A Fresnel lens is a type of lens invented by French physicist Augustin-Jean Fresnel.1 A binary Fresnel lens consists of alternating transparent and opaque zones with respect to the incident irradiation which allow it to act as a lens.2 However, reflective binary Fresnel lenses fabricated so far all suffer from reflections from the opaque zones and hence degradation in focusing and the lensing properties. Here we find a solution to this problem by developing carbon nanotube Fresnel lens, where we exploit the darkest man-made material ever,3 i.e., low-density vertically aligned carbon nanotube arrays. Such arrays can produce a near-perfect optical absorption material (reflectance ∼0.045%) due to extremely low index of refraction and nanoscale surface roughness.3–5 We present for the first time an array of nanotube Fresnel lenses made by exploiting the near-perfect optical absorption property of the nanotubes together with silicon nanofabrication techniques. Each nanotube Fresnel lens in the array has a 38 μm radius and fifteen zones. The optical performance analysis shows well defined sharp focusing from the nanotube lens array. This finding is a major achievement in realizing efficient optical components on silicon based electronics for making miniaturised photonic chips in various applications, such as in integrated optics, optical interconnects, beam focusing, maskless lithography systems, deflecting and collimating tasks in optical sensor systems, optical computers, optical data transfer and optical communication.6–10 Another main application is the generation of very efficient 2D source arrays for neural network architectures where a lens array can be easily integrated with electronics on the silicon chip.
Carbon nanotubes (CNTs) were first discovered by Iijima in 1991.11 Since then nanotubes have attracted a great deal of interest due to their exceptional electrical properties, extraordinary flexibility and resilience combined with high strength.12–14 The mechanical and electrical properties of CNTs depend largely on the chiral angle of the graphene sheet and diameter, which can vary from a few nanometers for single-walled carbon nanotubes to tens of nanometers for multi-walled carbon nanotubes.15 Single-walled carbon nanotubes can be either metallic or semiconducting, depending on the direction about which the graphite sheet is rolled, whereas multi-walled carbon nanotubes are mostly metallic and carry high current densities.
Vertically grown carbon nanotube arrays act as extremely black objects because of their low reflection, high absorption and random surface scattering.3 It has been reported from both theoretical calculations4 and experimental measurements3, 5 that materials displaying extremely low refractive indices (n = 1.01–1.10) can be prepared using low-density carbon nanotube arrays. Yang and co-workers16 have reported high absorption coefficients for low density aligned nanotubes in a direction parallel to the CNTs. They also observed extremely low refractive indices for light in the visible wavelength regime. This arrangement provides a material having a rough surface with no repeating topology, causing light to scatter in random directions and, thereby, making the surface extremely black. We exploit this near perfect absorption of the extremely black carbon nanotube forest to realize a Fresnel lens array with excellent contrast and focusing capability. A Fresnel lens has concentric circular zones with their radii proportional to the square root of integer multiples of wavelength.17 Long f-number Fresnel lenses also offer substantial advantages over equivalent reflective devices due to their better tolerance to surface-figure errors which enhances the precision of the mounting structure. Fresnel lenses are also straightforward to mount as they require a flat membrane rather than a curved shape.18
The focal length f of the lens is related to radius r of successive zone edges by the equation (n = 1, 2, 3, ….), hence r2 = fnλ, i.e., × constant and λ is the wavelength of light.19 In the nanotube Fresnel lenses presented here, the centre zone radius was set at 10 μm by keeping the focal length at 158 μm and the wavelength at 633 nm. The nanotube Fresnel lens array was modeled using finite element method (FEM) to analyze the wave propagation and focusing performance. Due to the cylindrical symmetry and for the purpose of simplicity, a 2D model was established depicting the cross-section of the Fresnel lens, as shown in Figure 1. The regions comprising of carbon nanotube forests were modeled as high density periodic arrays of nanotubes with radius of 50 nm and lattice constant of 500 nm. The diameter of the centre zone was 20 μm.
The dielectric constant of individual multi-wall carbon nanotube is defined by their frequency dependent dielectric function ϵ(ω), which is anisotropic in nature20 and matches very closely with that of bulk graphite.21–23 We incorporated the dielectric constant into our simulation as a function of frequency. Light propagation across the lens was simulated for a wavelength of 800 nm in transmission mode and strong focusing was observed. As presented in the intensity plot in Figure 1a, the incident light from the top of the lens is mostly blocked by the carbon nanotube arrays and forward propagation only occurs through the gaps. Due to the phase differences between the gaps, a strong focus spot is produced at a distance of about 120 μm at 800 nm wavelength which is equivalent to 158 μm at 633 nm from the lens. The intensity profiles plotted across the distance from the centre of the lens and in the focal plane illustrate the focal length and high intensity focal point produced. Our simulation results confirm that the carbon nanotube arrays grown in this fashion act as Fresnel diffractive lenses. Based on the simulation results an array of carbon nanotube Fresnel lenses was fabricated using photolithography and chemical vapour deposition (CVD). A scanning electron microscope (SEM) picture of the fabricated Fresnel lens array is shown in Figure 2.
The fabricated CNT Fresnel lens array was characterized under an optical microscope (Olypus-BH2) with a magnification of 10×. Figure 3a shows the lens array under the microscope. It was clear from the images that the dark carbon nanotubes were acting as near perfect absorbers. Figure 3b shows the lens array focusing the light. The focal length was experimentally measured as 160 μm, which is in close agreement with the simulation result of 158 μm. The slight variation in the value is well within the fabrication tolerances. Figure 4 shows the magnified version of a single carbon nanotube Fresnel lens and focal point along with the light intensity profile across the horizontal and vertical directions. It was clear from the intensity profiles that there was a well defined focal point with good contrast. The light intensity profile was smooth along the both horizontal and vertical directions. The sharpness of the focus can be further increased by tuning the density and length of the nanotubes and by increasing the number of zones in each lenslet. The efficiency of the nanotube Fresnel lens array or diffraction efficiency was calculated from the ratio of light intensity at the focal point to the total light intensity falling on lenslet. The measurement gave around 12% efficiency from the lenslets for the optical spectrum.
The fabricated carbon nanotube Fresnel lenses offers new possibilities in designing highly flexible and efficient interconnection networks with massive parallelism. They can be used for efficient focusing, deflecting and collimating tasks in optical sensor systems, optical computers, optical data transfer and optical communication. Another main application is the generation of 2D source arrays for neural network architectures where a lens array can be easily integrated with electronics on the silicon chip. The current design is superior to existing binary Fresnel lens array for generating 2D source array in terms of high contrast, efficient focusing because the reflection from the opaque zone was almost absent. Another method of generating 2D beam arrays from a single beam is to use binary phase Dammann gratings.24 But the binary phase pattern of a Dammann grating is complicated because the position of the transitions and the phase depth need to be optimized for the desired beam configuration.
In conclusion, we have developed a novel carbon nanotube Fresnel lens array with high contrast and efficient focusing on silicon substrate using the extremely low index of refraction and nanoscale surface roughness carbon nanotube forest. The performance of the lens array was modeled using finite element method to fix the design parameters. Then the lens array was fabricated using lithography and CVD. The superior performance of the lens array was experimentally verified using optical characterization. This lens array is a major achievement in realizing efficient optical components on silicon based electronics for making miniaturized photonic chips.