Complete Phase-Strain Model for Structurally Embedded Interferometric Optical Fiber Sensors

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Abstract
The relation between a three-dimensional state of strain and the optical phase retardation in a single mode optical fiber is formalized by drawing together classical three-dimensional crystal optics and classical waveguide theory. Neumann's strain optic relations are described in a form usable in optical fiber sensor design. These relations are then combined with weakly guiding fiber theory to develop an integral which relates the optical phase shift in a structurally embedded interferometric optical fiber strain sensor to the induced three-dimensional strain field. This process leads to a previously undisclosed, additional waveguide dispersion term which contributes on the same order to the total strain induced phase retardation as does the term derived by Butter and Hocker (1978). Still, however, waveguide dispersion effects are found to be negligibly small, even in three- dimensional loading. Butter and Hocker's equation and the complete phase-strain model developed herein can give very similar results when both are applied to certain embedded sensors. This anomaly can lead to the false conclusion that Butter and Hocker's results are equally valid for any structurally embedded sensor.