Direct experimental visualization of waves and band structure in 2D photonic crystal slabs

Ofori-Okai, Benjamin K.; Sivarajah, Prasahnt; Werley, Christopher A.; Teo, Stephanie M.; Nelson, Keith A.

doi:10.1088/1367-2630/16/5/053003

Cited by 15 publications

(12 citation statements)

References 51 publications

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“…Another powerful principle of spectroscopy is the Fourier transform (FT) method, which has recently become more attractive because of advances in optical- and data-processing technologies as demonstrated by phonon-polariton spectroscopy 15 16 17 18 . In the FT method, all possible waves are excited at once, and power spectra are obtained by calculating the FT of the excited waveform.…”

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confidence: 99%

All-optical observation and reconstruction of spin wave dispersion

et al. 2017

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To know the properties of a particle or a wave, one should measure how its energy changes with its momentum. The relation between them is called the dispersion relation, which encodes essential information of the kinetics. In a magnet, the wave motion of atomic spins serves as an elementary excitation, called a spin wave, and behaves like a fictitious particle. Although the dispersion relation of spin waves governs many of the magnetic properties, observation of their entire dispersion is one of the challenges today. Spin waves whose dispersion is dominated by magnetostatic interaction are called pure-magnetostatic waves, which are still missing despite of their practical importance. Here, we report observation of the band dispersion relation of pure-magnetostatic waves by developing a table-top all-optical spectroscopy named spin-wave tomography. The result unmasks characteristics of pure-magnetostatic waves. We also demonstrate time-resolved measurements, which reveal coherent energy transfer between spin waves and lattice vibrations.

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confidence: 99%

All-optical observation and reconstruction of spin wave dispersion

et al. 2017

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“…2c. Many interesting features of LT 2D PhC slabs have been revealed in a previous study using this methodology 12 . Figure 2c shows the measured dispersion of the LN PhC slab; the primitive lattice vectors are oriented at 45…”

Section: Methodsmentioning

confidence: 68%

What is the Brillouin zone of an anisotropic photonic crystal?

et al. 2016

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The concept of the Brillouin zone (BZ) in relation to a photonic crystal fabricated in an optically anisotropic material is explored both experimentally and theoretically. In experiment, we used femtosecond laser pulses to excite THz polaritons and image their propagation in lithium niobate and lithium tantalate photonic crystal (PhC) slabs. We directly measured the dispersion relation inside PhCs and observed that the lowest bandgap expected to form at the BZ boundary forms inside the BZ in the anisotropic lithium niobate PhC. Our analysis shows that in an anisotropic material the BZ -defined as the Wigner-Seitz cell in the reciprocal lattice -is no longer bounded by Bragg planes and thus does not conform to the original definition of the BZ by Brillouin. We construct an alternative Brillouin zone defined by Bragg planes and show its utility in identifying features of the dispersion bands. We show that for an anisotropic 2D PhC without dispersion, the Bragg plane BZ can be constructed by applying the Wigner-Seitz method to a stretched or compressed reciprocal lattice. We also show that in the presence of the dispersion in the underlying material or in a slab waveguide, the Bragg planes are generally represented by curved surfaces rather than planes. The concept of constructing a BZ with Bragg planes should prove useful in understanding the formation of dispersion bands in anisotropic PhCs and in selectively tailoring their optical properties.

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“…hexagonal lattice), the intensity can be collapsed along the y-dimension because of the use of a line-source excitation, which most significantly projects onto modes that are spatially uniform along y. The validity of this approach is proven by strong agreement of the experimental dispersion curves with simulations [29].…”

Section: Methodsmentioning

confidence: 99%

The homogenization limit and waveguide gradient index devices demonstrated through direct visualization of THz fields

et al. 2015

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Electromagnetic homogenization approximation calculates an effective refractive index of a composite material as a weighted average of its components, and has found uses in gradient refractive index and transformation optics devices. However, the utility of the homogenization approximation is hindered by uncertainty in its range of applicability. Harnessing the capability of time-resolved imaging provided by the terahertz polaritonics platform, we determined the dispersion curves of slab waveguides with periodic arrays of holes, and we quantified the breakdown of the homogenization approximation as the period approached the terahertz wavelength and the structure approached the photonic bandgap regime. We found that if the propagation wavelength in the dielectric waveguide was at least two times as large as the Bragg condition wavelength, the homogenization approximation held independent of the detailed geometry, propagation direction, or fill fraction. This value is much less demanding than the estimate of 10:1 often assumed for homogenization. We further used the experimental capabilities to extract the effective refractive index of the photonic crystals in the homogenization approximation limit, and we used this to analyze the predictive strength of analytical formulas. These formulas enabled rapid design of a Luneburg lens and a bi-directional cloak in a waveguide platform without the need for numerical simulations. Movies of terahertz waves interacting with these structures, which were fabricated using femtosecond laser machining, reveal excellent performance. The combination of an analytical formula and confidence in the homogenization approximation will aid in fast design and prototyping of gradient index devices.

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Direct experimental visualization of waves and band structure in 2D photonic crystal slabs

Cited by 15 publications

References 51 publications

All-optical observation and reconstruction of spin wave dispersion

All-optical observation and reconstruction of spin wave dispersion

What is the Brillouin zone of an anisotropic photonic crystal?

The homogenization limit and waveguide gradient index devices demonstrated through direct visualization of THz fields

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