The theory of electric polarization in crystals defines the dipole moment of an insulator in terms of a Berry phase (geometric phase) associated with its electronic ground state. This concept not only solves the long-standing puzzle of how to calculate dipole moments in crystals, but also explains topological band structures in insulators and superconductors, including the quantum anomalous Hall insulator and the quantum spin Hall insulator, as well as quantized adiabatic pumping processes. A recent theoretical study has extended the Berry phase framework to also account for higher electric multipole moments, revealing the existence of higher-order topological phases that have not previously been observed. Here we demonstrate experimentally a member of this predicted class of materials-a quantized quadrupole topological insulator-produced using a gigahertz-frequency reconfigurable microwave circuit. We confirm the non-trivial topological phase using spectroscopic measurements and by identifying corner states that result from the bulk topology. In addition, we test the critical prediction that these corner states are protected by the topology of the bulk, and are not due to surface artefacts, by deforming the edges of the crystal lattice from the topological to the trivial regime. Our results provide conclusive evidence of a unique form of robustness against disorder and deformation, which is characteristic of higher-order topological insulators.

Electromagnetically induced transparency (EIT) [1,2] provides a powerful mechanism for controlling light propagation in a dielectric medium, and for producing slow and fast light. EIT traditionally arises from destructive interference induced by a nonradiative coherence in an atomic system. Stimulated Brillouin scattering (SBS) of light from propagating hypersonic acoustic waves [3] has also been used successfully for the generation of slow and fast light [4][5][6][7]. However, EIT-type processes based on SBS were considered infeasible because of the short coherence lifetime of hypersonic phonons. Here, we report a new Brillouin scattering induced transparency (BSIT) phenomenon generated by acousto-optic interaction of light with long-lived propagating phonons [8,9]. We demonstrate that BSIT is uniquely non-reciprocal due to the propagating acoustic phonon wave and accompanying momentum conservation requirement. Using a silica microresonator having naturally occurring forward-SBS phasematched modal configuration [8,9], we show that BSIT enables compact and ultralow-power slow-light generation with delay-bandwidth product comparable to state-of-the-art SBS systems. [3,10,11] is a fundamental materiallevel nonlinearity occurring in all states of matter [12] in which two optical fields are coupled to a traveling acoustic wave through photoelastic scattering and electrostriction. The light fields scatter from the periodic photoelastic perturbation generated by the traveling acoustic wave, while simultaneously writing a spatiotemporally beating electrostriction force whose momentum and frequency matches the acoustic wave. Phase matching for SBS is thus defined by both 1 arXiv:1408.1739v2 [physics.optics] 11 Aug 2014 energy and momentum conservation, and is satisfied in back-scattering only by multi-GHz phonon modes in most solids. SBS is frequently used for optical gain [3,13], laser linewidth narrowing [14], optical phase conjugation [15], dynamic gratings [16], and even material characterization and microscopy [17][18][19][20][21][22]. The applications of SBS in superluminal and slow light experiments have been recognized as well [4][5][6][7]. However, unlike the case of electromagnetically induced transparency (EIT) [1,2], the generation of transparency with SBS has never been demonstrated. This is because in typical Brillouin scattering pump-probe systems the lifetimes of phonons at multi-GHz frequencies are much shorter than the photon lifetimes [3,23,24], effectively disabling the coherent interference of probe Stokes scattering and pump anti-Stokes scattering pathways. In a forward-scattering SBS system however, this lifetime relationship can be reversed by coupling the light fields through a low-frequency long-lived phonon mode as shown recently in the experimental demonstration of forward-SBS lasing [8] and Brillouin cooling [9]. Stimulated Brillouin scattering (SBS)Nonlinear optical processes such as EIT need to satisfy the energy-momentum conservation, leading to the phase-matching requirement. For...

Although bolometric- and ponderomotive-induced deflection of device boundaries are widely used for laser cooling, the electrostrictive Brillouin scattering of light from sound was considered an acousto-optical amplification-only process(1-7). It was suggested that cooling could be possible in multi-resonance Brillouin systems(5-8) when phonons experience lower damping than light(8). However, this regime was not accessible in electrostrictive Brillouin systems(1-3,5,6) as backscattering enforces high acoustical frequencies associated with high mechanical damping(1). Recently, forward Brillouin scattering(3) in microcavities(7) has allowed access to low-frequency acoustical modes where mechanical dissipation is lower than optical dissipation, in accordance with the requirements for cooling(8). Here we experimentally demonstrate cooling via such a forward Brillouin process in a microresonator. We show two regimes of operation for the electrostrictive Brillouin process: acoustical amplification as is traditional and an electrostrictive Brillouin cooling regime. Cooling is mediated by resonant light in one pumped optical mode, and spontaneously scattered resonant light in one anti-Stokes optical mode, that beat and electrostrictively attenuate the Brownian motion of the mechanical mode

A recent renaissance in Brillouin scattering research has been driven by the increasing maturity of photonic integration platforms and nanophotonics. The result is a new breed of chip-based devices that exploit acousto-optic interactions to create lasers, amplifiers, filters, delay lines and isolators. Here we provide a detailed overview of Brillouin scattering in integrated waveguides and resonators, covering key concepts such as the stimulation of the Brillouin process, in which the optical field itself induces acoustic vibrations, the importance of acoustic confinement, methods for calculating and measuring Brillouin gain, and the diversity of materials platforms and geometries. Our review emphasizes emerging applications in microwave photonics, signal processing and sensing, and concludes with a perspective for future directions.

stimulated Brillouin interaction between sound and light, known to be the strongest optical nonlinearity common to all amorphous and crystalline dielectrics, has been widely studied in fibres and bulk materials but rarely in optical microresonators. The possibility of experimentally extending this principle to excite mechanical resonances in photonic microsystems, for sensing and frequency reference applications, has remained largely unexplored. The challenge lies in the fact that microresonators inherently have large free spectral range, whereas the phase-matching considerations for the Brillouin process require optical modes of nearby frequencies but with different wave vectors. Here we rely on high-order transverse optical modes to relax this limitation and report the experimental excitation of mechanical resonances ranging from 49 to 1,400 mHz by using forward Brillouin scattering. These natural mechanical resonances are excited in ~100 µm silica microspheres, and are of a surface-acoustic whispering-gallery type.