Poisson’s spot with molecules

In the Poisson-spot experiment, waves emanating from a source are blocked by a circular obstacle. Due to their positive on-axis interference an image of the source (the Poisson spot) is observed within the geometrical shadow of the obstacle. In this paper we report the observation of Poisson’s spot using a beam of neutral deuterium molecules. The wavelength independence and the weak constraints on angular alignment and position of the circular obstacle make Poisson’s spot a promising candidate for applications ranging from the study of large molecule diffraction to patterning with molecules.

Figure 1

(Color online). Poisson-spot experimental setup: A beam of neutral ${\text{D}}_2$ is created in a supersonic expansion from a $10\mu \text{m}$ nozzle at 11 bar source pressure, and cooled with liquid nitrogen to a temperature of 101 K. This results in a terminal beam velocity of $v=1060{\text{ms}}^{-1}$, as determined from time-of-flight spectra, corresponding to a de Broglie wavelength of $\lambda =0.096\text{nm}$. The measured velocity spread is $\Delta v/v=0.054$. The source size is defined by the $50\mu \text{m}$-diameter source skimmer made from a glass pipette [10]. A shadow is cast by a free-standing circular disk of $60\mu \text{m}$ diameter located at $g=1496\text{mm}$ and sampled at distances $b=321$, 641, and 801 mm using an $11\mu \text{m}$-aperture skimmer (prevents back streaming) mounted on an $x\text{−}y$ piezo table. An electron-bombardment ionization region together with a magnetic sector for mass selection and a channeltron are used for detection of the beam.

Figure 2

(Color online). Electron and optical microscopy images of the circular obstacle. It is a free-standing silicon nitride $\left({\text{SiN}}_x\right)$ disk, $60\mu \text{m}$ in diameter, less than $1\mu \text{m}$ in thickness and suspended by four narrow support bars. It was fabricated at the NanoStructures Laboratory of MIT. The pattern was written by scanning-electron-beam lithography and transferred into the ${\text{SiN}}_x$ using reactive-ion etching. (a) The scanning-electron micrograph shows the edge of the free-standing circular disk at the corner of the left-most support bar in the same orientation as in the larger scale micrographs. The edge roughness is close to minimal there and measures about 250 nm peak-to-peak. The scanning-electron micrograph in (b) reveals additional edge roughness in the form of remnants from etching protruding up to 500 nm from the disk edge. (c) Optical micrograph showing the outer aperture of $400\mu \text{m}$ diameter.

Figure 3

2D image of a molecular-beam Poisson spot. The contour lines show the higher intensity regions along the edge of the shadow, revealing the positions of the support bars. They are separated by 200 counts per second. The central part of the shadow is amplified as a grayscale image plot. The image is the sum of 24 images recorded consecutively at a sampling distance of 321 mm (2.8 h recording time per image). The images were summed with a variable pixel shift, determined from minimizing the sum of squared pixel-value differences. This was done to compensate for misalignment due to temperature drifts. A 2-by-2 Savitzky-Golay filter was applied to reduce noise.

Figure 4

The Poisson spot for three different disk-to-sampling plane distances: (a) 321 mm, (b) 641 mm, and (c) 801 mm. The data set in (a) is the horizontal profile of the image in Fig. 3 with an accumulated measurement time per data point of 136 s. The measurement time per data point was 120 s for the medium sampling distance and 60 s for the largest. The error bars show statistical uncertainty only. The unobstructed count rates were $3800{\text{s}}^{-1}$, $2500{\text{s}}^{-1}$, and $1700{\text{s}}^{-1}$, respectively, giving diffraction efficiencies of about 1%–2%. The lines show the result of model calculations, taking into account the actual measured unobstructed beam intensities. The dashed lines show the diffraction pattern to be expected from an ideally shaped circular disk, while the continuous lines show model results taking into account roughness, which was modeled by a fourth power sine with a period of about $1\mu \text{m}$ and a peak-to-peak amplitude of 300 nm added to the edge of the ideal disk. Fitting the data to the calculation was achieved solely by subtracting background (approximately $475{\text{s}}^{-1}$) and adjusting for any lateral misalignment. When an edge corrugation of 300 nm is incorporated there is an excellent agreement between simulated and measured intensity profiles. This level of edge corrugation also corresponds very well to the observed defects (Fig. 2).