Experimental probe of a complete 3D photonic band gap

Abstract

The identification of a complete three-dimensional (3D) photonic band gap in real crystals always employs theoretical or numerical models that invoke idealized crystal structures. Thus, this approach is prone to false positives (gap wrongly assigned) or false negatives (gap missed). Therefore, we propose a purely experimental probe of the 3D photonic band gap that pertains to many different classes of photonic materials. We study position and polarization-resolved reflectivity spectra of 3D inverse woodpile structures that consist of two perpendicular nanopore arrays etched in silicon. We observe intense reflectivity peaks (R > 90%) typical of high-quality crystals with broad stopbands. We track the stopband width versus pore radius, which agrees much better with the predicted 3D photonic band gap than with a directional stop gap on account of the large numerical aperture used. A parametric plot of s-polarized versus p-polarized stopband width agrees very well with the 3D band gap and is model-free. This practical probe provides fast feedback on the advanced nanofabrication needed for 3D photonic crystals and stimulates practical applications of band gaps in 3D silicon nanophotonics and photonic integrated circuits, photovoltaics, cavity QED, and quantum information processing. arXiv:1909.01899v2 [physics.optics]

Polymer-based self-assembled photonic crystals to tune light transport and emission

“…34 After a plethora of experimental efforts, the emergence of a photonic band gap was reported in 3D photonic crystal formulated by discrete engineering. 35,36 3D photonic crystals with diamond-like lattice symmetry were made via stacking layers of dielectric rods (see Fig. 3a) or via drilling cylindrical holes in a block of a high-refractive-index material, and these are commonly called woodpile and inverse woodpile structures, respectively.…”

Reflectivity of three-dimensional GaAs photonic band-gap crystals of finite thickness

“…Following Ref. [27], we estimate the error margins in the stop band edges and therefore the stop band width. We estimate the standard deviation in the minimum reflectivity at frequencies below the stop band, and the standard deviation of the maximum reflectivity, which both propagate into the determination of the gap edges.…”

“…When the frequency of light lies in a gap in the dispersion relations for a certain wave vector tending from the origin to the Brillouin zone boundary, light cannot propagate in the corresponding direction as a result of Bragg diffraction [9]. Such a directional gap or stop gap is usually probed with reflection or transmission experiments where a reflectivity peak or transmission trough occurs, also known as a stop band [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. To first order, the width of a stop band is proportional to the ratio of the dominant Fourier component of the dielectric function and the average dielectric constant [28,29].…”

Controlled light propagation in random, periodic, and superperiodic silicon nanophotonic materials

“…The resultant 3D crystal structure is cubic with a diamond-like symmetry, as illustrated in Figure 2.2(a) and also in an animation [106]. Inverse woodpile crystals have a broad 3D photonic band gap (see Figure 2.3) on account of their diamond-like structure [107][108][109][110]. The inset of Figure 2.3 shows the first Brillouin zone of the inverse woodpile structure with the high-symmetry points identified and the origin at Γ.…”

“…The band structures were calculated for pore radii corresponding to those obtained at the probing location, with the method from chapter 5 and Ref. [110] 2 . The band structure shows that the cavity superlattice sustains two types of bands inside the 3D band gap, namely flat bands typical of Cartesian light, and dispersive bands in the upper half of the band gap.…”