Transcending shift-invariance in the paraxial regime via end-to-end inverse design of freeform nanophotonics.

Traditional optical elements and conventional metasurfaces obey shift-invariance in the paraxial regime. For imaging systems obeying paraxial shift-invariance, a small shift in input angle causes a corresponding shift in the sensor image. Shift-invariance has deep implications for the design and functionality of optical devices, such as the necessity of free space between components (as in compound objectives made of several curved surfaces). We present a method for nanophotonic inverse design of compact imaging systems whose resolution is not constrained by paraxial shift-invariance. Our method is end-to-end, in that it integrates density-based full-Maxwell topology optimization with a fully iterative elastic-net reconstruction algorithm. By the design of nanophotonic structures that scatter light in a non-shift-invariant manner, our optimized nanophotonic imaging system overcomes the limitations of paraxial shift-invariance, achieving accurate, noise-robust image reconstruction beyond shift-invariant resolution.

High-performance hybrid time/frequency-domain topology optimization for large-scale photonics inverse design.

We present a photonics topology optimization (TO) package capable of addressing a wide range of practical photonics design problems, incorporating robustness and manufacturing constraints, which can scale to large devices and massive parallelism. We employ a hybrid algorithm that builds on a mature time-domain (FDTD) package Meep to simultaneously solve multiple frequency-domain TO problems over a broad bandwidth. This time/frequency-domain approach is enhanced by new filter-design sources for the gradient calculation and new material-interpolation methods for optimizing dispersive media, as well as by multiple forms of computational parallelism. The package is available as free/open-source software with extensive tutorials and multi-platform support.

End-to-end metasurface inverse design for single-shot multi-channel imaging.

We introduce end-to-end inverse design for multi-channel imaging, in which a nanophotonic frontend is optimized in conjunction with an image-processing backend to extract depth, spectral and polarization channels from a single monochrome image. Unlike diffractive optics, we show that subwavelength-scale "metasurface" designs can easily distinguish similar wavelength and polarization inputs. The proposed technique integrates a single-layer metasurface frontend with an efficient Tikhonov reconstruction backend, without any additional optics except a grayscale sensor. Our method yields multi-channel imaging by spontaneous demultiplexing: the metaoptics front-end separates different channels into distinct spatial domains whose locations on the sensor are optimally discovered by the inverse-design algorithm. We present large-area metasurface designs, compatible with standard lithography, for multi-spectral imaging, depth-spectral imaging, and "all-in-one" spectro-polarimetric-depth imaging with robust reconstruction performance (≲ 10% error with 1% detector noise). In contrast to neural networks, our framework is physically interpretable and does not require large training sets. It can be used to reconstruct arbitrary three-dimensional scenes with full multi-wavelength spectra and polarization textures.

Fullwave Maxwell inverse design of axisymmetric, tunable, and multi-scale multi-wavelength metalenses.

We demonstrate new axisymmetric inverse-design techniques that can solve problems radically different from traditional lenses, including reconfigurable lenses (that shift a multi-frequency focal spot in response to refractive-index changes) and widely separated multi-wavelength lenses (λ = 1 µm and 10 µm). We also present experimental validation for an axisymmetric inverse-designed monochrome lens in the near-infrared fabricated via two-photon polymerization. Axisymmetry allows fullwave Maxwell solvers to be scaled up to structures hundreds or even thousands of wavelengths in diameter before requiring domain-decomposition approximations, while multilayer topology optimization with ∼105 degrees of freedom can tackle challenging design problems even when restricted to axisymmetric structures.

Overlapping domains for topology optimization of large-area metasurfaces.

We introduce an overlapping-domain approach to large-area metasurface design, in which each simulated domain consists of a unit cell and overlapping regions from the neighboring cells plus PML absorbers. We show that our approach generates greatly improved metalens quality compared to designs produced using a locally periodic approximation, thanks to ∼10× better accuracy with similar computational cost. We use the new approach with topology optimization to design large-area (200λ) high-NA (0.71) multichrome and broadband achromatic lenses with high focusing efficiency (∼50%), greatly improving upon previously reported works.

Topology optimization of freeform large-area metasurfaces.

We demonstrate optimization of optical metasurfaces over 105-106 degrees of freedom in two and three dimensions, 100-1000+ wavelengths (λ) in diameter, with 100+ parameters per λ2. In particular, we show how topology optimization, with one degree of freedom per high-resolution "pixel," can be extended to large areas with the help of a locally periodic approximation that was previously only used for a few parameters per λ2. In this way, we can computationally discover completely unexpected metasurface designs for challenging multi-frequency, multi-angle problems, including designs for fully coupled multi-layer structures with arbitrary per-layer patterns. Unlike typical metasurface designs based on subwavelength unit cells, our approach can discover both sub- and supra-wavelength patterns and can obtain both the near and far fields.

Inverse design of compact multimode cavity couplers.

Efficient coupling between on-chip sources and cavities plays a key role in silicon photonics. However, despite the importance of this basic functionality, there are few systematic design tools to simultaneously control coupling between multiple modes in a compact resonator and a single waveguide. Here, we propose a large-scale adjoint optimization approach to produce wavelength-scale waveguide-cavity couplers operating over tunable and broad frequency bands. We numerically demonstrate couplers discovered by this method that can achieve critical, or nearly critical, coupling between multi-ring cavities and a single waveguide at up to six widely separated wavelengths spanning the 560-1500 nm range of interest for on-chip nonlinear optical devices.

Inverse design of large-area metasurfaces.

We present a computational framework for efficient optimization-based "inverse design" of large-area "metasurfaces" (subwavelength-patterned surfaces) for applications such as multi-wavelength/multi-angle optimizations, and demultiplexers. To optimize surfaces that can be thousands of wavelengths in diameter, with thousands (or millions) of parameters, the key is a fast approximate solver for the scattered field. We employ a "locally periodic" approximation in which the scattering problem is approximated by a composition of periodic scattering problems from each unit cell of the surface, and validate it against brute-force Maxwell solutions. This is an extension of ideas in previous metasurface designs, but with greatly increased flexibility, e.g. to automatically balance tradeoffs between multiple frequencies or to optimize a photonic device given only partial information about the desired field. Our approach even extends beyond the metasurface regime to non-subwavelength structures where additional diffracted orders must be included (but the period is not large enough to apply scalar diffraction theory).

400%/W second harmonic conversion efficiency in 14 µm-diameter gallium phosphide-on-oxide resonators.

Second harmonic conversion from 1550 nm to 775 nm with an efficiency of 400% W-1 is demonstrated in a gallium phosphide (GaP) on oxide integrated photonic platform. The platform consists of doubly-resonant, phase-matched ring resonators with quality factors Q ∼ 104, low mode volumes V ∼ 30(λ/n)3, and high nonlinear mode overlaps. Measurements and simulations indicate that conversion efficiencies can be increased by a factor of 20 by improving the waveguide-cavity coupling to achieve critical coupling in current devices.

Topology optimization of multi-track ring resonators and 2D microcavities for nonlinear frequency conversion.

We exploit recently developed topology-optimization techniques to design complex, wavelength-scale resonators for enhancing various nonlinear χ(2) and χ(3) frequency conversion processes. In particular, we demonstrate aperiodic, multi-track ring resonators and two-dimensional slab microcavities exhibiting long lifetimes Q≳104, small modal volumes V≳(λ/2n)3, and among the largest nonlinear overlaps (a generalization of phase matching in large-etalon waveguides) possible, paving the way for efficient, compact, and wide-bandwdith integrated nonlinear devices.

Enhanced Spontaneous Emission at Third-Order Dirac Exceptional Points in Inverse-Designed Photonic Crystals.

We formulate and exploit a computational inverse-design method based on topology optimization to demonstrate photonic crystal structures supporting complex spectral degeneracies. In particular, we discover photonic crystals exhibiting third-order Dirac points formed by the accidental degeneracy of monopolar, dipolar, and quadrupolar modes. We show that, under suitable conditions, these modes can coalesce and form a third-order exceptional point, leading to strong modifications in the spontaneous emission (SE) of emitters, related to the local density of states. We find that SE can be enhanced by a factor of 8 in passive structures, with larger enhancements ∼sqrt[n^{3}] possible at exceptional points of higher order n.

Integrated high quality factor lithium niobate microdisk resonators.

Lithium Niobate (LN) is an important nonlinear optical material. Here we demonstrate LN microdisk resonators that feature optical quality factor ~10(5), realized using robust and scalable fabrication techniques, that operate over a wide wavelength range spanning visible and near infrared. Using our resonators, and leveraging LN's large second order optical nonlinearity, we demonstrate on-chip second harmonic generation with a conversion efficiency of 0.109 W(-1).

Effects of 24 Weeks of a Supervised Walk Training on Knee Muscle Strength and Quality of Life in Older Female Total Knee Arthroplasty: A Retrospective Cohort Study.

Poor supervision, impaired exercise adherence, and low compliance with exercise regimens result in inconsistent effects regarding exercise interventions. A supervised-walk training regimen (9 km/week) may have a positive effect on functional recovery in female total knee arthroplasty (TKA). This study aimed to evaluate the effect of a supervised walking regimen on lower limb muscle strength, functional fitness, and patient-reported outcomes in female TKA. Twenty-eight female TKA were allocated into a control (CON) (n = 14) or walk training (WT) (n = 14) group. WT on treadmills was initiated 12 weeks after TKA. All patients were examined for lower muscle strength (including extension and flexion of hip and knee), physical function (including a 6-min walk test, 8-foot up-and-go test, and 30-s chair stand test), and Knee Injury and Osteoarthritis Outcome Score (KOOS) questionnaire. Knee flexor (WT: CON; 64.4 ± 4.1 nm/kg: 43.7±3.3 nm/kg; p = 0.001; effect size: 5.62) and extensor strengths (WT: CON; 73.1 ± 7.5 nm/kg: 48.2 ± 2.4 nm/kg; p = 0.001; effect size: 4.47) statistically increased in the WT group compared to the CON group. The 6-min walk test (from 341.3 ± 20.5 m to 405.5 ± 30.7 m; p = 0.001; effect size: 2.46) and 8-foot up-and-go test (from 9.5 ± 0.7 s to 8.3 ± 0.7 s; p = 0.002; effect size: 1.71) tests also showed significant improvements in the WT group in the follow-up compared to the baseline. An increase in quality of life score according to the KOOS questionnaire (WT: CON; 91.0 ± 2.8: 68.1 ± 5.8; p = 0.001; effect size: 5.02) was noted in the WT group compared to the CON group in the follow-up. WT facilitated improvements in knee muscle strength and functional outcomes in TKA patients.

Taming the flow of light via active magneto-optical impurities.

We demonstrate that the interplay of a magneto-optical layer sandwiched between two judiciously balanced gain and loss layers which are both birefringent with misaligned in-plane anisotropy, induces unidirectional electromagnetic modes. Embedding one such optically active non-reciprocal unit between a pair of birefringent Bragg reflectors, results in an exceptionally strong asymmetry in light transmission. Remarkably, such asymmetry persists regardless of the incident light polarization. This photonic architecture may be used as the building block for chip-scale non-reciprocal devices such as optical isolators and circulators.

A framework for scintillation in nanophotonics.

Bombardment of materials by high-energy particles often leads to light emission in a process known as scintillation. Scintillation has widespread applications in medical imaging, x-ray nondestructive inspection, electron microscopy, and high-energy particle detectors. Most research focuses on finding materials with brighter, faster, and more controlled scintillation. We developed a unified theory of nanophotonic scintillators that accounts for the key aspects of scintillation: energy loss by high-energy particles, and light emission by non-equilibrium electrons in nanostructured optical systems. We then devised an approach based on integrating nanophotonic structures into scintillators to enhance their emission, obtaining nearly an order-of-magnitude enhancement in both electron-induced and x-ray-induced scintillation. Our framework should enable the development of a new class of brighter, faster, and higher-resolution scintillators with tailored and optimized performance.

Unidirectional invisibility induced by PT-symmetric periodic structures.

Parity-time (PT) symmetric periodic structures, near the spontaneous PT-symmetry breaking point, can act as unidirectional invisible media. In this regime, the reflection from one end is diminished while it is enhanced from the other. Furthermore, the transmission coefficient and phase are indistinguishable from those expected in the absence of a grating. The phenomenon is robust even in the presence of Kerr nonlinearities, and it can also effectively suppress optical bistabilities.

Twenty-four-week hospital-based progressive resistance training on functional recovery in female patients post total knee arthroplasty.

BACKGROUND: After total knee arthroplasty (TKA) surgery, a decline in muscle strength is associated with a decrease in function. The aim of this study was to demonstrate the effect of a further 24 weeks of hospital-based resistance training under supervision, and precise dose on knee functional recovery and daily activities for female TKA patients. METHODS: Twenty-nine patients who underwent unilateral primary TKA were allocated into either resistance training (RT) (n = 14) or control (CON) (n = 15) groups. All patients were assessed, with an isokinetic dynamometer, for hip and knee flexor and extensor muscle strength, physical function test, and Knee Injury and Osteoarthritis Outcome Score (KOOS). Resistance training was initiated three months after index surgery. The assessments were performed before exercise (Baseline), in the middle of the resistance training at 12 weeks (Mid-exercise), completion of the resistance training (Post-exercise), and 12 weeks after resistance training completion (Follow-up). A statistical test was performed by using generalized estimating equations. RESULTS: Patients in RT had more of an increase in both knee extensor and flexor muscle strength than those in CON at the Post-exercise assessment. The six-minute walk test distance was more in RT compared with CON at the same Post-exercise assessment. Furthermore, the RT group had increases in Activities of daily living and Sports subscales compared to the CON group. CONCLUSIONS: A further 24 weeks of hospital-based progressive resistance training facilitated improvement in knee muscle strength and functional outcome in TKA patients. Active hospital-based progressive resistance training is recommended for rehabilitation following TKA surgery.

The effects of high impact exercise intervention on bone mineral density, physical fitness, and quality of life in postmenopausal women with osteopenia: A retrospective cohort study.

Osteoporosis and osteopenia prevailed in postmenopausal women and predisposed to osteoporotic fractures that increase mortality, morbidity, and the cost of social care. Here, we investigated the effect of 24 weeks of aerobic dancing on the bone miner density, physical fitness and health-related quality of life (HRQoL) in postmenopausal women with osteopenia. Total 80 participants (control [CON]: 40; exercise [EX]: 40) were included in the final analysis. The EX group underwent a 24-week aerobic dance intervention. Bone mineral density (BMD), physical fitness, and SF-36 questionnaire were assessed at baseline and 24-weeks. The BMD change in the femoral neck at the 24-weeks were significantly different between the 2 groups (CON: -1.3 ±â€Š2.7%, EX: 3.1 ±â€Š4.6%, P = .001). Grip strength, sidestep and physical functional domain of HRQoL in the EX group were significantly improved compared to the CON. The results were suggested 24-week aerobic dance intervention could result in the lower the incidence of bone fracture through increasing BMD and decreasing fall risk for postmenopausal women.

Circuit training enhances function in patients undergoing total knee arthroplasty: a retrospective cohort study.

BACKGROUND: The number of patients receiving total knee arthroplasty (TKA) has been rising every year due to the aging population and the obesity epidemic. Post-operative rehabilitation is important for the outcome of TKA. METHODS: A series of 34 patients who underwent primary unilateral TKA was retrospectively collected and divided into either exercise group (n = 16) and control group (n = 18). The exercise group underwent a 24-week course of circuit training beginning 3 months after total knee arthroplasty (TKA). The effect of circuit training on TKA patients in terms of motion analysis, muscle strength testing, Knee injury and Osteoarthritis Outcomes Score (KOOS) questionnaire and patient-reported outcome measurement Short-Form Health Survey (SF-36) at the pre-operation, pre-exercise, mid-exercise, and post-exercise. RESULTS: Motion analysis revealed the stride length, step velocity, and excursion of active knee range of motion significantly improved in the exercise group when compared to those in the control group. KOOS questionnaire showed a greater improvement in pain, ADL, and total scores in the exercise group. The SF-36 questionnaire revealed a significant improvement in general health, bodily pain, social function, and physical components score in the exercise group. CONCLUSIONS: The post-operative circuit training intervention can facilitate recovery of knee function and decrease the degree of pain in the TKA and might be considered a useful adjunct rehabilitative modality. The ultimate influence of circuit training on TKA needs further a prospective randomized clinical trial study and long-term investigation. TRIAL REGISTRATION: NCT02928562.

Effects of circuit exercise and Tai Chi on body composition in middle-aged and older women.

AIM: To investigate the impact of circuit exercise and Tai Chi exercise on body composition in middle-aged and older women. METHODS: The present cohort study included 180 women (aged 45-75 years) who were divided into a circuit exercise group, Tai Chi group and control group. The exercise program consisted of 60 min of exercise three times per week for 12 weeks. The circuit exercises were carried out with intensity controlled by heart rate (60-80% of work). The Tai Chi group practiced Yang style with the same frequency, but with intensity of 50-60% of work. Blood pressure and body composition were assessed. The differences in all variables and the relative changes between baseline and 12 weeks' follow up were evaluated. RESULTS: The circuit exercise group showed a significant decrease in body mass index, systolic blood pressure and body fat mass, and an increase in total body muscle mass, lean body mass, bone mineral content and basal metabolic rate. The Tai Chi group showed a decrease in systolic blood pressure. Increases in the basal metabolic rate (1.3 ± 3.0%), total body muscle mass (1.8 ± 4.3%), lean body mass (1.9 ± 4.3%) and bone mineral content (1.8 ± 4.2%), and decreases in body mass index (-2.2 ± 7.8%), body fat (-6.5 ± 10.7%) and diastolic pressure (-1.2 ± 9.4%) were significantly greater in the circuit exercise group than in Tai Chi or control group. CONCLUSION: Circuit exercise for 12 weeks increases lean body mass and basal metabolic rate more effectively than Tai Chi exercise.