Original author: **Chibuikem Ukaegbe** Revised and edited by: **Jacky Song** ## Background Project Elara seeks to send maser beams over long distances, but beam divergence causes the signal to lose its coherence as it travels. This divergence occurs at a rate inversely proportional to the aperture size, so the smaller apertures that are more realistic to construct experience more divergence. as they travel. To counteract this, a technique developed by Project Elara's researchers, known as **coherent beam synthesis**, will be used to increase effective aperture size and thus reduce the divergence of the beam. The synthesized beam is created by coherently combining two beams spaced apart from each other, with the mutual destructive and constructive interference this creates simulating a larger aperture beam, and reducing beam divergence. ## Objective In this experiment, the calculations in [[Principles of coherent beam synthesis]] are to be challenged using 2 He-Ne lasers, primarily the derived formula for the diameter $d$ of the primary beam envelope: $ d = \sqrt{ 2\lambda z } $ While it would be ideal to test this using 2 masers, the maser prototypes are not complete at this point. In addition, masers are typically much larger than visible light masers, so conducting this experiment using them would increase the scales too significantly for our optics table to accommodate. It was determined in [[Merits and Limitations of Maser Technology, Literature Review]] that masers and lasers do not exhibit significantly different behavior in the absence of large particles which may cause diffraction, so the results from this experiment can be scaled up reasonably for Project Elara's application. ## Equipment - 2 633 nm He-Ne lasers - Photodiode or digital photodetector[^1] - 4 Iris apertures[^1] - Computer with software that can record the photodetector output - Thin film or filter wheel - Optical rangefinders ## Procedure #### I. Photodetector Test **Objective** - Ensure that the photodetector/photodiode is functioning correctly and that the interference pattern can be observed using the software. **Setup** - Place the photodetector and 1 He-Ne laser on the optical table - Place a thin film or filter wheel in the path of the photodetector. If the intensity of the He-Ne lasers can be adjusted, set them to the lowest intensity at which you can see the beam instead. - Move the He-Ne laser such that its beam is incident on the photodetector. **Analysis** - Observe the photodetector output and ensure that beam intensity remains stable. #### II. Beam-Combining **Objective** - Observe the interference pattern caused by the combination of the 2 coherent lasers. **Setup** - Place the photodetector and He-Ne lasers on the optical table - Place a thin film or filter wheel in the path of the photodetector. If the intensity of the He-Ne lasers can be adjusted, set them to the lowest intensity at which you can see the beam instead. If using a filter wheel, reduce the beam transmission to ~10% to prevent damage to the photodetector. - Place both a distance $z$ from the photodetector and a distance $D_b$ from the center of the photodetector. Use optical rangefinders to measure precise distances if available. *(Note) The angle and distances will depend on the equipment used and the scale at which the experiment takes place. Since the derivation assumes $z\gg D_b$, $z$ should be on the order of $\pu{10-100 cm}$ if $D_b$ is on the order of $\pu{1-10 mm}$ to maintain proportionality.[^1]* - Angle the lasers such that they each strike the photodetector at the same angle. Use optical rangefinders to measure precise distances if available. - Place 2 (open) iris apertures in the path of each beam near the photodetector. - Ensure that all equipment is aligned and both lasers meet at the photodetector. - Thin the beams using the iris apertures. - Ensure that the photodetector is receiving both beams and that the software is displaying a stable signal. Increase beam intensity of the lasers or beam transmission of the filter wheel if needed. ![[beam-combining-experiment-procedure.svg]] **Record Data** - Block laser B and record the intensity profile of laser A from the photodetector for a few minutes. - Unblock laser B. - Block laser A and record the intensity profile of laser B from the photodetector for a few minutes. - Unblock laser 2. - Record the intensity profile on the photodetector for a few minutes. ## Analysis - Download all data recorded from the photodetector - For the recordings where only Laser A and only Laser B were active, calculate the average intensities $I_A$ and $I_B$​. - For the recording with both lasers active, plot the time-averaged intensity over space. The presence of a stable, periodic oscillation in the intensity (interference fringes) confirms coherent combination. - Compare the interference pattern recorded by the photodetector to the theoretical interference pattern $I(r,z)$ determined analytically in [[Principles of synthetic apertures]], given by: $ I(r, z) = I_0 \cos^2 \left(\dfrac{kr^2}{2R(z)}\right)e^{-2r^2/w(z)^2} $ - Calculate the theoretical beam envelope diameter $d_{theoretical} = \sqrt{ 2 \lambda z }$ from the initial parameters (i.e. the known wavelength $\lambda = \text{633 nm}$ and the known distance between the lasers and the source). - Compare with the measured the experimental beam envelope diameter $d_{experimental}$ from taking the central lobe with from a curve fit of the experimentally-measured interference pattern - Calculate experimental error and suggest possible sources. [^1]: We thank [Dr. Ingrid Wilke](https://faculty.rpi.edu/ingrid-wilke) of Rensselaer Polytechnic Institute for giving us these equipment and experimental suggestions, as well as meeting with us to give feedback on the [initial version of our design](https://codeberg.org/elaraproject/beam-combining-experiment).