Optics: measuring and testing – By polarized light examination – Of surface reflection
Reexamination Certificate
2001-06-27
2003-04-15
Allen, Stephone B. (Department: 2878)
Optics: measuring and testing
By polarized light examination
Of surface reflection
C250S225000
Reexamination Certificate
active
06549283
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Technical Field of the Invention
The present invention relates in general to determining the degree of polarization of light having unknown polarization and, more particularly, to determining the degree of polarization by minimizing the effects of polarization dependence of a light-wave power meter.
2. Description of Related Art
Light is a transverse electromagnetic wave. If light has an electric field vector that resides in a particular fixed plane, the light is said to be polarized in that particular fixed plane. Two orthogonal polarized planar light waves of the same frequency result in a polarized electric field. The light's polarization state is determined by the relative amplitudes and phases of these two light waves.
Unpolarized natural light, such as, for example, sunlight, can be conceptualized as a plurality of randomly-oriented atomic sources, with each source emitting a source of polarized light for only tens of nanoseconds. When electromagnetic waves of equal frequency are super-imposed on one another, they yield a polarized resultant electromagnetic wave. When uncorrelated electromagnetic waves are continuously emitted by a natural light source, such as, for example, the sun, the polarization state of the light emitted by the natural light source varies randomly. If the period of the emitted light's polarization state is shorter than what can be perceived, the light is said to be unpolarized.
Light is most typically a mixture of polarized and unpolarized light and is, therefore, said to be partially polarized. Some percentage of the partially-polarized light has a non-random phase relationship. The degree of polarization (DOP) of light is defined as:
DOP
=
I
pol
I
pol
+
I
unpol
(
1
)
wherein I
pol
and I
unpol
are measured intensities of a polarized light component and of an unpolarized light component, respectively. DOP is a ratio of the polarized light component (I
pol
) to the total light (I
pol
+I
unpol
). DOP can range from 0 to 1. Sometimes DOP is referred to as a percentage.
If the DOP of a source of linearly-polarized light is to be measured, a linear polarizer can be rotated in the path of the linearly-polarized light. At some angle during the rotation of the linear polarizer, a maximal transmitted light intensity will be found. Perpendicular to the angle at which the maximal transmitted light intensity is found, a corresponding minimal transmitted intensity of the light will be found. If the light is 100% linearly polarized, the minimal transmitted intensity will equal 0 and the DOP will equal 1. If, however, the DOP of totally unpolarized light is measured, as the polarizer is rotated, the transmitted light will have the same intensity for all orientations of the linear polarizer. In this case, the DOP equals 0.
Most light is neither totally polarized nor totally unpolarized, but is rather a combination thereof. When partially-linearly polarized light is transmitted through a linear polarizer and the linear polarizer is rotated about an axis of propagation of the light, the partially-linearly-polarized light will have a maximal, as well as a minimal, non-zero, transmitted intensity. The maximal and the minimal non-zero transmitted intensities will be 90° apart from one another in rotation of the linear polarizer about the axis of propagation of the light.
The polarized transmitted intensity component of the light is represented by:
I
pol
=I
max
−I
min
(2)
A resolved unpolarized component of the light contributes:
I
min
=
I
unpol
2
(
3
)
Therefore, substituting equations 2 and 3 into equation 1 yields:
DOP
=
I
max
-
I
min
I
max
+
I
min
(
4
)
The above-described technique for measuring the DOP of partially-linearly-polarized light has been presented in many optical texts. However, linear polarization is an extreme example of elliptical polarization. Most typically, light is partially-elliptically polarized. When the light is partially-elliptically polarized, the measurement technique described above will not yield satisfactory results, because the technique requires the polarized component of the light to be linear. A more general technique is required to measure the DOP for any polarization state.
In Mueller calculus, power and polarization of light can be completely defined by the Stokes vector of the light. The Stokes vector (S) comprises four vectors: S
0
, S
1
, S
2
, and S
3
, which define the intensity, preference for horizontal polarization, preference for +45° polarization, and preference for right-circular polarization, respectively. S is usually written as a column vector as follows:
S
=
[
S
0
S
1
S
2
S
3
]
(
5
)
All possible polarization states of light can be uniquely represented by a Stokes vector pointing from the center of a sphere to a point on the surface of the sphere.
Any optical component, such as, for example, a wave plate (e.g., a retarder) or a polarizer, can be expressed as a 4×4 matrix called a Mueller matrix. Below are Mueller matrices for a linear polarizer, a quarter-wave plate, and a half-wave plate, respectively, as a function of rotation about an axis of propagation of a light source:
M
pol
(
c
)
=
[
1
cos
(
2
c
)
sin
(
2
c
)
0
cos
(
2
c
)
cos
2
(
2
c
)
sin
(
2
c
)
cos
(
2
c
)
0
sin
(
2
c
)
sin
(
2
c
)
cos
(
2
c
)
sin
2
(
2
c
)
0
1
0
0
0
]
(
6
)
M
qwp
(
e
)
=
[
1
0
0
0
0
0.5
[
cos
(
4
e
)
+
1
]
0.5
sin
(
4
e
)
-
sin
(
2
e
)
0
0.5
sin
(
4
e
)
0.5
[
-
cos
(
4
e
)
+
1
]
cos
(
2
e
)
0
sin
(
2
e
)
-
cos
(
2
e
)
0
]
(
7
)
M
hwp
(
b
)
=
[
1
0
0
0
0
cos
(
4
b
)
sin
(
4
b
)
0
0
sin
(
4
b
)
-
cos
(
4
b
)
0
0
0
0
-
1
]
(
8
)
The linear polarizer (M
pol
) is rotated an angle c, the quarter-wave plate (M
qwp
) is rotated an angle e, and the half-wave plate (M
hwp
) is rotated an angle b about the axis of propagation of the light source.
An incident polarized light wave, characterized by a Stokes vector S
in
, interacts with an optical component, characterized by its Mueller matrix M
device
, such that an emerging light wave can be characterized by an output Stokes vector S
out
, wherein:
S
out
=M
device
·S
in
(9)
More generally, if a series of optical components represented by M
n
. . . ·M
3
·M
2
·M
1
are encountered by the incident polarized light wave represented by S
in
, the Stokes vector S
out
that describes light transformed by the series of components can be represented as:
S
out=
M
n
. . . ·M
3
·M
2
·M
1
·S
in
(10)
A polarizer in effect acts as a discriminator that passes a maximal transmitted intensity of light having a polarization state that coincides with the polarization of the polarizer and a minimal transmitted intensity at a polarization state orthogonal thereto. In addition to linear polarizers, elliptical and circular polarizers are also known.
The intensity of the light emerging from the polarizer is typically measured using a light-wave power meter. An ideal light-wave power meter has no polarization dependence (PD) and also has perfect linearity throughout a measurement range of the light-wave power meter. One of the keys to accurate measurement of the DOP of light of unknown polarization is the ability of the polarizer to discriminate between different states of polarization.
To measure the DOP of linearly-polarized light, the linear polarizer must be rotated at least 180° about the axis of propagation of the light in order to capture the minimal and maximal transmitted intensities of the light. However, rotation of the polarizer causes problems. As the polarizer is rotated, the light-wave power meter is subjected to a plurality of states of polarization, which lead to measurement uncertainty due to polarization dependence (PD) of the light-wave power meter. PD is a power-loss mechanism that varies as the polarization of an
Agilent Technologie,s Inc.
Allen Stephone B.
Spears Eric J
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