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We propose and demonstrate the improvement of conventional Galilean refractive beam shaping system for accurately generating near-diffraction-limited flattop beam with arbitrary beam size. Based on the detailed study of the refractive beam shaping system, we found that the conventional Galilean beam shaper can only work well for the magnifying beam...
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... w 0 is the beam waist, is a dimensionless parameter and determines the range over, which the irradiance rolls off exponentially, R 0 is the radius at which the irradiance has fallen to half of its value on axis. For the sake of simplicity and consistency, only one parameter is changed in the following discussion. Numerical simulations are based on the MATLAB. In addition, the angular spectrum method combined with MATLAB is used for modeling the propagation of the input beam [18]. 2.1 Influence of target beam size ( R 0 ) Because the surface and phase distributions of dual aspheric lenses are related with the ratio of the target beam size to the input beam size, we focus on the influence of target beam size ( R 0 ). In simulation, the parameters are selected as w 0 = 3 mm , β = 16, d = 350 mm , n = 1.45 and λ = 1064 nm . Based on Eqs. (5), (6) and the energy conversation principle, we can get the 1 relationship R = h ( r ) and r = h ( R ). From Eqs. (1) and (2), we can see that the point R = r is a singularity and we cannot obtain the analytical solution of the surface profile distribution at this point. In simulation, numerical discrete method is used. In the present and following analysis, the surface profile of the discrete point proximate the singular point is used to represent the surface profile of the singular point. From the following analysis, we can found that the point R = r is not only a singularity, but also the point of inflexion of the phase distribution curve. Figure 2 shows the phase distributions of dual aspheric lenses for the transformation of input beam into target beam with different size ( R 0 ). There exists point of inflexion on the phase distribution curve and the point of inflexion moves outside along with the increase of target beam size ( R 0 ). The corresponding irradiance and phase distributions of the output beam along with the change of target beam size are shown in Figs. 3(a) and 3(b). According to Figs. 3(a) and 3(b), it can be found that the larger the target beam size ( R 0 ) results in smaller difference between output beam and target beam. The flattop area of phase distribution of the output beam becomes larger and larger with the increase of target beam size. In order to give a quantitative analysis of shaping effect, the shaping error between the output beam and target beam is defined ...
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Citations
... Note our choice to express δ as a frequency, rather than an angular frequency. The field amplitude E 0 (x) includes the spatial profile of the laser beam, which is taken to be a top-hat shape (as, e.g., in Ref. [32]) approximated by a super-Gaussian function of the form ...
A full density-matrix simulation is performed for optical deflection of a barium monofluoride (Ba138F19) beam using the bichromatic force, which employs pairs of counterpropagating laser beams that are offset in frequency. We show that the force is sufficient to separate BaF molecules from the other products generated in a helium-buffer-gas-cooled ablation source. For our simulations, the density-matrix and force equations are numerically integrated during the entire time that the molecules pass through a laser beam to ensure that effects of the evolution of the Doppler shift and of the optical intensity and phase at the position of the molecule are properly included. The results of this paper are compared to those of a deflection scheme [A. Marsman, D. Heinrich, M. Horbatsch, and E. A. Hessels, Phys. Rev. A 107, 032811 (2023)] which uses π pulses to drive frequency-resolved transitions. This paper is part of an effort by the EDM3 collaboration to measure the electric dipole moment of the electron using BaF molecules embedded in a cryogenic argon solid. Separation of BaF molecules will aid in producing a sufficiently pure solid.
... Note our choice to express δ as a frequency, rather than an angular frequency. The field amplitude E 0 (x) includes the spatial profile of the laser beam, which is taken to be a top-hat shape (as, e.g., in Ref. [32]) approximated by a super-gaussian function of the form ...
A full density-matrix simulation is performed for optical deflection of a barium monofluoride ($^{138}$Ba$^{19}$F) beam using the bichromatic force, which employs pairs of counter-propagating laser beams that are offset in frequency. We show that the force is sufficient to separate BaF molecules from the other products generated in a helium-buffer-gas-cooled ablation source. For our simulations, the density-matrix and force equations are numerically integrated during the entire time that the molecules pass through a laser beam to ensure that effects of the evolution of the Doppler shift and of the optical intensity and phase at the position of the molecule are properly included. The results of this work are compared to those of a deflection scheme (Phys. Rev. A 107, 032811 (2023)) which uses $\pi$ pulses to drive frequency-resolved transitions. This work is part of an effort by the EDM$^3$ collaboration to measure the electric dipole moment of the electron using BaF molecules embedded in a cryogenic argon solid. Separation of BaF molecules will aid in producing a sufficiently pure solid.
... The frequencies, wave vectors, phases, polarizations, and amplitudes are represented by ω p /(2π ), k p , φ p ,ˆ p , and E 0p ( r, t ), respectively. The latter includes both the time profile of the laser pulses (Fig. 2) and the spatial profile of the laser beam, which is taken to be a top-hat shape (as, e.g., in Ref. [22]) approximated by an elliptical super-Gaussian function of the form ...
A full density-matrix simulation is performed for optical deflection of a barium monofluoride (BaF) beam. Pairs of counterpropagating laser pulses are used for absorption followed by stimulated emission. The scheme produces a force which is nearly an order of magnitude larger than that obtainable using continuous-wave laser deflection, and yields a force-to-spontaneous-decay ratio which is more than an order of magnitude larger. The large reduction in spontaneous decay is key to optical deflection of molecules, where branching ratios to other vibrational states do not allow for cycling transitions. This paper is part of an effort by the EDM3 collaboration to measure the electric dipole moment of the electron using BaF molecules embedded in a cryogenic argon solid. Deflection of BaF molecules will separate them from the other ablation products coming from a buffer-gas-cooled ablation source, before embedding them into the argon solid. Our simulations show that sufficiently large deflections for this separation are feasible.
... The frequencies, wavevectors, phases, polarizations and amplitudes are represented by ω p /(2π), k p , φ p ,ˆ p and E 0p ( r, t), respectively. The latter includes both the time profile of the laser pulses (Fig. 2) and the spatial profile of the laser beam, which is taken to be a top-hat shape (as, e.g., in Ref. [21]) approximated by an elliptical super-gaussian function of the form ...
A full density-matrix simulation is performed for optical deflection of a barium monofluoride (BaF) beam. Pairs of counter-propagating laser pulses are used for stimulated absorption followed by stimulated emission. The scheme produces a force which is nearly an order of magnitude larger than that obtainable using continuous-wave laser deflection, and yields a force-to-spontaneous-decay ratio which is more than an order of magnitude larger. The large reduction in spontaneous decay is key to optical deflection of molecules, where branching ratios to other vibrational states do not allow for cycling transitions. This work is part of an effort by the EDM$^3$ collaboration to measure the electric dipole moment of the electron using BaF molecules embedded in a cryogenic argon solid. Deflection of BaF molecules will separate them from the other ablation products coming from a buffer-gas-cooled ablation source, before embedding them into the argon solid. Our simulations show that sufficiently large deflections for this separation are feasible.
... The applicability analysis of the obtained data can be demonstrated on the Galileo lens system, which is widely used in laser technology for laser beam shaping [47,48]. In optical systems operating with laser radiation, an important characteristic is the polarization sensitivity of the optical system [48,49]. ...
We have studied the basic polarization properties of variously shaped lenses for the on-axis beam in the exit pupil and present the data obtained. The Mueller calculus and three-dimensional polarization calculus methods were applied for polarization ray tracing. The calculation methods were compared on different samples. We have demonstrated that taking into account the shape of lenses when designing lens optical systems contributes to the minimization of the diattenuation magnitude.
... Current beam-shaping methods mainly include aspherical-lens systems [4][5][6][7], diffractive optical elements [8], liquid-crystal spatial light modulators [9,10], and metasurfaces and metamaterials [11,12]. Aspherical cylindrical lenses are the most effective beam-shaping method for an intense laser beam-shaping system. ...
In this study, the circular Gaussian spot emitted by a laser light source is shaped into a rectangular flat-top beam to improve the scanning efficiency of a selective laser sintering scanning system. A CO2 laser with a power of 200 W, wavelength of 10.6 μm, and spot diameter of 9 mm is shaped into a flat-top spot with a length and width of 0.5 × 0.1 mm, and the mapping function and flat-top Lorentzian function are calculated. We utilize ZEMAX to optimize the aspherical cylindrical lens of the shaping system and the cylindrical lens of the focusing system. We then calculate the energy uniformity of the flat-top line-shaped beam at distances from 500 to 535 mm and study the zoom displacement of the focusing lens system. The results indicated that the energy uniformity of the flat-top beam was greater than 80% at the distances considered, and the focusing system must precisely control the displacement of the cylindrical lens in the Y-direction to achieve precise zooming.
... References [14,15] numerically solve partial differential equations, Ref. [16] designs on-axis lenses with the supporting quadric method (SQM), and Refs. [17,18] numerically solve integral equations to get paired aspherical lenses with a desired aspherical apodization. Reference [19] numerically designs Fresnel lenses, and Ref. [20] implements normalized root mean square deviations (NRMSDs) to get an aspherical lens with desired aspherical apodization, to mention a few. ...
Here we present an optical system composed of two mirrors such that at the input/output, the light is a plane wave but with a user-defined apodization factor. The model presented is an analytic closed form with no numerical approximations or iterations. We test the model with illustrative scenarios, and the results are as expected; the system is stigmatic with the desired apodization factor. Thus, this system has several potential applications in high contrast imaging.
... A while ago, the Wireless Gigabit Alliance proposed the use of the millimetre waves in the license-free 60 GHz band, where 7 Gbps short-range wireless links are available for 7 GHz bandwidth. The 60 GHz band is considered as a part of the IEEE 802.11ad structure for very high data throughput in Wireless Local Area Networks (WLANs) using MIMO techniques [13]. Still, the wireless technologies Bluetooth, BLE and Wi-Fi have become victims of their own success. ...
... The low frequency of the EM field can penetrate kilometers of rock and soil; therefore, the signal will reach surface from deep underground making it suitable for different underground applications. Many investigations regarding the EM waves' propagation (600 Hz-60 MHz) through rock have been developed by researchers in different parts of the world [12,13] and a reliable communication has been proved and settled (at 200 m depth) in coal mines in South Africa [14]. ...
... According to the working principle, the refractive shaping system can be divided into two categories: Galilean (Figure 3.11a, b, c) and Keplerian (Figure 3.11d) light beam shaping systems [13]. All the shaping systems above give us a clear perspective of the kind of the lenses necessary to be used in order to obtain a long distance, beam light that has to be spotted on the active area of the PD. ...
Optical wireless communication (OWC) refers to any kind of communication based on light as a wireless transmission medium.
... Controlling the irradiance and wavefront simultaneously has been a basic problem of geometrical optics and optical design. Various design methods have been developed to design two optical surfaces for beam-shaping applications, including rotational aspheric surfaces [8][9][10][11][12] and freeform surfaces [13][14][15][16][17][18][19][20][21][22][23][24]. However, with the development of engineering and industry, some applications give higher requests for beam-shaping technology such as dynamic output beams with prescribed irradiances and sizes. ...
Recently, the optical design of refractive beam-shaping systems has been extensively studied, although such study remains focused on two optical surfaces. Designing a beam-shaping system with variable output beam sizes and prescribed irradiance profiles remains a challenging but rewarding task. Here, we present a design framework, including calculation of the initial system and optimization process, to achieve variable-diameter beam-shaping systems with high zoom ratios. We introduce the whole process of designing a compact $8\times $ 8 × zoom system of superior optical performance by transforming a Gaussian beam into flat-top beams with different magnifications. We also present a design of a zoom beam-shaping system transforming a Gaussian beam into variable beams with inverse Gaussian distributions to demonstrate the robustness and efficiency of the proposed method.
... A while ago, the Wireless Gigabit Alliance proposed the use of the millimetre waves in the license-free 60 GHz band, where 7 Gbps short-range wireless links are available for 7 GHz bandwidth. The 60 GHz band is considered as a part of the IEEE 802.11ad structure for very high data throughput in Wireless Local Area Networks (WLANs) using MIMO techniques [13]. Still, the wireless technologies Bluetooth, BLE and Wi-Fi have become victims of their own success. ...
... The low frequency of the EM field can penetrate kilometers of rock and soil; therefore, the signal will reach surface from deep underground making it suitable for different underground applications. Many investigations regarding the EM waves' propagation (600 Hz-60 MHz) through rock have been developed by researchers in different parts of the world [12,13] and a reliable communication has been proved and settled (at 200 m depth) in coal mines in South Africa [14]. ...
... According to the working principle, the refractive shaping system can be divided into two categories: Galilean (Figure 3.11a, b, c) and Keplerian (Figure 3.11d) light beam shaping systems [13]. All the shaping systems above give us a clear perspective of the kind of the lenses necessary to be used in order to obtain a long distance, beam light that has to be spotted on the active area of the PD. ...
This book provides a chronological literature review of optical wireless communication, followed by a detailed blueprint of a visible light communication (VLC) setup with the key characteristics of LEDs and photodetectors. Next, the optical channel impulse response and its description for different possible topologies is presented together with a description of the optical and electrical setup for both optical transmitters (oTx) and optical receivers (oRx). Different single carrier and multi-carrier modulations particularly applied in visible light communication setups are also presented. Both the optical and electrical modules of oTx and oRx are simulated and then prototyped and tested as embedded devices in an underground positioning and monitoring system for a continuous real time identification of the personnel on the main underground galleries where the illumination network is already installed.
• Presents a comprehensive look at visible light communication technology, both in description and application;
• Shows where and how VLC has been launched on the market as an alternative or partner technology to the existing wireless communication technologies based on radio frequency;
• Includes special focus on underground positioning and monitoring with embedded VLC.
