Jones Matrix Research Articles

Simulation analysis of temperature effects on all-fiber optic current sensor

Temperature is the main factor restricting the application of all-fiber current sensors. To comprehensively analyze temperature influences, the influences of temperature on Verdet constant, birefringence, and phase delay of the quarter-wave plate are modeled and simulated by the Jones matrix and Matlab. Basing on the normalized scale coefficient, the relationship between the normalized ratio coefficient and temperature is discussed. Finally, we get the conclusion that the normalized proportional coefficient of feedback phase shift fluctuates on both sides of the reference temperature. Keeping the temperature in a narrow range is a practical scheme to improve the system performance.

A switchable multi-wavelength EDFL using cascaded Sagnac fiber loops with mode differential delay line

We propose and experimentally demonstrate a switchable multi-wavelength Erbium-doped fiber laser that employs cascaded weakly-coupled few-mode fiber (FMF) Sagnac fiber loops with mode differential delay line. A comb filter of multiple specific wavelengths is performed by incorporating a weakly-coupled FMF in cascaded Sagnac fiber loops. The incorporation of the weakly-coupled FMF is realized with all-fiber mode multiplexer/demultiplexer (MUX/DEMUX), which can simultaneously generate transversal LP01 and LP11 modes. The comb filter characteristics of cascaded Sagnac fiber loops are simulated and analyzed by Jones matrix. By adjusting the polarization controllers (PCs), the fiber laser can operate in single-, dual-, and triple-wavelength laser states around C band. The side mode suppression ratio is larger than 30.0 dB. Moreover, the laser output stabilities for single-, dual-, and triple-wavelength lasing are investigated in a range of over 30 min at room temperature. Experimental results indicate that this work has potential applications in WDM systems, sensing, and instrument testing.

Lattice Boltzmann and Jones matrix calculations for the determination of the director field structure in self-propelling nematic droplets.

Nematic droplets immersed in aqueous surfactant solutions can show a self-propelled motion induced by a Marangoni flow in the droplet surface. In addition to the self-propulsion, the Marangoni flow induces within the droplet a convective flow which considerably influences the nematic director field of the droplet. We report numerical simulations aiming at the determination of the director field in the self-propelling droplet. The convective flow and the resulting structure of director field are described by a lattice Boltzmann model. The reliability of the obtained structures is proved by subsequent Jones matrix calculations which enable the direct comparison of experimental polarizing microscopy images of self-propelling droplets with calculated images based on the simulated structures.

Label-free functional and structural imaging of liver microvascular complex in mice by Jones matrix optical coherence tomography

We demonstrate label-free imaging of the functional and structural properties of microvascular complex in mice liver. The imaging was performed by a custom-built Jones-matrix based polarization sensitive optical coherence tomography (JM-OCT), which is capable of measuring tissue’s attenuation coefficient, birefringence, and tiny tissue dynamics. Two longitudinal studies comprising a healthy liver and an early fibrotic liver model were performed. In the healthy liver, we observed distinctive high dynamics beneath the vessel at the initial time point (0 h) and reappearance of high dynamics at 32-h time point. In the early fibrotic liver model, we observed high dynamics signal that reveals a clear network vascular structure by volume rendering. Longitudinal time-course imaging showed that these high dynamics signals faded and decreased over time.

Study on compact polarized light beam splitting system for generating sodium guidestars constellation

A simple and compact polarized light beam splitting system is developed to split one sodium laser beam into multiple beamlets. Here, a polarizing beam splitter and a high reflection mirror is creatively synthesized to be one mirror as the special splitter-and-coupler, whose operation principle is introduced in detail. A Jones matrix model is utilized for theoretical analysis of the amplitude variation and energy distribution of the splitting beamlets. As a result, four yellow beamlets with the power ratio of 1:1:1:1 and orthogonally linearly polarized state are achieved within only 0.002 m2 working area. This approach opens up a new way to generate sodium guidestars constellation for the extended-field-of-view multi-conjugate adaptive optics telescopes.

Description of the Birefringence Effect in Optical Media With Several Types of Anisotropy

The paper proposes a method for finding the characteristics of the birefringence in optical media that possess several types of anisotropy simultaneously. It is proposed to characterize birefringence by a vector equal to the Stokes vector of the eigenpolarization multiplied by the phase shift between waves with eigenpolarizations. It is shown that such a vector of the complex birefringence is equal to the sum of such vectors corresponding to the component birefringences. The proposed method is well compatible with approaches to finding the polarization dynamics of propagating radiation based on the concepts of the Jones matrix and the Poincaré sphere.

Polarisation statistics of vector scattering matrices from the circular orthogonal ensemble

We study the polarisation properties of random N×N scattering matrices distributed according to the circular orthogonal ensemble. We interpret 2 × 2 sub-blocks of the scattering matrix as Jones matrices and study their statistical properties. Using the polar decomposition, we derive probability density functions for retardance and diattenuation from scattering matrices of arbitrary size and in the limit N→∞.

Compact common-path polarisation holographic microscope for measuring spatially-resolved Jones matrix parameters of dynamic samples in microfluidics

In this study, we propose a compact four-channel angular-multiplexing polarisation holographic microscope to quantify the spatially resolved Jones matrix of a dynamic sample in a microfluidic channel. To make the imaging system compact, a common-path off-axis configuration based on a simple object and a reference beam generator unit, consisting of a Wollaston prism and a converging lens, was introduced in the holographic microscope. Using this system and the retrieval method described in this paper, the spatially resolved Jones matrix parameters, as well as the polarisation information, including the diattenuation and phase retardation, of the target sample could be simultaneously retrieved from a single-shot hologram. We experimentally demonstrated the feasibility of our method by quantitatively measuring the birefringence parameters of a quarter-wave plate and extracting the 2-D Jones matrix and polarisation parameters of potato starch particles and C. elegans worms. The simple optical structure and common-path design reduce the system requirements for light source coherence and system stability, which provides a feasible approach for the development of a portable polarisation holographic microscope for microfluidics.

Jones Matrix Microscopy for Living Eukaryotic Cells

Polarization of light carries important information regarding the materials included by biological samples. A Jones matrix is a general tool for quantifying the degree of polarization, however, its measurement has been limited mostly to connective tissues with strong polarization response due to the lack of measurement sensitivity. Here, we demonstrate polarization phase microscopy capable of measuring a Jones matrix of a living eukaryotic cell. Our strategy combines synthetic aperture imaging with polarization phase microscopy to improve the polarization sensitivity. The resultant suppression of intrinsic phase noise in the measurement allows a Jones matrix of a single eukaryotic cell to be clearly visualized. Using the synthesized Jones matrices, the characteristic cellular polarization properties of normal and cancer cells were quantified, and substantial differences between the two kinds were quantitatively identified.

Intracavity field dynamics near avoided mode crossing in a concentric silicon-nitride ring resonator

Understanding the intra-cavity field dynamics in passive microresonator systems has already been intriguing. It becomes fascinating when the system is complex, such as a concentric dual microring resonator that exhibit avoided mode crossing (AMC). In this work, we present a systematic study of intra-cavity oscillatory field dynamics near AMC in a concentric silicon nitride microring resonator with the help of the coupled Lugiato-Lefever equation (LLE). We identify two regions viz. weakly coupled region (WCR) and strongly coupled region (SCR) based on eigenfrequency separation of the two-hybrid modes, which originate from mode coupling near AMC. In WCR, the mode coupling effect is dominant, leading to intra-cavity power oscillation between these two modes in a periodic manner and non-identical variation of their phases. In SCR, the mode coupling effect reduces gradually with nearly identical characteristics of both the modes. We further verify our numerical findings with the semi-analytical variational method, leading to an in-depth understanding of the mode coupling induced dynamics. We finally analyze the polarization evolving state, and the polarization locked state with the help of Stokes parameters and Jones vectors in WCR and SCR, respectively.

Theoretical and experimental studies of output coupling ratio tunable double-corner-cube-retroreflector ring cavity

The polarization state in a double-corner-cube-retroreflector (DCCR) ring cavity is analyzed using Jones matrix. Based on the analysis results, an output coupling ratio tunable DCCR ring cavity created by employing a polarization beam splitter, and wave plates (including λ / 2 plate and λ / 4 plate) is studied theoretically and experimentally. The theoretical output coupling ratio tuning ranges are calculated as 0.01 % ∼ 80.86 % by rotating the λ / 2 plate, 0 ∼ 89.32 % by rotating the λ / 4 plate, and 2.71 % ∼ 81.37 % by rotating corner-cube retroreflector (CCR). The experimental measurement results are consistent with theoretical expectations. An output coupling ratio tunable Er:YAG laser with a DCCR ring cavity is also set up to verify the beneficial effect of output coupling ratio tuning. At given pump power, by tuning the output coupling ratio, the laser obtains optimum operation efficiency and realizes wavelength conversion between 1645 and 1617 nm.

Two-point polarization correlations of random paraxial and nonparaxial electromagnetic fields

We investigate the two-point polarization correlation properties of random, statistically stationary, two-dimensional (2D) and three-dimensional (3D) electromagnetic fields. To this end two specific mutual polarization correlation functions are introduced, one based on a geometric approach using the Poincar\'e vectors and the other on the energy distribution employing the Jones vectors. Both approaches provide equivalent information about the space-time polarization correlations and enable one to associate with the field a polarization length over which the equal-time polarization states remain essentially unchanged. For fields obeying Gaussian statistics, the polarization correlation functions take on simple forms in terms of measurable quantities representing electromagnetic coherence. The formalism is demonstrated with two examples: blackbody radiation inside a cavity and in the far zone of a cavity wall aperture.

Vectorial Compound Metapixels for Arbitrary Nonorthogonal Polarization Steganography

Malus' law regulating the intensity of light when passed through a polarizer, forms the solid basis for image steganography based on orthogonal polarizations of light to convey hidden information without adverse perceptions, which underpins important practices in information encryptions, anti-counterfeitings, and security labels. Unfortunately, the restriction to orthogonal states being taken for granted in the common perceptions fails to advance cryptoinformation to upgraded levels of security. By introducing a vectorial compound metapixel design, arbitrary nonorthogonal polarization multiplexing of independent grayscale images with high fidelity and strong concealment is demonstrated. The Jones matrix treatment of compound metapixels consisting of double atoms with tailored in-plane orientation sum and difference allows point-by-point configuring of both the amplitude and polarization rotations of the output beam in an analytical and linear form. With this, both multiplexing two continuous grayscale images in arbitrary nonorthogonal polarization angles and concealing grayscale image on another in an arbitrary disclosure angle window are experimentally demonstrated in the visible TiO2 metasurface platform. The methods shed new light on multifarious metaoptics by harnessing the new degree of freedom and unlock the full potential of metasurface polarization optics.

Measurement error caused by quarter-wave plate in the dynamic interferometer: Theory and correction method

Quarter-wave plate (QWP) is one of the most important components of dynamic interferometer and its retardation can influence the measurement accuracy, which is usually manifested as periodic ripple error in the measurement results. Based on Jones matrix, the error formula is deduced in this paper, and the error correction method by rotating the half-wave plate (HWP) to change the intensity distribution in the four phase-shifted interferograms is proposed. In the experiment, the ripple error can be effectively suppressed when the background intensity of four interferograms tend to be the same. The performance of dynamic interferometer can be significantly improved through the proposed method.

Implementation of polarization rotation using microring resonator and its application to design all-optical switch

A compact microring resonator (MRR) and its implementation for polarization rotation-based all-optical switching are proposed. The polarization rotation has been achieved by enhancing geometry-induced birefringence of the device and with the insertion of polarization rotator in the race-track-shaped MRR. The proposed device has been modeled using Jones matrix and the finite-difference time-domain simulation method. The insertion loss and the extinction ratio have been found to be −0.13 and 19.39 dB, respectively.

Polarization-sensitive imaging based on incoherent holography.

The polarization-sensitive imaging technology is proposed based on incoherent holography. The distribution of state of polarization (SoP) of the object light field can be reconstructed by measuring the phase difference and amplitude ratio of two components of the Jones vector on the basis of incoherent self-interference theory and the accurate point spread function (PSF) of the incoherent holographic system. In the analysis of Fresnel diffraction, we develop a new method to greatly simplify the calculation of the accurate PSF by means of imaging property of lens and symbolic mathematics tools. In the recording process, we utilize the automation of phase shift, photography, and synthesization of color hologram to greatly shorten the total recording time of a group of phase-shifted holograms. The experimental results show that the proposed technology can accurately realize polarization-sensitive imaging and it is much simpler for complete linearly polarized light.

Jones matrix holography with metasurfaces.

We propose a new class of computer-generated holograms whose far-fields have designer-specified polarization response. We dub these Jones matrix holograms. We provide a simple procedure for their implementation using form-birefringent metasurfaces. Jones matrix holography generalizes a wide body of past work with a consistent mathematical framework, particularly in the field of metasurfaces, and suggests previously unrealized devices, examples of which are demonstrated here. In particular, we demonstrate holograms whose far-fields implement parallel polarization analysis and custom waveplate-like behavior.

Passband-Flattened Frequency-Tunable Optical Fiber Multiwavelength Filter with Composite Combination of Waveplates.

We propose a passband-flattened frequency-tunable optical multiwavelength filter with a composite combination of waveplates, which is realized by harnessing a polarization-diversified loop structure. The proposed filter comprises a polarization beam splitter (PBS), two polarization-maintaining fiber (PMF) segments of equal length, an ordered waveplate combination (OWC) of a half-wave plate (HWP) and a quarter-wave plate (QWP) before the first PMF segment, and an OWC of a QWP and an HWP before the second PMF segment. The second PMF segment is butt-coupled to one port of the PBS so that its slow axis is oriented at 22.5° for the horizontal axis of the PBS. Based on the filter transmittance derived through the Jones calculus, we found the orientation angle (OA) sets of the four waveplates, which could induce an extra phase shift Φ from 0° to 360° in the passband-flattened transmittance function. From the transmission spectra calculated at the eight selected OA sets, which caused Φ to increase from 0° to 315° by steps of 45°, it was confirmed that the passband-flattened multiwavelength spectrum can be continuously tuned by properly controlling the OAs. This indicates continuous wavelength tunability based on composite OWCs. Then, this theoretical prediction was verified by experimental demonstration.

16.2: An Analysis of Stress‐Mura in Curved Liquid Crystal Display

In curved liquid crystal display, the glass substrate is in the state of bending, and the bending stress is generated inside the glass. Under the effect of stress photoelastic effect, the display will produce light leakage, which is called stress‐Mura. Based on the theory of stress photoelasticity and the finite element analysis of panel forming, this paper deduces the light leakage intensity of curved LCD (liquid crystal display) by using the Jones matrix, and puts forward a scheme to improve the design of curved curvature of LCD, which is verified by experiments.

Digital holographic polarimeter using dual reference beam interferometry.

An off-axis digital holographic imaging polarimeter was developed to estimate the Jones matrices of an object. The Jones vector image of the electric field returned from the object is determined from a single holographic recording using the interference between the dual, nearly orthogonal, reference beams. The technique compensates for phase variations in the optical beam paths between the recorded holograms and relaxes the need to generate orthogonal illumination polarization states. A minimization algorithm was developed to compute an estimation of the Jones matrix image of an object based on a set of measured Jones vector images. A proof-of-concept demonstration was performed to compute an estimated Jones matrix image of a polarimetrically complex object using digital holograms recorded with 6 different illumination polarizations.