Fundamental Thermal Noise in Distributed Feedback Fiber Lasers

Comment on “Probing the Ultimate Limit of Fiber-Optic Strain Sensing”

“…An alternative formulation leading to a simplified expression for thermal noise in optical fiber was later presented by Wanser (7), who subsequently provided strong experimental evidence to support the validity of the proposed model (8) and which has been widely applied since. More recent theoretical work has provided a further formulation for equilibrium thermal noise in passive optical fibers and fiber lasers (9), which agrees within a few percent with Wanser's formulation.…”

Response to Comment on “Probing the Ultimate Limit of Fiber-Optic Strain Sensing”

“…For instance, the theory proposed in (12) yields a frequency response of the type 1= ffiffi ffi f p , and the temperature dependence is ffiffiffi ffi T p . This is in evident disagreement with other models (7,8), which predict, for passive fibers, an almost flat frequency response and a temperature dependence on T.…”

“…Over the past two decades, few experiments have confirmed this model for long-fiber interferometers-and those have been only in the acoustic range-whereas strong deviations were found at low frequency (9,10). A similar theory was developed for fiber lasers, but a discrepancy with Wanser's expression was pointed out, and the measured low-frequency noise was far from the predicted level as well (7). To explain this behavior, a different theoretical model was proposed for fiber lasers, based on the introduction of source terms in the stochastic heat diffusion equation (11).…”

“…Cranch and Foster (6) compare our strain noise with that predicted by their model with an effective fiber length equal to twice the FBGs distance (analogous to fiber lasers) (7). We remark that the definition of effective length given in (7) is difficult to match with the popular Wanser's model (8).…”

“…Actually, neither the model in (12) nor the more popular theories in (7,8) considered thermal effects due to light storage in fiber resonators. Photothermal effect caused by the optical loss in photosensitive fibers and Bragg gratings has to be taken into account as a source term for calculating thermal fluctuations in the fiber.…”