Sumetsky M
OFS Laboratories, 600 Mountain Avenue, Murray Hill, New Jersey 07974, USA.
Opt Lett. 2004 Jan 1;29(1):8-10. doi: 10.1364/ol.29.000008.
In a tapered optical fiber there exist localized light structures that, in analogy to the magnetic bottles used in plasma fusion, can be called whispering-gallery bottles (WGBs). These essentially three-dimensional structures are formed by the spiral rays that experience total internal reflection at the fiber surface and that also bounce along the fiber axis in response to reflection from the regions of tapering. It is shown that the Wentzel-Kramers-Brillouin quantization rules for the strongly prolate WGBs can be inversed exactly, thus determining the cavity shape from its spectrum. The approximation considered allows one to find the shape of the etalon bottle, which, similar to the one-dimensional Fabry-Perot etalon, contains an unlimited number of equally spaced wave-number eigenvalues. The problem of determining such a non-one-dimensional cavity is not trivial, because such a cavity does not exist among the uniformly filled cavities such as rectangular boxes, cylinders, and spheroids that allow separation of variables. The etalon cavity corresponds to the fiber radius variation p(z) = rho0/cos(deltakz)/, where deltak is the wave-number spacing. The latter result is in excellent agreement with ray-dynamics numerical modeling.
在锥形光纤中存在局部光结构，类似于等离子体聚变中使用的磁瓶，可称为回音壁瓶（WGBs）。这些本质上的三维结构由螺旋光线形成，这些光线在光纤表面经历全内反射，并且还会因来自锥形区域的反射而沿光纤轴反弹。结果表明，对于强长椭球形WGBs的Wentzel-Kramers-Brillouin量子化规则可以精确反转，从而根据其光谱确定腔的形状。所考虑的近似方法使人们能够找到标准具瓶的形状，它类似于一维法布里-珀罗标准具，包含无限多个等间距的波数本征值。确定这样一个非一维腔的问题并不简单，因为在诸如矩形盒、圆柱体和球体等允许变量分离的均匀填充腔中不存在这样的腔。标准具腔对应于光纤半径变化p(z) = rho0/cos(deltakz)/ ，其中deltak是波数间距。后一结果与射线动力学数值模拟非常吻合。
