I have to design the layout of an electro-optic modulator using a slot waveguide structure. In the papers from Christian Koos (Karlsruhe Institute of Technology), in particular Optics Express 15, N 10, p 5976 (2007), the modal effective area Aeff is the target of the optimization in order to increase the nonlinear effects. In the case of a slot waveguide, the Aeff within the nonlinear slot must be minimized. I'm wondering if this Aeff is related to the travelling optical field or to the applied electric field at the electrodes.
Aeff should be minimized with respect to optical field (because, nlo effects are proportional to optical intensity)
Dear Srikanth, I thank you for your reply.
I see what you say and I agree.
My question arises from the induced birefringence Dn in EO modulators that can be expressed as 1/2 (n3 r33 E), where E in this case is the E field related to the voltage applied at the contacts of the EO modulators. For a good design we should maximize the E-field intensity to optimized the Dn. This is not an optical field as it is related to an applied voltage. So I'm wondering if it is something whose effective area must be minimized, too, as we know from Maxwell equations that every E-field has a H-field related.
The nonlinearity inside the slot depends on the superposition of the evanescent optical fields propagating through the cores. So yes, Aeff (which must be quite small because high intensity is desired to reach nonlinear effects) is related to the traveling optical field! Best regards.
If you want to optimize an EO modulator with an active part in the SLOT, you must increase the overlapping between the optical and electrical field in the SLOT. Because if you look at the variation of the effective index of the TM like mode, it is related to the electro-optic overlap integral in the active area. See for example "H. Kogelnik, “Theory of optical waveguides”, Ch. 2, pp. 7-88 in Guided Wave Optoelectronics 2nd Ed. Springer Series in Electronics and Photonics Vol. 26, T. Tamir Ed. (1990)"
The different steps for such optimization are :
1) Optimization of the optical geometry for a monomodal propagation and a maximum of the optical power in the SLOT part.
2) Put the metallic electrode sufficiently far away of the optical waveguide in order to preserve the absorption losses at small value close to 1 dB/cm for example.
3) Optimization of electrode geometry for first matching the effective indexes of the optical and RF modes and second maximize the electro-optic overlap integral.
Regards
@Efrain and Regis: I really thank you for your useful suggestions.
In terms of math expressions, for what i understand keeping on studying, in the delta n Dn expression i reported above, that is a direct function of the Electric field, the optical field influence in the nonlinear material is expressed within the r33 coefficient. So if we develop the r33 we can find Dn depending on both the E-fields (travelling optical and applied electrical field).
Is that correct ?
Yes,
If you look at the mode coupling theory, the variation of the propagation constant of the optical mode is proportionnal to overlap between a first quantity (a tensor of the variation of the permittivity multiply by the electric field of the optical mode (Eopt)) multiply by the complex conjugate of the electric field of the optical mode (E*opt).
The variation of the permittivity is given by the product of the electro-optic tensor and electric field of the RF signal (Erf). If we use only the r33 coefficient, the variation of the propagation constant is proportional to r33*Erf*Eopt*E*opt.
This meens that optimization of the modulator involve the maximization of the overlap between the RF and optical mode.
Regards
Dear Regis,
i really thank you for your precious explanation.
Very best regards
- Badges
- Science method