一种新型光学模式转换器

提出了一种梯度折射率分布介质为基质的单体光学模式转换器,可以将两正交截面内瑞利长度相同、光腰重合的厄米-高斯光束转换为拉盖尔-高斯光束.这种转换器具有一体化且只有两个反射面的特点,因此易于调整、光能反射损耗小;对于两正交截面内瑞利长度不同、光腰不重合的厄米-高斯光束,提出了一种可调节其瑞利长度和光腰位置的光腰调节器,将光腰调节器与单体光学模式转换器组合使用,也可以将这种厄米-高斯光束转换为拉盖尔-高斯光束.     

Analytical propagation equation of astigmatic Hermite–Gaussian beams through a 4×4 paraxial optical system and their symmetrizing transformation

Starting from the Collins formula, a closed-form propagation equation of astigmatic Hermite–Gaussian (H–G) beams through a 4×4 paraxial optical system is derived, which permits us to calculate the irradiance distribution at any propagation plane and to study the symmetrization of astigmatic standard and elegant H–G beams. A detailed symmetrizing transformation of astigmatic H–G beams through a three-cylindrical-lens mode converter is illustrated both analytically and numerically. It is found that in accordance with the second-order moments characterization, there are two types of beam symmetrization. The transformation of standard H–G beams through the three-cylindrical-lens mode converter belongs to the perfect symmetrization, whereas the transformation of elegant H–G beams is the imperfect one.     

Fields of apertured polychromatic laser beams with Gaussian and Hermite–Gaussian transverse modes

Starting from the Huygens–Fresnel diffraction integral, the field expressions of apertured polychromatic laser beams with Gaussian and Hermite–Gaussian transverse modes are derived. Influence of the bandwidth on the intensity distributions of the laser beams is analyzed. It is found that when the bandwidth increases, the amplitudes and numbers of the intensity spikes decrease and beam uniformity is improved in the near field and the width of transverse intensity distribution of the apertured beams decreases in the far field. Thus, the smoothing and narrowing effects can be achieved by increasing the bandwidth. Also, these effects are found in the laser beams with Hermite–Gaussian transverse modes as the bandwidth increases.     

Kurtosis parameter of truncated standard and elegant Laguerre–Gaussian beams propagating through ABCD optical systems

On the basis of the propagation equation of truncated standard and elegant Laguerre–Gaussian beams, the closed-form propagation expressions for the kurtosis parameter K of standard and elegant Laguerre–Gaussian beams passing through apertured optical systems are derived, it is shown that the kutosis parameter K of standard and elegant Laguerre–Gaussian beams depend on order p and index m of Laguerre polynomial, the beam-truncated parameter δ and the generalized Fresnel number F. Detailed numerical examples are given to illustrate the analytical results.     

Focal switch of spherically aberrated Laguerre–Gaussian beams

Based on the Collins formula, we study the focal switch of spherically aberrated Laguerre–Gaussian (L–G) beams passing through an optical system with the aperture and lens separated. Our results demonstrate that the behavior of the focal switch of spherically aberrated L–G beams is generally dependent on the spherical aberration coefficient, truncation parameter, Fresnel number and mode indices. The spherical aberration affects the relative focal shift, critical position of the focal switch and the relative transition. We also illustrate that there exists a minimum in addition to a maximum in the truncation parameter. Only inside the region between the minimum and the maximum the focal switch effect can be expected. The region depends on the spherical aberration coefficient as well as the Fresnel number.     

Changes in the polarization, the coherence and the spectrum of partially coherent electromagnetic Hermite–Gaussian beams in turbulence

The unified theory of coherence and polarization is applied to an investigation of the changes in the polarization, the coherence and the spectrum of partially coherent electromagnetic Hermite–Gaussian (EHG) beams propagating through atmospheric turbulence. Based on the extended Huygens–Fresnel principle, the 2×2 electric cross-spectral density matrix of partially coherent EHG beams in turbulence is expressed analytically by using a quadratic approximation of Rytov's phase structure function. The analytical expressions for the degree of polarization, the degree of coherence and the spectrum of partially coherent EHG beams in turbulence are derived, and the corresponding analytical results of electromagnetic Gaussian Schell-model (EGSM) beams can be obtained when the order number of the Hermite polynomial is zero. Some interesting results are obtained, which are illustrated by using numerical examples.     

Generalized beam propagation factor of hard-edged circular apertured diffracted Bessel–Gaussian beams

Based on the truncated second-order moments method on the cylindrical coordinate systems and the incomplete gamma function, an analytical expression of the generalized beam propagation factor (M_G² factor) of hard-edged circular apertured diffracted Bessel–Gaussian beams is derived and illustrated numerically. It is shown that the M_G² factor of hard-edged diffracted BGBs mainly depends on the truncation parameter δ and the beam parameters m and η. The results can be reduced to that for the non-truncated Bessel–Gaussian beams case and that for the truncated fundamental Gaussian beams case under certain conditions, respectively. The power fraction is also discussed analytically and numerically.     

Propagation of the Hermite–Gaussian beams through misaligned optical system with a circular aperture

By means of expanding a hard-edged aperture into a finite sum of complex Gaussian functions, the approximate analytical formula of one kind of higher-order Gaussian beams called the Hermite–Gaussian beams (HGBs) passing through circular apertured and misaligned optical system is obtained in this paper. The result provides more convenience for studying its propagation than the usual way by using diffraction integral directly. Some numerical simulations are also given for illustrating the propagation properties of the HGBs through the circular apertured optical systems.     

Application of the Wigner distribution function to complex-argument Hermite– and Laguerre–Gaussian beams beyond the paraxial approximation

The Wigner distribution function (WDF) is applied to study the propagation of complex-argument Hermite–Gaussian (HG) and Laguerre–Gaussian (LG) beams beyond the paraxial approximation. The analytical expressions for their intensity distributions in free-space propagation are derived, which are expressed in terms of Hermite polynomials for nonparaxial complex-argument HG beams and in terms of the sum of finite Hermite polynomials for nonparaxial complex-argument LG beams. A detailed comparison of the WDF approach, series expansion method and paraxial expressions is made, which shows that in the paraxial regime the WDF approach and series expansion method deliver consistent results with that of paraxial expressions. Beyond the paraxial approximation, the WDF approach offers convergent results, whereas the series expansion method has a limited applicable range, within which it gives consistent results with that of WDF approach but beyond which it gives unrealistic and divergent results.     

Excitation of nonlinear surface modes by wave beams

We consider the interaction of 2-D and 3-D wave beams with an interface between linear and nonlinear media. The range of parameters of Gaussian beams exciting nonlinear surface waves (NSW) with high efficiency is analytically determined. Different regimes of NSW excitation are numerically studied. Analytical data are in good agreement with numerical results.Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, Nos. 3–4, pp. 246–255, March–April, 1995.     

Bessel–Gaussian Beams in an Inhomogeneous Medium

Solutions of the parabolic equation which describes propagation of Bessel–Gaussian beams along the axis of an axially-symmetric medium having quadratic inhomogeneity have been obtained and investigated. It is shown that in the process of propagation the parameters of the beams change nonmonotonically. In the case of a transparent medium the beams periodically recover their initial structure.     

Focal shift in Hermite–Gaussian beams based on the encircled-power criterion

The focal shift in Hermite–Gaussian beams, whose axial irradiance vanishes, is studied based on the encircled-power criterion, and the results are illustrated numerically. The related problems are discussed.     

Comparison of SRS thresholds under pumping by Gaussian and Bessel beams

In the paraxial approximation, it has been shown that the quasi-stationary SRS amplification coefficient in the near-threshold region is determined by the product of the pump intensity in the beam center and the overlap integral of the transverse structure of the pump and the Stokes component. Expressions for the overlap integral and the scattering powers have been obtained and analyzed for the following cases: the pump and the Stokes field are Gaussian beams; the pump and the Stokes field are Bessel beams; the pump is a Bessel beam and the Stokes field is an axial Gaussian beam. Relations between the SRS excitation thresholds in different cases have been found.Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 71, No. 6, pp. 778–787, November–December, 2004.This revised version was published online in April 2005 with a corrected cover date.     

Investigation of a Broadband Quasi-Optical Mode Converter for a Multi-Frequency 1 MW Gyrotron

A broadband quasi-optical (QO) mode converter for a multi-frequency gyrotron has been designed and tested at Forschungszentrum Karlsruhe (FZK). The launcher is optimized for the TE_22,8 mode at 140 GHz, but the radiated beams present an almost identically focused pattern for all 9 considered modes between 105 GHz (TE_17,6) and 143 GHz (TE_23,8). Combining with a beam-forming mirror system, which consists of a quasi-elliptical mirror and two phase-correcting mirrors with non-quadratic surface contour, further calculations show that efficiencies of more than 94% have been achieved for converting the rotating high-order cylindrical cavity modes into the usable fundamental Gaussian mode. Low power (cold) measurements show a good agreement with theoretical predictions. This QO mode converter can be used for the broadband operation of a multi-frequency 1 MW gyrotron.     

High-order mode Laguerre–Gaussian beam transformation using a 127-actuator deformable mirror: numerical simulations

Transforming high-order mode Laguerre–Gaussian beams in the far-field using a 127-actuator deformable mirror controlled by a stochastic parallel gradient descent algorithm is presented. As a phase shift of half wave exists between every neighboring lobes of high-order mode Laguerre–Gaussian beams, there are multiple lobes in the far-field. The suitable beam radius related to the aperture size of the deformable mirror is discussed. Three system performance metrics are evaluated, and encircled energy is preferred. Simulation results show that it is possible to compensate for the phase shifts and other phase aberrations of a high-order mode Laguerre–Gaussian beam and achieve a single bright lobe with this approach. Transforming the far-field intensity distribution of high-order mode Laguerre–Gaussian beams into Gaussian and super Gaussian distributions are also investigated.     

28 GHz/50 kW准光输出连续波回旋管

研制出国内首支基于电子回旋加热应用的28 GHz/50 kW准光输出大功率连续波回旋管。该回旋管采用了双阳极磁控注入枪,TE₀₂模式谐振腔,内置准光模式变换器,单级降压收集极。回旋管采用无液氦制冷超导磁体提供稳态磁场。实验中成功实现54.8 kW/1 s短脉冲输出和45.8 kW/30 s的连续波输出,工作频率为28.08 GHz,总效率达到57%。     

Rotation of multimodal Gauss–Laguerre light beams in free space and in a fiber

A gradient algorithm is proposed for design of phase diffractive optical elements (DOEs) that can form the light beams being effectively a superposition of a small number of nonradially symmetric Gauss–Laguerre modes with a preset energy contribution of each mode. We show that under certain conditions there is a rotation of the cross-section of such light beams. The rotation of multimodal Gauss–Laguerre light beams propagating in a fiber with quadratic dependence of the refractive index is discussed.     

High-Efficient Mode Converter for ITER Gyrotron

A high-efficiency mode converter of the ITER gyrotron operating mode into the Gaussian wave beam has been developed. It includes an irradiating waveguide with shallow deformation and profiled quasi-optical mirrors to increase the Gaussian content. Low-power tests were carried out with a TE_25.10 mode exciter and a mode converter. A prototype of the short-pulsed 170 GHz gymtmn with the new converter was manufactured and tested. Diffraction losses measured inside the tube were less then 2% at the 1 MW power level. A high Gaussian mode content in the output beam has been also demonstrated.     

The factor of nonparaxial Hermite–Gaussian beams and related problems

On the basis of the second-order moment of the power density and in the use of the series expansion, the expressions for the beam width, far-field divergence angle and M² factor of nonparaxial Hermite–Gaussian (H–G) beams are derived and expressed in a sum of the series of the Gamma function. The theoretical results are illustrated with numerical examples. The M² factor of nonparaxial H–G beams depends not only on the beam order m, but also on the waist-width to wavelength ratio w₀/λ. The far-field divergence angles of nonparaxial H–G beams with even and odd orders approach their upper limits θ_max=63.435 and 73.898, respectively, which results in M²<1 as w₀/λ→0. For the special case of m=0 our results reduce to those of nonparaxial Gaussian beams. Some problems related to the characterization of the nonparaxial beam quality are also discussed.     

Propagation properties of anomalous hollow beams in a turbulent atmosphere

Propagation of circular and elliptical anomalous hollow beams in a turbulent atmosphere is investigated in detail. Based on the extended Huygens–Fresnel integral, analytical formulae for the average irradiance of circular and elliptical anomalous hollow beams propagating in a turbulent atmosphere are derived. The irradiance and spreading properties of circular and elliptical anomalous hollow beams in a turbulent atmosphere and in free space are studied numerically. It is found that circular and elliptical anomalous hollow beams at short propagation distance in turbulent atmosphere have similar propagation properties to those of free space, while at long propagation distance, circular and elliptical anomalous hollow beams eventually become circular Gaussian beams in a turbulent atmosphere, which is much different from their propagation properties in free space. The conversion from an anomalous hollow beam to a circular Gaussian beam becomes quicker and the beam spot spreads more rapidly for a larger structure constant, a shorter wavelength and a smaller waist size of the initial beam.