Symmetric Optical Systems Research Articles

Symmetric optical multipass matrix systems and the general rapid design methodology

We proposed an original type of multipass cell named symmetric optical multipass matrix system (SMMS), in which the same matrix patterns of various sizes can be formed on both sides. According to its special symmetric configurations, the SMMS design problem is modeled as a variant of the classical traveling salesman problem, which can be rapidly solved by evolutionary optimization algorithms. Two sets of 3-mirror SMMSs are designed, analyzed and built, which show superior characteristics of high stability, desirable beam quality and adjustable optical path lengths. Additionally, they can support simultaneous detection of multiple species with multi-laser channels. The proposed method is further extended to design a 4-mirror SMMS, which verifies the universality and robustness of the design methodology. The experimental observations are in consistent with the theoretical calculations. The newly proposed SMMSs have a broad application prospect in trace gas measurement.

Light induced self-assembly of one-dimensional PT-symmetric optical system exhibiting pulling force.

Light induced self-assembly's non-contact and non-invasive nature, along with its versatility and dynamic assembly capabilities, make it particularly well-suited for the self-organization of particles. Previous self-assembly configurations are either in a static equilibrium state or in a dynamic equilibrium state driven by a pushing force. In this study, we introduce a one-dimensional parity-time symmetric (PT-symmetric) multilayer optical system consisting of balanced gain and loss, enabling the generation of a total pulling force on the structure. By conducting molecular dynamics simulations, we achieve the self-organized structure exhibiting pulling force. Furthermore, by reversing the direction of the incident light, we realized pushing force induced binding. The stability of the bound structure is also analyzed using linear stability analysis. Additionally, the light induced self-assembly exhibiting pulling and pushing force is achieved in the one-dimensional multilayer system with unbalanced gain and loss. This work provides an additional degree of freedom in the self-organization of particles.

Wavefront aberration determination in non-axially symmetrical optical systems.

Non-axially symmetrical optical systems can provide better solutions to several optical design problems. However, determining their wavefront aberrations is challenging due to the great diversity of their configurations. Accordingly, in the present study, the optical path length (OPL) between two boundaries in a non-axially symmetrical system is expanded by a Taylor series expansion with respect to the base ray. This expansion converts the OPL from a deep composite function to a polynomial form. The various order wavefront aberrations are then obtained from the coefficients of the polynomials in terms of the system independent variables. The proposed method is equally valid for axially symmetrical systems provided that the object is placed on the meridional plane. Overall, the method provides a systematic approach for analyzing the wavefront aberrations in a wide range of optical systems.

Study and validation of a fast ray tracing method to determine density flux for symmetric solar optical systems

In this research paper, a computational program called MCMRDF-3D, is developed and validated by comparison with a reference software. MCMRDF-3D is formulated on Multi-Ray Monte Carlo Method for the determination of the distribution of solar irradiation along the receiver of any solar- concentrating system that withstand translational or rotational symmetries. This code incorporate an advantageous approach that consist in estimating the overall distribution of irradiation of a large scale solar concentrating systems on the basis of a consistent sample, then saving computation time, processor capacity and storage memory. The paper presents the new approach and applied it to determine the distribution of irradiation provided by three concentrators. We compare the processing time, the irradiation map rendering, and the size of numeric data, to those provided by a Reference software. The obtained irradiation distribution and power harvesting quantities over the receiver matches very well. We conclude that MCMRDF-3D proves to easy, fast, accurate and reliable approach for the simulation of solar concentrator system. Among other implications, this work opens a path for saving time when studying numerous symmetrical imaged and non-imaged optical systems. For future work, this time saving and flexible program will be of a significant help to envision optical errors from real behavior of optical surface in concentrating systems.

Remote focusing optical tweezers for 3D imaging.

We present a remote focusing optical tweezer utilizing a 4f symmetrical optical system to compensate the high-order aberration during annular light refocusing. The position of the optical trap can be adjusted beyond the range of one hundred micrometers in the axial direction by means of tuning the position of the mirror placed in the focal region of the illumination objective lens. This optical tweezer can be combined with a sectioning microscope to realize three-dimensional (3D) imaging, e.g., a confocal microscope using a single water immersion objective lens. All optical elements are placed in one side of the sample, which is very useful for application in fields such as radiation biology, where radiation or magnetism disturbance must be introduced on the other side of the sample. In the experiment, a 10 µm diameter silicon dioxide microsphere and pollen cells immersed in the water are translated along the axis using the optical tweezer and, meanwhile, the sectioning images are obtained using the confocal microscope.

Singular optical propagation properties of two types of one-dimensional anti- PT -symmetric periodic ring optical waveguide networks

Two types of one-dimensional (1D) anti- PT -symmetric periodic ring optical waveguide networks, consisting of gain and loss materials, are constructed. The singular optical propagation properties of these networks are investigated. The results show that the system composed of gain materials exhibits characteristics of ultra-strong transmission and bidirectional reflection. Conversely, the system composed of loss materials demonstrates equal transmittance and reflectance at some frequencies. In both the systems, a new type of total reflection phenomenon is observed. When the imaginary part of the refractive indices of waveguide segments is smaller than 10−5, the system shows bidirectional transparency with the transmittance tending to be 1 and reflectivity to be smaller than 10−8 at some bands. When the refractive indices of the waveguide segments are real, the system will be bidirectional transparent at the full band. These findings may deepen the understanding of anti- PT -symmetric optical systems and optical waveguide networks, and possess potential applications in efficient optical energy storage, ultra-sensitive optical filters, ultra-sensitive all-optical switches, integrated optical chips, stealth physics, and so on.

Sigma vector calculations in nodal aberration theory and experimental validation using a Cassegrain telescope

Nodal Aberration Theory (NAT) was developed to explain the field dependency of aberration field centers in the image plane of nominally rotationally symmetric optical systems that have lost their symmetry through misalignments. A new insight into the theory led to calculating the sigma vectors, which locate the aberration field centers, using the angle between a real-ray trace of the optical axis ray (OAR) and the normal of the local surface where “local” refers to the object and image optical spaces of that surface. Here, we detail the sigma vector calculations for general optical systems and provide an experimental investigation of a misaligned system with a high-precision customized Cassegrain telescope. In the simulations, a Newtonian telescope, a Cassegrain telescope, and a three-mirror anastigmat telescope were misaligned intentionally in ray-tracing software. The sigma vectors were calculated analytically for the third-order aberrations of astigmatism and coma. Experimentally, the same perturbations were implemented for the Cassegrain telescope system, and the aberrations were quantified through interferometric measurements on a grid of field points in the image plane that verified the analytical derivation and simulations.

Simplified analysis and suppression of polarization aberration in planar symmetric optical systems.

Polarized remote sensing imaging has attracted more attention in recent years due to its wider detection information dimension compared to traditional imaging methods. However, the inherent instrument errors in optical systems can lead to errors in the polarization state of the incident and outgoing light, which is the polarization aberration of the optical system, resulting in a decrease in polarization detection accuracy. We propose a polarization aberration simplification calculation method for planar symmetric optical systems, by what only three ray samples are needed to obtain the distribution of polarization aberrations within the pupil. This method has a calculation accuracy close to traditional methods, and the sampling rate is 0.003 times that of traditional methods. Based on this, we designed a merit function that optimizes both wavefront and polarization aberrations simultaneously. It is found that diattenuation and retardance of the optical system are 62% and 58% of the original, and the polarization crosstalk term is reduced by 37% when the polarization weight factor takes an appropriate value. And at the same time, the wavefront aberration has also been well optimized.

Generation of an ultrashort pulse train through ultrafast parity-time symmetry switching.

We propose a scheme for the direct generation of an ultrashort pulse train as well as the further compression of pulsed lasers based on the nonlinearity inherent to parity-time (PT) symmetric optical systems. Implementation of optical parametric amplification in a directional coupler of χ(2) waveguides enables ultrafast gain switching through pump-controlled breaking of PT symmetry. We theoretically demonstrate that pumping such a PT symmetric optical system with a periodically amplitude-modulated laser enables periodic gain switching, which can directly convert a continuous-wave signal laser into a train of ultrashort pulses. We further demonstrate that by engineering the PT symmetry threshold, an apodized gain switching that enables the production of ultrashort pulses without side lobes. This work suggests a new approach for exploring the non-linearity inherent to various PT symmetric optical structures to extend optical manipulation capabilities.

Transverse ray aberrations determination innon-axially symmetrical optical imaging systemsusing Taylor series expansion.

Non-axially symmetrical optical systems can provide better solutions to several optical design problems. However, the determination of their aberrations is a challenge due to the great diversity of their configurations. To address this problem, this study extends previous work by the present group to determine the transverse ray aberrations in non-axially symmetrical optical imaging systems through the use of a Taylor series expansion. The expansion converts the coordinates of the incident point, which are highly composite functions, of a general ray on the image plane into polynomial functions. The various order transverse ray aberrations are then extracted directly from the corresponding terms of the polynomials. Notably, the derived expressions are exact since they are determined without any approximations. Furthermore, the proposed method can be equally applied to axially symmetrical systems provided that the object is confined on the meridional plane. Consequently, the proposed method offers a useful and generally applicable approach for the systematic analysis of the transverse ray aberrations in optical systems with the object at either finite or infinite positions.

Universal Subdiffusive Behavior at Band Edges from Transfer Matrix Exceptional Points.

We discover a deep connection between parity-time symmetric optical systems and quantum transport in one-dimensional fermionic chains in a two-terminal open system setting. The spectrum of one dimensional tight-binding chain with periodic on-site potential can be obtained by casting the problem in terms of 2×2 transfer matrices. We find that these non-Hermitian matrices have a symmetry exactly analogous to the parity-time symmetry of balanced-gain-loss optical systems, and hence show analogous transitions across exceptional points. We show that the exceptional points of the transfer matrix of a unit cell correspond to the band edges of the spectrum. When connected to two zero temperature baths at two ends, this consequently leads to subdiffusive scaling of conductance with system size, with an exponent 2, if the chemical potential of the baths are equal to the band edges. We further demonstrate the existence of a dissipative quantum phase transition as the chemical potential is tuned across any band edge. Remarkably, this feature is analogous to transition across a mobility edge in quasiperiodic systems. This behavior is universal, irrespective of the details of the periodic potential and the number of bands of the underlying lattice. It, however, has no analog in absence of the baths.

Dual polarization Fourier transform processor using geometric-phase lenses.

This work presents a novel optical system for polarization image processing using geometric-phase (Pancharatnam-Berry) lenses. Such lenses are half-wave plates where the orientation of the fast (slow) axis follows a quadratic relation with the radial coordinate, and they present the same focal length but opposite sign for left and right circular polarizations. Therefore, they split an input collimated beam in a converging beam and a diverging beam with opposite circular polarizations. This coaxial polarization selectivity introduces a new degree of freedom in optical processing systems and makes it interesting for imaging and filtering applications that require polarization sensitivity. Here we profit from these properties to build an optical Fourier filter system with polarization sensitivity. A telescopic system is used to have access to two real Fourier transform planes, one for each circular polarization. A second symmetric optical system is used to recombine the two beams onto a single final image. As a result, polarization sensitive optical Fourier filtering can be applied, as demonstrated with simple bandpass filters.

Peak-to-Average Ratio Suppression Algorithm for Non-Hermitian Symmetric Optical OFDM System Based on GA-PTS

Peak-to-Average Ratio Suppression Algorithm for Non-Hermitian Symmetric Optical OFDM System Based on GA-PTS

Realization of Bound States in the Continuum in Anti‐PT‐Symmetric Optical Systems: A Proposal and Analysis

AbstractNovel physical concepts that originate from quantum mechanics, such as non‐Hermitian systems (dealing mostly with PT and anti‐PT symmetry) and bound states in the continuum (BICs), have attracted great interest in the optics and photonics community. To date, BICs and anti‐PT symmetry seem to be two independent topics. Here, a parallel cascaded‐resonator system is proposed for the first time to achieve BICs and anti‐PT symmetry simultaneously. It is found that the requirements for the Fabry–Pérot BIC and anti‐PT symmetry can both be satisfied when the phase shift between any two adjacent resonators is an integer multiple of π. The cascaded‐resonator systems consisting of different numbers of resonators are further analyzed and their robustness to fabrication imperfections is demonstrated. The proposed structure can readily be realized on an integrated photonic platform, and can enable many applications that benefit from the advantages of both BICs and anti‐PT symmetry, such as optical delay and storage, all‐optical nonlinear processing, high‐sensitivity sensing, and chiral mode switching.

Comprehensive study of singular points in a PT-symmetric Thue-Morse multilayer

Parity-time symmetric optical systems have a non-Hermitian Hamiltonian with a purely real spectrum. These systems have been extensively explored owing to their ability to generate exotic photon transport phenomena. In this work, we report the spectral singularity of the one-dimensional aperiodic odd-generation Thue-Morse photonic lattice with parity time symmetry. We showed that this multilayer in addition to obvious unidirectional and bidirectional transparencies, displays interesting and singular properties including absorption, lasing and coherent perfect absorption-lasing singularities. Based on the transfer matrix and scattering matrix (S matrix) methods, the behavior of these singular points and reflectionless and invisibility properties of the structure is analyzed with respect to the thickness of the passive film sandwiched between active layers due to phase shift changes, frequency and incident angle of light. The available values of the structural parameters are investigated to obtain extraordinary transmission and reflection phenomena. These optical systems may possess the potential in the design of novel lasing and coherent perfect absorption optical devices with adjustable applications.

Alternative computation of the Seidel aberration coefficients using the Lie algebraic method.

We give a brief introduction to Hamiltonian optics and Lie algebraic methods. We use these methods to describe the operators governing light propagation, refraction, and reflection in phase space. The method offers a systematic way to find aberration coefficients of any order for arbitrary rotationally symmetric optical systems. The coefficients from the Lie method are linked to the Seidel aberration coefficients. Furthermore, the property of summing individual surface contributions is preserved by the Lie algebraic theory. Two examples are given to validate the proposed methodology with good results.

Multifocal wavefronts with prescribed caustics in axially symmetric optical systems

Multifocal and/or extended depth-of-focus designs are widely used in many optical applications. In most of them, the optical configuration has axial symmetry. A usual design strategy consists of exploring the optimal wavefronts that emerging out of the optical system would provide the desired multifocal properties. Those properties are closely related to light concentration on caustic surfaces. We present a systematic analysis of how to obtain those multifocal wavefronts given some prescriptions on the locations of caustics. In particular, we derive several multifocal wavefronts under archetypical prescriptions in the sagittal caustic alone, or combined with the tangential one at certain points, with some emphasis on visual optics applications.

Primary aberration optimization for double-plane symmetric beam shaping systems using a pair of curved reference surfaces.

The geometric aberration of centered refracting double-plane symmetric optical systems (DPSOS) is investigated. For DPSOS with different defocus values in the tangential plane and the sagittal plane (astigmatic wavefront), a pair of curved reference surfaces which vanishes the quadratic terms of the optical path difference (OPD) between a general ray and a reference ray are deduced. With the curved reference surfaces, the primary (fourth-order) wave aberration function for DPSOS is calculated and analyzed, which can be used for beam shaping designs with astigmatic input wavefront, such as slab lasers and semiconductor lasers. Further, the proposed curved reference surfaces can be applied to analyze the aberrations of general DPSOS.

Analysis of polarization characteristics of freeform surface optical system

Freeform surfaces are widely used in off-axis optical systems with large aperture, large field of view, and long focal length. The polarization effect caused by the non-rotationally symmetrical shape has an impact on the system’s polarization imaging quality and measurement accuracy. Based on Jones’ notation, this paper proposes a polarization aberration analysis method for fringed Zernike polynomial freeform optical systems and constructs a full-field polarisation aberration analysis model of non-rotationally symmetric freeform reflective optical systems. The light propagation vector k is added on the basis of the two-dimensional ray tracing algorithm. By tracing the full-field polarized light of the off-axis optical system in the field of view, the Jones pupil diagram is obtained. The phase aberration, diattenuation and retardance are separated by Pauli decomposition and SVD decomposition. The off-axis freeform surface optical system is designed. The analysis results show that the phase aberration of the off-axis freeform surface optical system is directly related to the surface shape of the freeform surface. The changes of the freeform surface to the diattenuation and retardance are both 56% of the diattenuation and retardance of the sistem. For deep-space telescopes and lithography systems, it is of great significance for improving system accuracy to master this change.

Singular characteristics of one-dimensional Fibonacci optical waveguide networks composed of PT-symmetric elements

In this paper, the singular optical properties of the interesting one-dimensional (1D) Fibonacci optical waveguide networks composed of parity-time-symmetric ( PT -symmetric) elements (FCOWNCPTSEs) are studied. It is found that there are three types of systematic phases defined by the modulus of the eigenvalues of the scattering matrix, eleven types of unidirectional transparency, and an approximate bidirectional transparency in the FCOWNCPTSEs, which have not been reported in PT -symmetric periodic optical systems and aperiodic Thue–Morse multilayers composed of PT -symmetric elements. It can be seen that the types of systematic phases and transparencies in FCOWNCPTSEs are more abundant than those of periodic systems and Thue–Morse systems. It further shows that with the decrease of symmetry the properties of the optical systems composed of PT -symmetric elements will be more abundant, which deepens people’s understanding of the relationship between symmetries and optical properties. In addition, we also find three sets of interesting Fibonacci numbers in transmitted and reflected spectra and an interesting quasiconstant in scattering spectra. Our results may be useful for the designing of novel structures with singular optical properties, e.g., invisible cloak and stealth aircraft, etc.