Optical frequency standards are necessary tools for accurate measurement of time and length. In practice these standards are stabilised laser systems locked to a known frequency reference. These references are typically the resonant frequencies of the atoms of an absorption medium that have been theoretically calculated to a high degree of accuracy. This thesis describes a combination of experimental and theoretical research performed on modulation transfer spectroscopy (MTS)--a technique used to frequency stabilise a laser in order to produce an accurate frequency reference--with emphasis placed on developing techniques and procedures to overcome the limitations found in existing MTS stabilised laser systems. The focus of the thesis is to generate a highly accurate frequency reference by researching the system parameters that will increase the signal to noise ratio and improve the accuracy of the reference through refinement of the signal structure. The early theoretical interpretation of MTS was effectively a low absorption approximation that occurs at low pressures. This approximation ignores the depletion of beam energy through absorption and is a distinct limitation of the theoretical model in its ability to accurately predict the influence of a range of system parameters on signal strength and structure. To overcome this limitation a 3-D (or volumetric) analysis was developed and is presented here for the first time. This volumetric model is a measure of two depleted beams interacting collinearly in an absorbing medium of iodine and is described to accurately predict the signal maximum as a function of pressure for all wavelengths. This model was found to be more accurate in predicting the influence of system parameters on the signal strength and structure, including that of pump beam intensity, pressure, saturation parameter, cell length and modulation parameters. The volumetric model is a novel approach to MTS theory but is more complex computationally than the traditional low pressure model and therefore more difficult to implement in many situations. To overcome this problem a hybrid model was developed as a combination of the low pressure and volumetric models. The comparison between the rigorous volume model and the hybrid model indicate that there is a deviation in the signal strength at high pressures. However, the agreement was very good in the pressure regimes that are commonly used to realise actual frequency references. Comparison of the hybrid model to experimental data was performed over a range of different wavelengths (532 nm, 543.5 nm, 612 nm and 633 nm) and found to be in close agreement. This gives confidence in the model to accurately predict signal strength and structure in any situation. Three mechanisms have been identified that limit the accuracy of frequency references due to the creation of residual amplitude modulation (RAM) where it shifts the frequency of the reference. The influence of RAM is included in the hybrid model as a ratio of the amplitude modulated and frequency modulated components of the saturating beam. These RAM production mechanisms result from the modulation of the saturating beam, the overlap of the beams in the medium, and the differential absorption of the sidebands in the medium. While the first mechanism has been previously reported the latter two are discussed here in detail for the first time. RAM generated by the modulators used (acousto-optic or electro-optic modulators) was typically of the order of 10% to 12%, depending on the excursion of the created sidebands. RAM generated by an asymmetric beam overlap with the modulators used was found to be as large as 30%. A combination of these two independent mechanisms can be used to provide a "RAM-free" state of the system by using one to cancel the effects of the other. The third RAM generation process--medium induced RAM--is difficult to remove but through a careful combination of absorption related parameters--namely, pump intensity, cell length, pressure and detector phase--the effects of RAM can be removed, leading to a distortion free MTS signal. Further investigation into the predictions provided by the hybrid model shows that there is a complex relationship between cell length and the optimum pressure required for maximum signal strength, such that longer cell lengths will not necessarily improve the signal strength. This is contrary to conventional thinking and is important in the MTS design process to reduce unnecessary costs and improve the signal to noise ratio and frequency accuracy. Optimisation of frequency stabilised laser systems using MTS are generally performed using trial and error. Comparison of these optimum parameter values to those predicted by the hybrid model show that for popular wavelengths such as 532 nm they are similar. In addition, the hybrid model is able to predict the frequency shifts that arise within the system parameters used and has shown that existing systems being used at 532 nm, 633 nm and 778 nm could improve their signal to noise ratio and accuracy through a variation in the parameters. A methodology based on the hybrid model is presented that can be used to calculate the optimum parameters for maximum signal strength and a "RAM-free" state for any wavelength. This systematic approach can therefore be used to guide the design of actual frequency stabilised laser systems prior to and during the design process.
| Identifer | oai:union.ndltd.org:ADTP/265658 |
| Date | January 2008 |
| Creators | Hopper, David J. |
| Publisher | Queensland University of Technology |
| Source Sets | Australiasian Digital Theses Program |
| Detected Language | English |
| Rights | Copyright David John Hopper |
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