Developments in the generation and measurement of vortex modes in solid-state lasers

Abstract

We have explored several methods of generating Laguerre-Gaussian doughnut modes with the eventual application of laser processing directing our research. These modes have potential in this field due to their increasing mode steepness with azimuthal phase and their potential for carrying orbital angular momentum (OAM). A key research goal has been to obtain such modes with high purity and the ability to select the handedness of the OAM, in a system with robust potential for power scaling. All of which are key in order to fully understand the impact of these modes on laser processing.
Initially we explored intra-cavity, gain shaping methods in Nd:YAG to achieve these goals. This maintains all the advantages of power scaling normally associated with solid state lasers, and has the potential for excellent beam quality. To the best of our knowledge, however, no concrete method has been presented for selecting the handedness within the cavity. We have selectively excited doughnut modes by coupling multi-modal laser diode pump light into capillary fibres and re-imaging the fibre end into a Nd:YAG gain medium. By using a fibre with a 0.8 aspect ratio between its inner and outer radius, we would be able to select higher order doughnut modes that have a steeper intensity profile and more OAM per photon. Through this we have generated Laguerre-Gaussian 'petal' modes up to an azimuthal order of 23. These high order modes exhibit greater intensity steepness but no OAM. These modes have little practical application.
In order to better investigate what governs the selection of the OAM handedness we moved to a ring laser design pumped using a capillary fibre with a 0.5 aspect ratio. This, whilst operating unidirectionally at a single frequency, produces a doughnut mode with an azimuthal order of one and a clear presence of the helical phase and therefore OAM. This has allowed us to examine such a mode in isolation. Through this we observed that reversing beam propagation direction in the ring cavity also reversed the handedness of the helical phase. We found this effect associated with the Faraday Rotator as it is the only known non-reciprocal effect in the cavity. We also found a similar effect in the highly chiral material, tellurium dioxide. The effects were replicated in a slightly multi-modal ring laser but were not observed in a standing wave laser. Tests in free space were unable to detect this effect, so either another mechanism is responsible or the effect was too weak for our detection methods.
We therefore moved to external methods for creating doughnut modes. We chose to focus on astigmatic mode converters as these can produce perfectly pure beams unlike methods using spiral phase plates or spatial light modulators. We have developed on the previous design by Beijersbergen et al. by replacing the cylindrical lenses with off-axis spherical mirrors. We have also expanded the theory of mode converters to apply to off-axis spherical mirrors. The mirrors allow for greater power scaling and wavelength flexibility. The key to this is producing high purity HG₀₁ modes. Initially these were produced by placing a slit in a cavity that naturally oscillated on the LG₀₁ mode. However there was a significant fundamental mode impurity. We improved this by developing a Nd:YVO₄ laser cavity pumped by two separate circular pump beams. This greatly improved the output power to 175mW as well as the mode quality. This method allows for control of the OAM by rotating the HG₀₁ though 90°. Feeding this through the converter produced a high purity LG₀₁ mode with negligible loss.
We also developed a diagnostic technique for analysing the purity of modes generated by a mode converter. As the most likely impurity is a HG01 mode from misaligning the converter this can be picked up by measuring the azimuthal symmetry of the Mach-Zehnder spiral interference pattern. A pure mode will generate a spiral with an even azimuthal intensity distribution. A HG₀₁ impurity will disrupt this. This can be measured with a virtual rotating slit. Our theoretical predictions of the amount of azimuthal variation a given level of impurity will cause matched extremely well when this method was tested with a real system. 
The need for high purity modes has led us to develop further diagnostic techniques to more quantitatively assess the quality of HG₀₁ and LG₀₁ modes. For both modes this involves analysing its intensity profile as recorded on a CCD camera. It provides quantitative analysis of key properties of the intensity profile in order to identify impurities. For the HG₀₁ mode it compares the evenness of the two intensity maxima and how close to zero the central node is. For the LG₀₁ it again measures how close to zero the central null is, the circularity of the beam, and the azimuthal symmetry. Further analysis generates a matching theoretical mode to the image and subtracts it to look at the residual power distribution. This allows us to identify specific modal impurities incoherently combined with the beam and quantify them. Further work is needed to take into account of distortions created by the CCD camera itself as well as general noise.
Finally we Q switched the HG₀₁ seed laser. This allowed for greater output power of 460mW without losing mode purity. It produced 24ns pulses with a 147kHz repetition rate. The pulses could be shortened further simply by shortening the cavity. Passing this through a double-pass bounce geometry Nd:YVO₄ slab amplifier; pumped with up to 55W of power we obtained an maximum amplified power of 17W. However some significant mode impurity was added as well as large amount of astigmatism. It was noticed there was damage on the amplifier crystal that may have been the cause of some of this. However amplification is clearly possible, whether by amplifying the HG₀₁ or LG₀₁ mode.

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