We introduce a new class of metamaterials that allow simultaneous spatial and temporal control of electromagnetic waveforms and present for the first time the generation of flying doughnuts, single-cycle pulses of toroidal topology

Fedotov, V.A.

Papasimakis, N.

Raybould, T.A.

Youngs, I.

Zheludev, N.I.

Southampton (e-Prints Soton)

   Generation of Flying Electromagnetic Doughnuts via Spatiotemporal Conversion of Transverse Electromagnetic Pulses  T. A. Raybould1, N. Papasimakis1, V. A. Fedotov1, I. Youngs2, and N. I. Zheludev1, 3 1.  Optoelectronics Research Centre & Centre for Photonic Metamaterials, University of Southampton, Highfield SO17 1BJ, UK  2.  Platform Systems Division, DSTL, Salisbury SP4 0JQ, UK 3.  TPI and Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore 637378, Singapore  Abstract: We introduce a new class of metamaterials that allow simultaneous spatial and temporal control of electromagnetic waveforms and present for the first time the generation of flying doughnuts, single-cycle pulses of toroidal topology.   Flying doughnut (FD) pulses are exact solutions to Maxwell’s equations, distinguished by a doughnut-like configuration of electric and magnetic fields, strong longitudinal field components along the propagation direction, and unique spatiotemporal coupling [1,2]. They are single-cycle, wide bandwidth pulses that propagate in free-space with the speed of light. In contrast to other families of pulses, their spatial and temporal dependence cannot be separated. FD pulses interact with matter in unique ways, including non-trivial field transformations upon reflection from interfaces and the excitation of strong toroidal response in dielectric particles [3].  Here we introduce a scheme for the generation of FDs based on spatially gradient metamaterial arrays. We employ a cylindrically symmetric metamaterial array (see schematic representation in Fig. 1a), reflecting the toroidal topology of the Flying Doughnut pulse. The spatiotemporal coupling is provided by varying the properties of the metamaterial elements across the array according to the parameters of the targeted FD pulse, the effective wavelength, q1, and Rayleigh length, q2. We consider illumination by a transverse, short, Gaussian pulse and calculate numerically the emitted electromagnetic fields. Similarly to ideal FD pulses, the generated pulse is of single-cycle duration and toroidal topology, as indicated by the electric field intensity profile of Fig. 1b. Importantly, the emitted pulse exhibits coupled spatial and temporal structure, with a spatially varying frequency spectrum (see inset to Fig. 1b).  Fig. 1 (a)	 Schematic	 representation	 of	 the	 flying	 doughnut	 generation	 scheme.	 A	 cylindrically	 symmetric	metamaterial	array	excited	by	a	transverse	electromagnetic	pulse	emits	a	flying	doughnut	pulse.	(b)	The	azimuthal	electric	field	intensity	of	the	metamaterial-generated	FD	pulse	in	a	cross-section	normal	to	the	y-axis.	The	generating	metamaterial	array	is	in	the	z=0	plane.	The	inset	shows	the	corresponding	Fourier	transform	highlighting	the	radially	gradient	spectral	content	with	low	frequencies	occupying	the	outer	regions	of	the	pulse,	and	higher	frequencies	close	to	its	centre.	All	units	are	normalized	to	q1,	which	is	the	effective	wavelength	of	the	FD	pulse	[2].		In summary, we demonstrate a practical scheme for the generation of FD pulses based on metamaterial arrays with simultaneous spatial and frequency dispersion. Possible applications include new schemes for information and energy transfer, as well as new forms of spectroscopy. References [1] R. W. Ziolkowski, “Exact solutions of the wave equation with complex source locations,” J. Math. Phys. 26, 861 (1985). [2] R.W.Hellwarth and P.Nouchi,“Focused one-cycle electromagnetic pulses,” Phys. Rev. E 54, 889 (1996). [3] T. A. Raybould, V. A. Fedotov, N. Papasimakis, I. J. Youngs, and N. I. Zheludev, “Focused electromagnetic doughnut pulses and their interaction with interfaces and nanostructures”, Opt. Express 24, 3150 (2016).    

Generation of flying electromagnetic doughnuts via spatiotemporal conversion of transverse electromagnetic pulses

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