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Abstract
We consider the Casimir force from a real frequency perspective, in a system consisting of two plasmonic metallic plates separated by a vacuum gap, in order to elucidate the connection between the Casimir force behavior and the underlying electromagnetic modes. This system supports a set of discrete modes including gap plasmon modes and guided modes. Previous works have shown that the behavior of the Casimir force in this system is well explained by the gap plasmon modes when the vacuum gap has a size of 10 nm or less. We show that in the intermediate regime where the gap size is approximately 100 nm, the contribution from the discrete modes, which are repulsive except for the lowest-order gap plasmon mode, is no longer sufficient to account for the behavior of the Casimir force. Instead, the contribution from a continuum spectrum, which is always attractive, plays a significant role. These two contributions, when integrated over the frequency, can be comparable in magnitude in the intermediate gap size regime. Our results show that including the contribution from the continuum spectrum is essential in understanding the attractive nature of the Casimir interaction. We further show that in a low-loss material system, the contributions of the discrete modes exhibit a resonant Lorentzian lineshape, and the peak resonance amplitude is proportional to the inverse of the resonance linewidth at each resonance, leading to the fact that the Casimir force is independent of the damping rate of a material.
© 2019 Optical Society of America
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