Conditions for higher-order resonant modes to be excited in a photonic-crystal fiber Bragg grating

The modal cutoff properties in a germanium-doped solid-core photonic-crystal fiber Bragg grating (PCFBG) are investigated with the beam propagation method. The results show that the normalized frequency V of a PCFBG depends not only on the normalized pitch Lambda/lambda but also on the normalized hole size d/Lambda. In addition, the single-mode-multimode boundary profile of the PCFBG shifts to the low normalized hole-size side in contrast to that of the pure-silica solid-core photonic-crystal fiber (pure-solid PCF). Furthermore, besides the phase-matching condition and the electric field overlapping with the grating region, the inequality VPCF>pi also should be fulfilled for the higher-order resonant modes to be excited in the PCFBG.

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