Continuously variable beam splitter

An optical beam splitter separates an input beam into two exit beams which angularly diverge from each other by a continuously variable amount. The degree of angular divergence is controlled by rotating a compound cylinder composed of a half-cylinder of birefringent material and a half-cylinder of glass about their common cylindrical axis. The cylinder is placed between a pair of plano-concave sections, which match the curvature and materials of the cylinder. The ordinary refractive index of the birefringent half-cylinder section is matched to that of the isotropic glass half-cylinder, which limits the changes in exit beam angular divergence to only one of the beams. A phase compensation block preceding the birefringent plano-concave section and the compound cylinder prevents the accumulation of optical phase between the two exit beams. The interfaces between the fixed birefringent plano-concave section and the birefringent half-cylinder as well as the glass half-cylinder and the fixed glass plano-concave sections are immersed in an index matching oil to minimize optical wavefront distortion at these interfaces.

FIELD OF THE INVENTION 
The present invention relates to a beam splitter for electromagnetic 
radiation, in particular for light. The beam splitter splits an incident 
beam into two output beams, the angle of divergence between which is 
continuously variable. 
BACKGROUND OF THE INVENTION 
A beam splitter is a commonly used element in optical apparatus. A beam 
splitter splits an incident beam into two output beams which diverge at a 
fixed angle. Other commonly used beam splitting prisms split an incident 
beam into two substantially parallel output beams such as described in the 
book of M. Francon, and S. Mallick, "Polarization Interferometers", 
Wiley-Interscience, 1971, pp. 25. However, these prisms have the 
disadvantage of the angle of separation between the two exit beams of the 
prism is fixed. Continuously variable beam splitters are described in the 
article of R. Drougard, and J. Wilczynski, "New Polarization 
Interferometer For Fourier Analysis", J. Opt. Soc. Am. 55, 1638 (1965) and 
in the book of M. Francon et al. at pages 40-42. However, the Drougard 
beam splitter requires complex matched counter rotation of two 
Wollaston prisms relative to a precisely-aligned, precision half-wave plate 
to avoid the generation of four exit beams from the variable beam 
splitter. This approach results in a variable beam splitter that is 
difficult to operate and that requires several expensive optical 
components. 
Optical apparatus such as the optical apparatus described in U.S. Pat. No. 
4,758,092 describes an apparatus and technique for probing dynamic sheet 
charged density variations in an integrated semiconductor device. This 
apparatus uses a beam splitting prism in a phase-contrast interferometer 
which optically detects the electrical signals in a functioning electronic 
circuit. The operation of such an apparatus can be substantially enhanced 
by a simple to use continuously variable beam splitter. The teaching of 
U.S. Pat. No. 4,758,092 is incorporated herein by reference. 
SUMMARY OF THE INVENTION 
It is an object of the present invention to provide an improved continuous 
variable beam splitter. 
It is another object of the present invention to provide a continuously 
variable beam splitter having a simple noncomplex mechanical motion. 
It is yet another object of the present invention 
A broad aspect of the present invention is an optical apparatus for 
splitting a beam into two diverging beams wherein the angle between the 
two diverging beams is continuously variable. 
The optical apparatus has an input subsystem and an output subsystem. The 
input subsystem splits the incident beam into a first and second 
component. 
The output subsystem causes the first and second components to diverge at a 
continuously variable angle. 
In a more particular aspect of the present invention, the optical apparatus 
has an input subsystem which separates an incident normally polarized beam 
into two colinear components having orthogonal polarization. 
In another more particular aspect of the present invention, the input 
subsystem is formed from a first and second block of birefringent 
material. The first and second blocks have the crystal axis orthogonally 
oriented with respect to each other. 
In another more particular aspect of the present invention, the output of 
the input subsystem has a concave cylindrical surface which matches a 
convex cylindrical surface on the output subsystem. 
In another more particular aspect of the present invention, the apparatus 
has an output subsystem formed from a cylindrical optical element. 
In another more particular aspect of the present invention, the cylindrical 
optical element is formed from two semicylinders adhesively attached along 
the plane surfaces of the semicylinder. One semicylinder is a birefringent 
material and the other is nonbirefringent material. 
In another more particular aspect of the present invention, at the 
interface of the semicylinders the incident beam is split into two beams 
diverging at an angle. 
The angle is determined by the relative angle between the semicylinder 
plane surface and the incident beam.

DETAILED DESCRIPTION 
FIGS. 1, 2 and 3 schematically show a side view of the basic structure of 
the apparatus of the present invention. Apparatus 100 has an input 
subsystem 102 and output subsystem 104. Input subsystem 102 is composed of 
a first part 106 and a second part 108. The first and second parts are 
formed from a birefringent material. The principal axis of the first and 
second parts are nonparallel and are preferably orthogonal. Part 108 has a 
concave output surface 114. Output subsystem 104 has a convex surface 116 
which is adapted for slidable engagement with surface 114. The radius of 
concave surface 114 is the same as convex surface 116. Between surfaces 
114 and 116 there is a fluid having the same index of refraction as the 
normal index of refraction of part 108 and subsystem 104, which permits 
surface 114 to slide with respect to surface 116. Part 104 is birefringent 
and has the same principal axis as part 108. Incident beam 110 has 
polarization 118 which is at angle 120 (preferably 45.degree.) with 
respect to y-axis 122. Birefringent part 106 splits incident beam 110 into 
two colinear beams having a polarization along x-axis 124 and y-axis 122. 
The phase of the x and y polarizations is changed by part 106. The 
orientation of the principal axis of part 108 and subsystem 104 is so that 
the phase difference is reversed. Therefore, the x polarized output beam 
126 and the y-polarized output beam 128 have the same phase. If part 106, 
part 108 and subsystem 104 are of the same birefringent material, to 
achieve equal phase at the output, distance 130 is equal to the sum of 
radius 134 and distance 132. Subsystem 104 is in the shape of a 
semicylinder having planar surface 136. When planar surface 136 is 
perpendicular to incident beam 110, beams 128 and 126 are not deviated 
from the direction of the incident beam. When surface 136 is not 
perpendicular to the direction of the incident beam 110 y-polarized beam 
128 is deviated from the direction of the incident beam as shown in FIGS. 
2 and 3 by angle 140 which is continuously variable to the direction of 
incident beam 110. The x-polarized beam 126 is not deviated if the 
ordinary index of refraction of output subsystem 104 is the same as the 
index of refraction of region 150 outside of surface 136. 
FIG. 4 shows a perspective diagram a specific embodiment of the 
continuously variable beam splitter according to the present invention. A 
cylinder composed of two sections, 6,8 is rotated about its axis 14. This 
action varies the angle of the interface between the birefringent portion 
6 and the glass portion 8 of the cylinder. By matching the refractive 
index of the glass portion of the cylinder 8 to the ordinary refractive 
index of the birefringent portion of the cylinder 6, light polarized along 
the x-axis 24 is not refracted at this interface 30. However, light 
polarized along the y-axis 26 will see a refractive index change at the 
interface between the birefringent 6 and glass 8 sections of the cylinder. 
Therefore, input light 16 polarized along the x-axis 24 will exit the 
variable beam splitter undeviated 18, while input light 16 polarized along 
the y-axis 26 will exit the variable beam splitter 20 with a slight 
divergence angle, .alpha., 34. 
Input light 16 to the variable beam splitter is polarized at 45 degrees to 
the x-axis in the x-y plane. This light travels through the birefringent 
material of section 2, which may be made of quartz. The y polarized 
portion of the input light travels at a phase velocity of c/n.sub.c, while 
light polarized along the x-axis travels with a phase velocity of 
c/n.sub.o, where c is the speed of light in a vacuum, and n.sub.e and 
n.sub.o are the extraordinary and ordinary indices of refraction 
respectively. After traveling through section 2, the x and y polarized 
portions of the input beam will have accumulated a phase difference of 
.DELTA..phi..sub.2 =(n.sub.e -n.sub.o)l.sub.2, where l.sub.2 is the length 
of section 2 along z-axis 28. Similarly, as the two polarizations travel 
through sections 4 and 6, the x and y polarizations will accumulate a 
phase difference between them of 
EQU .DELTA..phi..sub.4,6 =(n.sub.o -n.sub.e)(l.sub.4 +l.sub.6), 
where l.sub.4 is the minimum thickness of section 4 and l.sub.6 is the 
radius of the half-cylinder 6. Notice that if l.sub.2 =l.sub.4 +l.sub.6, 
the accumulated phase difference between the x and y polarizations will be 
zero. At the interface 30 between cylindrical sections 6 and 8, the x and 
y polarizations will refract differently. Since the ordinary refractive 
index along x-axis 24 of section 6 matches the isotropic refractive index 
of section 8, the x polarization will not refract at this interface. And 
hence, it will travel through the cylindrical section 8 and the 
plano-concave section 10 undeviated. However, the y polarized light will 
see a refractive index change of n.sub.c -n.sub.o at the interface 30 
between sections 6 and 8. Hence, this polarization will refract by an 
amount given by 
##EQU1## 
where .theta., 36, is the angle that the cylinder, composed of section 6 
and 8, has been rotated about its axis 14 relative to a vertical reference 
plane 22, and angle .alpha., 34, is the divergence angle between the two 
exit beams 18 and 20. For small values of the birefringence, the exit 
angle .alpha. is approximately given by 
EQU .alpha.=.DELTA.n.theta., 
where .DELTA.n=n.sub.e -n.sub.o. The concave 32 face of section 10 has a 
matching curvature to the half-cylinder section 8 and both sections are 
made of the same material, which may be Hoya FEL-1 glass. Sections 8 and 
10 provide an index matched glass path from the beam splitting interface 
30 to the outside of the matching oil bath 12 to minimize the effect of 
optical inhomogenetities and thermal blooming that would otherwise occur 
in the index matched bath. 
The continuously variable beam splitter, according to the present 
invention, can be used as beam splitter 14 of FIG. 1 of U.S. Pat. No. 
4,758,092 incorporated herein by reference above. 
A partial list of the birefringent materials from the Handbook of Optics, 
W. G. Driscoll, McGraw-Hill, p. 10-107 useful to practice the present 
invention are: 
Quartz 
Calcite 
Rutile (Titanium Dioxide) 
Cadmium Selenide 
Magnesium Flouride 
Cadmium Sulfide 
Apophyllite 
Zinc Sulfide 
Lithium Niobate 
Barium Titanate 
ADP 
AD*P 
KDP 
KD*P 
Sapphire 
Mica 
In summary, the present invention relates to a beam splitter for 
electromagnetic radiation, in particular for light. The beam splitter 
splits an incident beam into two output beams, the angle of divergence 
between which is continuously variable.