Hello,

I would like to ask how group index is used to calculate neff as a function of frequency in INTERCONNECT “Straight waveguide element”. It is considered that dn/dω is a constant value? Thanks in advance.

# Straight waveguide Interconnect

**evachat**#1

**bkhanaliloo**#2

Dear @evachat

The values for neff and ng are extracted from Mode simulations as is explained here and then are imported into INTERCONNECT.

This link also provides the details how software calculates group index in Mode solutions.

I hope I could answer your question.

**evachat**#3

Actually, I ask for the element Straight Waveguide here where I can set a single value for effective index and group index at a specific frequency I assume…

**bkhanaliloo**#4

Dear @evachat

Thank you for clarification.

In this case neff and group index are given at the central frequency. However, if you want to perform broadband calculation, software uses Taylor expansion to calculate effective index at other frequencies as is explained in the link that you provided.

For simplicity, lets assume that dispersion is zero. Software will use *ng* and *neff* to calculate the slope of refractive index at central frequency. Then will use a linear Taylor expansion to calculate the value of neff at the new frequency (w):

neff(w) = neff(w0) + ( ng(w0) - neff(w0) ) * (w - w0)/w0;

where ( ng(w0) - neff(w0) )/w0 is the slope of effective index (dn/dw) at w=w0. So, as you can see the value for ng and neff at central frequency are used to calculate new values at a new frequency of interest.

You can expand this calculations for cases where dispersion is not zero.

I hope I could answer your question.

**evachat**#5

Yes, but it is given for a certain frequency right? What if I run a

broadband simulation with a Network Analyzer?

Quoting Behzad Support Khanaliloo lumerical@discoursemail.com:

**gwang**#6

Hi @evachat,

The values are for a certain central frequency which is defined by the “frequency” in the “Standard” setting.

If you run a broadband simulation with an ONA, it is important to match the ONA’s central frequency to the waveguide’s central frequency. Then the effective index is calculated in respect to frequency as:

`neff(w) = neff(w0) + ( ng(w0) - neff(w0) ) * (w - w0)/w0;`

where w0 = 2*pi*f0.