A theoretical study on the sensitivity of the resonant wavelength of long-period waveguide gratings (LPWGs) to temperature and pressure is reported. Starting with the phase-matching condition of the LPWG, general expressions for the temperature and pressure sensitivities are derived. The temperature sensitivity considers the thermo-optic and thermal expansion effects, and the pressure sensitivity takes into account the elasto-optic and elastic deformation effects of the materials involved, as well as the modal dispersion effect. Focusing on the extensively studied glass and polymer waveguides, the contributions of these effects to the temperature or pressure sensitivity were roughly evaluated and illustrated in the form of histograms in order to show the roles of these effects straightforwardly. The results show that a LPWG based on a polymer waveguide is preferred to that based on a glass waveguide for obtaining high temperature or pressure sensitivity. The temperature sensitivity is dominated by the modal dispersion effect and the difference between the thermo-optic coefficients of the waveguide and the cover layer materials, while the thermal expansion effects make only a minor contribution to the sensitivity for the cases of both glass and polymer waveguides. The pressure sensitivity is dominated by the modal dispersion effect and the difference between the elasto-optic coefficients of the channel waveguide and the cover layer materials. In particular, in the case of the polymer LPWG the elastic deformation effects of the waveguide and grating materials make a moderate contribution to the pressure sensitivity and cannot be ignored. The minor contributions from the thermal expansion effects or the elastic effects may play a role in designing a temperature- or a pressure-insensitive LPWG device. Finally, the possibility that the waveguide loss affects the LPWG temperature/pressure sensitivity is discussed.
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