Power In Bucket Research Articles

Demonstration of horizontal free-space laser communication with the effect of the bandwidth of adaptive optics system

Abstract The performance of free-space laser communication (FSLC) is greatly decreased by horizontal atmospheric turbulence. Adaptive optics is used to overcome horizontal turbulence. This study investigated the effect of the 3 dB bandwidth of an adaptive optics system (AOS) on FSLC performance by using power-in-bucket (PIB) method, which considers the effect of receiving aperture and then, can accurately evaluate of the effect of system bandwidth on the communication performance. A 9 km horizontal maritime link experiment was performed through adaptive correction to validate the theoretical analysis. Results indicate that the effect of system bandwidth can be accurately evaluated using PIB method. This work provides a basis for designing and evaluating AOSs for FSLC.

Scrutinizing the effects of turbulence on partially coherent Gaussian beam propagating through Caspian Sea

In this paper, the total attenuation due to scattering, absorption and turbulence is considered in investigation of link parameters of the underwater horizontal optical communication system in the Caspian sea. In the present paper, based on extended Huygens-Fresnel principle and the unified theory of coherence and polarization, analytical formulas for Cross-Spectral Density (CSD) matrix elements and the Spectral Degree of Polarization (SDP) are derived. By using the matrix elements of cross-spectral density, some valuable analytical expression for defining Power In Bucket (PIB), Signal to Noise Ratio (SNR) and Bit Error Rate (BER) are presented. Then, the effects of some source and turbulent ocean factors on link parameters of partially coherent Gaussian beam propagating through turbulent water are scrutinized. It is deduced that underwater communication link parameters are affected by environment’s factors (e.g. Chlorophyll concentration (CC), turbulence parameters) and source parameters (e.g. laser wavelength). Investigating spectral degree of polarization shows that by increasing the strength of oceanic turbulence, the fluctuation of spectral degree of polarization becomes smaller. The obtained results are displayed with graphs.

Performance improvement of terrestrial free-space optical communications by mitigating the focal-spot wandering

Focal-spot wandering is the main cause for the major power loss in free-space optical communications. Thus,mitigating it is a primary requirement for the successful performance improvement. In order to prove this prerequisite, an experimental set-up using 155-Mbps data transmission is built for the link range of 0.5 km at an altitude of 15.25 m. In the experiment, the receiver is equiped with a control system to stabilize the received optical propagation at the detector plane which is called as focal-spot wandering mitigation control so as to couple the power in bucket perfectly to the photodetector. The performance improvements due to mitigating focal-spot wandering are regressively investigated in terms of various quality assessment key parameters. Maximum radial distance of 0.25 mm, maximum effective scintillation index of 0.17, optical signal-to-noise ratio of 9 dB, minimum eye-opening of ±0.37 V, minimum eye-height of ±0.51 V, controlled bit-error-rate of 6.45 × 10−9 to 7.09 × 10−8 and the link margin of 1.83 dB are attained even during strong turbulence level while mitigating focal-spot wandering.

Using Collins Formula with Scaling Factor to Analysis the Propagation Properties in Laser Focus System Design

A Collins formula method with a scaling factor between the target-and source-plane has been proposed for the laser propagation in the optical system design, which can be used to evaluate the laser optical system performance and the tolerance analysis. The laser propagation in the optical systems can be calculated by the Collins integral formula, and an angular spectrum method has been derived by coordinate substitution. A scaling factor m is introduced to make the choice of the observation-plane more flexibility and the calculation more accurate. The laser optical system has been designed, and its tolerance analysis is conducted by the Angular-Spectrum method. The evaluating criterion is the laser spot radius in the far field, which is defined by 86.5% power in bucket (PIB). The radius of the laser spot in 90m between 0.8mm and 1.4mm with the expectation of 0.92mm is calculated by the tolerance analysis, and the experimental result is 1.01mm. In the distance of 47m, the radius is between 0.42mm and 0.73mm with the expectation of 0.48mm calculated by the tolerance analysis, the experimental result is 0.46mm. The experiment agrees the result of the tolerance analysis well. The focal shift for laser propagation in the optical systems is validated. The experiment results confirm the calculation and it proved the use of the method in laser focus optical system design.

Numerical and experimental study on liquid crystal optical phased array beam steering combined with stochastic parallel gradient descent algorithm

In this paper, we present numerical and experimental study on beam steering with liquid-crystal optical phased array (LC-OPA) by means of stochastic parallel gradient descent (SPGD) algorithm. The numerical simulation, which is mainly based on the evolution of power-in-bucket (PIB), indicates that the beam steering strategy with LC-OPA is relatively robust, and the algorithm performs well most of the time. The results also reveal that the performance of SPGD algorithm is influenced by the order of Zernike polynomials, the radius of bucket and the steering angle. The order of Zernike polynomials and the radius of bucket are optimized to improve the accuracy and convergence of the algorithm. In a proof-of-concept experiment, the feasibility of the beam steering strategy with LC-OPA is demonstrated.

Numerical laser beam propagation using large eddy simulation of a jet engine flow field

In certain directed infrared countermeasure (DIRCM) situations, the laser beam path may have to pass close to the engine exhaust plume of the aircraft and models of plume turbulence are needed for DIRCM performance simulations. The jet engine plume was modeled using large eddy simulation (LES), providing time resolved information about the large scale turbulent eddies. The refractive index data from the LES calculations were integrated along the propagation path to produce time resolved phase screens for optical beam propagation. The phase screens were used to calculate laser beam parameters including beam wander and power-in-bucket (PIB). Numerical beam propagation resulted in a root-mean-square beam wander of 200 μrad for the small turbojet engine studied. The PIB was calculated for beams with 80 μrad and 2 mrad divergence having equal beam diameter when passing through the plume. For the beam with low divergence, the average PIB was reduced from 0.23 to 0.040, while the beam with wider divergence showed no significant reduction. In both cases, the plume introduced significant temporal variation of the instantaneous PIB. The beam wander is not affected by the divergence, but only depends on beam size.

Analysis of laser beam propagation properties with the Collins formula in a focused laser system

A Collins formula method with a scaling factor between the target and source plane is proposed for laser propagation in optical system design, which can be used to evaluate laser optical system performance and tolerance analysis. The laser propagation in optical systems can be calculated by the Collins integral formula, and an angular spectrum method is derived by coordinate substitution. It is introduced a scaling factor m, making the choice of the observation plane more flexible and the calculation more accurate. A laser optical system is designed, and its tolerance analysis is conducted by the angular spectrum method. The evaluation criterion is the laser spot radius in the far-field, which is defined by 86.5% power in bucket. The radius of the laser spot in 90 m distance is from 0.8 to 1.4 mm by the tolerance analysis, which the ideal expectation is 0.92 mm and the experimental result is 1.01 mm. In the distance of 47 m, the radius is from 0.42 to 0.73 mm by the tolerance analysis, which the ideal expectation is 0.48 mm and the experimental result is 0.46 mm. The experimental results agree with the results of the tolerance analysis well. The focal shift for laser propagation in optical systems is validated. The experimental results confirm the calculation and they prove the use of the method in laser focus optical system design.

坐标缩放激光角谱传输及在激光光学系统中的应用

An angular-spectrum method with a scaling factor between the observation and the source plane was proposed for the laser propagation in an optical system to evaluate its performance and to analyze its tolerance.As the laser diffraction propagation in the optical system could be calculated by the Collins integral formula,the formula coordinate was transformed and an angular spectrum method was derived by coordinate substitution.Then,a scaling factor was introduced to make the choice of the observation-plane more flexibility and the calculation of the laser propagation more accurate.A laser optical system was designed,and its tolerance was analyzed by the angular-spectrum method.The evaluating criterion was the laser spot radius in the far field,which was defined by 86.5% Powerin Bucket(PIB).Experiments show that when the radius of the laser spot is 0.8—1.4 mm in a distance of 90 m,the expected value calculated by the tolerance analysis is 0.92 mm and the measured result is 1.01 mm.Moreover,when that is 0.42—0.73 mm in the distance of 47 m,the expected value and the measured result are 0.48 mm and 0.46 mm,respectively.Both the experiment results match the data of the tolerance analysis well.The focal shift for laser propagation in the optical system was validated by the tolerance analysis.The theoretical analysis by the proposed method is verified experimentally,which confirms the feasibility proposed method in design of laser focus optical systems.

Probability density functions of power-in-bucket and power-in-fiber for an infrared laser beam propagating in the maritime environment

Irradiance fluctuations of an infrared laser beam from a shore-to-ship data link ranging from 5.1 to 17.8 km are compared to lognormal (LN), gamma-gamma (GG) with aperture averaging, and gamma-Laguerre (GL) distributions. From our data analysis, the LN and GG probability density function (PDF) models were generally in good agreement in near-weak to moderate fluctuations. This was also true in moderate to strong fluctuations when the spatial coherence radius was smaller than the detector aperture size, with the exception of the 2.54 cm power-in-bucket (PIB) where the LN PDF model fit best. For moderate to strong fluctuations, the GG PDF model tended to outperform the LN PDF model when the spatial coherence radius was greater than the detector aperture size. Additionally, the GL PDF model had the best or next to best overall fit in all cases with the exception of the 2.54 cm PIB where the scintillation index was highest. The GL PDF model also appears to be robust for off-of-beam center laser beam applications.

Propagation characteristics of tilted partially coherent rectangular flat-topped beam in turbulent atmosphere

In this paper, the effects of atmospheric turbulence on the intensity distribution of a tilted Rectangular Partially Coherent Flat-Topped (RPCFT) beam were studied. An analytical formula for the intensity distribution was derived. POWER In Bucket (PIB) value is calculated numerically. The effects of source parameters – such as correlation length, order of flatness and tilt coefficient – on the intensity were analyzed. Detailed analysis demonstrates that these parameters have an influence on beam propagation properties. The analyses are illustrated by numerical examples and graphs.

Reliability analysis of the flat-topped array beam FSO communication link

Free-space optical communication systems are affected by turbulent atmosphere. The atmospheric transmission is affected by absorption, scattering and turbulence. In this paper, the effects of absorption and scattering are taken into account using Beer’s law and the effects of turbulence are considered in calculating the average intensity distribution. An analytical expression for the average intensity distribution of a partially coherent flat-topped array (PCFTA) beam in turbulent atmosphere is derived based on the extended Huygens–Fresnel principle. The average intensity, power in bucket, signal to noise ratio, and bit error rate of this kind of beam are investigated in details. It is shown by numerical results and analytical methods that the average intensity and link parameters of PCFTA beams change during propagation and these changes are dependent upon both source parameters and weather conditions.

Experimental study on beam shaping in a reduced-scale relay mirror system

Improving power coupling efficiency of beam uplink propagation in a relay mirror system is under extensive research in recent years. A typical model of the relay mirror system is established and theory of beam shaping used to improve power coupling efficiency of the relay mirror system is analyzed in detail. A reduced-scale experimental relay mirror system is founded, which has the same Fresnel number as uplink propagation in the relay mirror system with 1.0 m-caliber transmitter and 30 km propagation distance. Phase distribution of the source is optimized by using the stochastic parallel gradient descent algorithm. The experimental results showed that power coupling efficiency of uplink propagation in the reduced-scale relay mirror system was improved from 72.67 to 87.88 % by beam shaping and the bucket power proportion in 5 pixels at the target was improved from 45.49 to 52.78 %.

Beam propagation analysis of a multi-laser diode FSO system through free space

In this paper beam propagation analysis of a multi-beam multi-collimator opticalcommunication system through free space is studied. For this purpose, the propagationproperties of Gaussian multi-beams through a multi-optical path including collimators intransmitters are studied and an analytical formula for intensity distribution is derived. Theeffects of beam divergence and beam separation distances on the propagation propertiesof Gaussian multi-beams are studied in detail by calculating the beam widthand power in bucket (PIB). The analyses are illustrated by numerical examples.

Beam propagation analysis of a multi beam FSO system with partially flat-topped laser beams in turbulent atmosphere

In this paper, the propagation properties of partially coherent flat-topped (PCFT) laser beams in multi-beam FSO communication links are analyzed. Analytical expressions for the average intensity and beam width of PCFT multi beams are derived based on extended Huygens–Fresnel principle by considering the effects of turbulent atmosphere. Also power in bucket (PIB) is calculated numerically based on analytical expression of average intensity. It is revealed that PCFT multi beams can be converted into a Gaussian beam after sufficiently large propagation distance. It is found that correlation length, order of flatness and beams’ separation distances in the source plane have strong effects on minimum distance required for this conversion as well as beam width and PIB. Obtained results are confirmed and illustrated with numerical examples and resulted graphs.

Propagation properties of radial partially coherent flat-topped array beams in a turbulent atmosphere

With the help of the tensor method, the analytical expression for the cross-spectral density of the radial partially coherent flat-topped array (RPCFTA) beams propagating in a turbulent atmosphere is derived, where the correlated superposition and uncorrelated superposition are considered. The average intensity, the spatial coherence properties and power in bucket (PIB) of these kinds of beams are investigated in detail. It is shown by numerical results and analysis that the average intensity and the spatial coherence of the correlated or uncorrelated RPCFTA beams will change on propagation and this change is dependent upon the correlation of the source's beamlets and atmospheric turbulence. In addition, the comparisons of the average intensity and the spatial coherence between the correlated and the uncorrelated RPCFTA beams propagating both in turbulent atmosphere and in free space are also given, and some interesting results are obtained. The laser power of focus ability of the single PCFT beam is worse than that of the correlated RPCFTA beam and but better than that of the uncorrelated RPCFTA beam when propagation distance in turbulent atmosphere is far-field plane.

Characterizing the divergence properties of the laser diode beams propagation through collimator and aperture ABCD optical system

The propagation properties of Gaussian laser beams through a complete optical path including free space and the optics of transmitter and receiver containing a collimator, an aperture and a lens is studied. Based on the Collins integral and using the second order moment method, analytical formulas for intensity distribution and Power In Bucket (PIB) along the propagation path are derived. The effects of initial beam divergence, collimator–source separation distance and beam width deviation on laser beams properties are investigated. Obtained results are confirmed and illustrated with numerical examples and resulted graphs.

An exact solution to paraxial propagation of laser beams in longitudinal inhomogeneous plasmas

An exact, general solution for laser beams propagating in longitudinally inhomogeneous plasmas is obtained in the form of the diffraction integral. The Gaussian beam and the Hermite–Gaussian beam are taken for example. In the case of an increasing plasma density along the propagation distance, natural diffraction of the Gaussian beam is retarded. This retardance has a less effect on the central part of the Hermite–Gaussian beam while a considerable rise of the power in bucket (PIB) occurs in the surrounding part of the beam.

Analyzing Beam Propagation through Atmospheric Turbulence for Different Degrees of Global Coherency

Studies of optical beam propagation through atmospheric turbulence are important for many applications. Fully coherent laser beams are very sensitive to the turbulence medium. Studies have shown that using partially coherent beams is an effective method to reduce this unsatisfactory feature. Unfortunately partially coherent beams are more expanded when they propagate thought turbulence medium, which is a limiting factor in most applications. In this paper we have determined a special degree of global coherency, which optimizes beam propagation with respect to limiting factors (sensitivity to the turbulence and broadening). Also we have shown that other beam characteristics such as beam quality, power in bucket (PIB) and strehl ratio are optimized in this special degree of coherency.

Higher order annular Gaussian laser beam propagation in free space

Propagation of higher order annular Gaussian (HOAG) laser beams in free space is examined. HOAG beams are defined as the difference of two Hermite-Gaussian (HG) beams; thus, they can be produced by subtracting a smaller beam from a larger beam, that are cocentered and both possess HG mode field distributions. Such beams can be considered as a generalization of the well-known annular Gaussian beams. We formulate the source and receiver plane characteristics and kurtosis parameter of HOAG beams propagating in free space and evaluate them numerically. In comparison to HG beams, HOAG beams have a broader beam size with outer lobes of kidney shape. The amount of received power within the same receiver aperture size, that is, power in bucket, is generally lower for higher order beams. The convergence of the kurtosis parameter to an asymptotic value for higher order beams takes much longer propagation distances compared to zero-order beams.

Paraxial propagation of partially coherent flat-topped beam

The propagation of flat-topped beam passing through a paraxial optical ABCD system is extended to partially coherent case and has been studied in detail. Based on Wigner distribution function (WDF), the irradiance distribution of partially coherent flat-topped beam is derived. Furthermore, two propagation parameters, such as M2-factor and Power in Bucket (PIB) are illustrated analytically and numerically.