First the obvious. The period of a fiber Bragg grating is half the optical wavelength in the fiber. So calculate this using the free space wavelength lambda0 and the effective (group) refractive index neff. Period = lambda0/2neff. You will have to measure or calculate neff. The strength of the grating coupling to the mode is a function of overlap of the mode and the grating. This is detailed in lots of places including here https://www.rp-photonics.com/fiber_bragg_gratings.html. A weak grating can produce a narrow reflection band while a strong grating can produce a wide reflection band. The formula for the spectral reflection is simple. Check out the Wikipedia page on fiber Bragg gratings. The coupling constant can vary over a wide range. If this gives you a start, good. If you want more specifics, please ask.

David A. Ackerman thanks a lot sir.

From the perspective of coupled mode theory:

[Recommended book: A. Yariv, P. Yeh, "Photonics - Optical Electronics in Modern Communication"]

Grating structures/periodic perturbations are used to couple (transfer energy) modes either in the same direction (co-directional coupling) or in the opposite direction (contra-directional coupling) at a particular wavelength.

In a single-mode fiber, where only fundamental mode is present, with the use of Bragg gratings incident power in the fundamental mode can be transferred to the same mode, but in the opposite direction (reflection) at the operating wavelength. In order for this power transfer to take place, a phase matching condition has to be satisfied. The general phase matching condition for contra-directional coupling is Beta1 + Beta2 = 2pi/Lambda, where Beta1 and Beta2 are the propagation constants of the coupled modes and Lambda is the grating period.

For single-mode FBG the incident mode and reflecting mode are the same, that is why Beta1 = Beta2, which leads to the equation lambda0 = 2*neff*Lambda, where lambda0 is the operating wavelength and neff is the effective refractive index of the fundamental mode at the operating wavelength.

Similarly, in the multimode waveguide, gratings can be used to couple two different modes. For example, the fundamental mode can be excited in the forward direction and the grating period can be set in such a way that the power is transferred to the higher-order mode, but in the backward direction.

1. So the grating period can be calculated from the phase matching condition depending on the effective index of the coupled modes at the operating wavelength.

2. Modulation depth is generally associated with modulation strength in the rectangular waveguides, because the gratings are surface corrugated (in most cases) on the rectangular waveguides. Higher the modulation depth, higher is the modulation strength. In case of fibers, gratings are periodic variation of high and low refractive indices. So the modulation strength is denoted by contrast (difference) between the high and low refractive indices. Higher the contrast, higher is the modulation strength. Higher modulation strength leads to higher reflection peak and wider bandwidth in the reflection spectrum. That means full reflection can be achieved at a smaller grating length.

Manoranjan Minz thank you so much.

Tomasz Osuch Thank you so much sir.

Thanks David A. Ackerman

For basic concept in FBG, I would like to recommend you a paper titled "Fiber Grating Spectra" by Turan Erdogan.

Krishna Mohan Dwivedi Thanks a lot

Biswajit Ghosh