The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

The overall goal of this procedure is to generate higher order lags optical beams at high purity for use in high precision interferometry. This is accomplished by first designing and prototyping the optimal phase conversion pattern to convert a fundamental mode optical beam into a desired higher or de mode using a spatial light modulator mode converter, and then manufacturing a phase plate converter based on the prototyping results. The second step is to inject a fundamental mode laser beam onto the manufactured phase plate to produce a beam at low purity.

The produced beam is carefully profiled, matched to desired new beam parameters by means of lenses to be eventually injected into the linear mode cleaner cavity. Next, the linear mode cleaner cavity operates as a mode selector to the injected beam. Locking the linear mode cleaner allows separating the desired the gilgo mode from the residual unwanted modes, rejecting these and eventually increasing the overall mode purity of the generated beam.

The final step is to design the mirrors required for the desired performance of the Lega GARS mode in a full scale detector. This is achieved by simulating subsystems of the detector and reducing certain shapes in the mirror surfaces until the desired performance is achieved. Ultimately, analysis of the intensity profile of the generated beam is used to assess its purity.

The main advantage of this technique over existing methods is it allows for generating a stable high purity beam. This also allows for a high degree of adaptability within experimental setup. Though this method can provide improvements in performing high precision interferometric measurements, it can also be applied to all areas of science, such as materials processing microscopy, motion sensors, biology, and more.

We had the idea for this method after reading in the literature about mode conversion using phase plates and spatial light modulators. We realized immediately that if we applied the mode cleaning technique, we should be able to greatly improve the purity of the modes that we generate in this way. After the development of this technique, researchers in the area of gravitational wave detection were able to explore the application of Leger gas beams in setups.

Representative of gravitational wave interferometers, including large scale interferometer prototypes and using high power laser systems, The first step is to generate a pure low noise power stabilized fundamental mode gian beam. The details of this setup are in the manuscript. Use a beam profiler with real-time image analysis software to measure the beam radius along the optical path and collect at least 10 data points, fit the measured radii and extract the beam waist size and position.

Next, select and place lenses along the optical path to reshape the beam waist size and position. Direct the beam into the spatial light modulator placed at the beam waist to help with alignment for a reflective type spatial light modulator. Adjust the incident angle to five degrees or less to avoid astigmatism in the generated beam.

Now apply the phase profile of the desired higher or lager GU beam to the spatial light modulator liquid crystal display using the dedicated computer program shown here is the phase modulation profile of the AL three three mode to be created in this experiment. This is the image as it appears on the spatial light modulator. When viewed with the polarizer, based on the size of the injected beam, select the appropriate phase.

Pattern size now overlap a blazing structure to the phase profile on the spatial light modulator. The inset on the bottom left initially shows the beam with only the phase conversion pattern at right applied to the spatial light modulator with the application of a blazing pattern to the phase profile light with the leggos profile is separated from light without it optimize the blazing angle to produce a diffraction angle into the first order that is greater than the divergence angle of the beam. Use the data on the optimal conversion pattern to manufacture a phase plate to replace the spatial light modulator.

It is convenient to position the phase plate at the waist of the injected fundamental mode beam to be converted. Place a CCD camera behind the phase plate for help with alignment. Monitor the camera output to carefully align the phase plate such that it is perpendicular to the initial beam and the beam is centered with respect to the phase structure.

Use a beam card to determine where the beams transmitted through the phase plate. Achieve a good separation of the higher diffraction orders. Once this is done, obscure the higher order beams with an aperture centered on the main diffraction order.

Ensure that the aperture has the desired results. Proceed by constructing a mode cleaner cavity to be placed where the leggos beam will be injected. Choose mirrors for the cavity.

Select the rigid spacer to support them, and a pieto electric ring element to allow for microscopic adjustments of the cavity length glue. The mirrors on the spacer and interpose piezo electric ring element between one of the mirrors and the spacer with the mode cleaner cavity in place and its geometry Defined mode matched the beam generated by the phase plate to the cavity egg in modes to profile the Legge GOs beam record its intensity distribution with a CCD camera at different positions along the beam path. To profile the Legge Gouss beam record its intensity distribution with a CCD camera at different positions along the beam path.

Place lenses and repeat measurements until the optimal beam size and location are found. Now vary the cavity length by moving the mirror with the piso electric crystal. Optimize the alignment of the injected beam into the cavity while monitoring the transmitted beam seen in the monitor.

Used measurements of the light transmitted by the mode cleaner shown here in the red trace as a function of the cavity length, which is shown in the yellow trace to investigate the mode content to the leggo beam generated by the phase plate. Now more carefully inspect the CCD images and identify parasitic modes. Here the beam profiles of the parasitic modes are shown as their peaks are traversed.

Evaluate the power of these modes using the photo diodes signal and compute the exact mode content of the overall beam. The measured results and exact mode content can be reproduced with and compared to numerical simulations as shown here. Continue by engaging the control loop to lock the cavity length to the main ance record images of the profile of the resulting beam transmitted by the cavity with the CCD camera to diagnose the produced beam.

Measure the power of the leggos beam with a laser power meter Care should be taken to avoid clipping leggo beams may exceed the dimensions of the sensitive area of most commercial instruments. Use a CCD camera to measure the beam intensity. Employ a fitting routine to find the parameters of the theoretical beam profile file.

Assess the purity of the beam by computing the squared inner product of the theoretical and measured amplitude distributions. The mirrors used in large scale interferometric experiments like advanced ligo are incredibly smooth state-of-the-art optics that have been designed for the fundamental mode use of the higher order. AL modes requires stricter requirements that are determined through simulations.

Begin by choosing a simulation tool in this case. Finesse for this video. The advanced LIGO dual recycled Michelson interferometer with fbri Perot arm cavities shown here is modeled.

Prepare the finesse input of the model, then test it with fundamental mode beams and validate its reliability. Adapt the finesse file for the LG three three mode. Taking care to alter the setup to give a similar beam size to the fundamental mode.

Repeat the tests using these beams. The results should be very similar to those of the fundamental mode. Now set up a realistic interferometer model incorporating data about the surface figures of the cavity mirrors.

Investigate and compare the performance of the hermit Gaussian zero zero mode and the higher order legian modes, for example, detecting the field at the dark port. The higher order modes are expected to perform worse. The mode degeneracy resulting in distorted beams which leak into the detection port to investigate the degeneracy effects present in this model simulate the fbri Perot arm cavities in which the degeneracy originates.

Use data from these simulations to identify unwanted modes in the circulating beam and any frequency splitting. In this part of the video, the mirror surface map is shown along the bottom left and a Zer polynomial content on the bottom right mirror surface shapes that cause significant coupling between the input beam and modes of the same order are adjusted to achieve greater purity of the circulating beam. The beam profile is shown in the upper left and its power in the upper right.

In this case, 99%purity of the circulating mode is ultimately achieved. The final mirror map represents mirror requirements for the leggos mode and can be used in simulations of the full scale interferometer to test improvements in performance. This is the intensity profile of the fundamental mode beam used as input to the system which was successfully converted to this legge Gauss three three beam.

In the example shown here, which shows results published in reference 21. Using this method, a lagals three three beam of 82.8 watts and 96%purity was generated. A sense of the purity of this beam can be seen in this plot of the fit residuals for this mode.

Once mastered, this technique can be done a few weeks if it is performed properly from design to completion of the apparatus. Attempting this procedure, one should pay extremely care to their design and the preliminary remodeling of this experimental setup and to the choice and the quality of optical components. Generally individual is new to this method, will struggle with the design, characterization and alignment of the higher order mode section of the apparatus.

After watching this video, you should have a good understanding of how to create higher order like a gause modes for use and high precision interferometry. Don't forget that working lasers can be extremely hazardous and precautions such as wearing certified laser safety goggles should always be taken while performing this procedure.