Near Field Propulsion Forces from Nonreciprocal Media

Arguments based on symmetry and thermodynamics may suggest the existence of a ratchetlike lateral Casimir force between two plates at different temperatures and with broken inversion symmetry. We find that this is not sufficient, and at least one plate must be made of nonreciprocal material. This setup operates as a heat engine by transforming heat radiation into mechanical force. Although the ratio of the lateral force to heat transfer in the near field regime diverges inversely with the plates separation, $d$, an Onsager symmetry, which we extend to nonreciprocal plates, limits the engine efficiency to the Carnot value ${\eta }_c$. The optimal velocity of operation in the far field is of the order of $c{\eta }_c$, where $c$ is the speed of light. In the near field regime, this velocity can be reduced to the order of $\overline{\omega }d{\eta }_c$, where $\overline{\omega }$ is a typical material frequency.

Figure 1

Two objects placed in vacuum. Object 1 is held at temperature $T_1$, while object 2 and the environment are held at zero temperature, for simplicity. Object 2 is translationally invariant in direction $y$, and we consider the force acting on it in that direction.

Figure 2

Two parallel plates at a distance $d$, at different temperatures. At close proximity, these may mimic, e.g., inner and outer parts of an engine axis (left). We consider the case where the lower plate is nonreciprocal, which may, e.g., be due to a magnetic field pointing in the direction as indicated in the figure.

Figure 3

Scaled motive force $F_{y}c$ (red diamonds), and heat transfer $H$ (gray circles) for a SiC plate and one of n-InSb subject to a magnetic field along the $x$ axis. The dots correspond to numeric calculations and the continuous lines to the small $d$ asymptotes from Eq. (11) and its equivalent for $H$. Note that the force changes sign from $+y$ to $-y$ (dark red to light red diamond) at large separation. Inset: left-hand side of Eq. (13) in units of $c/(\omega d)$ for $d=1\mathrm{nm}$. Figures’ parameters: $B=10T$, $T_1=300K$, $T_2=270K$.