Constant in Modes of Optical Fiber

[taimoortalpur]

Dear All,
Many thanks for reading this query. Actually, I am having problem in measuring the mode fields of Optical fiber at the core-cladding interface analytically for modes LP01 and LP11. The modes are normally given by eq 2.165 (image attached).

To my knowledge these constants A and C are Normalization constants to make the power in the mode equal to 1. But how to measure these Normalization constants. Is there any formula to measure them for LP01 and LP11 mode. Any sources will be highly appreciated.

I checked one source and found the formulas in attached images Eq A.9 and A.5 (where he defines LP11 mode by eq 4.9 in some way normalized again) but when I measure value with these Normalization coefficients I get answer in range of 10^6 (definitely there is something wrong) I will be helpful if someone can figure out some error or can give some guideline.

Many Thanks again..

 

[Claude Bile]

The normalization constants are derived from the boundary conditions for a given fiber geometry.

Claude.

 

[taimoortalpur]

Many thanks for your humble reply. I used the Normalization constant calculated for step index fiber LP11 mode (shown in figure) but the values are in range of 10^6 and later i use them for measuring smthng and get erronous results...Kindly inform me are there any formulas for LP01 and LP11 modes or any good source. If possible kindly inform me about the typical values.

Many Thanks in advance.