Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs

Linear extrapolation method based on multiple equiproportional models for thermal performance prediction of ultra-large array

Strong demand for developing the photothermal (PT) and electrothermal devices with ultra-large array is increasing. Thermal performance prediction is vital to optimize the key properties of the devices with ultra-large array. Finite element method (FEM) provides a powerful numerical approach for solving complex thermophysics issues. However, for calculating the performance of devices with ultra-large array, it is very memory-consuming and time-consuming to build an equal scale three-dimensional (3D) FEM model. For an ultra-large periodic array irradiated with a local heating source, the use of periodic boundary conditions could lead to considerable errors. To solve this problem, a linear extrapolation method based on multiple equiproportional models (LEM-MEM) is proposed in this paper. The proposed method builds several reduced-size FEM models to carry out simulation and extrapolation, which avoids dealing with the ultra-large arrays directly and greatly reduces the computation consumption. To verify the accuracy of LEM-MEM, a PT transducer with beyond 4000 × 4000 pixels is proposed, fabricated, tested and compared with the prediction results. Four different pixel patterns are designed and fabricated to test their steady thermal properties. The experimental results demonstrate that LEM-MEM has great predictability, and the maximum percentage error of average temperature is within 5.22% in four different pixel patterns. In addition, the measured response time of the proposed PT transducer is within 2 ms. The proposed LEM-MEM not only provides design guidance for optimizing PT transducers, but is also very useful for other thermal engineering problems in ultra-large array that requires facile and efficient prediction strategy.

Lifting restrictions on coherence loss when characterizing non-transparent hypersonic phononic crystals

Hypersonic phononic bandgap structures confine acoustic vibrations whose wavelength is commensurate with that of light, and have been studied using either time- or frequency-domain optical spectroscopy. Pulsed pump-probe lasers are the preferred instruments for characterizing periodic multilayer stacks from common vacuum deposition techniques, but the detection mechanism requires the injected sound wave to maintain coherence during propagation. Beyond acoustic Bragg mirrors, frequency-domain studies using a tandem Fabry–Perot interferometer (TFPI) find dispersions of two- and three-dimensional phononic crystals (PnCs) even for highly disordered samples, but with the caveat that PnCs must be transparent. Here, we demonstrate a hybrid technique for overcoming the limitations that time- and frequency-domain approaches exhibit separately. Accordingly, we inject coherent phonons into a non-transparent PnC using a pulsed laser and acquire the acoustic transmission spectrum on a TFPI, where pumped appear alongside spontaneously excited (i.e. incoherent) phonons. Choosing a metallic Bragg mirror for illustration, we determine the bandgap and compare with conventional time-domain spectroscopy, finding resolution of the hybrid approach to match that of a state-of-the-art asynchronous optical sampling setup. Thus, the hybrid pump–probe technique retains key performance features of the established one and going forward will likely be preferred for disordered samples.

Phononic and photonic properties of shape-engineered silicon nanoscale pillar arrays

We report the results of Brillouin-Mandelstam spectroscopy and Mueller matrix spectroscopic ellipsometry of the nanoscale 'pillar with the hat' periodic silicon structures, revealing intriguing phononic and photonic-phoxonic-properties. It has been theoretically shown that periodic structures with properly tuned dimensions can act simultaneously as phononic and photonic crystals, strongly affecting the light-matter interactions. Acoustic phonon states can be tuned by external boundaries, either as a result of phonon confinement effects in individual nanostructures, or as a result of artificially induced external periodicity, as in the phononic crystals. The shape of the nanoscale pillar array was engineered to ensure the interplay of both effects. The Brillouin-Mandelstam spectroscopy data indicated strong flattening of the acoustic phonon dispersion in the frequency range from 2 GHz to 20 GHz and the phonon wave vector extending to the higher-order Brillouin zones. The specifics of the phonon dispersion dependence on the pillar arrays' orientation suggest the presence of both periodic modulation and spatial localization effects for the acoustic phonons. The ellipsometry data reveal a distinct scatter pattern of four-fold symmetry due to nanoscale periodicity of the pillar arrays. Our results confirm the dual functionality of the nanostructured shape-engineered structure and indicate a possible new direction for fine-tuning the light-matter interaction in the next generation of photonic, optoelectronic, and phononic devices.

Determination of 1-propanol, ethanol, and methanol concentrations in water based on a one-dimensional phoxonic crystal sensor

In this research, the photonic and phononic response of one-dimensional multilayer phoxonic crystals (PxCs) with normal incident of electromagnetic and acoustic waves is discussed. The presented design can work as a highly sensitive sensor for measuring three binary alcohol/water mixtures (i.e., 1-propanol/water, ethanol/water, and methanol/water) for a wide range of concentrations. The PxC sensor is able to detect small changes in the refractive index and longitudinal sound velocity of the alcohol/water mixture with initially neglecting the acousto-optical interaction. The sensor design is a defective structure as [$({\rm Si}/{\rm SiO}_2)^4 (\rm mixture\;wt. \%) {({{\rm SiO}_2}/{\rm Si})^4}$(Si/SiO₂)⁴(mixturewt.%)(SiO₂/Si)⁴]. Also, we studied the effects of changing mixture concentrations from 0 wt. % to 100 wt. % on the physio-chemical parameters and resonant mode frequency. In our results, we have achieved high performance for the three alcohol mixtures in both phononic and photonic sensors especially for low concentrations. For example, in the photonic sensor we obtained sensitivity, $Q$Q value, and figure of merit of 873 nm/RIU, 755, and ${290}\;{{\rm RIU}^{ - 1}}$290RIU^-1, respectively, for methanol of concentration 10% in water. The phononic sensor showed higher results compared with the photonic sensor, as for ethanol with concentration 26.8% in water we obtained sensitivity, $Q$Q value, and figure of merit of ${37}\;{{\rm MHz/ms}^{ - 1}}$37MHz/ms^-1, 1604, and ${8.4}\;{({\rm m/s})^{ - 1}}$8.4(m/s)^-1, respectively. The proposed structure has different merits: operation at high temperatures, compact size, ease of fabrication, and feasibility of alcohol detection with two different methods that could be used in many chemical applications.

Nanocrystalline silicon optomechanical cavities

Silicon on insulator photonics has offered a versatile platform for the recent development of integrated optomechanical circuits. However, there are some constraints such as the high cost of the wafers and limitation to a single physical device level. In the present work we investigate nanocrystalline silicon as an alternative material for optomechanical devices. In particular, we demonstrate that optomechanical crystal cavities fabricated of nanocrystalline silicon have optical and mechanical properties enabling non-linear dynamical behaviour and effects such as thermo-optic/free-carrier-dispersion self-pulsing, phonon lasing and chaos, all at low input laser power and with typical frequencies as high as 0.3 GHz.

High-efficiency acousto-optic coupling in phoxonic resonator based on silicon fishbone nanobeam cavity

We investigate the acousto-optic coupling rates between different acoustic resonance modes and a specified optical resonance mode in a one-dimensional phoxonic crystal fishbone nanobeam formed by periodically arranging semi-cylinders of air on both sides of a suspended silicon waveguide. The gradually tapered unit cells form optical and acoustic resonators. In acousto-optic coupling rate calculation, the acoustic fields and optical fields are obtained by steady state monochromatic analysis and eigen-mode computation, respectively. Results showed that the acoustic polarizations and symmetries of the acoustic resonance modes are dominant factors in the acousto-optic coupling efficiency, and appropriate selection of these parameters can prevent cancellation of acousto-optic interactions, thereby enhancing acousto-optic coupling rates. This study provides important insights that can be applied to acousto-optic device designs.

Fourier synthesis of radiofrequency nanomechanical pulses with different shapes

The concept of Fourier synthesis is heavily used in both consumer electronic products and fundamental research. In the latter, pulse shaping is key to dynamically initializing, probing and manipulating the state of classical or quantum systems. In NMR, for instance, shaped pulses have a long-standing tradition and the underlying fundamental concepts have subsequently been successfully extended to optical frequencies and even to the implementation of quantum gate operations. Transferring these paradigms to nanomechanical systems requires tailored nanomechanical waveforms. Here, we report on an additive Fourier synthesizer for nanomechanical waveforms based on monochromatic surface acoustic waves. As a proof of concept, we electrically synthesize four different elementary nanomechanical waveforms from a fundamental surface acoustic wave at f1 ≈ 150 MHz using a superposition of up to three discrete harmonics. We use these shaped pulses to interact with an individual sensor quantum dot and detect their deliberately and temporally modulated strain component via the optomechanical quantum dot response. Importantly, and in contrast to direct mechanical actuation by bulk piezoactuators, surface acoustic waves provide much higher frequencies (>20 GHz; ref. 10) to resonantly drive mechanical motion. Thus, our technique uniquely allows coherent mechanical control of localized vibronic modes of optomechanical crystals, even in the quantum limit when cooled to the vibrational ground state.

On-chip optical mode conversion based on dynamic grating in photonic-phononic hybrid waveguide

We present a scheme for reversible and tunable on-chip optical mode conversion based on dynamic grating in a hybrid photonic-phononic waveguide. The dynamic grating is built up through the acousto-optic effect and the theoretical model of the optical mode conversion is developed by considering the geometrical deformation and refractive index change. Three kinds of mode conversions are able to be realized using the same hybrid waveguide structure in a large bandwidth by only changing the launched acoustic frequency. The complete mode conversion can be achieved by choosing a proper acoustic power under a given waveguide length.

Towards GHz-THz cavity optomechanics in DBR-based semiconductor resonators

Resonators based on acoustic distributed Bragg reflectors (DBRs) were optimized to work in the GHz-THz regime, and grown by molecular beam epitaxy. We show that in structures made of GaAlAs alloys a simultaneous optimal confinement of light in the visible range and phonons in the tens of GHz range can be achieved. We report time resolved differential optical reflectivity experiments performed with fs-ps laser pulses. The experimental results are in excellent agreement with simulations based on standard transfer matrix methods. The resonant behavior of the photoelastic coefficient is discussed. The perfect optic-acoustic mode overlapping, added to a strongly enhanced coupling mechanism, implies that these DBR-based cavities could be the base of highly efficient optomechanical resonators.

Breakdown of the linear acousto-optic interaction regime in phoxonic cavities

The limits of validity of the linear photoelastic model are investigated in a one-dimensional dual photonic-phononic cavity, formed by alternating layers of a chalcogenide glass and a polymer homogeneous and isotropic material, which supports both optical and acoustic resonant modes localized in the same region. It is shown that the linear-response regime breaks down when either the acoustic excitation increases or the first-order acousto-optic interaction coupling element vanishes by symmetry, giving rise to the manifestation of multiphonon absorption and emission processes by a photon. Our results provide a consistent interpretation of different aspects of the underlying physics relating to nonlinear acousto-optic interactions that can occur in such cavities.

Mode conversion based on forward stimulated Brillouin scattering in a hybrid phononic-photonic waveguide

We propose a scheme for on-chip all optical mode conversion based on forward stimulated Brillouin scattering in a hybrid phononic-photonic waveguide. To describe the mode conversion the theoretical model of the FSBS is established by taking into account the radiation pressure and the electrostriction force simultaneously. The numerical simulation is carried out for the mode conversion from the fundamental mode E11x to the higher-order mode E21x. The results indicate that the mode conversion efficiency is affected by the waveguide length and the input pump light power, and the highest efficiency can reach upto 88% by considering the influence of optical and acoustic absorption losses in the hybrid waveguide. Additionally, the conversion bandwidth with approximate 12.5 THz can be achieved in 1550nm communication band. This mode converter on-chip is a promising device in the integrated optical systems, which can effectively increase the capacity of silicon data busses for on-chip optical interconnections.

Lasing from active optomechanical resonators

Planar microcavities with distributed Bragg reflectors (DBRs) host, besides confined optical modes, also mechanical resonances due to stop bands in the phonon dispersion relation of the DBRs. These resonances have frequencies in the 10- to 100-GHz range, depending on the resonator's optical wavelength, with quality factors exceeding 1,000. The interaction of photons and phonons in such optomechanical systems can be drastically enhanced, opening a new route towards the manipulation of light. Here we implemented active semiconducting layers into the microcavity to obtain a vertical-cavity surface-emitting laser (VCSEL). Thereby, three resonant excitations--photons, phonons and electrons--can interact strongly with each other providing modulation of the VCSEL laser emission: a picosecond strain pulse injected into the VCSEL excites long-living mechanical resonances therein. As a result, modulation of the lasing intensity at frequencies up to 40 GHz is observed. From these findings, prospective applications of active optomechanical resonators integrated into nanophotonic circuits may emerge.

Simultaneous bandgaps in LiNbO3 phoxonic crystal slab

We study simultaneous photonic and phononic crystal slabs created in Z-cut lithium niobate membranes. Bandgaps for guided waves are identified using the three-dimensional finite element method (FEM). Three lattices are considered: the square, the hexagonal, and the honeycomb lattices. We investigate the evolution of band gaps as a function of geometrical parameters such as hole radius and membrane thickness. We show the existence of dual photonic and phononic bandgaps in the triangular lattice for suitable geometrical parameters and specific modal symmetries for both the elastic and the electromagnetic fields.

High-frequency acousto-optic effects in Bragg reflectors

Picosecond acoustic interferometry was used to study the acousto-optic properties of a distributed Bragg reflector (DBR) manufactured from two immiscible polymers (cellulose acetate and polyvinylcarbyzole). Picosecond strain pulses were injected into the structure and changes in its reflectance were monitored as a function of time. The reflectance exhibited single-frequency harmonic oscillations as the strain pulse traversed the DBR. A transfer matrix method was used to model the reflectance of the DBR in response to interface modulation and photo-elastic effects. This work shows that photo-elastic effects can account for the acousto-optic response of DBRs with acoustically matched layers.

Modeling of optomechanical coupling in a phoxonic crystal cavity in diamond

A photonic and phononic crystal (phoxonic crystal PxC) is a periodically patterned material that can at the same time localize optical and mechanical modes. Here we theoretically model one-dimensional PxC in diamond and find high quality mechanical resonances with very high frequencies > 10 GHz and optical properties comparable to those of PxC in other materials. The simultaneous confinement of photons and phonons leads to an optomechanical interaction that we calculate in a perturbation approach. The optomechanical coupling strengths reach values in the MHz range. We identify design rules to simultaneously achieve high optical and mechanical quality factors along with strong optomechanical coupling.

Sound and heat revolutions in phononics

The phonon is the physical particle representing mechanical vibration and is responsible for the transmission of everyday sound and heat. Understanding and controlling the phononic properties of materials provides opportunities to thermally insulate buildings, reduce environmental noise, transform waste heat into electricity and develop earthquake protection. Here I review recent progress and the development of new ideas and devices that make use of phononic properties to control both sound and heat. Advances in sonic and thermal diodes, optomechanical crystals, acoustic and thermal cloaking, hypersonic phononic crystals, thermoelectrics, and thermocrystals herald the next technological revolution in phononics.

Acoustic waveguiding by pliable conduits with axial cross sections as linear waveguides in two-dimensional sonic crystals

Pliable conduits composed of periodically arranged concentric aluminum tori in air, with their axial cross sections acting as linear waveguides in two-dimensional sonic crystals, are numerically shown to guide acoustic waves in three dimensions in a flexible manner. Waveguide band structures are obtained by exploiting axial symmetry in a super-cell approach through two-dimensional finite-element simulations under the periodic boundary conditions. One isolated band having a bandwidth of 19.66% or 10.10% is observed for each guide, whose cross section is either in square or triangular geometry, respectively. Corresponding mode profiles indicate efficient guiding, as the acoustic energy is mainly concentrated in the hollow-core region of the guides. Transmittance spectra calculated through finite-element simulations are in agreement with the computed guiding bands. Transmittance along the waveguides with square and triangular axial cross sections around mid-band frequencies of their guiding bands varies slightly from -6.05 and -6.65 dB to -5.98 and -8.86 dB, respectively, as the guide length is increased from 10 to 200 periods. Efficient guiding across the smooth bends over circular arcs up to 90 deg is also demonstrated through three-dimensional finite-element method simulations.

Three-dimensional dielectric phoxonic crystals with network topology

We theoretically demonstrate the existence of simultaneous large complete photonic and phononic bandgaps in three-dimensional dielectric phoxonic crystals with a simple cubic lattice. These phoxonic crystals consist of dielectric spheres on the cubic lattice sites connected by thin dielectric cylinders. The simultaneous photonic and phononic bandgaps can exist over a wide range of geometry parameters. The vibration modes corresponding to the phononic bandgap edges are the local torsional resonances of the dielectric spheres and rods. Detailed discussion is presented on the variation of the photonic and phononic bandgaps with the geometry of the structure. Optimal geometry which generates large phoxonic bandgaps is suggested.

Phonons in slow motion: dispersion relations in ultrathin Si membranes

We report the changes in dispersion relations of hypersonic acoustic phonons in free-standing silicon membranes as thin as ∼8 nm. We observe a reduction of the phase and group velocities of the fundamental flexural mode by more than 1 order of magnitude compared to bulk values. The modification of the dispersion relation in nanostructures has important consequences for noise control in nano- and microelectromechanical systems (MEMS/NEMS) as well as opto-mechanical devices.

Band structures of phononic-crystal plates in the form of a sandwich-layered structure

This study investigates the propagation of Lamb waves in phononic-crystal plates in the form of a sandwich-layered structure. The composite plates are composed of periodic layers bilaterally deposited on both sides of the homogeneous core layer. Using the analyses of the band structures and the transmission spectra, it is revealed that the core layer may induce significant modulations to the lower-order Lamb modes. The modulations are ascribed to the reshaped particle displacement fields of the eigenmodes. Prominently, the core layer made of soft material (rubber) combines the identical eigenmodes of the periodic layers into a pair of asymmetric and symmetric modes in which case the periodic layers vibrate independently. However, the core layer made of hard material (tungsten) or medium hardness material (silicon) couples the periodic layers tightly, in which case the composites vibrate as a whole. In addition, it is found that the phononic band gaps are very sensitive to the thickness of the core layer; this could be indispensable to practical applications such as bandgap tuning.

Simultaneous guidance of slow photons and slow acoustic phonons in silicon phoxonic crystal slabs

We demonstrate theoretically that photons and acoustic phonons can be simultaneously guided and slowed down in specially designed nanostructures. Phoxonic crystal waveguides presenting simultaneous phononic and photonic band gaps were designed in perforated silicon membranes that can be conveniently obtained using silicon-on-insulator technology. Geometrical parameters for simultaneous photonic and phononic band gaps were first chosen for optical wavelengths around 1550 nm, based on the finite element analysis of a perfect phoxonic crystal of circular holes. A plain core waveguide was then defined, and simultaneous slow light and elastic guided modes were identified for some waveguide width. Joint guidance of light and elastic waves is predicted with group velocities as low as c/25 and 180 m/s, respectively.

Quasi-two-dimensional optomechanical crystals with a complete phononic bandgap

A fully planar two-dimensional optomechanical crystal formed in a silicon microchip is used to create a structure devoid of phonons in the GHz frequency range. A nanoscale photonic crystal cavity is placed inside the phononic bandgap crystal in order to probe the properties of the localized acoustic modes. By studying the trends in mechanical damping, mode density, and optomechanical coupling strength of the acoustic resonances over an array of structures with varying geometric properties, clear evidence of a complete phononic bandgap is shown.