Abstract
The classification and calculation of the core modes of all-solid photonic
bandgap fibers (ASPBFs) are addressed. The first 12 modes of a multimode
ASPBF are calculated by a full-vector finite difference method (FDM) using a
Yee's cell in cylindrical coordinates. The modes of the ASPBFs are labeled
in analogy with step-index fibers based on their mode profile similarities,
and are classified into nondegenerate modes or degenerate pairs according to
the minimum waveguide sectors and the associated boundary conditions based
on results from symmetry analysis. Furthermore, an analytical effective
index model (EIM) for ASPBFs can be formulated, which yields highly accurate
results in calculating the effective indices of those 12 modes. The
advantages of simple and fast implementation of the EIM are demonstrated by
designing ASPBFs that can be used in second harmonic generation for a source
wavelength of 1.06 μm. The phase matching condition
is achieved between an index-guided fundamental HE<sub>11</sub> mode for the IR and
a bandgap-guided higher-order HE<sub>12</sub> mode for the second
harmonic. The fiber parameters determined by the EIM are confirmed by the
FDM.
© 2011 IEEE
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