Jones Matrix Formalism Research Articles

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.

Multivariable Analysis of Nonlinear Optical Loop Mirror Operating Parameters Using Jones Matrices and Three-Dimensional Renderings

Nonlinear optical loop mirrors (NOLMs) are used in modern fiber optic devices and optical communications. In this study, we present numerical analyses of the multiple variables involved in the operation of an NOLM in low- and high-power transmissions. The Jones matrix formalism was used to model linear and circular polarization inputs. We used three-dimensional (3D) plots to identify the characteristics required in the experimental operation of the NOLM. These characteristics, including the critical power, low- and high-power transmission, and dynamic range, depend on parameters such as the fiber loop length, input power, angle of retarder plate, and input polarization. A standard single-mode fiber (SMF-28) with high twist loop lengths of 100, 300, and 500 m and input powers of 0–100 W was simulated. Three-dimensional surface graphics provided a comprehensive view of the NOLM transmission and considerably enhanced the optimal transmission by manipulating adjustable device components including the power and polarization control plates. Optimal transmission facilitates its use in integrating ultrafast pulse generation, optical signal processing, optical communication systems, and photonic integrated circuit applications.

Spin-decoupling of vertical cavity surface-emitting lasers with complete phase modulation using on-chip integrated Jones matrix metasurfaces

Polarization response of artificially structured nano-antennas can be exploited to design innovative optical components, also dubbed “vectorial metasurfaces”, for the modulation of phase, amplitude, and polarization with subwavelength spatial resolution. Recent efforts in conceiving Jones matrix formalism led to the advancement of vectorial metasurfaces to independently manipulate any arbitrary phase function of orthogonal polarization states. Here, we are taking advantages of this formalism to design and experimentally validate the performance of CMOS compatible Jones matrix metasurfaces monolithically integrated with standard VCSELs for on-chip spin-decoupling and phase shaping. Our approach enables accessing the optical spin states of VCSELs in an ultra-compact way with previously unattainable phase controllability. By exploiting spin states as a new degree of freedom for laser wavefront engineering, our platform is capable of operating and reading-out the spin-momentum of lasers associated with injected spin carriers, which would potentially play a pivotal role for the development of emerging spin-optoelectronic devices.

Spin-orbit maximally discordant mixed states

We introduce a proposal to prepare spin-obit maximally discordant mixed states by a linear optical circuit, with quantum bits (qubits) encoded in the polarization and transverse mode degrees of freedom of photons. In particular, we discuss how to prepare non-balanced spin-orbit entangled states, applying this technique to obtain maximally discordant mixed states. We present a simulation of the optical circuit by using the Jones matrix formalism. We performed a study of entanglement, classical and quantum correlations. The results show excellent agreement with the underlying theory and open a new experimental approach for addressing quantum correlations in optical setups.

Toward an All-Optical Fingerprint of Synthetic and Natural Microplastic Fibers by Polarization-Sensitive Holographic Microscopy

Microplastic fibers from synthetic textiles have been indicated as a major source of pollution because millions of fibers are released into the environment by laundry washing. In fact, such types of microplastics usually bypass wastewater treatment processes and filters, thus reaching the oceans and other water natural reservoirs in huge quantities. Nowadays, several approaches are available for characterizing microplastics, but unfortunately, there is no unique and standard method for this aim. Among the various methodologies, several microscopy techniques such as optical microscopy (OM), scanning electron microscopy coupled with energy dispersive X-ray (SEM–EDX) analysis, or OM combined with molecular spectroscopy can be used for visual detection and measurements. Our proposal is a non-destructive method based on a digital holographic microscope in a configuration fully sensitive to the polarization of light transmitted by the fibers with a micron dimension. Our aim is to prove that the proposed approach allows for the precise characterization of synthetic and natural fibers in water. The method exploits all the advantages of digital holography such as numerical refocusing, non-invasive testing, and quantitative measurements of the complex wave field by adding access to the polarization of light that conveys meaningful information about materials. We intend to show that a unique all-optical fingerprint can be retrieved using the Jones-matrix formalism for the major classes of synthetic microfilaments used in the textile industry (i.e., polyamide 6, polyamide 6.6, polypropylene, and polyester) and for the most common natural fibers (i.e., wool and cotton) prepared according to previously developed appropriate protocols. Our results show that the proposed technology identifies new features for micron-sized fibers based on optical anisotropy through quantitative digital holography that could open future routes for automatic and all-optical identification of textile contaminants in water.

Design of broadband terahertz vector and vortex beams: II. Holographic assessment

In this paper, we demonstrate the capabilities of the terahertz pulse time-domain holography in visualisation, simulation, and assessment of broadband THz vortex beam formation dynamics upon its shaping by elements of beam converter, and further propagation and manipulation. By adding Jones matrix formalism to describe broadband optical elements, we highlight the differences in the spatio-spectral and spatio-temporal structure of the formed vortex and vector beams dependence on the modulator used and visualise their modal features. The influence of diffraction field structure from each element in the broadband vortex modulator is revealed in numerical simulation and the formed beams are analysed against the simplified Laguerre-Gaussian beam model.

Dynamic fusion of images from the visible and infrared channels of sightseeing system by complex matrix formalism

The employment of new mathematical and computer approaches for the fusion of target images from the visible and infrared channels of the sightseeing system (SSS) is one of the ways to increase the efficiency of the SSS of armored vehicles. Modern approaches to improving the efficiency of image fusion are aimed to increase the visibility of the target via improving the quality indices of fused images. This paper proposes a fundamentally new approach to image fusion, namely dynamic image fusion, at which the target is observed in the mode of a video clip composed of a sequence of stationary fused images obtained at different parameters of fusion, in contrast to traditional stationary image fusion, at which the decision is made from one fused image. Unlike stationary image fusion, aimed to increase the visibility of the target, the dynamic image fusion allows one to enhance the conspicuity of the target. The principle of dynamic image fusion proposed in this paper is based on matrix formalism, in which the fused image is constructed in the form of a complex vector function, which by its mathematical form is analogous to the Jones vector of elliptically polarized light wave, which in turn opens the possibility of matrix transformation of the complex vector of the fused image and consequently its parameterization by analogy with the Jones matrix formalism for the light wave. The article presents mathematical principles of matrix formalism, which is the basis for dynamic image fusion, gives examples of stationary and dynamic image fusion by the method of complex vector function and compares with the corresponding images, fused by algorithms of weight addition in the field of real and complex scalars. It is shown that by selecting weight coefficients, the general form of a complex amplitude vector image can be reduced to the algorithms of weight and averaged addition in the field of real scalars, weight amplitude and RMS-image in the field of complex scalar numbers, and geometric-mean image in the field of complex vectors, which, thereby, are partial cases of the general form of the complex amplitude image in the field of complex vectors.
 The animated images obtained by the method of complex vector function illustrate the increase of conspicuity of the object of observation due to the dynamic change of the fusion parameters.

Magneto-optical Kerr effect measurement in ultrafast Sagnac interferometry using the Jones matrix approach.

We report the Jones matrix formalism of the magneto-optic Kerr effect (MOKE) for ferromagnets using an ultrafast Sagnac interferometer. Compared to the time-resolved MOKE instrument, the Sagnac interferometer has the advantage of obtaining the real and imaginary parts of the differential MOKE signal as well as the differential reflectivity and the lattice displacement at the same time. In addition, a simple method to obtain the static values of Kerr rotation and ellipticity is presented.

Investigation of a polarization-based Cr:forsterite laser resonator cavity

A polarization-based laser resonator cavity with continuous variable output coupling is investigated using Cr:forsterite crystal as the gain medium. The confocal resonator cavity houses intracavity polarization optics for continuous tuning of the output coupler. The variation in the coupling efficiency is suitably explained by calculation based on Jones matrix formalism. The established resonator cavity is found to be advantageous for fine control over the cavity output energy, intracavity energy, cavity buildup time, laser pulse width, and threshold pump energy. The theoretically estimated output energy is in good agreement with the experimental results. The investigated system provides flexible optimization of the laser parameters and can be useful for all optical synchronization of multiple laser pulses as desired in many spectroscopic experiments.

Гомодинный квадратурный интерферометр перемещений. Моделирование

In this paper, based on the Jones matrix formalism, we describe the optical scheme of a single-pass homodyne displacement interferometer with a quadrature phase detection principle. The interferometer is built according to the Michelson scheme, and polarizing optical elements are used to obtain quadrature signals with a phase shift of 90°. The interferometer is supposed to be used as part of a new Russian standard of the kilogram based on watt balance for precision measurements of the displacement and speed of the coil in the vertical direction. The results of modeling the optical scheme of the interferometer are considered in order to assess the effect on the measurement accuracy of the imperfection of the polarizing elements and their alignment. An algorithm for correction of nonlinearity arising in the quadratic detection of interference signals is also considered. The results of experimental testing of a homodyne displacement interferometer with a quadrature principle of phase registration are carried out.

Research on the Methods and Algorithms Improving the Measurements Precision and Market Competitive Advantages of Fiber Optic Current Sensors.

An electromagnetic instrument transformer is a common device used to measure large current values in high-voltage electrical networks; it has been in use for more than a century. However, the optical current transformer, a promising technology also known as a fiber optic current sensor (FOCS), offers increased safety and ease of operation, as well as the absence of errors caused by the magnetic circuit of legacy transformers. Although the FOCS scheme is well known and has been actively developed for over a quarter century, it has certain disadvantages that limit its use. This paper describes the authors’ efforts to solve these problems in order to make FOCS technology competitive and widely adopted. We upgraded the FOCS optical circuit, expanded the frequency band of the captured current signal, and reduced the solution’s cost. We designed new signal processing algorithms to compensate for errors caused by internal factors in the measurement circuit, as well as those caused by environmental influences. We developed an FOCS computer model based on the Jones matrix formalism to enhance the experimental debugging. It allowed us to define the requirements for elements of the optical circuit and its production accuracy.

Tolerance analysis of non-depolarizing double-pass polarimetry

Double-pass polarimetry measures the polarization properties of a sample over a range of polar angles and all azimuths. Here, we present a tolerance analysis of all the optical elements in both the calibration and measurement procedures to predict the sensitivities of the double-pass polarimeter. The calibration procedure is described by a Mueller matrix based on the eigenvalue calibration method (ECM) [1]. Our numerical results from the calibration and measurement in the Mueller matrix description with tolerances limited by systematic and stochastic noise from specifications of commercially available hardware components are in good agreement with previous experimental observations. Furthermore, by using the orientation Zernike polynomials (OZP) which are an extension of the Jones matrix formalism, similar to the Zernike polynomials wavefront expansion, the pupil distribution of the polarization properties of non-depolarizing samples under test are expanded. Using polar angles ranging up to 25∘, we predict a sensitivity of 0.5% for diattenuation and 0.3∘ for retardance using the root mean square (RMS) of the corresponding OZP coefficients as a measure of the error. This numerical tool provides an approach for further improving the sensitivities of polarimeters via error budgeting and replacing sensitive components with those having better precision.

Generalized temporal synthesis method for a birefringent laser pulse shaper.

We propose a new method for the synthesis of arbitrary temporal output pulse profiles by using a birefringent laser pulse shaper. This shaper contains a series of N birefringent crystals placed between input and output polarizers. The synthesis method starts with the linear time-invariant system theory to determine the optimal amplitudes of the replica pulses at the output polarizer and the time delay between them, and then uses the temporal Jones matrix formalism to obtain the angle of each crystal. The design procedure is demonstrated for an eight-stage birefringent laser pulse shaper. Several examples of predefined output pulse profiles are given to show the potential of the proposed birefringent laser pulse shaper.

Photonic 60 GHz sub-bands generation with 24-tupled frequency multiplication using cascaded dual parallel polarization modulators

Abstract An energy efficient and all optical 24 tupled radio frequency multiplication is proposed to generate 60 GHz using two cascaded dual parallel polarization modulators (DPPolMs). Detailed theoretical analysis is carried out using Jones matrix formalism. ±12th order optical sidebands are obtained at the output of second DPPolM which beat at the photo-detector (PD) to produce frequency 24 tupled RF carrier. A good optical spurious suppression ratio (OSSR) of 34.4 dB is obtained for ±12th order optical sidebands and radio frequency spurious suppression ratio (RFSSR) of 25.8 dB is obtained for 24-tupled RF signal. We verify the accuracy of the analysis with simulations in OptiSystem and a close match between theory and simulation results are obtained. We showed a scheme to generate four subcarrier signals in 57–64 GHz license free band using subcarrier multiplexing with an additional polarization modulator placed after cascaded DPPolMs. 10 km single mode fiber transmission performance of the optical sidebands in 57–64 GHz sub-band shows negligible power penalty of 0.3 dB at BER 10 - 9 .

A Method to Generate Vector Beams with Adjustable Amplitude in the Focal Plane

We design and investigate an original optical component made of a c-cut uniaxial crystal and an optical system to generate cylindrical vector beams with an adjustable polarization state. The original optical component has a specific, nearly conical shape which allows it to operate like a broadband wave retarder with the fast axis oriented radially with respect to the optical axis. We show via numerical simulations, using the Debye–Wolf diffraction integral, that the focal spot changes depending on the polarization state, thus enabling the control of the focal shape. Non-symmetrical shapes can be created although the optical system and incoming beam are circularly symmetric. We explained, using Jones matrix formalism, that this phenomenon is connected with the Gouy phase difference acquired by certain modes composing the beam due to propagation to the focal plane. We present our conclusions in the context of two potential applications, namely, stimulated emission depletion (STED) microscopy and laser micromachining. The optical system can potentially be used for STED microscopy for better control of the point-spread function of the microscope and to decrease the unwanted light emitted from the surroundings of the focal point. We give an analytical expression for the shape of the original component using the aspherical lens formula for the two versions of the component: one for each potential application.

Modelling of polarised optical frequency domain reflectometry of axially twisted anisotropic optical fibres

This paper presents a mathematical model that describes the influence of defects in an anisotropic optical fibre on its polarised frequency domain reflectograms. The model relies on the Jones matrix formalism. Calculated reflectograms are presented for a uniform axial twist of an optical fibre. As input data for simulation, we use real distributed optical parameters of the fibre determined by polarised light Brillouin reflectometry.

Effect of Faraday mirror imperfections in a fiber optic current sensor dedicated to ITER

Plasma current measurements in ITER are safety-related and must therefore satisfy a very demanding specification. In this paper, the use of the Fiber Optics Current Sensor (FOCS) operating in the reflection mode with a Faraday mirror to perform plasma current measurements is analyzed. Based on the Jones matrix formalism, we performed numerical simulations to investigate the impact of the Faraday mirror detuning on the measurement accuracy. We show that the use of standard commercial components does not allow to satisfy the ITER requirements for the whole plasma current range. A simple solution to the problem is proposed, which consists in taking into account a mirror calibration in the current estimator. We show that the achievable mirror calibration accuracy is sufficient to fulfill the ITER requirements.

Geometrical-phase lens based optical system for the spin-splitting of vector beams

In this work, we present a new optical lens system based on a polarization directed flat lens (geometric phase lens) designed to provide circular polarization split focusing in two real foci located at two different axial planes. We find the conditions to obtain two real back focal planes of the system, and the same focal length of opposite sign. In this situation, the system acts as a bifocal SAM split system with equal scale for both real foci. We experimentally demonstrate the optical spin dependent dual focus effect of the system. Then, we illuminate the system with vortex and vector beams generated by a q-plate and provide theoretical explanation within the Jones matrix formalism for the different orbital angular momentum (OAM) and spin angular momentum (SAM) states experimentally observed at the two focal planes. Finally, we show the interference of the two split focused components of the vector beam at the intermediate plane between the two focal planes. The resulting spiral interference pattern indicates the sign and value of the vector beam's topological charge. It can also be used to identify the vector beam of a given charge by the shift on the interference fringes. Therefore, the optical system can be useful as a new tool for analyzing OAM and SAM beams.

Optical constants modelling in silicon nitride membrane transiently excited by EUV radiation.

We hereby report on a set of transient optical reflectivity and transmissivity measurements performed on silicon nitride thin membranes excited by extreme ultraviolet (EUV) radiation from a free electron laser (FEL). Experimental data were acquired as a function of the membrane thickness, FEL fluence and probe polarization. The time dependence of the refractive index, retrieved using Jones matrix formalism, encodes the dynamics of electron and lattice excitation following the FEL interaction. The observed dynamics are interpreted in the framework of a two temperature model, which permits to extract the relevant time scales and magnitudes of the processes. We also found that in order to explain the experimental data thermo-optical effects and inter-band filling must be phenomenologically added to the model.

Spectral performance of a zero-order liquid-crystal polymer commercial q-plate for the generation of vector beams at different wavelengths

Liquid-crystal polymer q-plates are commercial devices for generating vector beams at the design wavelength where the device exhibits half-wave (HW) retardance. Since they are not voltage addressable, the operational wavelength remains fixed. In this work we perform a broadband spectral characterization of the q-plate retardance as a function of wavelength, ϕ(λ), and identify the wavelengths with retardance values relevant for vector beam generation (π, π/2, and 3π/2). The wavelength is then used as a tuning parameter to change the device performance from a HW q-plate to a positive-QW or a negative-QW q-plate. These performances are analyzed using the Jones matrix formalism. We present a simple procedure to derive the polarization distribution of the vector beams expected at these QW wavelengths, as a superposition of the input polarization state and the output state of a HW q-plate. Experimental results using the red and blue lines of an Ar-Kr laser and an IR laser diode of 980 nm confirm the theoretical predictions. We show that for input linearly polarized light of 980 nm and 488 nm the device generates hybrid vector beams (where the ellipticity varies with the azimuthal angle), while for 647 nm pure radial vector beams with constant ellipticity are obtained. These results could extend the use of commercial q-plates for multicolour vector beam applications.