Single-crystal – oriented-crystal – and epitaxy growth processes; – Processes of growth with a subsequent step acting on the...
Reexamination Certificate
2001-03-30
2003-11-04
Kunemund, Robert (Department: 1765)
Single-crystal, oriented-crystal, and epitaxy growth processes;
Processes of growth with a subsequent step acting on the...
C117S003000, C117S915000, C438S406000, C438S407000, C438S408000, C216S062000, C216S087000, C385S130000
Reexamination Certificate
active
06641662
ABSTRACT:
FIELD OF THE INVENTION
This invention relates in general to the field of fabricating ultra thin, birefringent metal oxide single-crystal films. More particularly, the invention relates to a method for fabricating single-crystal metal oxide wave retarder plates and the use of such wave retarder plates in optical waveguide polarization mode converters.
BACKGROUND OF THE INVENTION
Wave retarder plates, such as quarter-wave plates and half-wave plates, are components having important uses in manipulating polarization in optical systems. Such components depend on different phase changes that occur between the normal modes of a light wave propagating in anisotropic media rather than on selective refraction or absorption. Referring to
FIG. 1
, there is shown the index ellipsoid
1000
of an arbitrary anisotropic crystal having principal crystallographic axes X, Y and Z. For a plane wave propagating in the anisotropic crystal in an arbitrary direction defined by a unit vector {right arrow over (u)}, its two normal modes (i.e., the two orthogonal plane polarized components into which the plane wave may be decomposed) propagate at velocites c
0
a
and c
0
b
, respectively, where c
0
is the velocity of the plane wave in vacuum, and n
a
and n
b
are the refractive indices along the minor and major normal mode axes
1001
and
1002
of the index ellipse
1003
, respectively. The plane of the index ellipse
1003
is perpendicular to the unit vector {right arrow over (u)}. If n
b
>n
a
and assuming that the two normal modes are in phase as they enter into the anisotropic crystal, a phase difference &dgr;&phgr; between the two normal modes grows as they propagate through the crystal. The phase difference after the plane wave has propagated a distance d through the anisotropic crystal is:
δφ
=
2
π
λ
[
n
b
(
λ
)
-
N
a
(
λ
)
]
d
.
(
1
)
The amplitudes of the two normal modes are A cos &thgr; and A sin &thgr;, where &thgr; is the angle between the incident plane of polarization and the major axis
1002
of the index ellipse
1003
, and A is the amplitude of the incident plane wave. Combining the normal modes after a phase difference &dgr;&phgr; produces a different state of polarization. For &dgr;&phgr;=&pgr;/2 the resulting polarization is an ellipse with its major axis parallel to the major axis
1002
of the index ellipse
1003
, while for &dgr;&phgr;=&pgr; the polarization is again plane but rotated by an angle of 2&thgr;. In the particular case where &thgr;=45° the ellipse becomes a circle, and circularly polarized light is produced, with the opposite hand of circular polarization obtained when &thgr;=135°. For &dgr;&phgr;=&pgr; and &thgr;=45°, the plane of polarization is rotated by 90°.
Where the plane wave propagates along one of the principal crystallographic axis X, Y or Z, the normal modes have phase velocities of c
0
2
and c
0
n
3
, c
0
, and c
0
3
, and c
0
, and c
0
2
, respectively. For off-axis propagation (i.e., not along one of the principal crystallographic axes) the two normal modes which are orthogonally polarized relative to one another will be spatially displaced due to the “walk-off effect,” where the two normal modes will be spatially displaced relative to one another after propagating a certain distance. However, for off-axis propagation in a thin anisotropic crystal having a thickness on the order of 10 &mgr;m, the spatial displacement, which is less than 0.3 &mgr;m, is small relative to the typical beam size used in integrated optics and can therefore be ignored. It is noted that the walk-off effect is not present when light is propagating along one of the three principal crystallographic axes X, Y or Z. Single crystal slabs having planar major surfaces perpendicular to one of the principal crystallographic axes X, Y and Z are referred to as X-cut, Y-cut and Z-cut crystals, respectively.
For a uniaxial birefringent crystal, such as a LiNbO
3
crystal, the Z principal crystallographic axis is referred to as the optic axis and n
1
=n
2
. The normal modes for a uniaxial crystal are referred to as the ordinary mode and the extraordinary mode, respectively.
Birefringent single crystal slabs that produce phase differences of
δφ
=
π
2
(
2
m
+
1
)
and &dgr;&phgr;=&pgr;(2m+1), where m=0, 1, 2, . . . , are known as wave retarder plates, or more specifically quarter-wave plates and half-wave plates, respectively, where m is the order of the wave retarder plate.
Recently, zeroth order half-wave plates have been used in integrated optic circuits to provide TE-TM polarization mode converters. As described in Y. Inoue et al., “Polarization Mode Converter with Polyimide Half-Wave Plate in Silica-Based Planar Lightwave Circuits,” IEEE Photon. Technol. Lett., Vol. 6, pp. 626-628, August 1994, an optical waveguide section that supports both TE and TM modes of propagation is provided with a groove perpendicular to the direction of light propagation in the optical waveguide section. A zeroth-order polyimide half-wave plate is inserted in the groove with its optic axis at 45° with respect to the electric field vector of the TE and the TM modes in the waveguide section, respectively. Using such an arrangement, a TE wave propagating through the half-wave plate is converted to a TM mode wave, and a TM wave propagating through the half-wave plate is converted to a TE mode wave. The Inoue et al. polarization mode converter uses a 14.5 &mgr;m thick zeroth-order half-wave plate made of polyimide and provides low-loss polarization-independent operation at 1550 nm with TE-TM conversion ratios of greater than 20 dB. However, polyimide plates are hygroscopic which adversely impacts the long term performance and stability of the polarization mode converter. In addition, because of its relatively low birefringence, polyimide half-wave plates are relatively thick, which increases the diffraction losses that normally become significant in waveguides with smaller guided mode size, as well as distortion of narrow pulses passing through the polyimide half-wave plate caused by dispersion in that material. Fabricating the half-wave plate using a material having a larger birefringence would permit the wave plate to be thinner, and therefore reduce the diffraction losses and dispersion.
The phase difference, &dgr;&phgr; between the normal modes of a light wave after propagating through a wave plate may be expressed as of &dgr;&phgr;=R2&pgr;, where R is the optical retardance. For a half-wave plate R=½(2m+1), and for a quarter-wave plate R=¼(2m+1), where m=0, 1, 2 . . . . Therefore, the thickness d of a wave retarder plate may be expressed as
d
=
R
λ
[
n
b
(
λ
)
-
n
a
(
λ
)
]
.
(
2
)
From equation (2) and the definitions of the optical retardance R, it is apparent that the thickness d of the wave retarder plate decreases with its order m and is inversely proportional to the difference between the indices of refraction &eegr;
b
(&lgr;) and &eegr;
a
(&lgr;) along the normal mode axes in the wave retarder plate, the difference being indicative of the degree of birefringence of the material of the wave retarder plate in the direction of light wave propagation.
As mentioned above, it is desirable for the thickness d of the wave retarder plate to be as small as possible in order to minimize the diffraction and attenuation losses, and dispersion. Therefore, it is desirable to fabricate wave retarder plates, preferably of zeroth order (m=0), from crystals having a large birefringence, such as birefringent metal oxide crystals including LiNbO
3
, LiIO
3
, &bgr;-BaB
2
O
4
and LiB
3
O
5
. However, forming such ultra thin (e.g., d=10.6 &mgr;m for a zeroth-order LiNbO
3
half-wave plate at &lgr;=1550 nm) wave retarder plates of birefringent metal oxide crystals where the wave retarder plate retains the optical properties of the b
Levy Miguel
Osgood, Jr. Richard M.
Radojevic Antonije M.
Baker & Botts LLP
Kunemund Robert
The Trustees of Columbia University in the City of New York
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