The Magic of Optics-An Overview of Recent Advanced Terahertz Diffractive Optical Elements

Abstract

Diffractive optical elements are well known for being not only flat but also lightweight, and are characterised by low attenuation. In different spectral ranges, they provide better efficiency than commonly used refractive lenses. An overview of the recently invented terahertz optical structures based on diffraction design is presented. The basic concepts of structure design together with various functioning of such elements are described. The methods for structure optimization are analysed and the new approach of using neural network is shown. The paper illustrates the variety of structures created by diffractive design and highlights optimization methods. Each structure has a particular complex transmittance that corresponds to the designed phase map. This precise control over the incident radiation phase changes is limited to the design wavelength. However, there are many ways to overcome this inconvenience allowing for broadband functioning.

Keywords: 3D printing; beam shaping; convolution approach; diffractive optical elements; neural-network-based optimization; on-axis and off-axis regime; terahertz optics.

Figure 1

The effective efficiency of the binary phase diffractive element for two different absorption coefficient values: $\alpha$ = 1 cm${}^{-1}$ (left diagram) and $\alpha$ = 3 cm${}^{-1}$ (right diagram). The effective efficiency values are given under assumption of considering only diffractive efficiency (diff. eff.), attenuation introduced by the thickness of the structure resulting from absorption coefficient value (att.), Fresnel losses resulting from the reflection of part of the radiation of the interface between two media with different refractive indices (FL) and considering both—attenuation coefficient influence and Fresnel losses (att. + FL). It can be noticed that for materials with larger attenuation the effective efficiency is larger for structures with smaller phase shift than resulting from theoretical diffraction efficiency due to the attenuation of material. The influence of Fresnel losses is increasing with the increase of the refractive index value.

Figure 2

Refractive indices and absorption coefficients of exemplary materials available for extrusion-based 3D printing technique. High density polyethylene (HDPE) is illustrated as a reference material but it cannot be processed using this technique. The group of biopolymers—FiberWood, FiberSilk, BioCREATE and BioWOOD, thermoplastic polyurethane (PolyFlex) and thermoplastic polyester elastomer (FiberFlex 40D) are characterized with largest absorption coefficient values—similar to polylactide (PLA). The butenediol vinyl alcohol co-polymer (BVOH) together with acrylonitrile styrene acrylate (ASA) have slightly smaller absorption coefficient value. The most transparent (not taking into account reference HDPE) is polypropylene (PP), then high impact polystyrene (HIPS) and nylon–poliamid 12 (PA12). The refractive index values for all illustrated materials are in the range between 1.5 and 1.65, which is very similar to the values of refractive index for glass for visible light.

Figure 3

Refractive indices and absorption coefficients of alternative THz optical materials. Different types of modelling clay with refractive index values ranging from 1.2 up to 2, papers, paraffin, chocolate. HDPE and PA12 are plotted as reference materials.

Figure 4

(a) The scheme of forming diffraction orders by the grating together with different diffraction grating types—different coding types: binary, sinusoidal, step-like, kinoform. (b) The scheme of focusing efficiency of diffractive converging lens. Colors corresponds to particular diffraction grating orders.

Figure 5

(a) The exemplary object used in simulations for 0.3 THz. (b) The image obtained in $4f$ imaging setup assuming no aperture, only calculation matrix size. (c) The image obtained in $4f$ imaging setup assuming lens apertures limited to 75 mm (marked with red dashed line) (d) The image obtained in $4f$ imaging setup assuming lens apertures limited to 50 mm (marked with red dashed line). Formed images are inverted as in $4f$ setups. The presented area corresponds to 90-mm-square area cut from 204.8-mm calculation matrix.

Figure 6

Different THz diffractive optical structures manufactured using: (a) laser cutting to manufacture hyperbolic lens [9] from paper, (b) extrusion-based 3D printing to make a mold to form converging lens from paraffin, (c) extrusion-based 3D printing from PA12 for off-axis focusing lens, (d) selective laser sintering (powder-based 3D printing) from PA12 to manufacture point-to-point redirecting lens and (e) ablation in silicone to fabricate Fibonacci lens (photograph courtesy Linas Minkevičius, FTMC, Vilnius).

Figure 7

The intensity patterns of: (a) Airy, (b) Bessel and (c) optical vortex beams. The upper panel illustrates the propagation along optical axis—$yz$ plane, while the lower panel corresponds to the $xy$ cross-sections at distances after optical element marked with red dashed lines. The structure is located on the left edge of $yz$ distributions.

Figure 8

Different diffractive structures redirecting and splitting the incident radiation. The upper panel illustrates the phase delay maps introduced by each structure. The lower panel illustrates the intensity distribution in the focal plane in (a). Additionally, due to the fact the distributions are symmetrical in (b–d) the focal plane is illustrated as two halves—left corresponding to amplitude distribution and right the intensity distribution. The structure in (a) is a shifted lens to redirect and focus the radiation out of the optical axis. The inset shows the magnification of focal spot which will have more aberrations when shifted further from the optical axis. The structure in (b) is the binary phase grating joined with the converging lens. It forms two strong spots aside optical axis. The structure in (c) is the sinusoidal phase grating joined with the converging lens. Due to the modified changes of the phase the spots corresponding to other order of diffraction than ±1st are also visible. The structure in (d) is the Dammann grating forming the matrix of 3 × 2 points joined with the converging lens. In this case additional orders are very noticeable. Thus, in case of redirecting the beam there in a need to optimized the phase delay map to suppress the influence of undesired spurious focal spots.

Figure 9

The comparison of different DOE design methods—(a) theoretical off-axis lens equations with 25 mm and 50 mm shifts, (b) iterative algorithm and (c) neural network optimization of phase distribution. The calculated phase distributions of the diffractive structures are shown as a grey scale image (lower panel) corresponding to introducing phase retardation from 0 (black) to $2\mathsf{\pi }$ (white). On the upper panel the corresponding reconstructed intensity patterns are given in color palette. The reconstructed area was the same size as the structure, but here was limited to the region marked with red rectangles on phase retardation maps. The cross-sections along the horizontal axis crossing the main optical axis (marked with red triangles) are shown in the middle panel.