Highly linear lithium niobate Michelson interferometer modulators assisted by spiral Bragg grating reflectors.

Highly linear electro-optic modulators are key components in analog microwave photonic links, offering on-chip direct mixing of optical and RF fields. In this work, we demonstrate a monolithic integrated Michelson interferometer modulator on thin-film lithium niobate (LN), that achieves linearized performance by modulating Bragg grating reflectors placed at the end of Michelson arms. The modulator utilizes spiral-shaped waveguide Bragg gratings on Z-cut LN with top and bottom electrodes to realize extensive reflectors, essential for linearized performance, in a highly integrated form. Optical waveguides are realized using rib etching of LN with precisely engineered bottom and top cladding layers made of silicon dioxide and SU-8 polymer, respectively. The compact design fits a 3 mm long grating in an 80 µm × 80 µm area, achieving a broad operating bandwidth up to 18 GHz. A spurious free dynamic range (SFDR) of 101.2 dB·Hz2/3 is demonstrated at 1 GHz, compared to 91.5 dB·Hz2/3 for a reference Mach-Zehnder modulator fabricated on the same chip. Further enhancement in SFDR could be achieved by reducing fiber-to-chip coupling loss. The proposed demonstration could significantly improve the linearity of analog modulator-based integrated optical links.

Compact MZI modulators on thin film Z-cut lithium niobate.

In this paper, we designed, implemented, and characterized compact Mach-Zehnder interferometer-based electro-optic modulators. The modulator utilizes spiral-shaped optical waveguides on Z-cut lithium niobate and the preeminent electro-optic effect which is applied using top and bottom electrodes. Optical waveguides are made of rib etched lithium niobate waveguides with bottom silicon oxide cladding, while SU8 polymer covers the top and sides of the rib waveguides. The proposed implementation resulted in low optical losses < 1.3 dB/cm. Moreover, we achieved compact modulators that fit 0.286 cm and 2 cm long optical waveguides in 110 µm × 110 µm and 300 µm × 300 µm areas, respectively. For single arm modulation, the modulators achieved a VπL of 7.4 V.cm and 6.4 V.cm and 3-dB bandwidths of 9.3 GHz and 2.05 GHz, respectively. Push-pull modulation is expected to cut these VπL in half. The proposed configuration avoids traveling wave modulation complexities and represents a key development towards miniature and highly integrated photonic circuits.

Fundamental electro-optic limitations of thin-film lithium niobate microring modulators.

We investigate the impact of waveguide curvature on the electro-optic efficiency of microring resonators in thin-film X-cut or Y-cut lithium niobate (in-plane extraordinary axis) and derive explicit relations on the response. It is shown that such microring modulators have a fundamental upper bound on their electro-optic performance (∼50% filling factor) which corresponds to a specific arrangement of metal electrodes surrounding the microring and yields nearly identical results for X-cut and Y-cut designs. We further show that this limitation does not exist (i.e., 100% filling factor is possible) with Z-cut microring modulators or can be circumvented (i.e., ∼100% filling factor is possible) in X-cut and Y-cut modulators that use a race-track configuration with segmented electrodes. Comparison of our analytical results with multiphysics simulations and measured electro-optic efficiencies of microring resonators in the literature demonstrates the validity and accuracy of our approach.

Ultra-efficient and fully isotropic monolithic microring modulators in a thin-film lithium niobate photonics platform.

The large electro-optic coefficient, r33, of thin-film lithium niobate (LN) on insulator makes it an excellent material platform for high-efficiency optical modulators. Using the fundamental transverse magnetic optical mode in Z-cut LN enables isotropic in-plane devices; however, realizing a strong vertical electric field to capitalize on r33 has been challenging. Here we present a symmetric electrode configuration to boost the vertical field strength inside a fully-etched single-mode LN waveguide. We use this design paradigm to demonstrate an ultra-compact fully isotropic microring modulator with a high electro-optic tuning efficiency of 9 pm/V, extinction ratio of 20 dB, and modulation bandwidth beyond 28 GHz. Under quasi-static operation, the tuning efficiency of the modulator reaches 20 pm/V. Fast, efficient, high-contrast modulation will be critical in future optical communication systems while large quasi-static efficiency will enable post-fabrication trimming, thermal compensation, and even complete reconfiguration of microring-based sensor arrays and photonic integrated circuits.

Sensing Sub-10 nm Wide Perturbations in Background Nanopatterns Using Optical Pseudoelectrodynamics Microscopy (OPEM).

Using light as a probe to investigate perturbations with deep subwavelength dimensions in large-scale wafers is challenging because of the diffraction limit and the weak Rayleigh scattering. In this Letter, we report on a nondestructive noninterference far-field imaging method, which is built upon electrodynamic principles (mechanical work and force) of the light-matter interaction, rather than the intrinsic properties of light. We demonstrate sensing of nanoscale perturbations with sub-10 nm features in semiconductor nanopatterns. This framework is implemented using a visible-light bright-field microscope with a broadband source and a through-focus scanning apparatus. This work creates a new paradigm for exploring light-matter interactions at the nanoscale using microscopy that can potentially be extended to many other problems, for example, bioimaging, material analysis, and nanometrology.

Voxelized topology optimization for fabrication-compatible inverse design of 3D photonic devices.

Topology optimization for photonic device design, has been mostly used to optimize binary structures based on refractive index as the free parameter for each design cell. Typically, a constraint on the optimization variable to be z-invariant and a smoothing operation on small features are applied to make the structure fabricable by conventional lithography. To enable topology optimization to design fabricable 3D structures using emerging methods like grayscale lithography and focused ion beam milling, we propose here a framework that uses the refractive index step position as the free parameter for each 3D voxel. This choice of framework enables us to reuse the same mesh in each iteration and thereby reduce the time for optimization. We apply the framework to the fabricable design of both free-space and integrated photonic devices, at different wavelengths, demonstrating high-efficiency ultra-compact designs with wide wavelength tunability.

Realization of alignment-tolerant grating couplers for z-cut thin-film lithium niobate.

We present the design, modeling, fabrication, and characterization of grating coupler devices for z-cut lithium niobate near 1550 nm. We first experimentally measure the sensitivity of the insertion loss of a conventional grating coupler to translational misalignment through a three-factor full factorial design of experiment. Next, we design grating couplers that are significantly less sensitive to misalignment. The fabricated devices experienced less than 7 dB of excess insertion loss for combined misalignments of up to ± 5 µm in plane and up to -2 µm or + 10 µm out of plane.

High performance fully etched isotropic microring resonators in thin-film lithium niobate on insulator platform.

We present our design, fabrication, and experimental results for very high-performance isotropic microring resonators with small radii (∼ 30 µm) based on single-mode strip waveguides and transverse magnetic (TM) polarization in a fully etched lithium niobate (Z-cut) thin-film on insulator. The loss of the devices is predicted to be < 10 dB/cm, and is measured to be ∼ 7 dB/cm. The measured optical responses of microring resonators exhibit an extinction of ∼ 25 dB (close to critical coupling), a 3 dB optical bandwidth of 49 pm (∼ 6 GHz) for all-pass structures, an extinction of ∼ 10 dB for add-drop structures, and a free spectral range of ∼ 5.26 nm, all of which are in excellent agreement with the design. This work is the first step towards ultra-compact and fully isotropic optical modulators in thin-film lithium niobate on insulator.

Regularized pseudo-phase imaging for inspecting and sensing nanoscale features.

Recovering tiny nanoscale features using a general optical imaging system is challenging because of poor signal to noise ratio. Rayleigh scattering implies that the detectable signal of an object of size d illuminated by light of wavelength λ is proportional to d6/λ4, which may be several orders of magnitude weaker than that of additive and multiplicative perturbations in the background. In this article, we solve this fundamental issue by introducing the regularized pseudo-phase, an observation quantity for polychromatic visible light microscopy that seems to be more sensitive than conventional intensity images for characterizing nanoscale features. We achieve a significant improvement in signal to noise ratio without making any changes to the imaging hardware. In addition, this framework not only retains the advantages of conventional denoising techniques, but also endows this new measurand (i.e., the pseudo-phase) with an explicit physical meaning analogous to optical phase. Experiments on a NIST reference material 8820 sample demonstrate that we can measure nanoscale defects, minute amounts of tilt in patterned samples, and severely noise-polluted nanostructure profiles with the pseudo-phase framework even when using a low-cost bright-field microscope.

Optical inspection of nanoscale structures using a novel machine learning based synthetic image generation algorithm.

In this paper, we present a novel interpretable machine learning technique that uses unique physical insights about noisy optical images and a few training samples to classify nanoscale defects in noisy optical images of a semiconductor wafer. Using this technique, we not only detected both parallel bridge defects and previously undetectable perpendicular bridge defects in a 9-nm node wafer using visible light microscopy [Proc. SPIE9424, 942416 (2015)], but we also accurately classified their shapes and estimated their sizes. Detection and classification of nanoscale defects in optical images is a challenging task. The quality of images is affected by diffraction and noise. Machine learning techniques can reduce noise and recognize patterns using a large training set. However, for detecting a rare "killer" defect, acquisition of a sufficient training set of high quality experimental images can be prohibitively expensive. In addition, there are technical challenges involved in using electromagnetic simulations and optimization of the machine learning algorithm. This paper proposes solutions to address each of the aforementioned challenges.

Spatial control of photonic nanojets.

For a long time, light focusing from microspheres has been intensively researched. The microsphere has been shown to be capable of generating a high intensity beam with sub-wavelength width, known as a photonic nanojet (PNJ). In this article, we present a detailed report on the properties of a new asymmetrical microstructure, consisting of a supporting stage and a spherical cap, and demonstrate precise engineering of the PNJ characteristics by simply selecting its geometrical dimensions. More importantly, we find that a single asymmetrical microstructure can generate an ultra-elongated PNJ on the shadow side and the cascade of two asymmetrical elements can generate a PNJ with a full width at half maximum (FWHM) waist down to 0.27λ. In addition, because of the presence of energy convergence regions within the second element, an ultra-narrow PNJ can be generated even when the length of the second element in the cascade is many orders of magnitude greater than the wavelength or deviates somewhat from the optimal dimensions. This offers design flexibility and manufacturing tolerance, which has not been demonstrated in the conventional microsphere design or its derivatives. We believe that these remarkable performance features make the asymmetrical structure and its cascade attractive in numerous applications.

Quantitative phase imaging of weakly scattering objects using partially coherent illumination.

In this paper, we extend our recent work on partially coherent quantitative phase imaging (pcQPI) from two-dimensional (2D) to three-dimensional (3D) imaging of weakly scattering samples. Due to the mathematical complexity, most theoretical modeling of quantitative phase image formation under partial coherence has focused on thin, well-focused samples. It is unclear how these abberations are affected by defocusing. Also, as 3D QPI techniques continue to develop, a better model needs to be developed to understand and quantify these aberrations when imaging thicker samples. Here, using the first order Born's approximation, we derived a mathematical framework that provides an intuitive model of image formation under varying degrees of coherence. Our description provides a clear connection between the halo effect and phase underestimation, defocusing and the 3D structure of the sample under investigation. Our results agree very well with the experiments and show that the microscope objective defines the sectioning ability of the imaging system while the condenser lens is responsible for the halo effect.

Application of measurement configuration optimization for accurate metrology of sub-wavelength dimensions in multilayer gratings using optical scatterometry.

Critical dimension measurement accuracy in optical scatterometry relies not only on the systematic noise level of instruments and the reliability of forward modeling algorithms, but also heavily on the measurement configuration. To construct a set of potentially high-accuracy configurations, we apply a general measurement configuration optimization method based on error propagation theory and singular value decomposition, by which the measurement accuracy is approximated as a function of a pseudo Jacobian with respect to the measurement configurations. Simulations and experiments for the optical metrology of a sub-wavelength deep-etched multilayer grating establish the feasibility of the proposed method.

Grating integrated single mode microring laser.

Microring and microdisk lasers are potential candidates for small footprint, low threshold in-plane integrated lasers; however, they exhibit multimode lasing spectra and bistability. Here, we theoretically propose and experimentally demonstrate a novel approach for achieving single mode lasing in microring lasers. Our approach is based on increasing the radiation loss of all but one of the resonant modes of microring resonators by integrating second order gratings on the microrings' waveguide. We present single mode operation of electrically pumped semiconductor microring lasers whose lasing modes are lithographically selected via the second order grating. We also show that adding the grating does not increase the lasing threshold current significantly.

Measuring the Nonuniform Evaporation Dynamics of Sprayed Sessile Microdroplets with Quantitative Phase Imaging.

We demonstrate real-time quantitative phase imaging as a new optical approach for measuring the evaporation dynamics of sessile microdroplets. Quantitative phase images of various droplets were captured during evaporation. The images enabled us to generate time-resolved three-dimensional topographic profiles of droplet shape with nanometer accuracy and, without any assumptions about droplet geometry, to directly measure important physical parameters that characterize surface wetting processes. Specifically, the time-dependent variation of the droplet height, volume, contact radius, contact angle distribution along the droplet's perimeter, and mass flux density for two different surface preparations are reported. The studies clearly demonstrate three phases of evaporation reported previously: pinned, depinned, and drying modes; the studies also reveal instances of partial pinning. Finally, the apparatus is employed to investigate the cooperative evaporation of the sprayed droplets. We observe and explain the neighbor-induced reduction in evaporation rate, that is, as compared to predictions for isolated droplets. In the future, the new experimental methods should stimulate the exploration of colloidal particle dynamics on the gas-liquid-solid interface.

Nanoscale topography and spatial light modulator characterization using wide-field quantitative phase imaging.

We demonstrate an optical technique for large field of view quantitative phase imaging of reflective samples. It relies on a common-path interferometric design, which ensures high stability without the need for active stabilization. The technique provides single-shot, full-field and robust measurement of nanoscale topography of large samples. Further, the inherent stability allows reliable measurement of the temporally varying phase retardation of the liquid crystal cells, and thus enables real-time characterization of spatial light modulators. The technique's application potential is validated through experimental results.

Fast and accurate finite element analysis of large-scale three-dimensional photonic devices with a robust domain decomposition method.

A fast and accurate full-wave technique based on the dual-primal finite element tearing and interconnecting method and the second-order transmission condition is presented for large-scale three-dimensional photonic device simulations. The technique decomposes a general three-dimensional electromagnetic problem into smaller subdomain problems so that parallel computing can be performed on distributed-memory computer clusters to reduce the simulation time significantly. With the electric fields computed everywhere, photonic device parameters such as transmission and reflection coefficients are extracted. Several photonic devices, with simulation volumes up to 1.9×10(4) (λ/n(avg))3 and modeled with over one hundred million unknowns, are simulated to demonstrate the application, efficiency, and capability of this technique. The simulations show good agreement with experimental results and in a special case with a simplified two-dimensional simulation.

Effects of spatial coherence in diffraction phase microscopy.

Quantitative phase imaging systems using white light illumination can exhibit lower noise figures than laser-based systems. However, they can also suffer from object-dependent artifacts, such as halos, which prevent accurate reconstruction of the surface topography. In this work, we show that white light diffraction phase microscopy using a standard halogen lamp can produce accurate height maps of even the most challenging structures provided that there is proper spatial filtering at: 1) the condenser to ensure adequate spatial coherence and 2) the output Fourier plane to produce a uniform reference beam. We explain that these object-dependent artifacts are a high-pass filtering phenomenon, establish design guidelines to reduce the artifacts, and then apply these guidelines to eliminate the halo effect. Since a spatially incoherent source requires significant spatial filtering, the irradiance is lower and proportionally longer exposure times are needed. To circumvent this tradeoff, we demonstrate that a supercontinuum laser, due to its high radiance, can provide accurate measurements with reduced exposure times, allowing for fast dynamic measurements.

Inverse scattering solutions using low-coherence light.

We present a new wave-vector-space approach for solving inverse scattering problems. In our formulation, the theories for diffraction tomography and coherence gating are combined to explain 3D reconstruction with low-coherence light. Specifically, we apply this method to solve the scattering problem with broadband fields for transmission and reflection measurements. Our results can be applied to any interferometric measurements with low-coherence light, including optical coherence tomography, angle-resolved low-coherence interferometry, and white-light diffraction tomography.

Diffraction phase microscopy: monitoring nanoscale dynamics in materials science [invited].

Quantitative phase imaging (QPI) utilizes the fact that the phase of an imaging field is much more sensitive than its amplitude. As fields from the source interact with the specimen, local variations in the phase front are produced, which provide structural information about the sample and can be used to reconstruct its topography with nanometer accuracy. QPI techniques do not require staining or coating of the specimen and are therefore nondestructive. Diffraction phase microscopy (DPM) combines many of the best attributes of current QPI methods; its compact configuration uses a common-path off-axis geometry which realizes the benefits of both low noise and single-shot imaging. This unique collection of features enables the DPM system to monitor, at the nanoscale, a wide variety of phenomena in their natural environments. Over the past decade, QPI techniques have become ubiquitous in biological studies and a recent effort has been made to extend QPI to materials science applications. We briefly review several recent studies which include real-time monitoring of wet etching, photochemical etching, surface wetting and evaporation, dissolution of biodegradable electronic materials, and the expansion and deformation of thin-films. We also discuss recent advances in semiconductor wafer defect detection using QPI.