Optical: systems and elements – Lens – Anamorphic
Reexamination Certificate
2002-06-11
2003-12-09
Dang, Hung Xuan (Department: 2873)
Optical: systems and elements
Lens
Anamorphic
Reexamination Certificate
active
06661582
ABSTRACT:
FIELD OF THE INVENTION
This invention relates to optical transmitters for use in communications systems, and to anamorphic lenses for use in such transmitters.
BACKGROUND OF THE INVENTION
The bandwidth explosion driven by Internet usage has created a demand for an adaptable, high performance optical network. One of the key technologies in delivering high performance over a long haul network is pump laser technology, particularly Raman Laser technology. From a market perspective, device output power is the most important performance characteristic of such devices. There is considerable commercial pressure to maximise the overall device output power and efficiency. It is of course an advantage to operate at high laser powers as this can increase the spacing between amplifier stations in an amplified system and thus provide a significant cost reduction. Unfortunately, high power laser sources tend to produce highly elliptical beam and highly divergent shapes which, for the reasons discussed below, substantially reduce the coupling efficiency and hence the effective device output power. In particular, it has been found that the high power lasers now becoming available have such a high degree of beam divergence and ellipticity that this cannot be fully corrected by the use of conventional anamorphic lenses.
A typical optical transmitter comprises a laser capable of producing a divergent beam, and a lens whereby that divergent beam is collimated into a parallel beam for launch into an optical wave guide. In general, the laser output comprises an elliptical beam, and it has been found that this ellipticity increases as higher power laser are employed. This is a particular problem as high beam ellipticity substantially reduces the coupling efficiency of the laser output into a circular fibre. Lack of overlap between the elliptical laser beam and the fibre mode reduces the coupling efficiency. This effect is illustrated in
FIGS. 1
a
to
1
c
of the accompanying drawings.
FIG. 1
a
is a cross-sectional view of an elliptical laser beam
10
.
FIG. 1
b
is a cross-sectional view of a typical optical fibre core
12
which is substantially circular in cross section.
FIG. 1
c
shows the mismatch effect in which the lobes
10
a
,
1
b
, fail to enter the fibre or waveguide
12
and thus represent lost energy. If for example the ellipticity of the laser beam is e, then the maximum theoretical coupling efficiency into a circular cross section fibre is given by the expression:
MaxEfficiency
=
4
e
[
1
+
e
]
2
For a typical laser beam ellipticity of about 3.0, the coupling efficiency is thus reduced to about 75%, which translates into a loss of 1.25 dB without taking into account other losses. Since, for most pump laser products, output power is an exceptionally strong market driver, there is great incentive to solve this problem. To correct this loss of efficiency resulting from beam ellipticity, a number of workers have employed anamorphic lenses in conjunction with the laser. In a conventional anamorphic lens design, the two lens surfaces are crossed toroidal surfaces. An example of an anamorphic lens might for example be crossed cylinders, each of appropriate radius of curvature. One surface may comprise a cylindrical lens surface that collimates the laser beam in one plane and the second surface is a cylindrical lens that collimates the beam in the orthogonal plane. A general expression for the surface contour of each surface of such a lens is typically a polynomial expression of the form:
2
)
z
=
y
2
R
y
+
R
y
2
-
(
1
+
k
y
)
y
2
+
α
1
y
2
+
α
2
y
4
+
α
3
y
6
+
α
4
y
8
+
α
5
y
10
+
α
6
y
12
+
…
3
)
z
=
x
2
R
x
+
R
x
2
-
(
1
+
k
x
)
x
2
+
α
1
x
2
+
α
2
x
4
+
α
3
x
6
+
α
4
x
8
+
α
5
x
10
+
α
6
x
12
+
…
The first term on the left of each expression represents the curvature of the respective lens surface, and the remaining polynomial terms provide aberration correction. However, it has been found that the above designs only provide effective aberration correction along the x and y axes. The even aspheric surfaces set out in equations 2) and 3) provide aberration correction using a respective conic term, k
x
or k
y1
, plus even polynomial terms, a sufficient number of terms being taken to achieve the desired accuracy. For the sake of simplicity, one can regard the quadratic terms as supplying the lens curvature, whereas any quartic terms may be thought of as applying correction for third order aberration, and so on.
Aberration is often expressed as a wave front distortion, in which case, the amount of distortion is proportional to the fourth power of the lens NA (numerical aperture) and the focal length. A good rule of thumb for substantially ‘aberration free’ performance is that the wave distortion must not exceed &lgr;/4 across the aperture. To demonstrate the lack of efficiency of a conventional lens structure, a ray tracing program was used to calculate the distortion for a typical anamorphic lens at 45° to the vertical and horizontal planes. This lens had a refractive index of 1.87, a correction ratio (anamorphic ratio) of 2.56 and a geometric mean focal length of 1 mm.
This calculation revealed that the wave front distortion at 1.48 &mgr;m is given by:
4) &Dgr;&phgr;=41NA
g
2
NA
y
2
(in waves)
Where NA
x
is the horizontal numerical aperture in waves and NA
y
is the vertical numerical aperture. It is convenient to express equation 4) in terms of a ‘geometrical’ numerical aperture defined by:
5) NA
g
={square root over (NA
x
NA
y
)}
Thus, expressing equation 4) in terms of the geometrical NA, we have:
6) &Dgr;&phgr;=41NA
g
4
for the &lgr;/4 condition to be fulfilled, then:
7) 41NA
g
4
<0.25 or NA
g
<0.27.
For a typical current laser design, NA
x
=0.144 and NA
y
=0.387, giving NA
g
=0.24. This is just within the ‘limit’ defined above. However, future higher power laser chip designs will have a much higher NA in order to maximise ex-facet power. For these designs, the current anamorphic lens design will no longer be effectively aberration free. Although current lens designs can correct aberration in the horizontal and vertical planes, they are, when presented with a highly divergent elliptical beam, significantly less effective in the correction of aberration in the planes at 45° to the horizontal and vertical planes. This reduces the energy that can be coupled into a circular cross-section fibre and partially negates the advantage of introducing a high power source.
OBJECT OF THE INVENTION
An object of the invention is to overcome or at least to mitigate the above disadvantage.
A further object of the invention is to provide an improved anamorphic lens construction.
A further object of the invention is to provide an improved optical pump source for an amplifier.
SUMMARY OF THE INVENTION
According to a first aspect of the invention there is provided an anamorphic lens having first and second curved surfaces having mutually perpendicular planes of symmetry, wherein each said surface is defined from a generator polynomial including cross terms in first and second independent variables so as to correct aberration of light from a widely divergent source.
The generator polynomial comprises a function defining the curvature of the surface summed with a plurality of polynomial terms providing correction of aberration.
In a preferred embodiment, each lens surface is defined by a polynomial expression of the form,
z
=
x
2
R
x
+
R
x
2
-
(
1
+
k
x
)
y
2
+
y
2
R
y
+
R
y
2
-
(
1
+
k
y
)
y
2
+
α
10
x
2
+
α
01
y
2
+
α
20
x
4
+
α
11
x
2
&it
Dang Hung Xuan
Nortel Networks Limited
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