Layers with gradient refractive-index profile are an attractive alternative to conventional homogeneous stack coatings. However, the optical characterization and monitoring of the graded refractive-index profile is a complex issue, which has been typically solved by using a simplified model of mixed materials. Although this approach provides a solution to the problem, the precision, which can be expected from optical characterization of the refractive index gradient, remains unclear. In this work, we study optical characterization of SiO_xN_y layers deposited via reactive dual ion beam sputtering. To characterize the deposited layers, we use several methods including reflectance, and transmittance spectra at a broad range of incident angles, together with spectral ellipsometry. All the data were simultaneously fitted with a general profile of refractive index. The expected profile used in our fit was based on characterization of SiO_xN_y layers with a varying stoichiometry. By altering of the profile, we discussed sensitivity of such alternation on fit quality and we studied ambiguity of merit-function minimization. We demonstrate that while the scanning of particular parameters of the profile can be seemingly very precise, we obtain a very good agreement between the experimental data and model for a broad range of gradient shapes, where the refractive-index value on major part of the profile can differ as much as 0.02 from the mean value.
Terbium doped silicon oxynitride host matrix is suitable for various applications such as light emitters compatible with CMOS technology or frequency converter systems for photovoltaic cells. In this study, amorphous Tb3+ ion doped nitrogen-rich silicon oxynitride (NRSON) thin films were fabricated using a reactive magnetron co-sputtering method, with various N2 flows and annealing conditions, in order to study their structural and emission properties. Rutherford backscattering (RBS) measurements and refractive index values confirmed the silicon oxynitride nature of the films. An electron micr…
The development of versatile and novel material platforms for integrated photonics is of prime importance in the perspective of future applications of photonic integrated circuits for quantum information and sensing. Here we present a low-loss material platform based on high-refractive index silicon oxynitride (\ce{SiON}), which offers significant characteristics for linear and non-linear optics applications in a wide range of red/near-infrared wavelengths. The demonstrated propagation loss $<1.5$~dB/cm for visible wavelengths enables the realization of long and intricate circuitry for photon …
Nonlinear optical effects including stimulated Brillouin scattering (SBS) and four-wave mixing (FWM) play an important role in microwave photonics, optical frequency combs, and quantum photonics. Harnessing SBS and FWM in a low-loss and versatile integrated platform would open the path to building large-scale Brillouin/Kerr-based photonic integrated circuits. In this letter, we investigate the Brillouin and Kerr properties of a low-index (n=1.513 @ 1550 nm) silicon oxynitride (SiON) platform. We observed, for the first time, backward SBS in SiON waveguides with a Brillouin gain coefficient of …
Strong second harmonic generation (SHG) in silicon nitride has been extensively studied-among others, in terms of laser-induced SHG enhancement in Si3N4 waveguides. This enhancement has been ascribed to the all-optical poling induced by the coherent photogalvanic effect. Yet, an analogous process for Si3N4 thin films has not been reported. Our article reports on the observation of laser-induced 3-fold SHG enhancement in Si3N4 thin films. The observed enhancement has many features similar to all-optical poling, such as highly nonlinear power dependence, cumulative effect, or connection to the S…
On-chip optical resonators have proven to be a promising platform for generating Kerr frequency combs. Whispering gallery mode resonators are particularly attractive because of their small footprint as well as low threshold and power consumption. This performance can be attributed to two characteristics: the cavity quality factor (Q) and the cavity dispersion. The input optical field into the cavity is amplified by the cavity Q, enabling nonlinear processes to occur with low input powers. In addition, the total span of the optical comb is governed by the dispersion. In an optical cavity-based …
There are two main physical properties needed to fabricate 1D photonic structures and form perfect photonic bandgaps: the quality of the thickness periodicity and the refractive index of their components. Porous silicon (PS) is a nano-structured material widely used to prepare 1D photonic crystals due to the ease of tuning its porosity and its refractive index by changing the fabrication conditions. Since the morphology of PS changes with porosity, the determination of PS's refractive index is no easy task. To find the optical properties of PS we can use different effective medium approximatio…
Thermodynamic noise places a fundamental limit on the frequency stability of dielectric optical resonators. Here, we present the characterization of thermo-refractive noise in photonic-chip-based silicon nitride microresonators and show that thermo-refractive noise is the dominant thermal noise source in the platform. We employed balanced homodyne detection to measure the thermo-refractive noise spectrum of microresonators of different diameters. The measurements are in good agreement with theoretical models and finite element method simulations. Our characterization sets quantitative bounds o…
Dispersion engineering in silicon nitride (SiX NY ) waveguides is investigated through the optimization of the waveguide transversal dimensions and refractive indices in a multi-cladding arrangement. Ultra-flat dispersion of -84.0 +/- 0.5 ps/nm/km between 1700 and 2440 nm and 1.5 +/- 3 ps/nm/km between 1670 and 2500 nm is numerically demonstrated. It is shown that typical refractive index fluctuations as well as dimension fluctuations during the fabrication of the SiX NY waveguides are a limitation for obtaining ultra-flat dispersion profiles. Single- and multi-cladding waveguides are fabricat…
Temperature dependent refractive index of silicon and germanium
硅和锗可能是固态器件技术以及最近的微加工和纳米技术背景下最广为人知的两种半导体材料。同时，这两种材料在红外镜头设计领域也有重要的应用。为这两种材料透射的波长范围设计的光学仪器在冷却至低温时实现最佳性能，以增强来自场景的信号超过仪器背景辐射。为了实现在低温下使用硅和锗的高质量透镜设计，我们使用NASA戈达德太空飞行中心的低温高精度折射测量系统（CHARMS）测量了这两种材料的多个棱镜的绝对折射率，作为波长和温度的函数。对于硅，我们报告的绝对折射率和热光系数（dn/dT）在温度范围从20至300 K，波长从1.1至5.6微米，而对于锗，我们覆盖的温度范围从20至300 K和波长从1.9至5.5微米。我们将我们的测量结果与文献中的其他测量结果进行比较，并根据我们的数据提供依赖于温度的Sellmeier系数，以便将指数精确插值到其他波长和温度。引用文献中这两种材料折射率的各种数值，我们重申，当绝对精度要求大于+/-5 x 10^-3时，测量来自同一批原材料的样品的折射率是非常重要的。
For erbium-doped amorphous oxides, such as those that are used in compact lightwave devices interfaced with silicon, values of the refractive indices are commonly obtained empirically. This work, combining experimental and theoretical studies, examines silica as the exemplary host and the influence of erbium doping on the refractive index. Analysis of data is presented for the spectral refractive index in the ultraviolet to near infrared wavelength range of heavily erbium-doped silica thin films prepared by spin coating a sol-gel precursor on silicon and subsequent vacuum annealing. Effective …
Mode-division multiplexing offers a promising solution to increase the data capacity for optical communications. Waveguide mode conversion is essential for on-chip mode-division multiplexing. Previously reported mode converters have been limited to the conversion from a fundamental mode to one particular high-order mode. It is challenging to simultaneously satisfy the phase matching conditions during multiple mode conversion processes. Here, we propose a scalable design method that overcomes this limitation and realizes the simultaneous conversion of multiple modes via an all-dielectric two-di…
Portable and cost-effective gas sensors are gaining demand for a number of environmental, biomedical and industrial applications, yet current devices are confined into specialized labs and cannot be extended to general use. Here, we demonstrate a part-per-billion-sensitive refractive index gas sensor on a photonic chip based on silicon nitride waveguides functionalized with a mesoporous silica top-cladding layer. Low-concentration chemical vapors are detected by monitoring the output spectral pattern of an integrated Mach-Zehnder interferometer having one coated arm exposed to the gas vapors. …
Precise measurement of the refractive index of stable silicon isotopes $^{28}$Si, $^{29}$Si, $^{30}$Si single crystals with enrichments above 99.9 at.% and a silicon single crystal $^{nat}$Si of natural isotopic composition is performed with the Fourier-transform interference refractometry method from 1.06 to more than 80 mkm with 0.1 cm$^{-1}$ resolution and accuracy of $2 \times 10^{-5} ... 1 \times 10^{-4}$. The oxygen and carbon concentrations in all crystals are within $5 \times 10^{15}$ cm$^{-3}$ and the content of metal impurities is $10^{-5} ... 10^{-6}$ at.%. The peculiar changes of t…
The index of refraction n(E_γ)=1+δ(E_γ)+iβ(E_γ) is split into a real part δand an absorptive part β. The absorptive part has the three well-known contributions to the cross section σ_{abs}: the photo effect, the Compton effect and the pair creation, but there is also the inelastic Delbrück scattering. Second-order elastic scattering cross sections σ_{sca} with Rayleigh scattering (virtual photo effect), virtual Compton effect and Delbrück scattering (virtual pair creation) can be calculated by integrals of the Kramers-Kronig dispersion relations from the cross section σ_{abs}. The real elastic…
Broadband Chromatic Dispersion of Thermo-refractive Coefficients and its Impact in Silicon Nitride Nonlinear Photonics
Joint Quantum Institute, NIST/University of Maryland（联合量子研究所，美国国家标准与技术研究院/马里兰大学）；Microsystems and Nanotechnology Division, National Institute of Standards and Technology（微系统与纳米技术部，美国国家标准与技术研究院）
Graphene has been considered as a promising material for opto-electronic devices, because of its tunable and wideband optical properties. In this work, we demonstrate electro-refractive phase modulation in graphene at wavelengths from 1530 to 1570 nm. By integrating a gated graphene layer in a silicon-waveguide based Mach-Zehnder interferometer, the key parameters of a phase modulator like change in effective refractive index, insertion loss and absorption change are extracted. These experimentally obtained values are well reproduced by simulations and design guidelines are provided to make gr…
The use of the Silicon-on-Insulator (SOI) platform has been prominent for realizing CMOS-compatible, high-performance photonic integrated circuits (PICs). But in recent years, the silicon-nitride-on-silicon-dioxide (SiN-on-SiO$_2$) platform has garnered increasing interest as an alternative to the SOI platform for realizing high-performance PICs. This is because of its several beneficial properties over the SOI platform, such as low optical losses, high thermo-optic stability, broader wavelength transparency range, and high tolerance to fabrication-process variations. However, SiN-on-SiO$_2$ b…
The unique material property of silicon carbide (SiC) and the recent demonstration of low-loss SiC-on-insulator integrated photonics platform have attracted considerable research interests for chip-scale photonic and quantum applications. Here, we carry out a thorough investigation of the Kerr nonlinearity among 4H-SiC wafers from several major wafer manufacturers, and reveal for the first time that their Kerr nonlinear refractive index can be significantly different. By eliminating various measurement errors in the four-wave mixing experiment and improving the theoretical modeling for high-in…
Tight confinement of light in photonic cavities provides an efficient template for the realization of high optical intensity with strong field gradients. Here we present such a nanoscale resonator device based on a one-dimensional photonic crystal slot cavity. Our design allows for realizing highly localized optical modes with theoretically predicted Q factors in excess of 106. The design is demonstrated experimentally both in a high-contrast refractive index system (silicon), as well as in medium refractive index contrast devices made from aluminum nitride. We achieve extinction ratio of 21dB…
Dielectric metasurfaces require high refractive index contrast materials for optimum performance. This requirement imposes a severe restraint; devices have either been demonstrated at wavelengths of 700nm and above using high-index semiconductors such as silicon, or they use lower index dielectric materials such as TiO$_{2}$ or Si$_{3}$N$_{4}$ and operate in the visible wavelength regime. Here, we show that the high refractive index of silicon can be exploited at wavelengths as short as 532 nm by demonstrating a silicon metasurface with a transmission efficiency of 47% at this wavelength. The …
High-permittivity dielectric particles with resonant magnetic properties are being explored as constitutive elements of new metamaterials and devices in the microwave regime. Magnetic properties of low-loss dielectric nanoparticles in the visible or infrared are not expected due to intrinsic low refractive index of optical materials in these regimes. Here we analyze the dipolar electric and magnetic response of loss-less dielectric spheres made of moderate permittivity materials. For low material refractive index there are no sharp resonances due to strong overlapping between different multipo…
Optical complex materials offer unprecedented opportunity to engineer fundamental band dispersion which enables novel optoelectronic functionality and devices. Exploration of photonic Dirac cone at the center of momentum space has inspired an exceptional characteristic of zero-index, which is similar to zero effective mass in fermionic Dirac systems. Such all-dielectric zero-index photonic crystals provide an in-plane mechanism such that the energy of the propagating waves can be well confined along the chip direction. A straightforward example is to achieve the anomalous focusing effect witho…
High-refractive-index semiconductor optical waveguides form the basis for modern photonic integrated circuits (PICs) , but the conventional methods of achieving optical confinement require a thick lower-refractive-index support layer that impedes large-scale co-integration with electronics. To address this challenge, we present a general architecture for single-mode waveguides that confine light in a high-refractive-index material on a native substrate. Our waveguide consists of a high-aspect-ratio fin of the guiding material surrounded by lower-refractive-index dielectrics and is compatible w…
In the recent article by Feng et al. [Science 333, 729-733 (2011)] a system is proposed with a periodic spatial modulation of refractive index and absorption. It is claimed that this system is nonreciprocal and can be used as an optical isolator. The authors use an unconventional definition of reciprocity and thus make wrong conclusions on the applicability of the described phenomena for optical isolators. (Submitted to Science on October 7, 2011)
Precise measurements of the geometrical thickness of a sample and its refractive index are important for materials science, engineering, and medical diagnosis. Among the possible non-contact evaluation methods, optical interferometric techniques possess the potential of providing superior resolution. However, in the optical frequency region, the ambiguity in the absolute phase-shift makes it difficult to measure these parameters of optically thick dispersive materials with sufficient resolution. Here, we demonstrate that dual frequency-comb spectroscopy can be used to precisely determine the a…
In this work, we demonstrate an integrated platform comprising a refractive index (RI) sensor based on Photonic Molecule (PM) that effectively mitigates the influence of environmental perturbations using a differential measurement scheme while providing high quality-factor (Q) resonances. The RI sensor consists of an exposed microdisk resonator coupled to an external clad microring resonator fabricated on silicon-on-insulator (SOI) platform. We report a RI sensitivity of 23 nm/RIU, achieving a limit of detection (LOD) of 1.6 x 10-3 refractive index units (RIU) with improved stability in a comp…
We create a non-magnetic CMOS-compatible optical isolator on a silicon chip. The isolator is based on indirect interband photonic transition, induced by electrically-driven dynamic refractive index modulation. We demonstrate an electrically-induced non-reciprocity: the transmission coefficients between two single-mode waveguides become dependent on the propagation directions only in the presence of the electrical drive. The contrast ratio between forward and backward directions exceeds 30dB in simulations. We experimentally observe a strong contrast (up to 3 dB) limited only by our electrical …
We report fabrication of optical waveguides embedded in oxidised porous silicon in a mask-less process. Patterned pore-filling was attained by means of inkjet printing, enabling lateral modification of the waveguide's index of refraction and other optical properties thus providing full two-dimensional refractive index control of the optical waveguide. The waveguides were created by applying a KDP salt solution over a porous silicon film by means of a material printer. Light guiding was demonstrated at wavelengths 1.064 and 1.550 microns. Measured values of the intensity attenuation at these wa…
Future laser-interferometric gravitational wave detectors (GWDs) will potentially employ test mass mirrors from crystalline silicon and a laser wavelength of $1550\,\rm{nm}$, which corresponds to a photon energy below the silicon bandgap. Silicon might also be an attractive high-refractive index material for the dielectric mirror coatings. Films of amorphous silicon (a-Si), however, have been found to be significantly more absorptive at $1550\,\rm{nm}$ than crystalline silicon (c-Si). Here, we investigate the optical absorption of a Si/SiO$_2$ dielectric coating produced with the ion plating t…
In order to overcome the challenge of obtaining high modulation depth due to weak graphene-light interaction, a graphene-on-silicon nitride (SiNx) microring resonator based on graphene's gate-tunable optical conductivity is proposed and studied. Geometrical parameters of graphene-on-SiNx waveguide are systematically analyzed and optimized, yielding a loss tunability of 0.04 dB/μm and an effective index variation of 0.0022. We explicitly study the interaction between graphene and a 40-μm-radius microring resonator, where electro-absorptive and electro-refractive modulation are both taken into a…
Controlling the propagation and coupling of light to sub-wavelength antennas is a crucial prerequisite for many nanoscale optical devices. Recently, the main focus of attention has been directed towards high-refractive-index materials such as silicon as an integral part of the antenna design. This development is motivated by the rich spectral properties of individual high-refractive-index nanoparticles. Here, we take advantage of the interference of their magnetic and electric resonances, to achieve remarkably strong lateral directionality. For controlled excitation of a spherical silicon nano…
Chemical vapor deposition-based growth techniques allow flexible design of CMOS-compatible materials. Here, we report the deuterated silicon-rich nitride films grown using plasma-enhanced chemical vapor deposition. The linear and nonlinear properties of the films are characterized. We compare the absorption at 1550nm wavelength region for films grown with $SiH_4$ and $SiD_4$, and experimentally confirm that the silicon-rich nitride films grown with $SiD_4$ eliminates Si-H related absorption. Waveguides fabricated on the films are further shown to possess a linear and nonlinear refractive index…
Frequency domain spectroscopy allows an experimenter to establish optical properties of solids in a wide frequency band including the technically challenging 10 THz region, and in other bands enables metrological comparison between competing techniques. We advance a method for extracting the optical properties of high-index solids using only transmission-mode frequency domain spectroscopy of plane-parallel Fabry-Perot optical flats. We show that different data processing techniques yield different kinds of systematic error, and that some commonly used techniques have inherent systematic errors…
Polycrystalline silicon core fibers (SCFs) fabricated via the molten core drawing (MCD) method are emerging as a flexible optoelectronic platform. Here, the optical transmission properties of MCD SCFs that have been tapered down to a few micrometer-sized core dimensions are characterized from the Telecom band to the mid-infrared spectal regime. The SCFs exhibit low linear losses on the order of a few dB/cm over the entire wavelength range. Characterization of the two-photon absorption coefficient \b{eta}_TPA and nonlinear refractive index n_2 of the SCFs reveals values consistent with previous…
As the optical analogue to integrated electronics, integrated photonics has already found widespread use in data centers in the form of optical interconnects. As global network traffic continues its rapid expansion, the power consumption of such circuits becomes a critical consideration. Electrically tunable devices in photonic integrated circuits contribute significantly to the total power budget, as they traditionally rely on inherently power-consuming phenomena such as the plasma dispersion effect or the thermo-optic effect for operation. Here, we demonstrate ultra-low-power refractive inde…
We evaluate the nonlinear coefficient of graphene-on-silicon waveguides through the coincidence measurement of photon-pairs generated via spontaneous four-wave mixing. We observed the temporal correlation of the photon-pairs from the waveguides over various transfer layouts of graphene sheets. A simple analysis of the experimental results using coupled-wave equations revealed that the atomically-thin graphene sheets enhanced the nonlinearity of silicon waveguides up to ten-fold. The results indicate that the purely $χ^{(3)}$-based effective nonlinear refractive index of graphene is on the orde…
Perturbations to the effective refractive index from nanometer-scale fabrication variations in waveguide geometry plague high index-contrast photonic platforms including the ubiquitous sub-micron silicon-on-insulator (SOI) process. Such variations are particularly troublesome for phase-sensitive devices such as interferometers and resonators, which exhibit drastic changes in performance as a result of these fabrication-induced phase errors. In this Letter, we propose and experimentally demonstrate a design methodology for dramatically reducing device sensitivity to silicon width variations. We…
Adaptable, reconfigurable and programmable are key functionalities for the next generation of silicon-based photonic processors, neural and quantum networks. Phase change technology offers proven non-volatile electronic programmability, however the materials used to date have shown prohibitively high optical losses which are incompatible with integrated photonic platforms. Here, we demonstrate the capability of the previously unexplored material Sb$_2$Se$_3$ for ultralow-loss programmable silicon photonics. The favorable combination of large refractive index contrast and ultralow losses seen i…
We report an invisibility carpet cloak device, which is capable of making an object undetectable by visible light. The cloak is designed using quasi conformal mapping and is fabricated in a silicon nitride waveguide on a specially developed nano-porous silicon oxide substrate with a very low refractive index. The spatial index variation is realized by etching holes of various sizes in the nitride layer at deep subwavelength scale creating a local effective medium index. The fabricated device demonstrates wideband invisibility throughout the visible spectrum with low loss. This silicon nitride …
We demonstrate highly efficient coupling of light from an optical fiber to a silicon photonic crystal optomechanical cavity. The fiber-to-cavity coupling utilizes a compact (L ~ 25 um) intermediate adiabatic coupler. The optical coupling is lithographically controlled, broadband, relatively insensitive to fiber misalignment, and allows for light to be transferred from an optical fiber to, in principle, any photonic chip with refractive index greater than that of the optical fiber. Here we demonstrate single-sided cavity coupling with a total fiber-to-cavity optical power coupling efficiency of…
A method to engineer the refractive indices of functional materials (TiO2, ZnO, SnO2, SiO2), by nanostructuring in the deep sub-wavelength regime (<20nm), is presented. Block-copolymer templating combined with a wet processing route is used to realize 3D functional nanostructures with continuously adjustable refractive indices from 1.17 to 2.2. Wet processing accessed refractive index engineering can be applied to address a variety of realizability concerns in attaining design specified refractive index values and refractive index gradients in 1D, 2D, and 3D that arise as the results of optica…
The concept of high refractive index subwavelength dielectric nanoresonators, supporting electric and magnetic optical resonances, is a promising platform for waveguiding, sensing, and nonlinear nanophotonic devices. However, high concentration of defects in the nanoresonators diminishes their resonant properties, which are crucially dependent on their internal losses. Therefore, it seems to be inevitable to use initially crystalline materials for fabrication of the nanoresonators. Here, we show that the fabrication of crystalline (low-loss) resonant silicon nanoparticles by femtosecond laser …
In this paper, we present the theoretical studies of a refractive index map to implement a Gauss to J0-Bessel-Gauss convertor. We theoretically demonstrate the viability of such device by solving the inverse electromagnetic problem. The computed conversion efficiency is 90%. The theoretical results, obtained from the beam conversion efficiency, self-regeneration, and propagation through an opaque obstruction; demonstrate that a 2D graded index map of the refractive index can be used to transform a Gauss beam into a J0-Bessel-Gauss beam. To the best of our knowledge, this is the first demonstra…
We present the design, simulation, and planned fabrication process of a flat high resistivity silicon gradient index (GRIN) lens for millimeter and submillimeter wavelengths with very low absorption losses. The gradient index is created by subwavelength holes whose size increases with the radius of the lens. The effective refractive index created by the subwavelength holes is constant over a very wide bandwidth, allowing the fabrication of achromatic lenses up to submillimeter wavelengths. The designed GRIN lens was successfully simulated and shows an expected efficiency better than that of a …
