Lens Design, OPTI 517
Laser diode optics
Laser diodes and optical fibers are important optical components. A fiber optic has a glass core, a glass
cladding, and a plastic buffer. The numerical aperture of a multimode fiber is about 0.21 and for a single
mode fiber is about 0.12. The core diameters are typically 50 and 5-8 microns respectively, the cladding
diameter is 125 microns, and the buffer diameter is 250 microns. Single-mode laser diodes have numerical
apertures in the fast direction of 0.5 and in the slow direction of 0.18. Newer Vertical Cavity Emitting
Lasers have a numerical aperture of about 0.2 and the beam is circular.
Lens designers are often asked for lenses to couple light from lasers to fibers. To have a high coupling
efficiency mode matching must occur. This implies that the amplitude, polarization, phase, alignment, and
NA of the incoming light from the laser must match those associated with the fiber. Since many lasers do
not have a circular beam cross section or the appropriate numerical aperture some optics must be used to
circularize the beam, change the NA, and focus the light into the fiber.
In this homework we are going to design a collimating lens with the following specifications:
Clear aperture: 5 mm
NA = 0.5
Wavelength = 850 nm
Glass BK7
a) Set a plano convex lens 4 mm in thickness that meets these requirements. Light from infinity is incident
on the flat surface. Set the observation plane at the rear focal point. Evaluate the peak to valley spherical
aberration. (note that with a spherical surface there will be total internal reflection for rays at and near the
0.5 NA; therefore reduce the NA (clear aperture) to the point rays are refracted) 5 points.
b) Set the convex surface to be a hyperboloid with an eccentricity equal to the index of refraction and
verify that this perfectly corrects for spherical aberration. For a semi field-angle of 0.5 degree see how
much coma is present. The stop is located at the first surface. 5 points.
c) Set now the lens so that the convex surface is the front one. Change the radius of curvature to meet the
NA requirement Make this surface a general aspheric and free the conic constant, the 6th, 8th, and 10th
order aspheric coefficients. Set the program default error function. Set the image plane at the rear focal
plane. The field angle should be zero. Optimize till you correct for spherical aberration, that is, minimize
the opd rms or spot rms. Examine the coma for a 0.5 degree field. 5 points
d) Increase by hand the index of refraction till coma is corrected. Use the optimization to correct only for
spherical aberration (set first the field angle to zero). At this point the lens is an aplanat. 5 points.
e) Get back to lens as in c). Bend the lens till coma is corrected. 5 points. Bending a lens means changing
the surface curvatures while maintaining the same optical power.
Neatly present your work. Have a clear and concise explanation on what you did, a lens plot, and a
wavefront plot (zero and 0.5 degrees) for each case.
In many applications a lens must be corrected for both spherical aberration and coma (aplanat) so that
alignment becomes feasible. The lens of point b) would be difficult to align to a laser diode because
essentially it has no useful field of view. The lens on d) may be easier to make and mount because of the
flat surface.