3D-printed Optical Devices with Refractive Index Control forMicrowave Applications

D. Isakov1, 2, Y. Wu2, B. Allen3, C. J. Stevens3 and P. S. Grant2

1 WMG, University of Warwick, Coventry CV4 7AL, United Kingdom, d.isakov@warwick.ac.uk2 Department of Materials, University of Oxford, Oxford OX1 3PH, United Kingdom3 Department of Materials, University of Oxford, Oxford OX1 3PH, United Kingdom

ABSTRACT

We present the design, simulation, fused depositionmodelling (FDM) 3D printing and characterisation ofseveral structures with spatial variations in refractiveindex. The 3D-printed structures represent optical de-vices such as a gradient refractive index (GRIN) lens, aquarter-wave plate, band-absorbers and a GRIN spiralphase plate, all designed to operate in the 12–18 GHzfrequency range. The devices were fabricated by usingtwo printheads and bespoke filaments with ‘high’ and‘low’ dielectric permittivity to provide high contrast (upto ∆n = 2) in refractive index thus allowing structureswith reduced size. The manufactured devices showed agood agreement with simulation and theoretically pre-dicted performance.

Keywords: RF, gradient index, phase plate, 3D print-ing

1 Introduction

Achieving sub-wavelength spatial variations in therelative permittivity εr and permeability µr to controlthe propagation of the electromagnetic radiation opensup many opportunities for the development of new de-vices with improved or novel functionality [1]. However,while the progress in Transformational Optics (TO) the-ory continues to suggest many beneficial designs andfunctions, the application of this principle in practicehas remained complicated due to the difficulty of fab-ricating structures with the required controlled spatialdistribution of permittivity and/or permeability.

Recent rapid development of additive manufactur-ing and related 3D printing techniques have shown howthese approaches might reduce the production time andsimplify the manufacturing process of materials and de-vices with the required control of the spatial distributionof the demanded properties [2, 3, 4]. 3D printing offers aflexible and scalable capability for the fabrication of ob-jects with a complex form factor [5, 6] and may providea significant contrast in the spatial variation of refrac-tive index [7]. Recently, the ability to fabricate newFDM feedstock filament materials with high dielectricpermittivity up to εr = 11 suitable for mass-market 3D

printing has been demonstrated [8]. Utilising such fila-ment would allow rapid prototyping of devices for RFand microwave applications where high contrast in theindex of refraction n is required and may open new pos-sibilities for implementation of principles of TO in prac-tice. Another benefit of high-ε filament is that devicescan be fabricated with reduced size (along the directionof propagation) without a change in overall optical pathnl and device performance [7].

In this paper, we summarise our recent progress indesign, fabrication, and characterisation of several elec-tromagnetic devices able to manipulate the propagatedwave through a spatially graded refractive index. Fourall-dielectric devices such as a metamaterial tunable ab-sorber, a GRIN lens, a spiral phase plate and a quarter-wave phase plate were 3D printed using fused deposi-tion modelling and our bespoke feedstock composite fil-aments with dielectric permittivity in the range 7 to 11.Although these optical elements were designed mainlyto operate at single frequency 15 GHz, they show goodcapability in the broad frequency range in 12–18 GHz.

2 Results

2.1 Metamaterial absorber andanisotropic phase plate

A simple 3D-printed all-dielectric metamaterial ab-sorber, as described in [9], consists of arrays of alternat-ing low permittivity (ABS plastic) and high permittivity(ceramic composite) stripes with thickness much lowerthan the wavelength aligned along the H-field of thepropagating wave. For investigation of any metamate-rial features, the printed striped sample was placed ina Ku-band waveguide flange, as shown in Figure 1(a).The alternating dielectric stripes present a periodic ar-ray of rectangular-shaped dielectric resonators and canproduce a Mie-type magnetic resonance induced by alarge displacement current in dielectric stripes with highpermittivity, and can be attributed to the creation of anartificial magnetic dipole [10].

Figure 1(b) shows measured transmittance T = |S21|2,reflectance R = |S11|2, and absorption A = 1 − R − Tobtained from a 3D-printed sample containing 2 highpermittivity stripes with ε2 = 11 + i0.078 interleaved

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12 14 16 18

Frequency, GHz

0

0.2

0.4

0.6

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sorp

tion

T

R

A

E, kV/m-2 0 2

φ,

rad

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-π2

0

π2

π

Frequency, GHz

14.2 14.4 14.6 14.8

Ey Ex

∆φ

,ra

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π2

π

12 14 16 18

Frequency, GHzEx−Ey,

dB

-5

0

5

(a)

(b)

(c)

(d)

(e)

(f)

Figure 1: (a) Photograph of the 3D-printed dielectriccoupon 16 × 8 × 2 mm3 with alternating stripes withε1 = 2.56 · (1 + i0.002) and ε2 = 11 · (1 + i0.007); (b)the transmission T , reflection R and absorption A pa-rameters measured in the coupon made of 4-stripes; (c)electric field distribution in the coupon at the resonance.(d) Photograph of the 3D-printed piramidal horn an-tenna and a quarter-wave plate; (e) the phases φ of therecieved y and x components of the electrtic field; (f)the phase difference ∆φ between x and y components ofthe polarization in the P-QWP45-S arrangement show-ing that the linear polarisation of the incident wave istransformed into circular (elliptical) polarisation in the12–18 GHz frequency range.

between low permittivity stripes with ε1 = 2.56+i0.005.An absorption of 50% was obtained near 1.38 GHz. Fig-ure 1(c) shows simulated distributions of the transverseelectric field inside the sample at the resonant frequency.The circular component of electric field, shown as con-centric curves in the z-plane, resulted in a strong mag-netic field and was associated with the first TE11 modeof the Mie resonance.

According to effective medium theory [11], a periodictwo-component structure with alternating permittivityε1 and ε2 will have an anisotropy in effective relativedielectric permittivity εeff with values between low andhigh Wiener bounds: ε−1

min = fε−12 + (1 − f)ε−1

1 andεmax = fε2 + (1− f)ε1, where f is the volume fill frac-tion of the high permittivity component. This opensup the possibility for design the anisotropic structureswith controlled birefringence to transform or control themode of polarization in electromagnetic waves. One ofthe examples of such device is a quarter-wave and/orhalf-wave plate. Figure 1(d) presents a 3D-printed quarter-

wave plate (QWP) designed in such a way that an op-tical path difference ∆l between vertical and horizon-tal components of the plane wave will result in phasedelay δ = ±π/2. Figure 1(e) shows the experimentalresults for the phase of the linearly polarised wave (ver-tical P-polarization) passing through the QWP orientedat 45◦ to their principal axes to the polarisation of in-cident beam (P) and analysed by the receiver antennawith either vertical polarisation (Ex component) or lin-ear horizontal S polarisation (Ey component). Figure1(f) presents the phase (red) and amplitude (blue) dif-ference between orthogonal components of the electricfield. These results show that original linearly polarisedwave (with only Ex component) has been transformedby the QWP to the circularly (elliptically) polarisedwave with nearly equal Ex and Ey amplitudes and aphase difference of approximately π/2.

2.2 Gradient index devices

Gradient index devices present an alternative ways tomanipulate and control an electromagnetic wave, whichpassing through a boundary between two homogeneousmedia will experience a phase delay proportional to thedifference in refractive index of the media. Thus inGRIN devices, the beam manipulation mechanism isbased on the phase shift of the electromagnetic waveresulting from its interaction with a medium with a spa-tially graded refractive index.

Figure 2(a) shows 3D-printed H-plane sectoral hornwith relatively small length R0 = 2λ and a 3D-printedflat GRIN lens over the horn aperture to produce im-proved directivity. The desired functionality of the GRINlens was achieved through the appropriate distributionof the refractive index using a ray tracing principle of thecompensation of the ray phase retardation δ = 2π

λ Ln,where λ is a wavelength, and Ln is an optical pathwayof the ray [7]. Figure 2(b) shows 2D simulations of thefar-field radiation pattern for the shortened horn anddiscretised GRIN lens in a predicting excellent directiv-ity at 15 GHz. The experimental results (Figure 2(c))are in good agreement with simulation. The horn withlength only 2λ coupled with 3D-printed GRIN lens hasthe same directivity of approximately 18 dBi as a high-directivity horn with optimal length 6λ. Overall, whenthe GRIN lens is combined with an open aperture hornwith a reduced length of 2λ, improved antenna directiv-ity is achieved while simultaneously reducing the overallantenna physical length by over a factor of three.

Besides GRIN lens, TO approaches with a spatiallyvarying refractive index can be utilised to design manyother devices, such as cloaks, photonics crystals, powerdividers [13] or a spiral phase plate (SPP). The laterone is able to manipulate the plane wave into a he-lically phased beam with orbital angular momentum(OAM) [12]. Such phase plates are very promising for

Informatics, Electronics and Microsystems: TechConnect Briefs 2018 93

−π −π/2 0 π/2 π

— Simulation— Experiment

0

-20

-40

-60S21,

dB

Angle, radS21,

dB

-40

-50

-60

-70

π

π2

0

−π2

−π

Ph

ase

,ra

d

(a)

(b)

(c)

(d)

(e)

(f)

Figure 2: (a) Photograph of the 3D-printed H-planeshort (2λ) horn with 3D-printed GRIN lens attachedat the front aperture; (b) simulated electric field distri-bution in the horn-lens arrangements; (c) experimentaland simulated far-field radiation patterns of the shorthorn with 3D-printed GRIN lens. (d) Photograph ofthe 3D-printed horn antenna with GRIN spiral phaseplate (the plate with azimuthal dependent thickness isalso shown); (e) and (f) experimental measurements ofthe 15 GHz radiation signal from the GRIN spiral phaseplate in the plane with area 70× 70 cm2 perpendicularto the propagation vector.

applications required high data transfer rates. This ispossible due to the multiplexing of parallel data streamsthrough several independent orbital angular momentummodes.

In general, a spiral phase plate is a dielectric mate-rial with an azimuthally dependent height (usually indiscrete height steps) that imparts an azimuthal phaseshift onto incident radiation resulting in OAM. The totalstep height is that the total phase shift around the centreof the plate is ±m2π, where m is an integer denoting themode of the OAM. Alternatively, a GRIN spiral phaseplate can be obtained when the azimuthal phase shift isinstead induced through the azimuthally varied refrac-tive index. Both such plates (with azimuthally varyingheight and refractive index) have been 3D-printed andare shown in Figure 2(d).

Figures 2(e) and 2(f) present the experimental re-sults of the amplitude and phase profiles of the z-planeperpendicular to the direction of propagation, obtainedfrom a 3D-printed GRIN spiral phase plate, measuredwith a millimetre step resolution scanning system at thedistance about 50λ from the SPP. The amplitude pat-

tern in Figure 2(e) exhibits the expected vortex witha null intensity in the centre, whereas the spatial phaseprofile in Figure 2(f) exhibits the phase profile related toan OAM m = −1. It should be noted that although theGRIN SPP was designed to operate at single frequency15 GHz, it remains a good capability in the 12–18 GHzfrequency range.

3 Conclusion

Our recent achievements in formulation and fabrica-tion of feedstock filaments with high dielectric permit-tivity for FDM 3D printing allows convenient implemen-tation of the principles of transformation electromagnet-ics for the design and fabrication of several types of op-tical devices to be operated in the microwave frequencyband. Despite their relative simplicity, the experimentalrealisation of these graded refractive index devices showsthat there is a significant opportunity for 3D printing toenable TO-inspired devices in the microwave domain, es-pecially as higher dielectric constant materials suitablefor 3D printing become available.

Acknowledgment

This work was funded by the UK Engineering andPhysical Sciences Research Council (EP/I034548/1 andEP/P005578/1). BA is grateful to the support of theRoyal Society Industry fellowship scheme under awardnumber IF160001.

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