Optical forces through the effective refractive index.

Area of Science:

• Physics
• Nanotechnology
• Optomechanics

Background:

• Energy-based methods (dispersion relation, response theory of optical forces) are commonly used for optical force calculations in nano-optomechanical devices.
• These methods are often contrasted with the Maxwell stress tensor formalism.

Purpose of the Study:

• To demonstrate the theoretical agreement between energy-based methods and the Maxwell stress tensor in linear lossless systems.
• To extend the application of the response theory of optical forces to complex optical scenarios.
• To identify potential misinterpretations and inaccuracies in the dispersion relation method.

Main Methods:

• First-principles derivation to establish the equivalence of methods.
• Application of the multi-port response theory of optical forces.
• Analysis of the dispersion relation method concerning effective index derivatives.

Main Results:

• Explicit proof that energy-based methods (DR, RTOF) must agree with the Maxwell stress tensor (MST) in linear lossless systems.
• The response theory of optical forces can be extended to analyze multiple light sources, broadband sources, and multimode devices with multiple degrees of freedom.
• The dispersion relation method, when formulated using the derivative of the effective index at a fixed wave vector, can lead to misinterpretations and overestimated force calculations.

Conclusions:

• The equivalence of energy-based methods and MST provides a robust framework for optical force calculations.
• The extended RTOF formalism offers a versatile tool for analyzing complex optical systems in nano-optomechanics.
• Careful application and interpretation of the dispersion relation method are crucial to avoid inaccuracies in optical force determination.