Using a multimode fiber as a high-resolution, low-loss spectrometer

i-PHAOS: An Overview with an Open-Source Collaborative Database on Miniaturized Integrated Spectrometers

On-chip spectrometers are increasingly becoming tools that might help in everyday life needs. The possibility offered by several available integration technologies and materials to be used to miniaturize spectrometers has led to a plethora of very different devices, that in principle can be compared according to their metrics. Having access to a reference database can help in selecting the best-performing on-chip spectrometers and being up to date in terms of standards and developments. In this paper, an overview of the most relevant publications available in the literature on miniaturized spectrometers is reported and a database is provided as an open-source project to which researchers can have access and participate in order to improve the share of knowledge in the interested scientific community.

Speckle wavemeter based on a multi-core fiber and compressive imaging

Random speckle patterns contain valuable information about the incident light. Researchers have successfully constructed spectrometers and wavemeters by utilizing the speckles generated by inter-mode interferences of a multimode fiber (MMF). However, cameras were often employed to record the speckle data in previous reports. The camera's high cost (especially in the near-infrared range), large size, and low response speed limit the applications in optical communications, metrology, and optical sensing. A seven-core fiber (SCF) was fused with an MMF to capture the speckle pattern, where each core coupled part of the speckle field. Furthermore, we take advantage of the space division multiplexing capability of the SCF by incorporating an optical switch. This allows the variety of speckles generated by the incidence of different cores into the MMF. A convolutional neural network (CNN) regression algorithm was designed to analyze the complicated speckle data. The experimental results show that the proposed wavemeter can resolve adjacent wavelengths of 1 pm with an error of about 0.2 pm. We also discussed how different lengths of MMF influence the wavelength resolution. In conclusion, our research presents a robust and cost-effective approach to a wavelength measurement device by use of a seven-core optical fiber.

Lensless single-fiber ghost imaging

We demonstrate lensless single-fiber ghost imaging, which allows illumination and collection using a single optical fiber without a transmission-type system. Speckle patterns with relative coincidence degrees of 0.14 were formed by image reconstruction using improved differential ghost imaging. Employing fiber with a diameter of 105 µm, we achieved a spatial resolution of 0.05 mm in an observing area of 9m m 2, at a working distance of 10 mm. Compared to a conventional neuroendoscope at a power density of 94m W/c m 2, our imaging could be realized by extremely weak illumination at a laser power density of 0.10m W/c m 2. Using our lensless single-fiber ghost imaging, with 30,000 speckle patterns and implementing a diffuser, we attained an average coincidence degree of 0.45.

High-resolution compact spectrometer based on periodic tapered coreless fiber

This Letter proposes a method that balances miniaturization and high performance of fiber optic speckle spectrometers. The periodically tapered coreless fiber is used as the scattering element to excite more higher-order modes in the coreless fiber. As a result, a remarkable spectral resolution of 0.03 nm in the near-infrared spectrum can be achieved with a 5-cm-long fiber. Narrow linewidth and broadband spectra in the wavelength of 1540-1560 nm are reconstructed separately, demonstrating the excellent performance of the designed all-fiber spectrometer. The spectral resolution of our proposed spectrometer is comparable to that of a 2-m multimode fiber spectrometer and has a significant improvement in miniaturization.

Compact wavemeter incorporating femtosecond laser-induced surface nanostructures enabled by deep learning

Miniature spectrometers have the advantage of high portability and integration, making them quick and easy to use in various working environments. The speckle patterns produced by light scattering through a disordered medium are highly sensitive to wavelength changes and can be used to design high-precision wavemeters and spectrometers. In this study, we used a self-organized, femtosecond laser-prepared nanostructure with a characteristic size of approximately 30-50 nm on a sapphire surface as a scattering medium to effectively induce spectral dispersion. By leveraging this random scattering structure, we successfully designed a compact scattering wavelength meter with efficient scattering properties. The collected speckle patterns were identified and classified using a neural network, and the variation of speckle patterns with wavelength was accurately extracted, achieving a measurement accuracy of 10 pm in multiple wavelength ranges. The system can effectively suppress instrument and environmental noise with high robustness. This work paves the way for the development of compact high-precision wavemeters.

High-speed RF spectral analysis using a Rayleigh backscattering speckle spectrometer

Persistent wideband radio frequency (RF) surveillance and spectral analysis is increasingly important, driven by the proliferation of wireless communication and RADAR technology. However, conventional electronic approaches are limited by the ∼1 GHz bandwidth of real-time analog-to-digital converters (ADCs). While faster ADCs exist, high data rates prohibit continuous operation, limiting these approaches to acquiring short snapshots of the RF spectrum. In this work, we introduce an optical RF spectrum analyzer designed for continuous, wideband operation. Our approach encodes the RF spectrum as sidebands on an optical carrier and relies on a speckle spectrometer to measure these sidebands. To achieve the resolution and update rate required for RF analysis, we use Rayleigh backscattering in single-mode fiber to rapidly generate wavelength-dependent speckle patterns with MHz-level spectral correlation. We also introduce a dual-resolution scheme to mitigate the trade-off between resolution, bandwidth, and measurement rate. This optimized spectrometer design enables continuous, wideband (15 GHz) RF spectral analysis with MHz-level resolution and a fast update rate of 385 kHz. The entire system is constructed using fiber-coupled off-the-shelf-components, providing a powerful new approach for wideband RF detection and monitoring.

Reconstructive spectrometers taper down in price

The development of a low-cost compact reconstructive spectrometer paves the way towards portable pm-resolution spectroscopy.

Swept-source multimode fiber imaging

High-resolution compressive imaging via a flexible multimode fiber is demonstrated using a swept-laser source and wavelength dependent speckle illumination. An in-house built swept-source allowing for independent control of bandwidth and scanning range is used to explore and demonstrate a mechanically scan-free approach for high-resolution imaging through an ultrathin and flexible fiber probe. The computational image reconstruction is shown by utilizing a narrow sweeping bandwidth of [Formula: see text] nm while acquisition time is decreased by 95% compared to conventional raster scanning endoscopy. Demonstrated narrow-band illumination in the visible spectrum is vital for the detection of fluorescence biomarkers in neuroimaging applications. The proposed approach yields device simplicity and flexibility for minimally invasive endoscopy.

A Machine Learning Specklegram Wavemeter (MaSWave) Based on a Short Section of Multimode Fiber as the Dispersive Element

Wavemeters are very important for precise and accurate measurements of both pulses and continuous-wave optical sources. Conventional wavemeters employ gratings, prisms, and other wavelength-sensitive devices in their design. Here, we report a simple and low-cost wavemeter based on a section of multimode fiber (MMF). The concept is to correlate the multimodal interference pattern (i.e., speckle patterns or specklegrams) at the end face of an MMF with the wavelength of the input light source. Through a series of experiments, specklegrams from the end face of an MMF as captured by a CCD camera (acting as a low-cost interrogation unit) were analyzed using a convolutional neural network (CNN) model. The developed machine learning specklegram wavemeter (MaSWave) can accurately map specklegrams of wavelengths up to 1 pm resolution when employing a 0.1 m long MMF. Moreover, the CNN was trained with several categories of image datasets (from 10 nm to 1 pm wavelength shifts). In addition, analysis for different step-index and graded-index MMF types was carried out. The work shows how further robustness to the effects of environmental changes (mainly vibrations and temperature changes) can be achieved at the expense of decreased wavelength shift resolution, by employing a shorter length MMF section (e.g., 0.02 m long MMF). In summary, this work demonstrates how a machine learning model can be used for the analysis of specklegrams in the design of a wavemeter.

Efficient dispersion modeling in optical multimode fiber

Dispersion remains an enduring challenge for the characterization of wavelength-dependent transmission through optical multimode fiber (MMF). Beyond a small spectral correlation width, a change in wavelength elicits a seemingly independent distribution of the transmitted field. Here we report on a parametric dispersion model that describes mode mixing in MMF as an exponential map and extends the concept of principal modes to describe the fiber's spectrally resolved transmission matrix (TM). We present computational methods to fit the model to measurements at only a few, judiciously selected, discrete wavelengths. We validate the model in various MMF and demonstrate an accurate estimation of the full TM across a broad spectral bandwidth, approaching the bandwidth of the best-performing principal modes, and exceeding the original spectral correlation width by more than two orders of magnitude. The model allows us to conveniently study the spectral behavior of principal modes, and obviates the need for dense spectral measurements, enabling highly efficient reconstruction of the multispectral TM of MMF.

Wavefront shaping: A versatile tool to conquer multiple scattering in multidisciplinary fields

Optical techniques offer a wide variety of applications as light-matter interactions provide extremely sensitive mechanisms to probe or treat target media. Most of these implementations rely on the usage of ballistic or quasi-ballistic photons to achieve high spatial resolution. However, the inherent scattering nature of light in biological tissues or tissue-like scattering media constitutes a critical obstacle that has restricted the penetration depth of non-scattered photons and hence limited the implementation of most optical techniques for wider applications. In addition, the components of an optical system are usually designed and manufactured for a fixed function or performance. Recent advances in wavefront shaping have demonstrated that scattering- or component-induced phase distortions can be compensated by optimizing the wavefront of the input light pattern through iteration or by conjugating the transmission matrix of the scattering medium. This offers unprecedented opportunities in many applications to achieve controllable optical delivery or detection at depths or dynamically configurable functionalities by using scattering media to substitute conventional optical components. In this article, the recent progress of wavefront shaping in multidisciplinary fields is reviewed, from optical focusing and imaging with scattering media, functionalized devices, modulation of mode coupling, and nonlinearity in multimode fiber to multimode fiber-based applications. Apart from insights into the underlying principles and recent advances in wavefront shaping implementations, practical limitations and roadmap for future development are discussed in depth. Looking back and looking forward, it is believed that wavefront shaping holds a bright future that will open new avenues for noninvasive or minimally invasive optical interactions and arbitrary control inside deep tissues. The high degree of freedom with multiple scattering will also provide unprecedented opportunities to develop novel optical devices based on a single scattering medium (generic or customized) that can outperform traditional optical components.

Learning to sense three-dimensional shape deformation of a single multimode fiber

Optical fiber bending, deformation or shape sensing are important measurement technologies and have been widely deployed in various applications including healthcare, structural monitoring and robotics. However, existing optical fiber bending sensors require complex sensor structures and interrogation systems. Here, inspired by the recent renewed interest in information-rich multimode optical fibers, we show that the multimode fiber (MMF) output speckles contain the three-dimensional (3D) geometric shape information of the MMF itself. We demonstrate proof-of-concept 3D multi-point deformation sensing via a single multimode fiber by using k-nearest neighbor (KNN) machine learning algorithm, and achieve a classification accuracy close to 100%. Our results show that a single MMF based deformation sensor is excellent in terms of system simplicity, resolution and sensitivity, and can be a promising candidate in deformation monitoring or shape-sensing applications.

Design Study of Broadband and Ultrahigh-Resolution Imaging Spectrometer Using Snapshot Multimode Interference in Fiber Bundles

Imaging spectrometry plays a significant role in various scientific realms. Although imaging spectrometers based on different schemes have been proposed, the pursuit of compact and high-performance devices is still ongoing. A compact broadband and ultrahigh-resolution imaging spectrometer (CBURIS) is presented, which comprises a microlens array, multiple fiber bundles, a microscope, and a two-dimensional detector array. The principle of the device is to spatially sample and integrate the field information via the front microlens array and then further process with the fiber bundles and imaging system based on the multimode interference theory. From both the theoretical and numerical analysis, this CBURIS design is a superior concept that not only achieves a 0.17° spatial resolution and ultrahigh spectral resolution (resolving power exceeds 2.58 × 106 at 1.55 µm) from the visible to mid-infrared region but also has the advantages of snapshot measurement, thermal stability, and a compact footprint compared with most existing imaging spectrometers.

Chip-scale atomic wave-meter enabled by machine learning

The quest for miniaturized optical wave-meters and spectrometers has accelerated the design of novel approaches in the field. Particularly, random spectrometers (RS) using the one-to-one correlation between the wavelength and an output random interference pattern emerged as a promising tool combining high spectral resolution and cost-effectiveness. Recently, a chip-scale platform for RS has been demonstrated with a markedly reduced footprint. Yet, despite the evident advantages of such modalities, they are very susceptible to environmental fluctuations and require an external calibration process. To address these challenges, we demonstrate a paradigm shift in the field, enabled by the integration of atomic vapor with a photonic chip and the use of a machine learning classification algorithm. Our approach provides a random wave-meter on chip device with accurate calibration and enhanced robustness against environmental fluctuations. The demonstrated device is expected to pave the way toward fully integrated spectrometers advancing the field of silicon photonics.

Compact fiber-integrated scattering device based on mixed-phase TiO2 for speckle spectrometer

A universal, repeatable, and controllable integration of single-mode optical fiber and mixed-phase TiO₂ is used to manufacture a compact fiber-integrated scattering device. Based on the device, we achieve a high-performance and compact fiber-based speckle spectrometer, which has a resolution of 20 pm over a bandwidth of 15 nm, in the 1550 nm range. We test the capability of our proposed spectrometer to reconstruct narrow linewidth and broadband optical spectrums, and compare the performance with that of a traditional optical spectrum analyzer.

Core-shell NaErF4@NaYF4 upconversion nanoparticles qualify as a NIR speckle wavemeter for a visible CCD

Speckle patterns have been widely employed as a method for precisely determining the wavelength of monochromatic light. In order to achieve higher wavelength precision, a variety of optical diffusing waveguides have been investigated with a focus on their wavelength sensitivity. However, it has been a challenge to find a balance among the cost, compactness, precision, and stability of the waveguide. In this work, we designed a compact cylindrical random scattering waveguide (CRSW) as the light diffuser by mixing TiO₂ particles and ultra-violate adhesive. In the CRSW, speckle patterns are generated by input light scattering off TiO₂ particles multiple times. Additionally, a thin layer of upconversion nanoparticles (UCNPs) was sprayed on the end face of CRSW to allow near-infrared (NIR) light to be converted to visible light, breaking the imaging limitations of visible cameras in the NIR range. We, then, further designed a convolution neural network (CNN) to recognize the wavelength of the speckle patterns with excellent robustness and ability to transfer learning. This resulted in the achievement of a high wavelength precision of 20 kHz (∼0.16 fm) at around 1550 nm with a temperature resistance of ±2 °C. Our results demonstrate a low-cost, compact, and simple NIR wavemeter, which is capable of ultra-high wavelength precision and good temperature stability. It has significant value for applications in high-speed and high-precision laser wavelength measurements.

Enhancing sensitivity in absorption spectroscopy using a scattering cavity

Absorption spectroscopy is widely used to detect samples with spectral specificity. Here, we propose and demonstrate a method for enhancing the sensitivity of absorption spectroscopy. Exploiting multiple light scattering generated by a boron nitride (h-BN) scattering cavity, the optical path lengths of light inside a diffusive reflective cavity are significantly increased, resulting in more than ten times enhancement of sensitivity in absorption spectroscopy. We demonstrate highly sensitive spectral measurements of low concentrations of malachite green and crystal violet aqueous solutions. Because this method only requires the addition of a scattering cavity to existing absorption spectroscopy, it is expected to enable immediate and widespread applications in various fields, from analytical chemistry to environmental sciences.

Spectrally resolved point-spread-function engineering using a complex medium

Propagation of an ultrashort pulse of light through strongly scattering media generates an intricate spatio-spectral speckle that can be described by means of the multi-spectral transmission matrix (MSTM). In conjunction with a spatial light modulator, the MSTM enables the manipulation of the pulse leaving the medium; in particular focusing it at any desired spatial position and/or time. Here, we demonstrate how to engineer the point-spread-function of the focused beam both spatially and spectrally, from the measured MSTM. It consists of numerically filtering the spatial content at each wavelength of the matrix prior to focusing. We experimentally report on the versatility of the technique through several examples, in particular as an alternative to simultaneous spatial and temporal focusing, with potential applications in multiphoton microscopy.

Rayleigh speckle-based wavemeter with high dynamic range and fast reference speckle establishment process assisted by optical frequency combs

Compact speckle-based spectrometers that acquire lightwave wavelength from the speckle generated by turbid media are promising for high-resolution spectral analysis. For these devices, the reference establishment process is time consuming, and it is very difficult to obtain reference speckles covering a wide bandwidth with high resolution, which restricts the dynamic range in frequency (the ratio of bandwidth to resolution). In this Letter, we introduce optical frequency combs (OFCs) to the system to overcome these problems, which exist in the wavemeter based on Rayleigh speckle obtained from a single-mode fiber. In the experiment, the proposed wavemeter has a 1.5 nm bandwidth with 60 am resolution, covering a dynamic range in the frequency of 2×10⁷, and a fast reference speckle establishment process that takes only 0.9 ms. The proposed method assisted by OFCs is a good prospect for a more practical speckle-based wavemeter with higher dynamic ranges.

Spectral speckle-correlation imaging

We present a method for single-shot spectrally resolved imaging through scattering media by using the spectral memory effect of speckles. In our method, a single speckle pattern from a multi-colored object is captured through scattering media with a monochrome image sensor. The color object is recovered by correlation of the captured speckle and a three-dimensional phase retrieval process. The proposed method was experimentally demonstrated by using point sources with different emission spectra located between diffusers. This study paves the way for non-invasive and low-cost spectral imaging through scattering media.

Comparison of round- and square-core fibers for sensing, imaging, and spectroscopy

Multimode fibers (MMFs) show great promise as miniature probes for sensing, imaging, and spectroscopy applications. Different parameters of the fibers, such as numerical aperture, refractive index profile and length, have been already optimized for better performance. Here we investigate the role of the core shape, in particular for wavefront shaping applications where a focus is formed at the output of the MMF. We demonstrate that in contrast to a conventional round-core MMF, a square-core design does not suffer from focus aberrations. Moreover, we find that how the interference pattern behind a square-core fiber decorrelates with the input frequency is largely independent of the input light coupling. Finally, we demonstrate that a square core shape provides an on-average uniform distribution of the output intensity, free from the input-output correlations seen in round fibers, showing great promise for imaging and spectroscopy applications.

Image reconstruction through a multimode fiber with a simple neural network architecture

Multimode fibers (MMFs) have the potential to carry complex images for endoscopy and related applications, but decoding the complex speckle patterns produced by mode-mixing and modal dispersion in MMFs is a serious challenge. Several groups have recently shown that convolutional neural networks (CNNs) can be trained to perform high-fidelity MMF image reconstruction. We find that a considerably simpler neural network architecture, the single hidden layer dense neural network, performs at least as well as previously-used CNNs in terms of image reconstruction fidelity, and is superior in terms of training time and computing resources required. The trained networks can accurately reconstruct MMF images collected over a week after the cessation of the training set, with the dense network performing as well as the CNN over the entire period.

Real-time multispeckle spectral-temporal measurement unveils the complexity of spatiotemporal solitons

The dynamics of three-dimensional (3D) dissipative solitons originated from spatiotemporal interactions share many common characteristics with other multi-dimensional phenomena. Unveiling the dynamics of 3D solitons thus permits new routes for tackling multidisciplinary nonlinear problems and exploiting their instabilities. However, this remains an open challenge, as they are multi-dimensional, stochastic and non-repeatable. Here, we report the real-time speckle-resolved spectral-temporal dynamics of a 3D soliton laser using a single-shot multispeckle spectral-temporal technology that leverages optical time division multiplexing and photonic time stretch. This technology enables the simultaneous observation on multiple speckle grains to provide long-lasting evolutionary dynamics on the planes of cavity time (t) - roundtrip and spectrum (λ) - roundtrip. Various non-repeatable speckly-diverse spectral-temporal dynamics are discovered in both the early and established stages of the 3D soliton formation.

Disordered Optics: Exploiting Multiple Light Scattering and Wavefront Shaping for Nonconventional Optical Elements

Advances in diverse areas such as inspection, imaging, manufacturing, telecommunications, and information processing have been stimulated by novel optical devices. Conventional material ingredients for these devices are typically made of homogeneous refractive or diffractive materials and require sophisticated design and fabrication, which results in practical limitations related to their form and functional figures of merit. To overcome such limitations, recent developments in the application of disordered materials as novel optical elements have indicated great potential in enabling functionalities that go beyond their conventional counterparts, while the materials exhibit potential advantages with respect to reduced form factors. Combined with wavefront shaping, disordered materials enable dynamic transitions between multiple functionalities in a single active optical device. Recent progress in this field is summarized to gain insight into the physical principles behind disordered optics with regard to their advantages in various applications as well as their limitations compared to conventional optics.

Ultra-high resolution and broadband chip-scale speckle enhanced Fourier-transform spectrometer

Recent advancements in silicon photonics are enabling the development of chip-scale photonics devices for sensing and signal processing applications, among which on-chip spectrometers are of particular interest for precision wavelength monitoring and related applications. Most chip-scale spectrometers suffer from a resolution-bandwidth trade-off, thus limiting the uses of the device. Here we report on a novel passive, chip-scale, hybrid speckle-enhanced Fourier transform device that exhibits a two order-of-magnitude improvement in finesse (bandwidth/resolution) over the state-of-the art chip-scale speckle and Fourier transform spectrometers. In our proof-of-principle device, we demonstrate a spectral resolution of 140 MHz with 12-nm bandwidth for a finesse of 10⁴ that can operate over a range of 1500-1600 nm. This chip-scale spectrometer structure implements a typical spatial heterodyne discrete Fourier transform interferometer network that is enhanced by speckle generated from the wafer substrate. This latter effect, which is extremely simple to invoke, superimposes the high wavelength resolution intrinsic to speckle generated from a strongly guiding waveguide with a more broadband but lower resolution discrete Fourier transform modality of the overarching waveguide structure. This hybrid approach signifies a new pathway for realizing chip-scale spectrometers capable of ultra-high resolution and broadband performance.

Study of a fiber spectrometer based on offset fusion

A near-infrared spectrometer based on offset fused multimode fiber (MMF) is investigated in this study. The light spectrum is recovered by analyzing the speckle images when light is passing through the MMF. In order to generate adequate speckles, a polarization maintaining fiber (PMF) and a 30 cm long MMF are fused with a vertical offset. Seven different offset displacements are implemented in the fiber fusion. The follow-up experiments show that the fiber offset fusion has a significant influence on the spectral correlation and the resolution. Larger offset fusion can excite more high-order modes in the MMF, and it greatly improves the spectrometer's performance. The simulation results also show that more modes are excited in MMF, and the increase of mode number leads to lower correlation coefficients of the neighboring spectral channels. However, large offset fusion increases the fusion and the insertion loss of the whole system, which may bring difficulties in the low-light cases. In addition, an image denoising algorithm based on dynamic threshold filtering and a spectral reconstruction algorithm originated from complete orthogonal decomposition were used to remove the speckle pattern noise and recover the spectrum. The final speckle-based spectrometer has a spectral resolution of 0.6∼0.016nm depending on the different offset fusions.

Multimode-fiber-based single-shot full-field measurement of optical pulses

Multimode fibers are explored widely for optical communication, spectroscopy, imaging, and sensing applications. Here we demonstrate a single-shot full-field temporal measurement technique based on a multimode fiber. The complex spatiotemporal speckle field is created by a reference pulse propagating through the fiber, and it interferes with a signal pulse. From the time-integrated interference pattern, both the amplitude and the phase of the signal are retrieved. The simplicity and high sensitivity of our scheme illustrate the potential of multimode fibers as versatile and multi-functional sensors.

Quantitative strain sensing in a multimode fiber using dual frequency speckle pattern tracking

We report an amplitude-measuring multimode fiber sensor capable of making quantitative strain measurements and extracting the algebraic sign of the strain. The Rayleigh-based sensor probes the fiber with pulses of alternating optical frequency and records the backscattered speckle patterns on a high-speed camera. We show that measuring the change in the speckle pattern induced by a change in optical frequency provides a form of in situ calibration, enabling the sensor to recover the magnitude and algebraic sign of the strain. The sensor, which can be positioned anywhere along 2 km of fiber, has a linear strain response, a 10 kHz bandwidth, and a strain noise of ${10.2}\;{\rm p}\unicode{x03B5} /\surd {{\rm Hz}} $10.2pε/√Hz.

Deep learning reconstruction of ultrashort pulses from 2D spatial intensity patterns recorded by an all-in-line system in a single-shot

We propose a simple all-in-line single-shot scheme for diagnostics of ultrashort laser pulses, consisting of a multi-mode fiber, a nonlinear crystal and a camera. The system records a 2D spatial intensity pattern, from which the pulse shape (amplitude and phase) are recovered, through a fast Deep Learning algorithm. We explore this scheme in simulations and demonstrate the recovery of ultrashort pulses, robustness to noise in measurements and to inaccuracies in the parameters of the system components. Our technique mitigates the need for commonly used iterative optimization reconstruction methods, which are usually slow and hampered by the presence of noise. These features make our concept system advantageous for real time probing of ultrafast processes and noisy conditions. Moreover, this work exemplifies that using deep learning we can unlock new types of systems for pulse recovery.

Single-shot depth profiling by spatio-temporal encoding with a multimode fiber

Computational imaging with random encoding patterns obtained by scattering of light in complex media has enabled simple imaging systems with compelling performance. Here, we extend this concept to axial reflectivity profiling using spatio-temporal coupling of broadband light in a multimode fiber (MMF) to generate the encoding functions. Interference of light transmitted through the MMF with a sample beam results in path-length-specific patterns that enable computational reconstruction of the axial sample reflectivity profile from a single camera snapshot. Leveraging the versatile nature of MMFs, we demonstrate depth profiling with bandwidth-limited axial resolution of 13.4 µm over a scalable sensing range reaching well beyond one centimeter.

High-performance compact spectrometer based on multimode interference in a tapered spiral-shaped waveguide

Multimode interference patterns are strongly dependent on spectral components and can be used as fingerprints to reconstruct a spectrum with random amplitudes. Motivated by this concept, we designed and realized a high-performance compact spectrometer based on a tapered spiral-shaped waveguide with a detector array integrated directly on top. The device relies on imaging the multimode interference from leaky modes, resulting in a resolution of 20 pm in the visible range and a bandwidth from 545 to 725 nm with a 250 µm radius structure. Spectra of multiple narrow lines and synthesized broadband are well reconstructed. The ability to achieve such high resolution and broad bandwidth in a compact footprint is expected to have a significant role in low-cost and multifunctional integrated systems.

Optical fiber-based dispersion for spectral discrimination in fluorescence lifetime imaging systems

The excited state lifetime of a fluorophore together with its fluorescence emission spectrum provide information that can yield valuable insights into the nature of a fluorophore and its microenvironment. However, it is difficult to obtain both channels of information in a conventional scheme as detectors are typically configured either for spectral or lifetime detection. We present a fiber-based method to obtain spectral information from a multiphoton fluorescence lifetime imaging (FLIM) system. This is made possible using the time delay introduced in the fluorescence emission path by a dispersive optical fiber coupled to a detector operating in time-correlated single-photon counting mode. This add-on spectral implementation requires only a few simple modifications to any existing FLIM system and is considerably more cost-efficient compared to currently available spectral detectors.

Speckle-based strain sensing in multimode fiber

The diversity of spatial modes present within a multimode fiber has been exploited for a wide variety of imaging and sensing applications. Here, we show that this diversity of modes can also be used to perform quantitative strain sensing by measuring the amplitude of the Rayleigh backscattered speckle pattern in a multimode fiber. While most Rayleigh based fiber sensors use single mode fiber, multimode fiber has the potential to provide lower noise due to the higher capture fraction of Rayleigh scattered light, higher non-linear thresholds, and the ability to avoid signal fading by measuring many spatial modes simultaneously. Moreover, while amplitude measuring single mode fiber based Rayleigh sensors cannot provide quantitative strain information, the backscattered speckle pattern formed in a multimode fiber contains enough information to extract a linear strain response. Here, we show that by tracking the evolution of the backscattered speckle pattern, the sensor provides a linear strain response and is immune to signal fading. The sensor has a noise floor of 2.9 pɛ/√Hz, a dynamic range of 74 dB at 1 kHz, and bandwidth of 20 kHz. This work paves the way for a new class of fiber optic sensors with a simplified design and enhanced performance.

Simulative study on speckle-spectral properties of a random pixelated grating

Speckle spectrometers based on disordered media have shown great prospects and attracted more and more attention. To obtain a larger bandwidth and higher light-energy utilization ratio, a novel speckle spectrometer scheme is proposed based on a random pixelated grating. The speckle generation mechanism of the random pixelated grating is derived by using the diffraction and Fourier transform theory, and the speckle-spectral correlation properties are analyzed through numerical simulation. The influences of system parameters, such as variation ranges of grating periods and orientations, lens focal length, grating pixel size, and pixel number, are investigated. According to the simulation results, the speckle spectrometer system is optimized, and a spectral resolution of up to 0.01 nm can be achieved.

Deep learning enabled real time speckle recognition and hyperspectral imaging using a multimode fiber array

We demonstrate the use of deep learning for fast spectral deconstruction of speckle patterns. The artificial neural network can be effectively trained using numerically constructed multispectral datasets taken from a measured spectral transmission matrix. Optimized neural networks trained on these datasets achieve reliable reconstruction of both discrete and continuous spectra from a monochromatic camera image. Deep learning is compared to analytical inversion methods as well as to a compressive sensing algorithm and shows favourable characteristics both in the oversampling and in the sparse undersampling (compressive) regimes. The deep learning approach offers significant advantages in robustness to drift or noise and in reconstruction speed. In a proof-of-principle demonstrator we achieve real time recovery of hyperspectral information using a multi-core, multi-mode fiber array as a random scattering medium.

Deep learning the high variability and randomness inside multimode fibers

Multimode fibers (MMF) are remarkable high-capacity information channels. However, the MMF transmission is highly sensitive to external perturbations and environmental changes. Here, we show the successful binary image transmission using deep learning through a single MMF subject to dynamic shape variations. As a proof-of-concept experiment, we find that a convolutional neural network has excellent generalization capability with various MMF transmission states to accurately predict unknown information at the other end of the MMF at any of these states. Our results demonstrate that deep learning is a promising solution to address the high variability and randomness challenge of MMF based information channels. This deep-learning approach is the starting point of developing future high-capacity MMF optical systems and devices and is applicable to optical systems concerning other diffusing media.

Overcoming the speckle correlation limit to achieve a fiber wavemeter with attometer resolution

The measurement of the wavelength of light using speckle is a promising tool for the realization of compact and precise wavemeters and spectrometers. However, the resolution of these devices is limited by strong correlations between the speckle patterns produced by closely spaced wavelengths. Here, we show how principal component analysis of speckle images provides a route to overcome this limit. Using this, we demonstrate a compact wavemeter that measures attometer-scale wavelength changes of a stabilized diode laser, eight orders of magnitude below the speckle correlation limit.

Snapshot fiber spectral imaging using speckle correlations and compressive sensing

Snapshot spectral imaging is rapidly gaining interest for remote sensing applications. Acquiring spatial and spectral data within one image promotes fast measurement times, and reduces the need for stabilized scanning imaging systems. Many current snapshot technologies, which rely on gratings or prisms to characterize wavelength information, are difficult to reduce in size for portable hyperspectral imaging. Here, we show that a multicore multimode fiber can be used as a compact spectral imager with sub-nanometer resolution, by encoding spectral information within a monochrome CMOS camera. We characterize wavelength-dependent speckle patterns for up to 3000 fiber cores over a broad wavelength range. A clustering algorithm is employed in combination with l₁-minimization to limit data collection at the acquisition stage for the reconstruction of spectral images that are sparse in the wavelength domain. We also show that in the non-compressive regime these techniques are able to accurately reconstruct broadband information.

Multimode fiber Φ-OTDR with holographic demodulation

We propose and demonstrate a method to perform quantitative phase-sensitive optical time domain reflectometry (Φ-OTDR) using multimode fiber. While most Φ-OTDR sensors use single-mode fiber, multimode fiber exhibits higher thresholds for non-linear effects, a larger capture fraction of Rayleigh backscattered light, and the potential to avoid signal fading by detecting many spatial modes in parallel. Previous multimode fiber based OTDR sensors discarded most of the backscattered light and thus failed to take advantage of these noise-reducing factors. Here, we show that by performing off-axis holography with a high-speed camera, we can record the entire Rayleigh backscattered field, maximizing the detected light level and making the sensor immune to fading. The sensor exhibits a high degree of linearity, a minimum phase noise of -80 dB [rel. rad²/Hz], and 20 kHz bandwidth.

Demonstration of speckle-based compressive sensing system for recovering RF signals

We demonstrate measurement of RF signals in the 2-19 GHz band using a photonic compressive sensing (CS) receiver. The RF is modulated onto chirped optical pulses that then propagate through a multimode fiber that produces the random projections needed for CS via optical speckle. Our system makes 16 independent measurements per optical pulse and we demonstrate several calibration techniques to obtain the CS measurement matrix from these measurements. Then a standard penalized l₁ norm method recovers amplitude, phase, and frequency of single-tone and two-tone RF signals with about 100 MHz resolution in a single 4.5 ns pulse. A novel subspace method recovers the frequency to about 20 kHz resolution over 100 pulses in a 2.8 microsecond time window. These experiments use discrete fiber-coupled optical components, but all necessary functions can be realized in photonic and electronic integrated circuits.

Complete polarization control in multimode fibers with polarization and mode coupling

Multimode optical fibers have seen increasing applications in communication, imaging, high-power lasers, and amplifiers. However, inherent imperfections and environmental perturbations cause random polarization and mode mixing, causing the output polarization states to be different from the input polarization states. This difference poses a serious issue for employing polarization-sensitive techniques to control light-matter interactions or nonlinear optical processes at the distal end of a fiber probe. Here, we demonstrate complete control of polarization states for all output channels by only manipulating the spatial wavefront of a laser beam into the fiber. Arbitrary polarization states for individual output channels are generated by wavefront shaping without constraining the input polarization. The strong coupling between the spatial and polarization degrees of freedom in a multimode fiber enables full polarization control with the spatial degrees of freedom alone; thus, wavefront shaping can transform a multimode fiber into a highly efficient reconfigurable matrix of waveplates for imaging and communication applications.

Compact broadband spectrometer based on upconversion and downconversion luminescence

In this Letter, a compact spectrometer based on upconversion and downconversion luminescence for operation in the infrared, visible, and ultraviolet bands is presented. The proposed spectrometer has three components that are used for dispersion, frequency conversion, and detection. The conversion component converts the incident signal beam into a spectral window appropriate for the detection component. The detection component images the speckle pattern generated by scattering or diffraction in the random structure of the dispersion component. With the two-dimensional intensity data captured from both the speckle pattern and a calibration measurement process, one can reconstruct the spectra of the signal beam by solving a matrix equation. A smoothing simulated annealing algorithm has been implemented to improve the accuracy of the spectral reconstruction. We have analyzed possible sources of error in the algorithm and the corresponding limits of operation. The reported broadband, compact, high-resolution, luminescence-based spectrometer is well suited for portable spectroscopy applications.

Critical phenomenon in tapered dielectric structures

We demonstrate the existence of a critical behavior of a single electromagnetic mode propagating in a tapered dielectric structure. This behavior is described in terms of a critical phase velocity in the case of an adiabatic tapering. In the vicinity of this critical phase velocity, the tapered structure no longer confines the radiation and a significant fraction of the power escapes transversely.

Fiber-Optic Point-Based Sensor Using Specklegram Measurement

Here, we report a fiber-optic point-based sensor to measure temperature and weight based on correlated specklegrams induced by spatial multimode interference. The device is realized simply by splicing a multimode fiber (MMF) to a single-mode fiber (SMF) with a core offset. A series of experiments demonstrates the approximately linear relation between the correlation coefficient and variation. Furthermore, we show the potential applications of the refractive index sensing of our device by disconnecting the splicing point of MMF and SMF. A modification of the algorithm in order to improve the sensitivity of the sensor is also discussed at the end of the paper.

Compact broadband high-resolution infrared spectrometer with a dihedral reflector

We demonstrate a compact broadband high-resolution spectrometer approach. A dihedral reflector is used to reflect the dispersed light back to the grating for a second diffraction, folding the light path in a compact space, and enhancing the spectral resolution. The theoretical formulas for the system are strictly derived. In addition, a prototype of this spectrometer for fiber communication in the infrared wavelength range has been built. The optics can fit inside a volume of 12 cm × 14 cm × 5 cm and its spectral resolution is 57 pm over a wide wavelength range from 1250 nm to 1650 nm.

Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization

The accurate determination and control of the wavelength of light is fundamental to many fields of science. Speckle patterns resulting from the interference of multiple reflections in disordered media are well-known to scramble the information content of light by complex but linear processes. However, these patterns are, in fact, exceptionally rich in information about the illuminating source. We use a fibre-coupled integrating sphere to generate wavelength-dependent speckle patterns, in combination with algorithms based on the transmission matrix method and principal component analysis, to realize a broadband and sensitive wavemeter. We demonstrate sub-femtometre wavelength resolution at a centre wavelength of 780 nm, and a broad calibrated measurement range from 488 to 1,064 nm. This compares favourably to the performance of conventional wavemeters. Using this speckle wavemeter as part of a feedback loop, we stabilize a 780 nm diode laser to achieve a linewidth better than 1 MHz.

Speckle-based hyperspectral imaging combining multiple scattering and compressive sensing in nanowire mats

Encoding of spectral information onto monochrome imaging cameras is of interest for wavelength multiplexing and hyperspectral imaging applications. Here, the complex spatiospectral response of a disordered material is used to demonstrate retrieval of a number of discrete wavelengths over a wide spectral range. Strong, diffuse light scattering in a semiconductor nanowire mat is used to achieve a highly compact spectrometer of micrometer thickness, transforming different wavelengths into distinct speckle patterns with nanometer sensitivity. Spatial multiplexing is achieved through the use of a microlens array, allowing simultaneous imaging of many speckles, ultimately limited by the size of the diffuse spot area. The performance of different information retrieval algorithms is compared. A compressive sensing algorithm exhibits efficient reconstruction capability in noisy environments and with only a few measurements.

Universal sensitivity of speckle intensity correlations to wavefront change in light diffusers

Here, we present a concept based on the realization that a complex medium can be used as a simple interferometer. Changes in the wavefront of an incident coherent beam can be retrieved by analyzing changes in speckle patterns when the beam passes through a light diffuser. We demonstrate that the spatial intensity correlations of the speckle patterns are independent of the light diffusers, and are solely determined by the phase changes of an incident beam. With numerical simulations using the random matrix theory, and an experimental pressure-driven wavefront-deforming setup using a microfluidic channel, we theoretically and experimentally confirm the universal sensitivity of speckle intensity correlations, which is attributed to the conservation of optical field correlation despite multiple light scattering. This work demonstrates that a light diffuser works as a simple interferometer, and presents opportunities to retrieve phase information of optical fields with a compact scattering layer in various applications in metrology, analytical chemistry, and biomedicine.

Characterization of digital dispersive spectrometers by low coherence interferometry

We propose a procedure to determine the spectral response of digital dispersive spectrometers without previous knowledge of any parameter of the system. The method consists of applying the Fourier transform spectroscopy technique to each pixel of the detection plane, a CCD camera, to obtain its individual spectral response. From this simple procedure, the system-point spread function and the effect of the finite pixel width are taken into account giving rise to a response matrix that fully characterizes the spectrometer. Using the response matrix information we find the resolving power of a given spectrometer, predict in advance its response to any virtual input spectrum and improve numerically the spectrometer's resolution. We consider that the presented approach could be useful in most spectroscopic branches such as in computational spectroscopy, optical coherence tomography, hyperspectral imaging, spectral interferometry and analytical chemistry, among others.