Optical Propulsion and Levitation of Metajets

1. Problem Statement

Traditional optical manipulation techniques (e.g., optical tweezers) are predominantly limited to microscopic and sub-microscopic scales. While metasurfaces have revolutionized the control of light itself (manipulating polarization, phase, and amplitude), using them to control the motion of macroscopic or structured objects remains a challenge.

• The Limitation: Conventional optical forces (radiation pressure, gradient forces) typically act parallel or perpendicular to the light propagation direction. Standard refraction and reflection at interfaces follow Snell's law ($k_{out}^\parallel - k_{in}^\parallel = 0$), which results in zero net in-plane (lateral) force, preventing lateral propulsion of objects like solar sails.
• The Goal: To develop a mechanism capable of generating fully controllable, three-dimensional optical forces (both in-plane propulsion and out-of-plane levitation) on structured objects ("metajets") that are not limited by the object's size, potentially scaling from micro-devices to interstellar light sails.

2. Methodology

The authors employed a combination of first-principles theoretical modeling, electromagnetic simulations, and experimental validation using silicon-based metasurfaces.

• Theoretical Framework:

  • Derived a first-principles theory based on Newton's laws ($F = dp/dt$) applied to photon momentum transfer at an interface.
  • Introduced a spatially distributed phase gradient ($k_\phi = d\phi/dx$) via metasurfaces to modify Snell's law: $k_{out}^\parallel - k_{in}^\parallel = k_\phi$.
  • This modification allows for the generation of an effective wavevector component, enabling non-zero lateral forces.
  • Derived equations for in-plane force ($F_x$) and out-of-plane force ($F_z$) as functions of light power ($P$), refractive index ($n$), efficiency ($\eta$), and the phase gradient.

• Design and Simulation:

  • Metajet Structure: Designed "metajets" consisting of silicon nanopillars (500 nm height) on a silicon dioxide base (100 nm thick) arranged in a supercell pattern.
  • Phase Engineering: Used a "saw-tooth" phase profile created by varying the diameter of silicon pillars within a supercell (ranging from 3 to 8 pillars) to achieve a $0$ to $2\pi$ phase shift.
  • Tools:
    • Tidy3d (FDTD): Simulated unit cell behavior, phase shifts, and diffraction efficiencies.
    • COMSOL: Calculated the Maxwell stress tensor to determine the total optical force vectors acting on the supercell configurations.

• Fabrication:

  • Used Electron Beam Lithography (EBL) and Reactive Ion Etching (RIE) to pattern amorphous silicon pillars.
  • Employed a sacrificial chromium layer to detach the metajets from the substrate, allowing them to float freely in a liquid cell for motion studies.

• Experimental Setup:

  • Illuminated the metajets with a linearly polarized femtosecond laser (1000 nm wavelength) from below.
  • Measured diffraction efficiency in momentum space.
  • Recorded 3D motion (propulsion and levitation) using high-speed microscopy and video post-processing.

3. Key Contributions

1. Introduction of "Metajets": Defined a new class of vehicles constructed from metasurfaces that use the very light they manipulate to propel themselves.
2. First-Principles Theory of Metaphotonic Force: Established a theoretical model demonstrating that optical forces can be engineered to act at arbitrary angles (not just parallel/perpendicular to propagation) by manipulating the phase gradient.
3. 3D Motion Control: Successfully demonstrated simultaneous in-plane propulsion and out-of-plane levitation driven solely by optical forces.
4. Scalability Insight: Proved that the metaphotonic force scales with light power but is not limited by the size of the object, suggesting applicability to macroscopic scales (e.g., space exploration).

4. Key Results

• Force Directionality:
  • In-Plane Propulsion ($F_x$): The metajet moves in the direction opposite to the phase gradient ($k_\phi$). The force magnitude is proportional to the phase gradient ($d\phi/dx$) and diffraction efficiency.
  • Out-of-Plane Levitation ($F_z$): A vertical force component was observed, lifting the metajet against gravity (or buoyancy in liquid). This force depends on the refraction/reflection angle and efficiency.
• Supercell Optimization:
  • Experiments compared supercells with 3 to 8 pillars.
  • 3-Pillar Supercell: Produced the highest phase gradient ($d\phi/dx$), resulting in the largest refraction angle, highest diffraction efficiency (~58% measured), and maximum horizontal propulsion speed.
  • 8-Pillar Supercell: Produced a lower phase gradient, resulting in weaker propulsion but stronger vertical levitation forces.
• Experimental Validation:
  • Diffraction: Measured 58% diffraction efficiency into the $m=+1$ order, confirming the theoretical design.
  • Motion: Video analysis confirmed that metajets moved linearly along the x-axis while simultaneously levitating along the z-axis. The motion was stable and controllable by adjusting the laser power and supercell geometry.
  • Correlation: Experimental speed data matched the theoretical prediction that $F_x \propto - (d\phi/dx)$.

5. Significance and Impact

• Beyond Microscopy: This work breaks the size barrier of optical manipulation. Unlike traditional optical tweezers that struggle with large objects, metaphotonic forces scale with power, making them viable for macroscopic applications.
• 3D Control: It moves beyond simple 1D propulsion to full 3D vector control, allowing for complex trajectories (levitation + translation) without mechanical parts.
• Interstellar Applications: The authors highlight the potential for interstellar light sails. Since the force is not size-limited, large-scale metasurface sails could be propelled by high-power lasers for deep-space exploration.
• New Paradigm: It shifts the paradigm from "using light to move small particles" to "engineering structures to harness light momentum for macroscopic vehicle propulsion," opening new avenues in metaphotonics, robotics, and aerospace engineering.