Sensitivity analysis and optimization of sub-wavelength optical gratings using adjoints.

Area of Science:

• Photonics and Optical Engineering
• Computational Electromagnetics
• Device Design and Optimization

Background:

• Numerical optimization of photonic devices is computationally intensive.
• The finite-differences gradient method requires numerous electric field calculations, proportional to design parameters.
• This limits the efficiency and scope of photonic device optimization.

Purpose of the Study:

• To introduce and derive the adjoint formalism for efficient gradient computation in photonic device optimization.
• To demonstrate the practical application of adjoint-based optimization.
• To overcome the computational limitations of traditional gradient methods.

Main Methods:

• Derivation of the adjoint formalism for electromagnetic field computations.
• Application of the adjoint method to optimize a waveguide slab.
• Utilizing the adjoint method for designing optical sub-wavelength gratings.

Main Results:

• Adjoint-based optimization requires only two electric field computations, regardless of design parameters.
• Demonstrated successful application in optimizing waveguide slabs.
• Successfully applied to the design of optical sub-wavelength gratings, showcasing efficiency gains.

Conclusions:

• Adjoint-based optimization offers a computationally efficient alternative to finite-differences methods for photonic devices.
• The derived adjoint formalism is a valuable tool for accelerating the design of complex photonic structures.
• This approach significantly reduces computational cost, enabling more complex and rapid optimization of optical devices.