Overlap integral is required to calculate the phase shift in the pn junction based optical modulator i.e. Δϕ =2πΔΓΔnL/λ.
Here ΔΓ is related to the overlap of the depletion width Δx with optical confinement, which is determined by the waveguide geometry, location of the p-n junction and the impurity doping concentrations.
I want to know the exact formula of ΔΓ.
Thanks in anticipation.
Dear Subhash,
this depends strongly on your application. In case of pn-junction, however, I would recommend to use the overlap integral of the optical field in the waveguide over the electrical field insight the waveguide. As alternative to the overlap integral, you can use the field confinement factor (FCF), as you have mentioned. The FCF in high index contrast waveguides, e.g. silicon-on-insulator waveguides, is defined as the time averaged power flow in the waveguide over the time averaged power flow insight the whole system (see attached papers for more information).
First remark: You should bear in mind that the FCF (for what you are looking for) is just a factor to avoid overestimation of the phase shift.
Second remark: In your formula you use Delta Gamma. However, the change of FCF is negligible.
Conference Paper Silicon-On-Insulator Slot-Waveguide Design Trade-Offs
Chapter Design Optimization of Silicon-on-Insulator Slot-Waveguides ...
Dear Patrick,
Thank you very much for fast and appropriate response.I shall read your recommended articles. Thanking you again.
Dear Patrick,
In line of your suggestion that ,"I would recommend to use the overlap integral of the optical field in the waveguide over the electrical field insight the waveguide."
If I take the ratio of area under the curve of Electric Field norms of OPTICAL FIELD and area under the curve of Electric field (y component) of TM mode of ELECTRIC FIELD for the range where these field interact most, will give me ΔΓ.
Waiting your response.
Thanking you.
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