Susan N. Houde-Walter

Mode determination for planar waveguide using the four-sheeted dispersion relation

A numerical method for the determination of the modes of planar, multilayer waveguides is presented. It is possible, with this algorithm, to guarantee that all the solutions within any finite region of the complex plane representing the propagation constant are found; neither prior knowledge of the number of solutions nor their approximate locations within the region is required. This method is formulated using the four-sheeted Riemann surface of the analytic function that defines the waveguide dispersion relation and whose zeros correspond to the proper and improper modes of the structure. Both TE and TM modes can be determined for guides that incorporate materials with complex indexes. >

Design of a gradient-index photographic objective

A two-element gradient-index photographic objective was designed. It operates at f/2 and has a focal length of 50 mm. The half-field of view is 21.8 degrees . The design is compared to the six-element new double Gauss photographic objective and performs well in comparison.

Desired concentration-dependent ion exchange for micro-optic lenses

The required concentration-dependent diffusion coefficients for both ideal one-dimensional and ideal radial gradient-index profiles are determined. The modified quasi-chemical diffusion model is used to relate the diffusion coefficient to optimum glass composition. Adding aluminum to sodium silicate glasses facilitates the approach to the desired concentration dependence of the diffusion coefficient for silver-sodium ion exchange. A parabolic one-dimensional index profile is fabricated in one of the glasses. It deviates from ideal values by less than 2%.

Delta-n control in GRIN glass by additives in AgCl diffusion baths

The uptake of silver from a molten silver chloride bath by an aluminosilicate glass is highly sensitive to the presence of sodium in the salt bath under both equilibrium and nonequilibrium conditions. The delta-n resulting from the silver dopant is reduced by nearly an order of magnitude by the addition of just 5-mol % sodium chloride to the melt. The addition of zinc chloride or lead chloride can be used to maintain high delta-n values in the presence of sodium in the melt.

Unfolding the multivalued planar waveguide dispersion relation

Conventional 2*2 matrix techniques give an implicit dispersion relation for planar waveguides that involves multivalued functions. This multivalued form can cause complications and confusion. It is shown that it is possible to derive a single-valued form that avoids all such difficulties. The resulting formulation allows the unique identification of all the proper and improper modes of a structure and simplifies their numerical determination. >

Gradient-index profile control by field-assisted ion exchange in glass

Field-assisted ion exchange has been used to extend the profile repertoire and to speed the ion exchange process for gradient-index (GRIN) applications. Profiles are predicted for various ion mobility ratios and time-varying electric fields. Profile control is demonstrated by silver for sodium exchange in an aluminosilicate glass. Diffusion depths of the order of a millimeter are obtained in a few hours using modest field strengths.

Gradient-index eyepiece design

A study of gradient-index eyepieces was conducted. The general performance of homogeneous eyepieces having two and three elements was examined. Axial gradients were introduced into the eyepieces in an attempt to increase the half-fields of view to 25 degrees and extend the eye reliefs to 12 mm. The homogeneous eyepieces examined were of the Huygenian, Ramsden, and Kellner configurations. These eyepieces were scaled to the specifications of f/13, 21.4-mm focal length, and magnifying power of 10X. These classic systems were optimized to produce two- and three-element homogeneous eyepieces to determine how homogeneous systems could perform with the extended eye relief and larger field of view. Axial gradient eyepieces having two and three elements were designed to the same specifications. The balance of third-order aberrations, color, and distortion was maintained or improved compared to the homogeneous systems.. The additional degrees of freedom associated with the gradient made it possible to extend the eye relief and increase the field of view of these eyepieces.

Fabrication tolerances and metrology requirements for ion-exchanged micro-optic lenses: What's good enough?

Allowable deviations in index profiles, dopant distributions, and concentration dependence of diffusion coefficients are determined for collimating microlenses. Examples of high (and low) numerical aperture lenses are given for silver/sodium (and lithium/sodium) ion exchanges. Using the full lens aperture, one can ensure diffraction-limited performance only when the index is measured to within 1.0 x 10(-4) (4.3 x 10(-5)) of the optimum values. Fabrication tolerances for diffraction-limited performance over 80% of the numerical aperture are expressed in terms of the concentration-dependent diffusion coefficient, which typically must be held to within +/-4.7% (+/-11.5%) of ideal values.

Gradient-index binocular objective design

A two-element binocular objective with one axial gradient-index element was designed and compared with a three-element homogeneous objective. The index was constrained so that the gradient could be fabricated.

Recent Progress In Gradient-Index Optics

A brief summary of gradient-index (GRIN) optical principles is given, followed by a state-of-the-art review. Much of the important recent work has been in the area of GRIN materials, specifically: new glasses for ion exchange, new ion exchange techniques, GRIN sol-gel glasses and plastic GRIN. New metrology techniques and fabricated GRIN imaging systems are also discussed.