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Convolution Neural Network Based Degenerated Mode Decomposition Via Near-Field Images from Linear and Circular Polarizers
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Radially polarized light has various advantages on sensing, thanks for its symmetric field distribution. To select radial component, metallic sub-wavelength concentric arrays are widely used. To increase the stability of the metallic nanostructure from mechanical or chemical hazards, a method to apply an additional protective layer has been proposed. The structure was numerically calculated, and optimized structure showed ~97.4% of transmittance for radially polarized component with ~20 dB of polarization extinction ratio compared to the azimuthally polarized component. This result is a 22% increase compared to the case without the protective layer. In addition, the utility the protective layer applied to metallic sub-wavelength concentric arrays is also discussed. The structure has been applied to a binary, concentric optical plate, and showed the same function with radially polarized input, but prohibited azimuthally polarized input. The proposed structure is expected to be applied on numerous centrosymmetric flat optical components.
We present a novel method for modal decomposition of a composite beam guided by a large-mode-area fiber by means of direct far-field pattern measurements with a multi-variable optimization algorithm. For reconstructing far-field patterns, we use finite-number bases of Hermite Gaussian modes that can be converted from all the guided modes in the given fiber and exploit a stochastic parallel gradient descent (SPGD)-based multi-variable optimization algorithm equipped with the D4σ technique in order for completing the modal decomposition with compensating the centroid mismatch between the measured and reconstructed beams. We measure the beam intensity profiles at two different distances, which justifies the uniqueness of the solution obtained by the SPGD algorithm. We verify the feasibility and effectiveness of the proposed method both numerically and experimentally. We have found that the fractional error tolerance in terms of the beam intensity overlap could be maintained below 1 × 10⁻⁷ and 3.5 × 10⁻³ in the numerical and experimental demonstrations, respectively. As the modal decomposition is made uniquely and reliably, such a level of the error tolerance could be maintained even for a beam intensity profile measured at a farther distance.
A binary metallic superoscillatory lens assisted with annular subwavelength slits is proposed, which generates a longitudinally-polarized super-resolution focal point. The annular slits are designed to selectively transmit radially-polarized light. Simulations using the finite element method show a 0.24 λ focal spot with 21.8 dB of polarization purity and only 0.342 dB reduction in efficiency compared to a standard superoscillatory lens.
Nanophotonics has been an active research field over the past two decades, triggered by the rising interests in exploring new physics and technologies with light at the nanoscale. As the demands of performance and integration level keep increasing, the design and optimization of nanophotonic devices become computationally expensive and time-inefficient. Advanced computational methods and artificial intelligence, especially its subfield of machine learning, have led to revolutionary development in many applications, such as web searches, computer vision, and speech/image recognition. The complex models and algorithms help to exploit the enormous parameter space in a highly efficient way. In this review, we summarize the recent advances on the emerging field where nanophotonics and machine learning blend. We provide an overview of different computational methods, with the focus on deep learning, for the nanophotonic inverse design. The implementation of deep neural networks with photonic platforms is also discussed. This review aims at sketching an illustration of the nanophotonic design with machine learning and giving a perspective on the future tasks.
We propose and investigate a metallic Fresnel zone plate (FZP/MFZP) implemented on a silver-coated optical fiber facet for super-variable focusing of light, the focal point of which can be drastically relocated by varying the wavelength of the incident light. We numerically show that when its nominal focal length is set to 20 μm at 550 nm, its effective focal length can be tuned by ~13.7 μm for 300-nm change in the visible wavelength range. This tuning sensitivity is over 20 times higher than that of a conventional silica-based spherical lens. Even with such high tuning sensitivity with respect to the incident wavelength change, the effective beam radius at the focal point is preserved nearly unchanged, irrespective of the incident wavelength. Then, we fabricate the proposed device, exploiting electron- and focused-ion-beam processes, and experimentally verify its super-variable focusing functionality at typical red, green, and blue wavelengths in the visible wavelength range, which is in good agreement with the numerical prediction. Moreover, we propose a novel MFZP structure that primarily exploits the surface-plasmon-polariton-mediated, extra-ordinary transmission effect. For this we make all the openings of an MFZP, which are determined by the fundamental FZP design formula, be partitioned by multi-rings of all-sub-wavelength annular slits, so that the transmission of azimuthally polarized light is inherently prohibited, thereby leading to super-variable and selective focusing of radially polarized light. We design and fabricate a proof-of-principle structure implemented on a gold-coated fused-silica substrate, and verify its novel characteristics both numerically and experimentally, which are mutually in good agreement. We stress that both the MFZP structures proposed here will be very useful for micro-machining, optical trapping, and biomedical sensing, in particular, which invariably seek compact, high-precision, and flexible focusing schemes.
We show that germanium-doped graded-index multimode silica fibers can exhibit relatively high conversion efficiencies ( ∼ 6.5 % ) for second-harmonic generation when excited at 1064 nm. This frequency-doubling behavior is also found to be accompanied by an effective downconversion. As opposed to previous experiments carried out in single- and few-mode fibers where hours of preparation were required, in our system, these χ ( 2 ) related processes occur almost instantaneously. The efficiencies observed in our experiments are, to the best of our knowledge, among the highest ever reported in unprepared fibers.
We use high-resolution imaging of Rayleigh scattered light through the side of few-mode optical fibers to measure the local spatial structure of propagating vector fields. We demonstrate the technique by imaging both pure modes and superpositions of modes in the LP01 and LP11 families. Direct imaging not only gives high-resolution beat length measurements, but also records the local propagation dynamics including those due to perturbations. The imaging setup uses polarization discrimination to monitor both the transverse and the longitudinal polarization components simultaneously.
Radially polarized beams can be focused to a tighter spot in the focal plane with a high numerical-aperture objective when combined with an optimally designed pupil filter. Based on the unique characters, a novel super-resolution radially polarized-light pupil-filtering confocal sensing technology (SRPCST) is proposed, and a sensor based on SRPCST is developed. By using a radially polarized beam and pupil-filtering technology, SRPCST can effectively improve its lateral resolution. In SRPCST a strong longitudinal field component can be generated in the focal plane by focusing a radially polarized light with a high numerical-aperture objective. Pupil-filtering technology will modify the pupil function of the optical system by optimally designing the parameters of pupil filter to higher resolution. Theoretical analyses and packaged SRPCST sensor experiments indicate that the lateral resolution of SRPCST can be improved by 15.23% and 32.12% through super-resolution image restoration compared with confocal microscopy under the same conditions.
We implement cross-correlated imaging in the frequency domain (fC²) in order to reconstruct different modes propagating in a multi-mode optical fiber, and measure their relative powers. Our system can complete measurements in under a second (950 ms), with a maximum signal to noise ratio of 25 dB. The system is capable of group-delay temporal resolution as high as 720 fs, and this number can be tailored for a variety of modal discrimination levels by choice of apodization functions and effective bandwidths of the tunable source we use. Measurements are made on a double-clad test fiber to demonstrate simultaneous reconstruction of six guided modes. Finally, the system is used to optimize alignment into the fiber under test and achieve mono-mode purity > 95%, underscoring the utility of fC² imaging for near-real-time modal content analysis.
We report the generation of cylindrical vector beams using a concentric metallic grating fabricated on optical fibers with a period smaller than the wavelength of the incident light. Similar to the wiregrid linear polarizer, such a subwavelength metallic annular structure strongly reflects azimuthal polarization and allows radial polarization to transmit through. Due to the polarization selectivity of the concentric metallic grating, a cylindrical vector beam is obtained when a circularly polarized light is launched into the fiber. Such a device is suitable for the end mirror coupler in an all-fiber laser design to produce radially polarized modes.
An optical low-coherence interferometry technique has been used to simultaneously resolve the mode profile and to measure
the intermodal dispersion of guided modes of a few-mode fiber. Measurements are performed using short samples of fiber (about
50 cm). There is no need for a complex mode-conversion technique to reach a high interference visibility. Four LP mode groups
of the few-mode fiber are resolved. Experimental results and numerical simulations show that the ellipticity of the fiber
core leads to a distinct splitting of the degenerate high-order modes in group index. For the first time, to the best of our
knowledge, it has been demonstrated that degenerate LP11 modes are much more sensitive to core shape variations than the fundamental
modes and that intermodal dispersion of high-order degenerate modes can be used for characterizing the anisotropy of an optical
waveguide.
The description of optical fields in terms of their eigenmodes is an intuitive approach for beam characterization. However, there is a lack of unambiguous, pure experimental methods in contrast to numerical phase-retrieval routines, mainly because of the difficulty to characterize the phase structure properly, e.g. if it contains singularities. This paper presents novel results for the complete modal decomposition of optical fields by using computer-generated holographic filters. The suitability of this method is proven by reconstructing various fields emerging from a weakly multi-mode fiber (V approximately 5) with arbitrary mode contents. Advantages of this approach are its mathematical uniqueness and its experimental simplicity. The method constitutes a promising technique for real-time beam characterization, even for singular beam profiles.
A new measurement technique, capable of quantifying the number and type of modes propagating in large-mode-area fibers is both proposed and demonstrated. The measurement is based on both spatially and spectrally resolving the image of the output of the fiber under test. The measurement provides high quality images of the modes that can be used to identify the mode order, while at the same time returning the power levels of the higher-order modes relative to the fundamental mode. Alternatively the data can be used to provide statistics on the level of beam pointing instability and mode shape changes due to random uncontrolled fluctuations of the phases between the coherent modes propagating in the fiber. An added advantage of the measurement is that is requires no prior detailed knowledge of the fiber properties in order to identify the modes and quantify their relative power levels. Because of the coherent nature of the measurement, it is far more sensitive to changes in beam properties due to the mode content in the beam than is the more traditional M(2) measurement for characterizing beam quality. We refer to the measurement as Spatially and Spectrally resolved imaging of mode content in fibers, or more simply as S(2) imaging.
In this paper, a deep learning method is proposed to fully characterize the degenerated mode of high-order mode (HOM) group in few-mode fibers (FMFs). The HOM consists of four-fold degenerated spatial modes composed of mode degeneracy and polarization degeneracy. Three polarization projection images are used to recover the modal coefficients. Using the well-trained deep convolutional neural network (CNN) models on randomly generated simulation datasets, a mapping relationship of the two-dimensional intensity distribution to the one-dimensional coefficients space of eigenmodes has been efficiently learned. Two metrics are then used for evaluation on the test samples: (1) the error of the modal coefficients between the original and predicted values; (2) the average image correlation of the original and reconstructed intensity image. The results show that the coefficient errors are only almost one percent while the correlation is up to 99%, which demonstrates the feasibility of the proposed method. In addition, the prediction performance and robustness of the CNN are also assessed based on different image resolutions and different percentages of the neighboring mode group power. The quantitative evaluations demonstrate the stability of the well-trained CNN.
Research in photonic computing has flourished due to the proliferation of optoelectronic components on photonic integration platforms. Photonic integrated circuits have enabled ultrafast artificial neural networks, providing a framework for a new class of information processing machines. Algorithms running on such hardware have the potential to address the growing demand for machine learning and artificial intelligence in areas such as medical diagnosis, telecommunications, and high-performance and scientific computing. In parallel, the development of neuromorphic electronics has highlighted challenges in that domain, particularly related to processor latency. Neuromorphic photonics offers sub-nanosecond latencies, providing a complementary opportunity to extend the domain of artificial intelligence. Here, we review recent advances in integrated photonic neuromorphic systems, discuss current and future challenges, and outline the advances in science and technology needed to meet those challenges.
We propose an effective numerical modal decomposition (MD) algorithm for few/multi-mode fibers using a deep convolution neural network (CNN) model in this paper. MD is an available method to reveal modal coefficients. However, with the increase of the superimposed eigenmodes number, the performance of MD will deteriorate due to the modal ambiguity. Our aim is to attain both modal amplitudes and phases from the near-field intensity profile, while minimizing the effect of modal ambiguity as much as possible. Specifically, we train the model with the combination of a modal coefficients loss and two reconstruction losses (near-field and far-field intensity reconstruction losses), which ensures the uniqueness of the solution. With extensive simulational results, we demonstrate that our model is able to mitigate the problem of modal ambiguity and attain accurate modal coefficients (The correlation is above 1.9937 for all modal cases) in a high-speed way. Additionally, the influence of noise and task weights are comprehensively studied. Our proposed technique is useful to mitigate the modal ambiguity.
Mode decomposition (MD) is essential to reveal the intrinsic mode properties of multimode fibers (MMFs). Real-time MD provides a powerful tool to analyze the dynamics in MMFs. In this paper, we demonstrated that real-time MD can be achieved with the help of deep learning technique. We use large amounts of simulated beam intensity profiles of MMFs to train a convolutional neural network (CNN) and then evaluated this trained CNN on both simulation and experimental data. When testing on the simulated beam profiles, the averaged correlation between the reconstructed patterns and measured patterns is above 0.9842 and the decomposing rate can reach about 200 Hz. While for the experimental case, the averaged correlation is above 0.8896 and the decomposing rate for modal weights is 29.9 Hz, which is restricted by the maximum frame rate of the CCD camera. The results of both simulation and experiment show the superb real-time ability of the deep learning-based MD methods.
Based on the symmetry reduction procedures, we introduce nonlinear solitonic analogues of coherent and squeezed states both for self-focusing and self-defocusing nonautonomous NLSE models with harmonic oscillator confining potentials. We demonstrate that chirping of the de Broglie wave is a key physical condition for the existence of squeezed states, and it is precisely this wave effect that opens the way to the fundamental extension of the squeezed state concept to different nonlinear physical systems. We show that a subtle interplay between nonlinearity and space dimensionality can result in a rich variety of nonlinear squeezed states. In one dimensional symmetry, nonlinear squeezed states are formed if and only if the nonlinear response of one-dimensional graded-index external potential (waveguide) is inversely proportional to the “hidden” squeezing parameter. And vice versa, in the case of three-dimensional symmetry, the nonlinearity is required to be proportional to the “hidden” squeezing parameter. This remarkable finding carries the germ of the idea of the 3-D soliton bullet formation and the self-focusing collapse suppression in the experimental setup arranged so that periodic variations of the nonlinearity and the maximum peaks of nonlinear squeezed states are being opposite in phases, and as the result, these two processes are alternating to each other. By means of direct computer experiments, we demonstrate the stability of soliton-like coherent and squeezed states, and reveal remarkable and complete analogies with their canonical linear progenitors.
We present a fast implementation of the spatial and spectral imaging (S2) technique for modal analysis of multimode optical fibers. It utilizes a continuously scanning tunable laser source with an InGaAs camera operating at 500Hz along with inline data processing to increase the measurement repetition rate, by reducing the run up/run down time between two successive scans (about 27 times faster as compared to the previous state of the art). This allows real-time mode content monitoring of a multimode fiber. We illustrate the potential of this tool by collecting an 110,000 wavelength S2 spectrogram of a 5 mode-group fiber in minutes, and tracking, in real-time, the four LP11 modes of the same fiber as the launch polarization is rotated.
We have demonstrated a highly efficient cladding-pumped ytterbium-doped fiber laser, generating >2.1 kW of continuous-wave output power at 1.1 μm with 74% slope efficiency with respect to launched pump power. The beam quality factor (M2) was better than 1.2. The maximum output power was only limited by available pump power, showing no evidence of roll-over even at the highest output power. We present data on how the beam quality depends on the fiber parameter, based on our current and past fiber laser developments. We also discuss the ultimate power-capability of our fiber in terms of thermal management, Raman nonlinear scattering, and material damage, and estimate it to 10 kW.
We demonstrate the formation of a sub-wavelength focal spot with a long depth of focus using a radially polarized, narrow-width annular beam. Theoretical analysis predicts that a tighter focal spot (approximately 0.4 lambda) and longer depth of focus (more than 4 lambda) can be formed by a longitudinal electric field when the width of the annular part of the beam is decreased. Experimental measurements using a radially polarized beam from a photonic crystal laser agree well with these predictions. Tight focal spots with long depths of focus have great potential for use in high-tolerance, high-resolution applications in optical systems.
Optical transmission through concentric circular nanoslits is studied in experiments and numerical simulations. Polarized optical microscopic imaging shows that the optical transmission through these apertures is spatially inhomogeneous, exhibiting colored fan texture patterns. Numerical simulations show that these colored fan texture patterns originate from the cylindrical vector polarization of the transmitted beam. Specifically, the transmitted light is in-phase radially polarized at long wavelengths due to the predominant transmission of the transverse magnetic (TM) waveguide modes; and in-phase azimuthally polarized at short wavelengths due to the increased optical transmission of the transverse electric (TE) waveguide modes. Additionally, the transmission shows a peak at the wavelength of Wood anomaly and a dip at the resonant wavelength of surface plasmon excitation; and the transmitted light at these wavelengths is a mixture of azimuthally and radially polarized fields. These interesting optical transmission behaviors of circular nanoslits provide a miniaturized way to generating radially and azimuthally polarized light.
We review our recent work toward designing large mode area fibers for high power applications. We show that appropriately designed doped multi-mode fibers can be used to provide robust single-mode output when used in fiber laser cavities. Single-mode (SM) fiber mode field diameters of ~35μm are demonstrated with record SM pulse energies of 0.5mJ at 1550nm with a repetition rate of 200 Hz. Energies approaching 1mJ are obtained with a slight compromise in mode quality. A modification in the laser cavity results in a passively modelocked laser giving femtosecond pulses with nanojoule energies.
