Jones Matrix Research Articles

Temperature stability analysis of the all-fiber current sensor with a loop structure

Abstract All-fiber optical current sensor (AFOCS) is a perfect product formed by the combination of fiber-optic sensing technology and the Faraday effect. It boasts significant advantages such as resistance to electromagnetic interference, a high measurement dynamic range and precision, low power consumption, low cost, and insulation. Additionally, it enables long-distance transmission, making it one of the main devices for current monitoring in smart grids. However, the birefringence within the sensing fiber is highly susceptible to changes in temperature, causing the polarization state of light to be extremely sensitive to temperature variations. This sensitivity significantly impacts the accuracy of current measurements. A novel loop structure AFOCS with a coupled fiber polarization rotator (FPR) is introduced in this paper. The operating principle of this structure is theoretically analyzed, and the Jones matrix is used to analyze the output light intensity signal and derive the error formula. After comparing the measurement accuracy of the basic AFOCS and the loop structure AFOCS, it is demonstrated that this novel structure can improve current sensitivity by enhancing the temperature robustness of the system. Additionally, the error generated by the FPR is controlled below 1%, meeting the requirements for stable system operation. Therefore, this novel structure effectively improves the accuracy of current measurement and exhibits strong temperature stability.

Broadband metamaterial polarizers with high extinction ratio for high-precision terahertz spectroscopic polarimetry

The demand for precise polarizers is increasing to investigate the polarization characteristics of materials non-invasively in the terahertz region. Recently, to address the low extinction ratio and fragile nature of conventional wire-grid polarizers, plasmonic structures and metasurfaces have been proposed. However, the challenge of achieving low transmittance compared to a high extinction ratio, along with the bulky structure due to a thick substrate, remains to be addressed. Here, we present high-efficiency broadband metamaterial polarizers consisting of cross-aligned double-layers of subwavelength metallic slit arrays, leveraging the extraordinary optical transmission and funneling effects. We obtained extinction ratios exceeding 70 dB over a broad frequency range, from 0.2 to 2.5 THz, reaching a maximum extinction ratio of ∼90 dB at 0.7 THz. To investigate the influence of high extinction ratio polarizers on actual measurement results, we measured a non-Hermitian metasurface with asymmetric polarization conversion and analyzed them using the Jones matrix formalism. The results confirmed that the extinction ratio of the polarizer has a significant impact on precise polarization-dependent measurements, especially on cross-polarization measurements. The enhanced performance of our polarizers offers significant potential for sensitive THz systems, paving the way for advancements in polarization analysis of emerging materials and chiral sensing.

Polarization self-modulation in a coaxially end-pumped orthogonally polarized laser

A scheme of orthogonally polarized laser (OPL) with polarization self-modulation (PSM) in the coaxial end-pumping configuration is proposed in this work. The gain medium consisted of two Nd:YVO4 crystals with orthogonal optical axes, and a quarter-wave plate served as a polarization-switching device. By rotating the electric vector during each cavity round trip, frequency degeneration and correlated operation of two polarization components were achieved. The polarization eigenstates in two orthogonal directions were analyzed using the Jones matrix and eigenequation. The spectral distribution was also briefly discussed based on thermal effects. The results showed that two eigenmodes located at 45° and 135° to the crystal axis, respectively, with a frequency difference equaled to half the free spectral range of the resonator. In the experiments, it was found for the first time that the modulation of eigenstates can be realized by adjusting pump parameters (including pump power, beam size, focusing position, and pump wavelength) and cavity anisotropy, which enables the manipulation of degree of polarization (DOP) and monitoring the resonator properties. Overall, tuning the laser polarization eigenstate offers a flexible method to switch the operational states of the OPL, including the longitudinal mode frequency difference, DOP, polarization angle, etc. It is believed this scheme provides a valuable reference to realize compact, high-beam-quality, and robust OPLs for applications such as dual-frequency light source development, precision measurement and polarization control.

On-chip multifunctional metasurfaces with full-parametric multiplexed Jones matrix

On-chip metasurface for guided wave radiation works as an upgrade of conventional grating couplers, enriching the interconnection between guided wave and free-space optical field. However, the number of controllable parameters in equivalent Jones matrix of on-chip metasurface is limited that restricts the channels for multiplexing. Here, a supercell design based on detour phase and geometric phase has been proposed to reach full-parametric modulation of Jones matrix. As proof of concept, four independent sets of amplitude-phase channels have been experimentally demonstrated through a single on-chip metasurface. Moreover, through joint modulation of three phase mechanisms including detour phase, geometric phase and propagation phase, the Jones matrix could be decoupled from forward- and backward-propagating guided waves for direction multiplexing. This work paves the way for guided wave radiation towards high-capacity multiplexing and may further extend its application in optical communications, optical displays and augmented/virtual reality.

Bidirectional Vectorial Holography Using Bi-Layer Metasurfaces and Its Application to Optical Encryption.

The field of optical systems with asymmetric responses has grown significantly due to their various potential applications. Janus metasurfaces are noteworthy for their ability to control light asymmetrically at the pixel level within thin films. However, previous demonstrations are restricted to the partial control of asymmetric transmission for a limited set of input polarizations, focusing primarily on scalar functionalities. Here, optical bi-layer metasurfaces that achieve a fully generalized form of asymmetric transmission for any input polarization are presented. The designs owe much to the theoretical model of asymmetric transmission in reciprocal systems, which elucidates the relationship between front- and back-side Jones matrices in general cases. This model reveals a fundamental correlation between the polarization-direction channels of opposing sides. To circumvent this constraint, partitioning the transmission space is utilizedto realize four distinct vector functionalities within the target volume. As a proof of concept, polarization-direction-multiplexed Janus vectorial holograms generating four vectorial holographic images are experimentally demonstrated. When integrated with computational vector polarizer arrays, this approach enables optical encryption with a high level of obscurity. The proposedmathematical framework and novel material systems for generalized asymmetric transmission may pave the way for applications such as optical computation, sensing, and imaging.

Directionally Asymmetric in Orbital Angular Momentum Generation Using Single‐Layer Dielectric Janus Metasurfaces

AbstractJanus metasurfaces, offering versatile light manipulation contingent on incident direction, are explored across microwave to mid‐infrared spectra. Nonetheless, prior designs often resort to spatial multiplexing or vertical stacking, entailing complex fabrication. Metallic Janus metasurfaces, owing to material properties, suffer notable Ohmic losses in the visible spectrum. In this study, Single‐layer TiO2‐based Janus metasurfaces with arbitrary polarization control is experimentally demonstrated, exhibiting directionally asymmetric functionalities in spin and orbital angular momentum (OAM). A novel Jones matrix formulation tailored for Janus metasurfaces is presented, enabling efficient generation of two asymmetric, high‐purity OAM states of vortex beams at wavelength of 532 nm, contingent on incidence direction. This innovation facilitates compact and versatile phase manipulation, encompassing applications such as lasers and optical combiners, thereby expanding its utility across diverse domains.

A terahertz chiral metamaterial with tunable dual-band to broadband circular dichroism based on Dirac semimetals

Chiral metamaterials play a crucial role in manipulating the electromagnetic waves. This paper intoduces a three-dimensional Dirac semimetal materials (3D DSM) metamaterial structure tailored for tunable and broadband circular dichroism (CD) effects at terahertz (THz) frequencies. Using the Jones matrix, electromagnetic multipole resonance theory, and the atomic orbital hybridization model, the resonant performance for the DSM based metamaterials in reflection and transmission design is systematically analyzed, in terms of the resonant peak and bandwidth. Simulation results show that the bilayer DSM metamaterial supports the chiral response with dual-band resonance in transmitted spectra, and its CD and working frequency could be tuned by adjusting the rotation angle between the upper and lower DSM metamaterial layers and Fermi level of DSM. Therefore, the tunable CD from 0 to 0.51 could be achieved across a wide THz frequency from 3.56 THz to 4.02 THz. Additionlly, the resonant frequency is highly sensitive to the surrounding refractive index (RI), yielding a RI sensing sensitivity up to 308.6 GHz/RIU. The proposed DSM based chiral metamaterial features a tunable and broadband design, offering a universal design method and potential applications for the modulation of light polarization, chiral sensing and imaging, and communications.

Reaching the efficiency limit of arbitrary polarization transformation with non-orthogonal metasurfaces

Polarization transformation is at the foundation of modern applications in photonics and quantum optics. Notwithstanding their applicative interests, basic theoretical and experimental efforts are still needed to exploit the full potential of polarization optics. Here, we reveal that the coherent superposition of two non-orthogonal eigen-states of Jones matrix can improve drastically the efficiency of arbitrary polarization transformation with respect to classical orthogonal polarization optics. By exploiting metasurface with stacking and twisted configuration, we have implemented a powerful configuration, termed “non-orthogonal metasurfaces”, and have experimentally demonstrated arbitrary input-output polarization modulation reaching nearly 100% transmission efficiency in a broadband and angle-insensitive manner. Additionally, we have proposed a routing methodology to project independent phase holograms with quadruplex circular polarization components. Our results outline a powerful paradigm to achieve extremely efficient polarization optics, and polarization multiplexing for communication and information encryption at microwave and optical frequencies.

Compact common-path polarization holography for measurement of the Jones matrix of polarization-sensitive materials

A compact common-path off-axis digital holographic imaging method is proposed utilizing polarization-angular-multiplexing for Jones matrix measurement. Our method employs a common-path off-axis configuration to capture multiplexed off-axis interferograms generated by orthogonally polarized object beams and a reference beam on a monochrome CCD camera. The modulation of the fringe direction is achieved by two homemade retro-reflector mirrors, allowing for the retrieval of the Jones matrix distribution of transparent specimens through a matrix-division algorithm. The stable common-path design and the expansive camera field of view facilitate the extraction of spatially resolved Jones matrix parameters. The feasibility of this method was validated through experiments involving standard objects and polarization-sensitive materials, conducted at both general and microscopic scales. Our system completed polarization imaging of cancerous tissues, unequivocally demonstrating its extraordinary potential in medical pathology diagnostics.

Polar magneto-optical Kerr effect spectroscopy with a microscope arrangement for studies on 2D materials.

We describe a setup for magneto-optical Kerr effect (MOKE) spectroscopy suitable for Kerr rotation (ϕ) and ellipticity (η) measurement on microscopic samples, such as flakes of two-dimensional materials. A spatial resolution of ∼25μm, limited by the demagnified monochromator exit slit image, was achieved. The use of mirrors allows for measurement in polar MOKE geometry with a conventional electro-magnet, without requiring holes in the magnet pole pieces. The microscope-like optics also has a 90° twisted periscope arrangement of two mirrors that helps transport light without change in its circular polarization state. A Jones matrix analysis of the setup brings out the influence of the beam-splitter on the measured signals. Its correction requires the ellipsometry parameters of the beam-splitter in transmission mode, which were measured separately. The working of the setup is tested by measuring the ϕ and η spectra of 2H-WS2 flakes at low temperature, verifying them using Kramers-Kronig analysis and extracting the Landé g-factor of the ground state exciton from them.

A handheld polarimetric imaging device and calibration technique for accurate mapping of terahertz Stokes vectors

In recent years, handheld and portable terahertz instruments have been in rapid development for various applications ranging from non-destructive testing to biomedical imaging and sensing. For instance, we have deployed our Portable Handheld Spectral Reflection (PHASR) Scanners for in vivo full-spectroscopic imaging of skin burns in large animal models in operating room settings. In this paper, we debut the polarimetric version of the PHASR Scanner, and describe a generalized calibration technique to map the spatial and spectral dependence of the Jones matrix of an imaging scanner across its field of view. Our design is based on placement of two orthogonal photoconductive antenna (PCA) detectors separated by a polarizing beam splitter in the PHASR Scanner housing. We show that as few as three independent measurements of a well-characterized polarimetric calibration target are sufficient to determine the polarization state of the incident beam at the sample location, as well as to extract the Jones propagation matrix from the sample location to the detectors. We have tested the accuracy of our scanner by validating polarimetric measurements obtained from a birefringent crystal rotated to various angles, as compared to the theoretically predicted response of the sample. This new version of our PHASR scanner can be used for high-speed imaging and investigation of heterogeneity of polarization-sensitive samples in the field.

Light Field Transformation of Metasurface Based on Arbitrary Jones Matrix

AbstractMetasurfaces are ultra‐thin micro‐nano elements, have abundant freedoms, and are widely used in light field transformation. The Jones matrix of single‐layer birefringent metasurfaces have at most 6 degrees of freedom, which limits the richness and diversity of light field transformation. Bilayer metasurfaces have more design channels and functionality than single‐layer metasurfaces. By mathematical derivation, the decomposition method of the bilayer metasurface unitary Jones matrix is provided. Further, inspired by double‐phase holography, arbitrary complex Jones matrix is decomposed and realized by bilayer metasurface and achieves analytical decoupling of all 4 complex components of the Jones matrix. As the theoretical verification, spin‐orbit angular momentum mapping and four‐channel complex holography are realized by the bilayer metasurface. The decomposition method is completely analytical, universal, and easy to implement. It is of great significance for the transformation of light field, information transmission, and optical encryption based on metasurfaces.

Unlocking ultra-high holographic information capacity through nonorthogonal polarization multiplexing

Contemporary studies in polarization multiplexing are hindered by the intrinsic orthogonality constraints of polarization states, which restrict the scope of multiplexing channels and their practical applications. This research transcends these barriers by introducing an innovative nonorthogonal polarization-basis multiplexing approach. Utilizing spatially varied eigen-polarization states within metaatoms, we successfully reconstruct globally nonorthogonal channels that exhibit minimal crosstalk. This method not only facilitates the generation of free-vector holograms, achieving complete degrees-of-freedom in three nonorthogonal channels with ultra-low energy leakage, but it also significantly enhances the dimensions of the Jones matrix, expanding it to a groundbreaking 10 × 10 scale. The fusion of a controllable eigen-polarization engineering mechanism with a vectorial diffraction neural network culminates in the experimental creation of 55 intricate holographic patterns across these expanded channels. This advancement represents a profound shift in the field of polarization multiplexing, unlocking opportunities in advanced holography and quantum encryption, among other applications.

Upper limit on the polarization-assisted amplitude modulation capability of cascaded single-cell wave-plate-like metasurfaces

The Jones matrix method offers a robust framework for designing polarization multiplexed metasurfaces (PMMs). Traditional PMMs design involves initially defining functions and working channels, then mapping feature functions to adjustable parameters of metasurfaces. However, this approach makes it difficult to predict how working channels affect metasurface features. Here, we employ the generalized Malus law and Rodriguez rotation matrix on the Poincare Sphere to analyze diverse working channels’ impact on PMMs’ amplitude modulation capacity. For single-celled waveplate-like PMMs, up to three distinct images can be displayed. We demonstrate this in both theoretic method and numerical simulations. Our study establishes a framework for multi-channel amplitude modulation design of metasurfaces, applicable in information encryption, optical computation, diffraction neural networks, etc.

Combination of Fourier transform Jones matrix and beam coherence polarization matrix: Application to a double polarizer rectangular aperture

In this work, we extend the Fourier transform Jones (FTJ) matrix approach to handle input scalar fields with spatially variant transverse profiles. Additionally, we integrate the FTJ matrix with the beam coherence-polarization (BCP) matrix, suitable for describing partially coherent and partially polarized light. This approach is particularly effective when the polarization diffractive optical element is illuminated with a quasi-monochromatic paraxial scalar field with transverse spatial coherence, but with any degree of polarization and transverse profile. We apply the method to a meaningful example: a rectangular aperture with orthogonal polarizers on each half, illuminated with uniform randomly polarized light. We provide experimental validation using a randomly polarized He-Ne laser and a specially fabricated double polarizer mask. Furthermore, by placing a polarizer behind the polarization diffractive optical element, we generate a scalar beam with spatial incoherence across two distinct zones, suggesting the potential use of randomly polarized lasers with binary patterned polarizers to encode arbitrary binary coherence functions.

Terahertz reflective metasurfaces realize wavefront modulation of circular polarization channels

The emergence of many efficient optical field modulation methods and planar optical devices is attributed to the continuous research of geometric phase. Nevertheless, conjugate symmetry of the geometric phase limits the multiplexing of metasurfaces. To overcome this limitation, integrating the propagation phase and the geometric phase to achieve self-decouped metasurfaces can effectively double channel capacity. Herein, a more in-depth derivation of Jones matrices is conducted, leveraging two degrees of freedom offered by the propagation phase and the geometric phase. This approach enables complete modulation in circular polarization channels. By designing the phase difference between a fast axis and a slow axis, energy allocation between different channels can be controlled. It means independent complex amplitude modulation is achieved. On this basis, the geometric phase is introduced to realize tri-channel multiplexing metasurfaces. To verify the feasibility of this method, two metasurfaces are designed, including a bifocal metasurface with adjustable energy allocation and a tri-channel multiplexing metasurface. The proposed multifunctional metasurface offers new insights into wavefront multiplexing for communication systems.

P‐185: Influence Factors of Dark Viewing Angle of Vertical‐Alignment Liquid Crystal Displays

Dark viewing angle is one of the important indicators for assessing the picture quality of display panels. By using simulation results and physical insight provided by Extended Jones Matrix Method, we explain why LC pre‐tilt is the crucial factor of dark viewing angle of VA LCD, and also discuss other possible factors.

Theoretical and experimental analysis of the complex dynamics of spectral RMS width of an erbium-doped figure eight fiber laser

There are a large number of different ultrashort light pulses; a particular case is called noise-like pulses (NLPs), which are ultrashort light pulses that have the characteristic that their electric field has a very complex internal structure. Due to this characteristic, the envelope can take various shapes (Gaussian, triangular, square, complex shape, etc.). Also its amplitude and temporal width vary with respect to the polarization within the cavity. In this work we carry out a theoretical and experimental study of the RMS widths of NLPs measured within the mode-locked regions generated with our laser cavity: an erbium-doped figure eight fiber laser (EDFEFL). The experimental measurements of the RMS widths of the NLPs were compared with the theoretical model of light intensity transmission based on Jones matrices and with the theoretical model of the NOLM. We find that the theoretical model partially fits with the experimental results. We analyze NLPs with a wavelength carrier of 960 nm, repetition rate of 60 MHz, and temporal profile with duration on the order of nanoseconds.

Full‐Parameter Symmetric Jones Matrix Construction and Non‐Orthogonal‐Polarization Multiplexed Wavefront Shaping Over a Lossy Metasurface

AbstractAccurate full‐parameter construction of the Jones matrix is of great significance for encoding multiple functions in a single metasurface. Supercells composed of several elements are used for this purpose through coherent superposition. But all the elements in the reported studies should be lossless with near‐unity transmission, which limits the material system and restricts the Jones matrix construction in a unitary manner. Here a non‐unitary matrix decomposition method is proposed to build the supercell using a pair of 0°‐oriented rods and a pair of 45°‐oriented rods for on‐demand design of arbitrary symmetric Jones matrices. This method is applicable for lossy metasurfaces and offers straightforward physical guidance for structure design without optimization. The accuracy of the on‐demand Jones matrix generation is demonstrated by several 3D‐printed alumina metalenses with 3‐, 4‐, and 6‐channel polarization‐multiplexed focusing. The study opens a new pathway for non‐silicon meta‐optics and holds great potential for dynamic or switchable applications.

Miura Origami‐Inspired Reconfigurable Phase Gradient Metasurface for Linearly and Circularly Polarized Differential Modulation

Miura origami's reconfigurable characteristic and structural asymmetry, combined with electromagnetic (EM) wave manipulation, crashed a unique spark. However, the complexity of the three‐dimensional (3D) origami structure after folding makes it challenging to study the phase regulation mechanism. Here, we propose a reconfigurable phase gradient metasurface based on Miura origami and derive the underlying mechanism of phase modulation in detail under linearly and circularly polarized (LP and CP) incidence. We adopt the one‐dimensional (1D) gradient design along the x direction to verify the idea. The phase calculation formulas are given under LP and CP incidence through the Jones matrix's derivation. The beam deflector angles corresponding to LP and CP waves are identical in the planar state. As the folding angle increases, the phase evolution rules corresponding to the LP and CP waves are discrepant, leading to differential beam steering. Finally, the origami sample is processed for verification, and the experimental data are consistent with the simulation and theoretically calculated values. We believe this work can help analyze the EM behavior of complex 3D origami structures and lay a foundation for designing a multifunctional EM origami metasurface.