Dispersion and optical gradient force from high-order mode coupling between two hyperbolic metamaterial waveguides

• The dependence of dispersion properties in hyperbolic metamaterials on the filling ratio is analyzed.
• It is possible that the optical gradient forces of high-order modes are larger than the fundamental mode.
• Optical gradient forces of high-order modes weaken much faster than the case of low-order modes.
• The influence of the dielectric surrounding on the coupling effect and optical gradient force are clarified.

We analytically study dispersion properties and optical gradient forces of different-order transverse magnetic (TM) modes in two coupled hyperbolic metamaterial waveguides (HMMWs). According to Maxwell's equations, we obtain the dispersion relation of symmetric and antisymmetric modes, and calculate optical gradient forces of different-order modes by using Maxwell stress tensor. Numerical results show that the dispersion properties are dependent on the filling ratio, and the optical gradient forces of high-order TM modes are larger than the fundamental mode when the gap between two HMMWs is very narrow, but they weaken much faster than the case of low-order TM modes with the gap width increasing. In addition, the effects of the dielectric surrounding of waveguides on the coupling effect and optical gradient force are clarified. These properties offer an avenue for various optomechanical applications in optical sensors and actuators.