Scanning two-grating free electron Mach-Zehnder interferometer

We demonstrate a two-grating free electron Mach-Zehnder interferometer constructed in a transmission electron microscope. A symmetric binary phase grating and a condenser lens system form two spatially separated, focused probes at the sample which can be scanned while maintaining alignment. The two paths interfere at a second grating, creating constructive or destructive interference in the output beams. This interferometer has many notable features: positionable probe beams, large path separations relative to beam width, continuously tunable relative phase between paths, and real-time phase information. Here we use the electron interferometer to measure the relative phase shifts imparted to the electron probes by electrostatic potentials as well as a demonstration of quantitative nanoscale phase imaging of a polystyrene latex nanoparticle.

Figure 1

(a) Diagram for 2GeMZI showing definitions of the different transverse planes as well as labels for the transverse wave functions in each plane, the magnetic lenses (L1, L2, L3), gratings (G1, G2), and beam-defining aperture $A\left(\mathbf{x}\right)$ are also shown. The three different images depict the three cases of when the different gratings are inserted or removed. The position of the second grating relative to the beam is denoted as ${\mathbf{x}}_0^{\prime }$. (b) Diffraction efficiencies of G1, measured when G2 is removed. (c) Diffraction efficiencies of G2, measured when G1 is removed. (d) Measured output intensities of the 2GeMZI for different relative grating shifts normalized to maximum output intensity. (e) Simulated output intensities of the 2GeMZI for different relative grating shifts.

Figure 2

Bright field (BF) STEM images showing the interferometer output spatially oscillating between the intensity minimum and maximum for (a) grounded vertical Ag nanorod, (b) insulated vertical Ag nanorod. Insets are STEM HAADF images of each nanorod. [(c) and (d)] Simulated 2GeMZI output for two probes passing through a $1/r$ electrostatic potential where (d) has 10 times the charge of (c). [(e) and (f)] Same as (c) and (d) but with a horizontally elongated Gaussian included with the potential to simulate the increased induced charging by the incidence of the higher diffraction orders. Insets in (c)–(f) are the projected potentials used to create the simulated images. All scale bars are 100 nm.

Figure 3

HAADF and 2GeMZI BF image scans of a latex nanoparticle both from (a) simulation and (b) experiment. The rows display (i) the HAADF image, the 2GeMZI image aligned at the maximally (ii) constructive (magenta) and (iii) destructive (blue) interferometer output, and (iv) the respective line profiles. The experimental cross section [b(iv)] shows a raw cross section (thin line) and the radially averaged signal (thick line). All scale bars are 10 nm.

Figure 4

Reconstructed azimuthally averaged phase images of a latex nanoparticle from the raw 2GeMZI BF images with (a) constructive alignment (magenta) and (b) destructive alignment (blue). The simulated outcome (c) is also shown. (d) The experimental and simulated cross-sections of the reconstructed particle phase with shaded regions to show the error. All scale bars are $10\text{nm}$.

Figure 5

(a) Vertical silver nanorod FIB nanofabrication steps (i)-(iv). (b) SEM micrograph at ${52}^{\circ }$ tilt after fabrication steps (i)–(iii). SEM micrographs after fabrication steps (i)–(iv) imaging from bottom of membrane at (c) $0^{\circ }$ and (d) ${52}^{\circ }$ tilt. All scale bars are 200 nm.