If δ = (n + ½)π where n = 0, 1, 2, . . . and a 1 = a 2 = a
E
2
x + E
2
y = a
2
(15.51)
Right-handed and left-handed circularly polarized light are described as in case (ii).