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Decreasing the index change of grating with trapezoid index modulation

Trapezoid index modulation (TIM) is introduced in long period fiber grating to decrease the index change. The coupled-mode equations of long period grating with trapezoid index modulation have been presented. The coupled interactions considered in these equations include not only the self-coupling of the core mode and the coupling between the fundamental core mode and the cladding modes, but also the self-coupling of the cladding modes. Compared with the long-period fiber grating with rectangle index modulation (RIM), the advantage of this novel grating is that it needs a smaller refractive index change. The value of refractive index change decreases with the increasing of the difference between the top width and the bottom width. When the difference between the top width and the bottom width is 30 μm, the refractive index change is only 80.2% of that of the long-period fiber grating with rectangle index modulation. Trapezoid index modulation can also be applied to the fiber Bragg and sampled grating to decrease the refractive index change. Sixteen uniform channels filtering with small refractive index change are also demonstrated.