Polarization analysis for laser optical system

This paper presents a theoretical and experimental comparison of two techniques of optical fiber current sensors (OFCS) based on the Faraday Effect: the power and the degree of polarization (DOP) methods. The DOP method is shown to be insensitive to state of polarization (SOP) changes induced by environmental conditions. A maximum variation of 0.4% in the DOP value in the entire range of applied current from 0 to 100 A was measured. It is the first time to our knowledge that this fact was experimentally verified. Also, for the first time known it is reported that zero current response, DOP = 0.996, is in agreement with the theoretical expected value of unitary DOP. Besides, the theoretical and experimental normalized DOP is shown to have a maximum difference of 0.33% in the entire range of applied current. On the other hand, the power method OFCS is greatly affected by SOP changes. In order to be used in a practical application, its complexity must be increased by the use, for example, of polarization maintaining fibers instead of standard fibers used in the DOP method, increasing the cost of the sensor element.

In this chapter, we consider the imaging properties of a system with a circular exit pupil by applying the general formulas derived in Chapter 1. We derive expressions for its point-spread function (PSF), optical transfer function (OTF), and encircled, ensquared, and excluded powers. The effect of aberrations on a PSF is first studied in terms of its central value, i.e., its Strehl ratio. An exact expression is obtained for the Strehl ratio and the results for primary aberrations are compared with those obtained from the approximate expressions based on the phase variance of the aberration across the pupil derived in Chapter 1. The tolerances for primary aberrations are given for a certain value of the Strehl ratio. Balanced primary aberrations are also discussed and they are identified with the Zernike circle polynomials. A defocused PSF is considered next, and it is shown that systems with large Fresnel numbers, such as photographic systems, have a very small depth of focus. However, systems with small Fresnel numbers, e.g., a laser transmitter, have a large depth of focus. Focused and collimated beams are discussed, and the concept of near- and far-field distances is introduced. It is shown that if the Fresnel number of the beam focused on a target is small, the axial irradiance is maximum at a point that is closer to the focusing optics. However, maximum central irradiance on a target at a given distance is obtained when a beam is focused on it, even though a larger irradiance is obtained at a closer point. Aberrated PSFs for rotationally symmetric aberrations are considered, and numerical results are obtained that show that the size of their central spot is practically independent of the aberration. Symmetry properties of the aberrated PSFs are considered next. Full PSFs for primary aberrations are shown graphically and pictorially. A brief comparison of the diffraction and geometrical PSFs is also given. The line of sight of an optical system is identified with the centroid of its PSF and discussed for aberrated systems. It is shown that only coma-type aberrations change the line of sight. The OTFs for primary aberrations are discussed, and the concept of contrast reversal is described. The OTF aberrated by coma is complex, and we give its real and imaginary parts as well as its modulus and phase. Aberration tolerances are given for a certain value of the Hopkins ratio. The geometrical OTF is also discussed and approximate expressions for it are obtained for the primary aberrations. It gives reasonably accurate results in the region of very low spatial frequencies, a region of practical interest when the MTF of an aberrated system at high frequencies is practically negligible. It is shown that the MTF averaged over all angular orientations of a spatial frequency vector is maximum when the standard deviation of the ray aberration [i.e., the root mean square (rms) radius of the spot diagram with respect to its centroid] is minimum. The diffraction OTF is shown to approach the geometrical OTF in the limit of zero wavelength. The differences between the diffraction and geometrical OTFs are summarized. The incoherent line- and edge-spread functions are discussed, and numerical results for both the aberration-free and the aberrated systems are given. The aberration tolerances for a certain value of the Struve ratio are also given.

The point spread function (PSF) of an optical system is a function of both the amplitude and phase of the electric field in the exit pupil. Interferometric testing of optics yields information regarding variations in phase, but not in amplitude. Typically the PSF, encircled energy function (EEF) and Strehl ratio are calculated from the phase information alone, implicitly assuming that the amplitude is uniform across the pupil. For incoherent, unvignetted imaging systems this assumption is generally valid. Coherent optical systems are a different case due to the Gaussian irradiance profile of lasers. The optics in such systems are non-uniformly illuminated, the amplitude function in the pupil being characterized by a Gaussian or truncated Gaussian profile. This effect of apodization is examined for aberrated and unaberrated beams. Analytic forms and numerical results are presented, as are measurements of laser diode based optical systems. In general, little effect from apodization is seen on parameters which are typically of interest (e.g., Strehl, FWHM of PSF, 80% encircled energy) except for cases of pupil irradiance decrease of greater than half from center to edge.

Cat’s eye lens make the laser beam retro-reflected exactly to the opposite direction of the incidence beam, called cat’s eye effect, which makes rapid acquiring, tracking and pointing of free space optical communication possible. Study the influence of cat’s eye effect to cat’s eye retro-reflector at large incidence angle is useful. This paper analyzed the process of how the incidence angle and focal shit affect effective receiving area, retro-reflected beam divergence angle, central deviation of cat’s eye retro-reflector at large incidence angle and cat’s eye effect factor using geometrical optics method, and presented the analytic expressions. Finally, numerical simulation was done to prove the correction of the study. The result shows that the efficiency receiving area of cat’s eye retro-reflector is mainly affected by incidence angle when the focal shift is positive, and it decreases rapidly when the incidence angle increases; the retro-reflected beam divergence and central deviation is mainly affected by focal shift, and within the effective receiving area, the central deviation is smaller than beam divergence in most time, which means the incidence beam can be received and retro-reflected to the other terminal in most time. The cat’s eye effect factor gain is affected by both incidence angle and focal shift.

In order to deeply analyze the application prospect of the boundary layer suction technique on the compressor, the flow control effect of endwall suction scheme on the tip leakage flow of a compressor cascade at a large incidence angle with complex internal flow structure and different loss proportion from the case at design incidence angle, was studied numerically, as well as on the overall aerodynamic performance. The results show that the suction scheme directly affects the structure of the tip leakage flow and makes the onset position of the tip leakage vortex move backward, which weakens the intensity and influence range of the tip leakage flow, thus improving the cascade performance in the tip region. At the large incidence angle, large flow suction makes the boundary layer separation in the low span area advance, and the corner separation region at the gap-free end expands to the upper. The position of the separation vortex shedding rises from 10% blade span under the condition without suction to about 70% blade span under the condition with the suction flow rate of 0.7%, and the separation loss increases. The overall performance of the cascade at the large incidence angle mainly depends on the increase of separation loss, while the effect of the decrease of leakage loss on it is greatly reduced. With suction, the total pressure loss coefficient of the cascade increases by about 5.7% at the incidence angle of +8°.

Forecasting state of polarization (SOP) in aerial fibers poses several challenges due to exposure to dynamic und unpredictable environmental factors, such as wind-induced vibrations, leading to multi-timescale SOP variations. Traditional statistical and deterministic approaches may struggle to accurately model the complex, nonlinear, and multi-scale dynamics of these SOP fluctuations, making them less effective for real-world scenarios. To address these challenges, this study proposes a weather-adaptive forecasting framework combining discrete wavelet transform and artificial neural networks to predict SOP changes across varying timescales. By integrating environmental data, the model effectively captures rapid fluctuations and gradual drifts, significantly improving forecasting accuracy. Validation using field data across two locations demonstrates the model's reliability for both short-term and long-term predictions. Including environmental factors namely wind speed, temperature, and humidity improves long-term forecasting accuracy by over 64.5% compared to models taking as input SOP change data alone. Wind gusts enhance short-term forecasting under extremely windy conditions. Our proposed framework outperforms conventional techniques, offering a reliable framework for SOP change prediction and advancing proactive optical system monitoring.

To evaluate clinical retinal optical image quality following implantation of an extended depth of focus intraocular lens (EDOF IOL) (Vivity; Alcon Laboratories, Inc), and to compare it with a monofocal and a trifocal IOL. This prospective, comparative, case-control study included 88 eyes implanted with: (1) 19 monofocal IOLs (AcrySof SA60AT; Alcon Laboratories, Inc); (2) 38 EDOF IOLs (AcrySof IQ Vivity); and (3) 31 trifocal IOLs (AT LISA tri 839MP; Carl Zeiss Meditec AG). Total root mean square, ocular lower (LOA) and higher (HOA) order aberrations, point spread function (PSF) Strehl ratio (PSF with LOA), and PSF Strehl ratio excluding LOA (PSF without LOA) were analyzed using a Pyramidal WaveFront-based sensor aberrometer Osiris (Costruzione Strumenti Oftalmici) at two different pupil sizes (3 and 4 mm). The trifocal IOL showed the highest PSF without LOA at both pupil sizes (0.52 ± 0.12 and 0.31 ± 0.07, respectively), followed by the AcrySof SA60AT (0.39 ± 0.10 and 0.27 ± 0.07) and AcrySof IQ Vivity (0.34 ± 0.11 and 0.24 ± 0.09) (P < .001). The AcrySof IQ Vivity and monofocal IOLs were comparable (P > .05). Despite the comparable postoperative low spherical equivalent among the IOL groups, the AT LISA tri 839MP retinal image quality (PSF with LOA) was the most severely affected by such residual refractive errors (dropped to 0.26 ± 0.06 at 3 mm; P < .001) compared to the monofocal AcrySof SA60AT (0.24 ± 0.07 at 3 mm) and EDOF Acrysof IQ Vivity (0.23 ± 0.06 at 3 mm) groups. The PSF with LOA was comparable (P > .05) among the three groups at both the 3-and 4-mm pupil size. Although trifocal IOLs provided significantly better retinal image quality if influence of LOA is excluded, they also demonstrated to be the most sensitive to residual refractive errors. Both the EDOF Acrysof IQ Vivity and mono-focal AcrySof SA60AT IOLs showed a comparable retinal image quality, and they are also comparable with trifocal IOLs when considering the clinically real PSF (PSF with LOA). [J Refract Surg. 2023;39(2):103-110.].

Heretofore, eye modelling is based on the emmetropic eye taking its ocular optical components value from the population-based studies. Howbeit, the effect of aberration of myopic refractive error by modelling the eye using the parameters from ocular biometrics and ray tracing method has not been systematically studied. An objective of this study was to determine the point spread function (PSF) of myopic refractive error using eye modelling and ray tracing technique. Three eye models had been successfully modelled in Zemax software, scilicet, emmetropic Liou and Brennan, myopic Liou and Brennan, and corrected myopic Liou and Brennan. The optical performance of the eye models was analysed using PSF, whereby the PSF is presented in the form of Strehl ratio. A comparison of the two results reveals the Strehl ratio value for myopic Liou and Brennan eye was the lowest compared to its emmetropic model. Further analysis shows that the Strehl ratio of the corrected myopic Liou and Brennan model was higher compared to the uncorrected myopic model. Natheless, the corrected myopic model produced lower Strehl ratio value compared with the emmetropic model of Liou and Brennan. From this research, the accuracy of the Strehl ratios for myopia correction and emmetropia were calculated. It has shown that the accuracy of the Strehl ratio value for corrected myopia was lower.

Accurate astrometry and photometry of saturated and coronagraphic point spread functions (PSFs) are fundamental to both ground- and space-based high contrast imaging projects. For ground-based adaptive optics imaging, differential atmospheric refraction and flexure introduce a small drift of the PSF with time, and seeing and sky transmission variations modify the PSF flux distribution. For space-based imaging, vibrations, thermal fluctuations and pointing jitters can modify the PSF core position and flux. These effects need to be corrected to properly combine the images and obtain optimal signal-to-noise ratios, accurate relative astrometry and photometry of detected objects as well as precise detection limits. Usually, one can easily correct for these effects by using the PSF core, but this is impossible when high dynamic range observing techniques are used, like coronagrahy with a non-transmissive occulting mask, or if the stellar PSF core is saturated. We present a new technique that can solve these issues by using off-axis satellite PSFs produced by a periodic amplitude or phase mask conjugated to a pupil plane. It will be shown that these satellite PSFs track precisely the PSF position, its Strehl ratio and its intensity and can thus be used to register and to flux normalize the PSF. A laboratory experiment is also presented to validate the theory. This approach can be easily implemented in existing adaptive optics instruments and should be considered for future extreme adaptive optics coronagraph instruments and in high-contrast imaging space observatories.

All-fiber current transformers, with their outstanding advantages of high safety, electromagnetic interference immunity, and wide frequency response range, have been widely applied in DC current measurement. The measurement performance of all-fiber current transformers is affected by polarization state changes in optical components. This paper proposes a quaternion-based polarization optical modeling method, establishing physical models for lasers, polarizers, couplers, modulators, polarization-maintaining fibers, sensing fibers, and waveplates. We investigate various polarization effects induced by temperature variations and quantitatively analyze how different polarization state changes impact measurement errors, providing an effective evaluation method for assessing temperature-induced effects on the measurement performance of all-fiber current transformers. Research results show that within the temperature range of -40° C to 70° C, measurement errors caused by the Faraday effect and circular birefringence variations are less than 0.1%, while errors caused by residual linear birefringence and beat length variations of linear birefringence exceed 1%.

We describe the passive Q-switching regime of a neodymium laser that contains a Cr4+:YAG saturable absorber inside the cavity. Two configurations of the laser cavity are modeled: the cavity containing a partial polarizer as an additional unit and the microchip laser cavity in which the functions of an active element and saturable absorber are combined in a single piece of a Nd3+:YAG/Cr4+:YAG crystal with reflecting facets. It is shown that both lasers are able to generate a giant pulse with a changing state of polarization. Both the kinetics of the state of polarization of the pulse and its impact on second-harmonic generation are treated numerically. We find that the up-conversion efficiency can be enhanced and that harmonic-pulse compression can be obtained by means of the proper orientations of the intracavity polarizing elements, for the first configuration, or by choosing the polarization of the longitudinal pump and angular orientation of the doubling crystal, for the second one. The ability of the doubling crystal to analyze the state of polarization of pulses with nonlinearly changing polarization is discussed.

In many practical applications, dielectric electromagnetic (EM) windows are usually under large-angle incidence of EM waves rather than normal incidence. To guarantee normal operation of devices inside, high transmission must be maintained under large incident angles, especially for TE-polarized waves. In this work, we propose a method of achieving broadband transmission of TE-polarized waves under large incident angles by embedding meta-atoms within dielectric plates. To this end, long metallic wires and S-shaped structures are embedded in the original dielectric plate, the former of which will dilute the effective permittivity due to plasma oscillation and the latter will increase the effective permeability due to induced strong current loops under large incident angles. In this way, two consecutive transmission peaks can be generated, forming a broad transmission band under large incident angles. A proof-of-principle Ku-band prototype was designed, fabricated, and measured to verify this strategy. Both simulated and measured results show that the prototype can operate in the whole Ku-band under incident angle [60°, 85°] for TE-polarized waves, with significantly enhanced transmission. This work provides an effective method of enhancing large-angle transmission of EM waves and may find applications in radar, communications and others.

Monitoring of optical signal polarization state in optical fiber networks can provide a variety of information for infrastructure owners. There is a rather limited choice of available techniques for monitoring the change in a polarization state of an optical signal over the transmission line. Mostly, as the typical measurement, the total optical line polarization mode dispersion (PMD) is determined, or the instantaneous change in polarization state at the line input or output is measured. But that does not allow determining the location and cause of sudden polarization changes in an optical fiber. The authors propose a polarization monitoring technique using a traditional commercially-used optical time-domain reflectometer (OTDR) with additional circuitry to generate polarization-dependent measurement traces. Such a technique can potentially be used for continuously tracking a physical impact on an optical fiber link.

SUMMARY This paper presents a numerical simulation of the effects of an underground ridge (UGR) on seismically-induced ground motion characteristics using 2.5-D modelling with variable grid size. The responses of models with and without an UGR, estimated group velocity of later arrivals, horizontal differential ground motion, snapshots and spectral analysis of surface waves have confirmed high frequency surface wave generation near the ridge. Exponential decay of surface wave amplitude with depth was obtained in the vertical component but not in the radial and transverse components. Changes of focal mechanism parameters mainly affected the amplitude but not the spectral shape or bandwidth of UGR-induced surface waves. We predict that anomalous macroseismic intensity due to UGR-induced surface waves might arise in a zone of width of about 2.2 km parallel to a ridge and at a distance of about 0.5 km from the ridge edge, for the model geometry and the soil parameters considered. The UGR-induced surface waves were observed even when a UGR was overlain by a soil deposit. Increased depth or changes in the slope of the flanks of the UGR causes decrease of spectral amplitudes but does not affect the spectral shape, bandwidth or dominant frequency of induced surface waves. The dominant frequency of Rayleigh waves appeared to be twice that the fundamental frequency ( f 0) of first soft soil layer. For Love waves, the dominant frequency was twice that of f 0 for f 0 ≤ 0.63 Hz and was more than twice f 0, when f 0 > 0.63 Hz. The lower cut-off frequency for surface wave generation was approximately f 0. Only spectral amplitudes were affected by a change of S-wave velocity in first soil layer but not the spectral bandwidth, spectral shape or dominant frequency when f 0 was maintained constant. An increase of spectral bandwidth with decrease of f 0 of the first soil layer was found. We obtained a decrease of surface wave amplitude in accordance with the decrease of amplitude of body waves with angle of incidence. The amplitude of surface waves on the side of incidence of body waves was more than the opposite side. Further, it was inferred that dominant frequency and spectral bandwidth were unaffected but spectral shape was highly dependent on the angle of incidence of body waves. The simulations revealed that UGR effects deserve particular attention for earthquake-resistant design and seismic microzonation.

We find for the first time that polarization mismatch of the sample and reference arms in optical-fiber-based optical coherence tomography (OCT) has critical effect on its depth resolution when the light source is partially polarized. When the polarization states of the two arms are matched, the measured point spread function (PSF) is almost identical to the theoretical prediction. When their polarization states are mismatched, the PSF can be so distorted that the depth resolution is degraded to several times the theoretical value. When we polarize the source light with a polarizer, then the degree of polarization (DOP) is unity, and the depth resolution becomes independent of the polarization mismatch. This discovery has fundamental importance for high-resolution OCT imaging of biological tissues. With DOP<1, the depth resolution can be quickly degraded by either birefringence or scattering in the sample. Adjusting polarization controllers can only improve the depth resolution at a certain depth in a sample if the polarization state of light changes along the depth. When DOP=1, uniform resolution along the depth of a sample can be achieved.