3D-Printed THz Fresnel Lenses
3D-Printed THz Fresnel Lenses
Terahertz (THz) systems operating roughly between 0.1 and 10 THz sit in a region of the electromagnetic spectrum where traditional optical components are expensive, fragile, or simply unavailable off the shelf. A practical and cost-effective alternative is to 3D print custom optics directly, exploiting the fact that many common polymers are largely transparent at THz frequencies. This project explores the design, simulation, and fabrication of 3D-printed Fresnel lenses tailored for use in THz spectroscopy and imaging systems.
A conventional plano-convex lens achieves focusing through a continuously curved surface. For THz wavelengths (λ ~ 0.3 mm at 1 THz), the required lens thickness grows quickly with aperture, leading to significant absorption even in low-loss materials. A Fresnel lens collapses this profile: rather than accumulating phase continuously, it resets the phase every 2π, allowing a much thinner flat structure to achieve the same focusing effect. The key insight is that only the phase gradient matters for focusing, not the absolute accumulated phase.
The lens profile is derived from the ideal sagitta of a spherical surface. For a lens with focal length f and material refractive index n, the radius of curvature is:
The ideal unwrapped thickness profile as a function of radial position r is then:
This represents the physically correct thickness a true spherical lens would have. To convert this to a Fresnel profile, the thickness is phase-wrapped modulo the height T₂π that produces a full 2π phase shift:
This sawtooth-like profile is what gives a Fresnel lens its characteristic ring structure.
A real 3D printer deposits material in discrete layers of height Δz (typically 0.1–0.2 mm). The continuous Fresnel profile must therefore be quantized to the nearest printable step:
This quantization introduces a small phase error at each zone boundary, but for well-chosen layer heights relative to λ the efficiency loss is minimal. The scripts developed for this project automate this calculation taking frequency, focal length, lens aperture, refractive index, and layer thickness as inputs and output both the full thickness profile and an STL-ready geometry for printing.
The phase shift imparted by the lens goes as:
while amplitude loss through the material is governed by the extinction coefficient k:
Selecting a material with low k at the operating frequency is therefore critical. For THz work, polymers such as HIPS (High Impact PolyStyrene) is characterized and used in this project, with refractive index typically in the range n ≈ 1.5–1.7 and relatively low absorption across much of the 0.2–0.5 THz window with increasing loss up to 1THz.