Flat-topped multi-Gaussian Beam Research Articles

Pulse Broadening Effects on Ranging Performance of a Laser Altimeter with Return-to-Zero Pseudorandom Noise Code Modulation.

A laser altimeter using code modulation techniques receives a backscattered pulse wider than the transmitted rectangular pulse when scanning a rough or sloped target surface. This leads to degrading the ranging performance in terms of signal-to-noise ratio (SNR) and detection probability. Unlike the pulsed techniques, little work has focused on the pulse broadening effect of the code modulation techniques. In this study, mathematical models were derived to investigate the pulse broadening effect on the ranging performance of a return-to-zero pseudorandom noise (RZPN) laser altimeter. Considering that the impulse response can be approximated by a Gaussian function, the analytical waveform was derived using a new flat-topped multi-Gaussian beam (FMGB) model. The closed-form expressions were also analytically derived for a peak cross-correlation, SNR, and detection probability in terms of the pulse broadening effect. With the use of a three-dimensional model of asteroid Itokawa for practical surface profiles, the analytical expressions were validated by comparing to the results obtained from numerical simulations. It was also demonstrated that the pulse broadening effect dropped down the peak cross-correlation and then deteriorated the ranging performance. These analytical expressions will play an important role in not only designing a laser altimeter using the RZPN code modulation technique but also analyzing its ranging performance.

Propagation of fully and partially coherent flat-topped multi-Gaussian beams through axicons.

Theoretically, we have investigated the propagation of fully and partially coherent flat-topped multi-Gaussian beams through classical and logarithmic axicons. The stationary phase method applied to the Fresnel diffraction integral for intensity distribution has led to applicable relationships. The influences of axicon base angle, beam width, beam flatness, and coherence length with intensity distribution were studied. A number of results have been analyzed and discussed revealing some important conclusions. During this investigation, a specific interest has been given toward producing uniform intensity and long focal depth.

Theoretical simulation analysis of long-pulse laser induced damage in a BK7:SiO2/HfO2 optical anti-reflective films

The three dimensions (3-D) temperature field distribution (TFD) equation is established based on Newton’s law of cooling, which is focusing on optical anti-reflection films (OARFs) irradiated by flat-topped multi-Gaussian laser beam. The TFD of HfO2/SiO2 composite films coating on BK7 substrate(BK7:SiO2/HfO2) irradiated by single long-pulse laser is obtained by means of numerical simulation. The result shows that the thermal effect of OARFs is significant when irradiated by the flat-topped long-pulse laser. Moreover, the main damage of OARFs after long-pulse laser strikes is not films fusion but delamination. The delamination is caused by thermal conduction from the films to the BK7 substrate, then the fusing of BK7 substrate, following by the separation of films. The results provide a theoretical basis for progress analysis and mechanism study of long-pulse laser induced damage in OARFs.

Polarization characteristic and control of the conical diffracted output field under annular beam

Conical diffraction, a unique optical phenomenon in biaxial crystal, has important applications for the manipulation of particles. In this paper, a new model of annular Gaussian beam is constructed based on the Tovar's flat-topped multi-Gaussian laser beams. The conical diffraction of annular Gaussian beam is calculated using Belsky-Khapalyuk-Berry theory. The polarization characteristics of conical diffracted output beams under the annular Gaussian beam are theoretically calculated and experimentally demonstrated by means of the linearly polarized annular Gaussian beams with different polarization directions. It is found that the same azimuth angles of the inner and outer rings of the conical diffracted output beams have orthogonal polarization characteristics. A combined polarizer (CP) composed of eight polarizing segments with different specific pass axes of polarization is presented to simulate the polarization characteristic of the optical field of conical diffraction. Furthermore the calculations for output-field control of conical diffraction under the annular beam by using the proposed CP are compared with the experimental results. The results show that the intensities of both the inner and outer rings are periodically varied with CP azimuth angle. And when the azimuth angle of CP is 0, only the conical diffracted outer ring is remained, while only the inner ring of conical diffraction is remained for 180. This tunable conical diffracted field has important applications in optical tweezers and wavelength division multiplexing.

Propagating property of flat-topped multi-Gaussian beams passing through a misaligned optical system with two-lens and two-diaphragm

The optical elements’ maladjustment is a potential threaten in optical systems, thus, the transmission feature of laser beams passing through a misaligned optical system is widely studied. By using approximate expansion of circle diaphragm and generalized Huygens-Fresnel diffraction formula, a universal analytic expression is deduced for the flat-topped multi-Gaussian beams passing through a misaligned optical system with two-lens and two-diaphragm. The study on the propagating property of fundamental-mode Gaussian beams and a flat-topped multi-Gaussian beam is carried out accordingly. The expansion of complex Gauss function of misaligned optical circle diaphragm is given, as well as a group of new parameter values of the expansion of complex Gauss function. By using the new parameter values, the influence of disadjust parameters on output intensity distribution is analyzed numerically. The result shows that the diaphragms’ offset can make the beams offset or covered, and the second diaphragm influences more; the angle deflection of diaphragms can make light beams compressed in the deflection direction, and the first diaphragm influences more; the offset of the first lens can weaken light intensity in the same direction of the lens offset, and the offset of the second lens can weaken light intensity in the opposite direction of the lens offset; the angle deflection of the first lens can make light beams move to the opposite direction, and the angle deflection of the second lens has no influence; when all the diaphragms and the lenses are disadjust, the angle deflection of the first lens has a vital influence to the output intensity distribution.

Fractional Fourier transform of flat-topped multi-Gaussian beams

The fractional Fourier transform (FRFT) of the flat-topped multi-Gaussian beam (FMGB) is investigated based on the three kinds of FRFT optical systems: Lohmann I, Lohmann II, and quadratic graded-index systems. The analytical expressions for the FRFT of the FMGB are derived based on the propagation of the FMGB through the three systems. By introducing a hard-edge aperture function, the analytical expressions for the FRFT of the FMGB carried out by the apertured FRFT optical systems are presented. The FRFT characteristics of the FMGB for the three kinds of FRFT optical systems with and without apertures are discussed in detail. Results show that the three types of FRFT optical systems have the same function when the apertures are ignored but that significantly different characteristics are exhibited when the apertures appear.

Propagation of flat-topped multi-Gaussian beams through an apertured ABCD optical system

The generalized analytical expression for the propagation of flat-topped multi-Gaussian beams through a misaligned apertured ABCD optical system is derived. Using this analytical expression, the propagation characteristics of flat-topped multi-Gaussian beams through a spatial filter are investigated. The analytical formula of the electric field distribution in the focal plane is also derived for revealing the effects of the misalignment parameters clearly. It is found that different misalignment parameters have different influences on the electric field distributions of the beam focus spot and the output beam characteristics. The intensity distribution of the beam is mainly determined by the misalignment matrix element E, and the phase distribution is affected by the misalignment matrix elements G and E.

Propagation of flat-topped multi-Gaussian beams through a double-lens system with apertures

A general model for different apertures and flat-topped laser beams based on the multi-Gaussian function is developed. The general analytical expression for the propagation of a flat-topped beam through a general double-lens system with apertures is derived using the above model. Then, the propagation characteristics of the flat-topped beam through a spatial filter are investigated by using a simplified analytical expression. Based on the Fluence beam contrast and the Fill factor, the influences of a pinhole size on the propagation of the flat-topped multi-Gaussian beam (FMGB) through the spatial filter are illustrated. An analytical expression for the propagation of the FMGB through the spatial filter with a misaligned pinhole is presented, and the influences of the pinhole offset are evaluated.

A new synthesis method for synthesizing on-axis flat-topped beams by using a defocusing telescope system

A new method for synthesizing on-axis flat-topped beams by using a defocusing telescope system is proposed, where the flat-topped multi-Gaussian beam is chosen as the ideal beam. Within the framework of the paraxial approximation and based on the Collins diffraction integral formula, the analytical expressions for the on-axis field and incident field are derived and analyzed physically. The effect of beam order N, flat-top length parameter L, position of the flat-top centre zc and central longitudinal spatial frequency Sc on the on-axis intensity distribution is illustrated by numerical examples. A comparison of our results with the method for simulating the ideal beam by use of the rectangular function shows the advantages of our method.

Propagation and transformation of flat-topped multi-Gaussian beams in a general nonsymmetrical apertured double-lens system

On the basis of expanding a hard-edged aperture function as a finite sum of complex Gaussian functions, an approximate analytical expression for the propagation of an input complex amplitude distribution passing through a general nonsymmetrical apertured double-lens system is derived. Then, the propagation result for two-dimensional flat-topped multi-Gaussian beams is given. It is shown that the apertured Lohmann's symmetrical double-lens system for fractional Fourier transform is a special case of the general apertured double-lens system. The numerical calculation, graphical illustration, and some discussions for the transformation of the two-dimensional flat-topped multi-Gaussian beam in apertured Lohmann's symmetrical double-lens systems are also presented.

Off-axis flat-topped multi-Gaussian beam and its propagation through paraxial optical system

Off-axis flat-topped multi-Gaussian beam is proposed as an extension of flat-topped multi-Gaussian beam. The electric field of off-axis flat-topped multi-Gaussian beam is expressed as a superposition of a series of off-axis Gaussian beams. Propagation formulae for off-axis flat-topped multi-Gaussian beam through aligned and misaligned optical system are derived. As a numerical example, propagation properties of off-axis flat-topped multi-Gaussian beam in free space and through a misaligned thin lens are discussed.

Fractional Fourier transform of flat-topped multi-Gaussian beams based on the Wigner distribution function

By using the Wigner distribution function, the fractional Fourier transform (FRFT) of flat-topped multi-Gaussian (FTMG) beams is studied. Analytical expressions for the intensity distribution, beam width, far-field divergence angle, M2 factor and K parameter of FTMG beams are derived. The influence of fractional order on transformation properties of FTMG beams in the FRFT plane is illustrated with numerical examples.

Study of the correspondence between flat-topped multi-Gaussian beams and super-Gaussian beams

Based on the Wigner distribution function and irradiance moments method, the characteristic parameters of flat-topped multi-Gaussian beams (FMGBs), such as the M2 factor and beam width, are derived analytically. Then, from a comparison of the propagation of FMGBs and super-Gaussian beams (SGBs), it is found that two FMGBs and SGBs with the same M2 factor exhibit a similar transverse irradiance distribution at a position of the equal generalized Fresnel number despite the fact that the beam width and propagation distance may be different.

Propagation of flat-topped multi-Gaussian laser beams.

The multi-Gaussian beam shape is proposed as a model for aperture functions and laser beam profiles that have a nearly flat top but whose sides decrease continuously. Beams and apertures of this type represent a simple, elegant, and intuitive alternative to super-Gaussian beams, which are important in a number of applications such as laser resonator design. Analytical formulas are developed for the propagation of these beams through free space and optical systems representable by ABCD matrices.