Dispersion design in gradient index elements using ternary blends.

We show that a gradient-index element designed from a blend of three materials allows a designer to specify independently the element's refractive index and its change in refractive index with respect to wavelength. We show further the effectiveness of this approach by comparing modeled chromatic performance of deflectors consisting of a single material, a binary blend of materials, and a ternary blend.

Refractive index measurements of poly(methyl methacrylate) (PMMA) from 0.4-1.6 µm.

Using a transmission-spectrum-based method, the refractive index of a 50 µm thick sample of poly(methyl methacrylate) (PMMA) was measured as a function of wavelength. To mitigate the effects of nonplane-parallel surfaces, the sample was measured at 16 different locations. The technique resulted in the measurement of index at several thousand independent wavelengths from 0.42 to 1.62 µm, with a relative RMS accuracy <0.5×10(-4) and absolute accuracy <2×10(-4).

Chromatic analysis and design of a first-order radial GRIN lens.

From the expression for optical power of a radial first-order graded-index (GRIN) lens with curved surfaces, we derive an expression for chromatic aberration. Our expressions for optical power and chromatic aberration are valid under the paraxial approximation. By applying a series of further simplifying assumptions, namely a thin lens and thin GRIN, we derive a set of equations with which one can design an achromatic GRIN lens. We also derive expressions for the dispersive property of a GRIN element. Our analysis enables us to derive the relationship between material pairs that indicate their suitability as a material pair for a GRIN achromat. We use this relationship to search a standard glass catalog for attractive GRIN material pairs for a particular achromat design. We compare the optical performance of our GRIN design to that of a conventional homogeneous doublet and demonstrate that our approach is capable of identifying material pairs that perform well for achromatic GRIN lenses which would not generally be considered for conventional achromatic design. We also demonstrate our approach is capable of designing GRIN achromats with superior performance.

Thin sample refractive index by transmission spectroscopy.

Transmission spectroscopy and a small number of refractometer index measurements are combined to provide refractive index measurements of transparent samples ~50 um thick at hundreds of wavelengths with absolute accuracies <1 x 10(-4). Key to the technique is the use of independent index measurements to circumvent the need for an independent thickness measurement of the sample. The method was demonstrated on glass samples where fits to Cauchy curves had RMS accuracies <3 x 10(-5) from 415 to 1610 nm. Issues that must be addressed to reach this level of accuracy are discussed.

Achromatic GRIN singlet lens design.

Gradient refractive index (GRIN) materials are attractive candidates for improved optical design, especially in compact systems. For GRIN lenses cut from spherically symmetric GRIN material, we derive an analogue of the "lens maker's" equation. Using this equation, we predict and demonstrate via ray tracing that an achromatic singlet lens can be designed, where the chromatic properties of the GRIN counterbalance those of the lens shape. Modeling the lens with realistic materials and realistic fabrication geometries, we predict we can make an achromatic singlet with a 19 mm focal length using a matrix of known polymers.

Counter-propagating optical trapping system for size and refractive index measurement of microparticles.

We propose and demonstrate a novel approach to measure the size and refractive index of microparticles based on two beam optical trapping, where forward scattered light is detected to give information about the particle. The counter-propagating optical trap measurement (COTM) system exploits the capability of optical traps to measure pico-Newton forces for microparticles' refractive index and size characterization. Different from the current best technique for microparticles' refractive index measurement, refractometry, a bulk technique requiring changing the fluid composition of the sample, our optical trap technique works with any transparent fluid and enables single particle analysis without the use of biological markers. A ray-optics model is used to explore the physical operation of the COTM system, predict system performance and aid system design. Experiments demonstrate the accuracy of refractive index measurement of Deltan=0.013 and size measurement of 3% of diameter with 2% standard deviation. Present performance is instrumentation limited, and a potential improvement by more than two orders of magnitude can be expected in the future. With further development in parallelism and miniaturization, the system offers advantages for cell manipulation and bioanalysis compatible with lab-on-a-chip systems.

Two-beam optical traps: refractive index and size measurements of microscale objects.

A counter-propagating optical trap measurement (COTM) system is proposed and analyzed based on the ray-optics model. In this system, refractive index and size of trapped objects can be estimated by using forward scattered light from the two-beam laser trap with resolution Delta n = 0.013 for the refractive index measurements and 3.3% for the size measurements, which is comparable with current bulk techniques, such as refractometry, and flow cytometry. The unique advantage of the COTM system over conventional approaches lies in its capability of marker-free single-particle characterization in whatever transparent buffer required by living cell, eliminating the necessity of changing the fluid composition of the sample in refractometry, and of tagging target with toxic fluorescence dyes in flow cytometry. Noise analysis predicts a potential improvement in the system resolution by more than two orders of magnitude. This non-invasive and sterile tool complements lab-on-a-chips with single cell manipulation and analysis in living friendly ambient.