5. The system is able to detect homogeneity in the sample and point absorbers, allowing investigation of their source and minimise inaccuracies in bulk measurements.
6.2 Summary of the results
In this thesis I have achieved the aims outlined above by creating a model and analysis technique to predict the wavefront distortion of a beam through a heated sample and an optimised experimental system to measure this wavefront distortion. By comparison of the predicted and measured wavefront distortion, I have demonstrated for a ZBLAN and N-BK7 sample that this system can reproducibly measure bulk and surface absorption coefficients, as low as 10s of ppm cm−1and ppm scales respectively, and can measure samples of different geometries. This system was also demonstrated to be sensitive to anomalous absorbers which could be localised along an axis of the sample. Thus, an understanding of the level of contamination in the sample was gained which is very valuable for glass developers.
The validity of these results is dependant on the quality of the COMSOLFEMdescribing the heating of the sample, which was verified through comparison to the Hello & Vinet analytical solutions for a thin disc geometry. In the process the limitations of the HV model’s thermal expansion solution when modelling samples which deviate from this thin disc geometries was discovered. Thus,FEMmodel must be used as it can be applied to any geometry and it will not be effected in the same manner.
A model of the change optical path length ∆OPL of a probe beam incident on the heated sample at an angle was formulated in chapter 3, using theFEM. The thermo-elastic, thermo- refractive and elasto-optic effects were considered with the latter proven to be negligible in glass samples. Thermo-elastic and thermo-refractive effects were demonstrated to counteract each other reducing the observable distortion in ZBLAN, highlighting the advantages of measuring longer samples where thermo-refractive effects dominate. A linearised function in terms ofα andβ for the∆OPL was then formed allowing the absorption coefficients to be found by completing a least-squares fit.
The accuracy of the fit was dependant on the sample parameters which may vary in novel development glasses due to changes in the composition and the system parameters. Thus, a verification measurement using a N-BK7 sample, which has well documented parame-
6.3 Future work 127 ters, was conducted in chapter 4, measuring bulk absorption accurate to the predicted value within 0.3%. Varying sample parameters such as the thermo-optic and thermal expansion coefficients was, however, demonstrated to have a proportional effect on the value ofα and increases the error in the fit. Modelling demonstrated that by sweeping the coefficients and finding the minimum error, the uncertainty inα could be reduced and even allow determina- tion of the correct coefficients. However, the experimental noise floor must be reduced by a factor of 10 to recover this information experimentally.
This thesis introduced an off-axis probe, on axis pump photo-thermal measurement sys- tem which was optimised to measure small, low-loss samples. In chapter 5, this system was demonstrated to be able to reproducibly measure bulk absorption as small as 47.2
±0.4 ppm cm−1 +7.9−8.6% when the system was configured for the highest SNR, however, β could not be determined due to the small angle required. It was demonstrated that at large angles the bulk and surface distortion profiles become very distinct allowing an upper limit of β =3.5 ppm to be determined. Consequently, when assuming this maximum surface absorption in the highest SNR configuration the bulk absorption is bound to α = 46.2
±0.4 ppm cm−1+7.9−8.6% . Thus, this demonstrates that this system is able to quantify bulk ab- sorption of a magnitude expected for fused silica at 2µm forGWapplications and currently available ZBLAN, and with improvements to increase signal size could be used to measure the intrinsic losses in ZBLAN.
6.3 Future work
I aim for this system to be used to measure samples with absorptions approaching the lowest predicted theoretical losses. Whilst it has been demonstrated that ZBLAN samples of the current quality can be quantified this system will need to be improved to reach this goal.
Thus, it is essential that future work is done to obtain a higher power pump beam or build a resonate cavity system to increase the effective power by approximately 1000 times. The uncertainty in the fit and the noise floor of the DHWS also limits how well surface and bulk absorption could be quantified. Additionally, to increasing the signal, fitting to the whole wavefront deformation map instead of just the cross section will reduce the uncertainty.
I envision that the methods of formation of crystals in ZBLAN can be investigated in future work. By determining the absorption loss and total loss in bulk glass the loss due to scatter
could be inferred and then verified using an integrating sphere. Crystallisation in ZBLAN increases during fibre drawing, but absorption should not be significantly increased in this process. Using cutback measurements to determining total loss and finding the difference from absorption loss I predict to be able to infer an increase in crystallisation and scatter during the drawing process.
This system was built to be capable of measuring many samples with small realignments so that it could be used not only for ZBLAN parametrisation but the precision measure- ment of optics for gravitational wave detection. Future work in this field aims to measure fused silica and silicon at this wavelength. Silicon in particular will require an increase pump power due to a larger thermal conductivity than ZBLAN and upgrading the system to include a cryogenic tank to replicate the desired 127 K environment in the proposed detectors.
Whilst I have identified a number of areas in which this measurement system and associated model can be improved, I have up to this point verified that this system can measure absorp- tion on the order of magnitude 10s of ppm cm−1and ppm surface absorptions. Successfully completing future work will allow absorption coefficients to be quantified below anything currently published whilst helping determine the wavelengths and materials for futureGW detectors and develop low-loss ZBLAN to revolutionise telecommunications.