Modal approach to optical forces between waveguides as derived by transformation optics formalism

Area of Science:

• Physics
• Optics
• Electromagnetism

Background:

• Optical forces are crucial in waveguide interactions.
• Two primary methods exist for calculating optical forces in waveguides: the Maxwell stress tensor and modal force analysis.
• The relationship between these methods, especially for arbitrary cross-sections, requires clarification.

Purpose of the Study:

• To analytically demonstrate the equivalence of the Maxwell stress tensor and modal force approaches for lossless waveguides.
• To extend this equivalence to waveguides with arbitrary cross-sections.
• To investigate the validity of this equivalence in the presence of material loss.

Main Methods:

• Utilizing transformation optics formalism.
• Analytical derivation of optical force expressions.
• Comparison of force calculations from both the Maxwell stress tensor and modal force methods.

Main Results:

• The equivalence between the Maxwell stress tensor and modal force approaches is analytically proven for lossless waveguides of any cross-section.
• The derivation encompasses both pressure and shear optical forces.
• A key finding is that this equivalence breaks down in the presence of waveguide loss.

Conclusions:

• The two distinct approaches to calculating optical forces in lossless waveguides are fundamentally equivalent.
• Transformation optics provides a unified framework for understanding these forces.
• Material loss introduces a critical difference, rendering the two methods non-equivalent.