I'm currently trying to calculate the effective refractive index n_(eff) of waveguides using the (measured) group index n_g and the wavelength lambda.

analianopolisca

analianopolisca

Answered question

2022-08-12

I'm currently trying to calculate the effective refractive index neff of waveguides using the (measured) group index n g and the wavelength λ.
I started with the relation between n e f f and n g :
n g = n e f f ( λ ) λ ( d d λ n e f f ( λ ) ) .
Here I am stuck - if I know n g and the wavelength λ, can I use the above relationship to determine n e f f , or is there another approach that I should use?

Answer & Explanation

Chaya Garza

Chaya Garza

Beginner2022-08-13Added 10 answers

We can rewrite the differential equation as:
1 λ d n e f f d λ n e f f λ 2 = d d λ ( n e f f λ ) = n g λ 2
So
n e f f λ = C n g λ 2 d λ
for some constant C, which you can establish using suitable boundary conditions.
To solve this using numerical data, as you have suggested in the comments, between 850   nm and 855   nm, you would replace the integral with a sum:
n g λ 2 d λ n g λ 2 Δ λ
where Δ λ is the wavelength spacing between measurements.

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