Exhibit 1

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Microsoft_HoloLens_WSOU000005738

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Microsoft_HoloLens_WSOU000005739

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Microsoft_HoloLens_WSOU000005740

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Microsoft_HoloLens_WSOU000005741

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Microsoft_HoloLens_WSOU000005742

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Microsoft_HoloLens_WSOU000006006

* 

POLARIZATION 5.23 

Vibration direction of 

ordinary ra.Y (fast axis) 

FIGURE 9 Light incident normally on the front surface of a retardation plate showing the vibration directions of the ordinary and extraordinary rays. In a positive uniaxial crystal, the fast and slow axes are 

as indicated in parentheses; in a negative uniaxial crystal, the two axes 

are interchanged. 

A retardation plate can be made from a crystal which is cut so that the optic axis lies in 

a plane parallel to the face of the plate, as shown in Fig. 9. Consider a beam of unpolarized 

or plane-polarized light normally incident on the crystal. It can be resolved into two 

components traveling along the same path through the crystal but vibrating at right angles 

to each other. The ordinary ray vibrates in a direction perpendicular to the optic axis, 

while the extraordinary ray vibrates in a direction parallel to the optic axis. In a positive 

uniaxial crystal ne > n0 , so that the extraordinary ray travels more slowly than the ordinary 

ray. The fast axis is defined as the direction in which the faster-moving ray vibrates; thus in 

a positive uniaxial crystal, the fast axis (ordinary ray) is perpendicular to the optic axis, 

while the slow axis ( extraordinary ray) coincides with the optic axis. For a negative 

uniaxial crystal, the fast axis coincides with the optic axis. 

Figure 10 shows how the state of polarization of a light wave changes after passing 

through retardation plates of various thicknesses when the incident light is plane-polarized 

at an azimuth of 45° to the fast axis of the plate. If the plate has a retardation of A/8, which 

means that the ordinary and extraordinary waves are out of phase by n/4 with each other, 

the transmitted light will be elliptically polarized with the major axis of the ellipse 

coinciding with the axis of the original plane-polarized beam. As the retardation gradually 

increases (plate gets thicker for a given wavelength or wavelength gets shorter for a given 

plate thickness), the ellipse gradually turns into a circle, but its major axis remains at 45° to 

the fast axis of the retardation plate. For a retardation of A/4, the emerging light is right 

circularly polarized. As the retardation continues to increase, the transmitted light 

becomes elliptically polarized with the major axis of the ellipse lying perpendicular to the 

plane of the incident polarized beam, and then the minor axis of the ellipse shrinks to zero 

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5.24 PHYSICAL OPTICS 

* * * * 45° 

* * * * 45° 45° 45° 

FIGURE 10 State of polarization of a light wave after passing through a crystal plate whose 

retardation is indicated in fractions of a wavelength (phase retardation 2n/ A times these 

values) and whose fast axis is indicated by the double arrow. In all cases the incident light is 

plane-polarized at an azimuth of 45° to the direction of the fast axis. 

and plane-polarized light is produced when the retardation becomes A/2. As the 

retardation increases further, the patterns change in opposite order and the polarized light 

is left circularly polarized when the retardation equals 3A/4. Finally, when the retardation 

is a full wave, the incident plane-polarized light is transmitted unchanged although the 

slow wave has now been retarded by a full wavelength relative to the fast wave. 

The most common type of retardation plate is the quarter-wave plate. Figure 11 shows 

how this plate affects the state of polarization of light passing through it when the fast axis 

is positioned in the horizontal plane and the azimuth of the incident plane-polarized light 

is changed from e = 0° to e = 90°. When e = 0°, only the ordinary ray (for a positive 

birefringent material) passes through the plate, so that the state of polarization of the 

beam is unchanged. When 0 starts increasing, the transmitted beam is elliptically polarized 

with the major axis of the ellipse lying along the fast axis of the A/4 plate; tan e = b/a, the 

* * * * 45° 

goo 

FIGURE 11 State of polarization of a light wave after passing through a A/4 plate (whose fast axis 

is indicated by the double arrow) for different azimuths of the incident plane-polarized beam. 

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POLARIZATION 5.25 

ratio of the minor to the major axis of the ellipse. In the next case, 0 = 15° and 

tan 0 = 0.268, and so the ellipse is long and narrow. When the plane of vibration has 

rotated to an azimuth of 45°, the emerging beam is right circularly polarized (the same 

situation as that shown in the second part of Fig. 10). For values of 0 between 45 and 90°, 

the light is again elliptically polarized, this time with the major axis of the ellipse lying 

along the direction of the slow axis of the A/4 plate. The angle shown in the figure is 60°, 

and tan 60° = 1.732, so that b/a (referred to the fast axis) is greater than unity. When 0 

increases to 90°, the plane of vibration coincides with the slow axis and the transmitted 

light is again plane-polarized. As 0 continues to increase, the transmitted patterns repeat 

those already described and are symmetric about the slow axis, but the direction of 

,rotation in the ellipse changes from right-handed to left-handed, so that left-circularly 

polarized light is produced when 0 = 135°. 

The definition of right- and left-circularly polarized light should be clear from Figs. 10 

and 11. When the rotation is clockwise with the observer looking opposite to the direction 

of propagation, the light is called right-circularly polarized; if the rotation is 

counterclockwise, the light is called left-circularly polarized. 26 When circularly polarized 

light is reflected from a mirror, the direction of propagation is reversed, so that the sense 

of the circular polarization changes; i.e., left-circularly polarized light changes on reflection 

into right-circularly polarized light and vice versa. Therefore, in experiments involving 

magnetic fields in which the sense of the circularly polarized light is important,27'

28 it is 

important to know which kind one started with and how many mirror reflections occurred 

in the rest of the light path. Cyclotron resonance experiments can sometimes be used to 

determine the sense of the circular polarization.28 Another method utilizing a polarizer and 

A/4 plate has been described by Wood.29 

The behavior of a half-wave plate in a beam of plane-polarized light is completely 

different from that of a quarter-wave plate; the transmitted light is always plane-polarized. 

If the incident plane of vibration is at an azimuth 0 with respect to the fast axis of the A/2 

plate, the transmitted beam will be rotated through an angle 20 relative to the azimuth of 

the incident beam. The case showing 0 = 45° where the phase of vibration is rotated 

through 90° is illustrated in the fourth part of Fig. 10. In this situation the extraordinary 

beam is retarded by half a wavelength relative to the ordinary beam (for a positive 

birefringent material), hence the name, half-wave plate. If the polarizer is fixed and the 

A/2 plate is rotated ( or vice versa), the plane of vibration of the transmitted beam will 

rotate at twice the frequency of rotation of the A/2 plate. 

Quarter-wave plates are useful for analyzing all kinds of polarized light. In addition, 

they are widely employed in experiments using polarized light, e.g., measurements of the 

thickness and refractive index of thin films by ellipsometry or measurements of optical 

rotary dispersion, circular dichroism, or strain birefringence. Polarizing microscopes, 

interference microscopes, and petrographic microscopes are usually equipped with A/4 

plates. In some applications the A/4 plate is needed only to produce circularly polarized 

light, e.g., for optical pumping in some laser experiments, or to convert a partially 

polarized light source into one which appears unpolarized, i.e., has equal amplitudes of 

vibration in all azimuths. For these and similar applications, one can sometimes use a 

circular polarizer which does not have all the other properties of a A/4 plate (see Pars. 73 

to 76 in Ref. 1). 

The customary application for a A/2 plate is to rotate the plane of polarization through 

an angle of 90°. In other applications the angle of rotation can be variable. Automatic 

setting ellipsometers or polarimeters sometimes employ rotating A/2 plates in which the 

azimuth of the transmitted beam rotates at twice the frequency of the A/2 plate. 

7. Matrix Methods for Computing Polarization In dealing with problems involving 

polarized light, it is often necessary to determine the effect of various types of polarizers 

(linear, circular, elliptical, etc.), rotators, retardation plates, and other polarizationsensitive devices on the state of polarization of a light beam. The Poincare sphere 

-"Ill 

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