Investigation of beam characteristics in toric unstable optical resonator

In this paper the characteristics of the output beam of a toric unstable resonator are investigated. Based on the Fresnel–Kirchhof integral and using numerical methods, the performance of toric unstable resonators is simulated and its output beam characteristics are also evaluated. Geometrical resonator parameters, i.e. Fresnel number and magnification as well as the output coupler diameter, are considered in this investigation. The radial and azimuthal modes of the resonator are calculated and the modal behavior of the resonator is described according to geometrical parameters. The power extraction for each specific laser mode has also been inspected by calculating the finesse factor. Using an iteration mode convergence diagram, the mode discrimination of the resonator is investigated.     

高功率激光稳定腔选模分析

讨论了在有限菲涅耳数时，稳定凹－凸腔的高功率激光选模特性，研究表明当稳定凹－凸腔工作在临近界稳区时，基模体积显著提高，具有良好的选模效果。     

Calculations,in the three-dimensional approximation,for a half-symmetric unstable resonator with internal axicon (HSURIA) in the three-dimensional diffraction approximation with annular shape of the active medium

6. Conclusions 1. It was shown that, compared with other methods, realization of the analytic Prony method increases strongly the effective establishment of the radiation of the mode structure of the radiation field in an empty cavity having o complex configuration, such as the HSURIA resonator. 2. We investigated the dependence of the losses of various azimuthal and radial modes in an empty HSURIA resonator on the value of N_eq. We have shown that in the region N_eq=20−25 and at M=2 the losses of the highest-Q zeroth and first azimuthal modes amount to ≈0.65 and ≈0.70 respectively, which ensures lasing in the single-mode regime in the case of a sufficiently homogeneous active medium. 3. We found the field distributions of various azimuthal and radial modes in the HSURIA resonator in the absence of a medium. 4. We have shown that in the case of lasing on one highest-Q mode the radiation intensity on the tip of a W-axicon is not more than 2–3 times larger than the average over the central region of the W-axicon. Translated from Preprint No. 31 of the Lebedev Physics Institute, Russian Academy of Sciences, Moscow, 1991.     

多元件谐振腔模式的有限元传输矩阵分析方法

建立了多元件谐振腔本征模的有限元传输矩阵模型。提出了模式计算相对误差概念及相应表达式,该表达式在数值上不受菲涅耳数的影响,能够很好反映有限单元划分方案对不同菲涅耳数的谐振腔的模式计算精度的影响。提出了有限单元划分精细度的概念和相应表达式,用以表征有限单元划分的精细程度。该表达式以菲涅耳数作为有限元传输矩阵法对腔镜单元格数划分的相对要求,用镜面实际划分的单元格数与菲涅耳数的比值来表征有限单元划分的精细程度。分析了不同谐振腔参数变化时模式计算相对误差与有限单元划分精细度的关系,建立了3种不同函数形式的经验表达式,并通过比较拟合残差选择了拟合效果较好的表达式。     

Coherence and polarization properties of electromagnetic laser modes

A recently formulated mode representation of stochastic electromagnetic fields, based on a unified theory of coherence and polarization is applied to determine the transverse laser resonator modes in any rotationally symmetric cavity. It is found that the electromagnetic modes can be expressed in a simple way in terms of the classic Fox-Li modes of the monochromatic scalar theory; and that, if there is no degeneracy, each mode is completely spatially coherent and its degree of polarization is the same at each point of the cavity mirror.     

激光非稳腔模式的快速计算方法

对Du Fort-Frankel差分格式用于谐振腔模式计算进行简要分析,以该差分格式为基础,提出基于移动矩阵法的非稳腔模式数值计算快速算法.对空腔共焦非稳腔模式进行数值模拟,将计算结果与参考文献进行对比,两者吻合较好.对有源共焦非稳谐振腔内增益区位置对谐振腔输出功率的影响进行数值计算,结果表明:对于采用共焦非稳腔的大功率激光器,当增益体积一定、小信号增益曲线相同时,随着谐振腔内增益区与凹面镜之间的距离的减小,激光器输出功率会有较为明显的提高.数值算例证明了本文方法的正确性和有效性.     

An anisotropic metamaterial-based rectangular resonant cavity

Resonance properties of a rectangular resonant cavity filled with an anisotropic metamaterial bilayer are investigated. Different from the isotropic case and the one-dimensional resonator, the resonance properties in such a cavity are closely related to the dispersion relation of the anisotropic medium. Three cases including six subcases of different combinations of metamaterials are discussed and it is found that subwavelength resonance modes may occur in all subcases. Particularly, the relation between resonance modes and the transverse cavity width is investigated, and calculated results show that there are infinite subwavelength resonance modes as the transverse cavity width approaches zero. Requirements of the material and geometry parameters to construct a subwavelength resonant cavity are revealed by theoretical analysis, which demonstrates that this kind of subwavelength resonator brings more design flexibility and tolerance. PACS 78.70.Gq; 81.05.Zx; 84.40.Ba     

光泵气体THz激光器用CO2泵浦源腔内光场模式

CO2泵浦源是光泵气体太赫兹激光器的核心器件之一,其性能直接关系到太赫兹激光器的工作稳定性。CO2泵浦源一般由闪耀光栅作为全反射尾镜,构成特殊的光栅腔实现波长的选支输出。采用传输矩阵的特征向量法对光栅谐振腔的腔内光场模式进行了理论分析与数值模拟,计算了光栅腔的一系列本征模式及相应的衍射损耗。结果表明光栅腔的腔内模式特性等效于一个平凹腔,而对于大菲涅尔数的光栅腔, Littrow波长的附近支线也可能具有衍射损耗较低的低阶模,可能优先于Littrow波长的高阶模起振,导致光栅腔的波长选择性降低。     

半导体超常媒质矩形谐振腔(英文)

设计并研究了两个有不同各向异性参数的半导体超常媒质矩形谐振腔,其中填充了部分右手半导体超常媒质和部分左手半导体超常媒质。通过作图法研究了充满非色散的右手半导体超常媒质和色散的左手半导体超常媒质的谐振腔中谐振模式的解。结果显示,谐振腔的谐振模式取决于半导体超常媒质的色散关系。讨论了每种谐振腔中包含的六种情况,分别表示两个区域的传播常数为实数和虚数的不同的组合,并且揭示了构建具有无相差特性的谐振腔的几何参数要求。     

圆镜共焦腔激光横模的传输矩阵法模拟和分析

共焦腔是一般稳定腔的特例,由于等价性,共焦腔中自再现模的振幅分布、损耗和光斑尺寸常常被用于讨论一般稳定腔。为了分析具有大菲涅尔数的圆镜共焦腔,本文利用传输矩阵方法对腔模进行计算和讨论。研究结果表明:传输矩阵方法的结果与Fox-Li积分迭代法的结果一致,并且传输矩阵方法实用于大菲涅尔数共焦腔。     

Extension of the Jones matrix formalism to higher-order transverse modes

The well-known Jones matrix formalism, which can be directly applied to the propagation of the polarization of fundamental (TEM(00)) laser resonator modes, has to be modified for higher-order transverse modes. It is shown that this can be done in straightforward manner by using N x N matrices instead of the 2 x 2 Jones matrices, where N denotes the number of orthogonal polarization states of the transverse mode under consideration. The most common case of TEM(01) Hermite-Gaussian modes, where N is four, is discussed in detail.     

Coaxial resonator for a megawatt 280 GHz gyrotron

To provide the required mode selectivity for a megawatt 280 GHz gyrotron, a coaxial resonator operating in a high order TE mode is considered. Mode discrimination is achieved both by exploring the differences in the transverse structures of the competing modes and investigating a suitable geometry for the coaxial insert. For modes with close eigenfrequencies the associated diffractionQ factors can be widely different in value, thereby ensuring an effective mode selection. In the resonator studied here, the frequency separation between the design mode TE_26,10,1 and its nearest competing mode TE_20,12,1 is about 0.6% and the ratio of the correspondingQ factors is as high as 6.5. Unlike the coaxial resonator, in the hollow cavity without the inner conductor the fundamental spectrum of eigenfrequencies is more dense, and all TE modes within the frequency interval 271–288 GHz have approximately the sameQ factor.     

Azimuthal behaviour of flow-excited diametral modes of internal shallow cavities

The aerodynamic excitation of ducted cavity diametral modes gives rise to complex flow-sound interaction mechanisms, in which the axisymmetric free shear layer interacts with the asymmetric acoustic modes. This results in various azimuthal patterns and behaviours depending on different flow and geometrical parameters. The azimuthal behaviour of this self-excitation mechanism is investigated experimentally. Axisymmetric shallow cavities in a duct have been tested over the range of cavity length to depth ratio from 1 to 6 and at Mach numbers up to 0.4. A set of pressure transducers flush mounted to the cavity floor is used to determine the acoustic mode amplitude and orientation. The excited acoustic modes are classified into spinning, partially spinning, and stationary diametral modes. An analytical representation based on the duct acoustics theory is used to analyse the measurements and provides a physical explanation of the observed behaviour of the diametral modes. Splitter plates are installed inside the cavity to form a geometrical preference. The acoustic response of this geometrically altered case show that pressure oscillations at different azimuthal angles along the cavity circumference can be uncorrelated, or even oscillate at different frequencies, while the diametral modes are still strongly excited. Two hot-wire probes are also used in a separate set of measurements to investigate the azimuthal behaviour of the shear layer oscillation. The results show that the shear layer oscillation has the same azimuthal distribution as that of the excited acoustic modes, indicating that the shear layer oscillation at different azimuthal angles can be not only uncorrelated but also occur at different frequencies.     

On the influence of spatial hole-burning on mode selection and mode synchronization in a CW laser

The influence of spatial saturation modulation of both the amplifier and absorber in a laser with a Fabry-Perot resonator, and of the associated Bragg-reflection, on the frequency-dependent losses necessary for single-frequency operation, as well as on the frequency synchronization of three modes, has been examined. Conditions for mode selection and mode synchronization are given. To achieve single-frequency operation in a laser with a Fabry-Perot resonator the loss difference between the mode to be selected and modes to be quenched has to be proportional to the Bragg losses of the selected mode suffered by its self-induced grating. The proportionality factor depends on the length and position of the amplifier in the cavity. In the case of a short amplifier and a short absorber inside the resonator, the discussion of conditions for synchronization of three modes shows that the synchronization regime is also determined by the position of the absorber.     

Finite-difference time-domain analysis of deformed square cavity filters with a traveling-wave-like filtering response by mode coupling

An add-drop filter based on a perfect square resonator can realize a maximum of only 25% power dropping because the confined modes are standing-wave modes. By means of mode coupling between two modes with inverse symmetry properties, a traveling-wave-like filtering response is obtained in a two-dimensional single square cavity filter with cut or circular corners by finite-difference time-domain simulation. The optimized deformation parameters for an add-drop filter can be accurately predicted as the overlapping point of the two coupling modes in an isolated deformed square cavity. More than 80% power dropping can be obtained in a deformed square cavity filter with a side length of 3.01 microm. The free spectral region is decided by the mode spacing between modes, with the sum of the mode indices differing by 1.     

Goos-Hänchen induced vector eigenmodes in a dome cavity

We demonstrate numerically calculated electromagnetic eigenmodes of a 3D dome cavity resonator that owe their shape and character entirely to the Goos-H?nchen effect. The V-shaped modes, which have purely TE or TM polarization, are well described by a 2D billiard map with the Goos-H?nchen shift included. A phase space plot of this augmented billiard map reveals a saddle-node bifurcation; the stable periodic orbit that is created in the bifurcation corresponds to the numerically calculated eigenmode, dictating the angle of its 'V.' A transition from a fundamental Gaussian to a TM V mode has been observed as the cavity is lengthened to become nearly hemispherical.     

Fundamental azimuthal modes of a constricted annular resonator: theory and measurement

The fundamental azimuthal modes of a constricted annular resonator are investigated. It is found that a given mode of an unconstricted resonator splits into two separate modes in the constricted resonator. One mode is of a higher frequency and has a pressure antinode centered in the constricted region. The other mode is of a lower frequency and has a pressure node centered in the constricted region. The resonance frequency of the higher-frequency modes increases linearly with a decrease in the constricted to unconstricted area ratio, whereas the lower frequency drops nonlinearly. Measurements and theory match to within 0.5% when end corrections and thermo-viscous losses are included in the system model. It was found that end correction impedances derived by mode-matching techniques were the only ones accurate enough to match the measurements and computation to within the error bounds.     

A laser cavity used as an etalon for interferometric control of its own field

A quantitative relationship between the cavity parameters and the angular structure of the emission scattered in a parallel-plane active cavity filled with an arbitrary set of optical elements has been determined. The multipath interference into the active cavity is demonstrated to have properties which differ radically from similar processes in the etalon—among other things the relatively low finesse of the cavity interference rings is independent of the mirror quality and is a function of the Fresnel number only. The use of the operating laser cavity as an etalon for precise control of its own mode wave parameters is discussed.     

Controlling mode locking in optical ring cavities

Imperfections in the surface of intracavity elements of an optical ring resonator can scatter light from one mode into the counterpropagating mode. The phase-locking of the cavity modes induced by this backscattering is a well-known example that notoriously afflicts laser gyroscopes and similar active systems. We experimentally show how backscattering can be circumvented in a unidirectionally operated ring cavity either by an appropriate choice of the resonant cavity mode or by active feedback control. PACS 42.60.Da; 45.40.Cc; 42.79.Bh; 42.55.-f     

Whispering-gallery modes in a barrel-shaped dielectric resonator

We experimentally study a new type of resonator, namely, a barrel-shaped dielectric resonator with whispering-gallery modes which is formed by the cutting dielectric hemisphere. Compared with a hemispherical dielectric resonator, the E type oscillation spectrum of such a resonator is rarefied with respect to the azimuthal index. Comparative analysis of the electromagnetic characteristics of the barrel-shaped dielectric resonator and half-disk dielectric resonators shows that the radiation losses of the mode energy from the spherical surface are smaller than those from the cylindrical surface. This fact stimulates the high values of the internal Q-factor of modes of the barrel-shaped dielectric resonator. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 12, pp. 1041–1048, December 2005.