Determination of stress-optical and thermal-optical coefficients of Nb ₂O₅ thin film material

The stress-optical and thermal-optical coefficients of Nb2 O5 in thin film narrow bandpass filters (NBPFs) are determined by using the experimental data of temperature-dependent shift of center wavelength. The five-cavity subnanometer NBPFs under consideration are made by the same Nb2 O5 and Si O2 film materials but deposited on two different substrates (WMS-02 and F-7) through ion-assisted deposition process. The shift of center wavelength in the bandpass filters due to temperature rise is theoretically formulated and related to a variety of factors including the change of refractive index and film thickness due to temperature rise as well as thermal stress. By using the experimental data of center wavelength shift, the unknown stress-optical and thermal-optical coefficients of Nb2 O5 thin film material are evaluated. These coefficients are equal to -95.1× 10-12 Pa-1 and 1.43× 10-5 ° C-1, respectively, at 1550 nm wavelength.