source: Β© 2006 Optical Society of America
In order to reconstruct the structure of a long-period grating, both the complex core-to-core transmission function and the complex core-to-cladding transmission function should be known. However, in practice, only the core-to-core transmission function of the grating can be measured. We demonstrate theoretically the reconstruction of long-period gratings from only the core-to-core transmission function. The reconstruction is performed by extracting the complex core-to-cladding transmission function of the grating from its core-to-core transmission function. Generally, the extraction is not unique; however, we show that by writing an additional grating in cascade to the interrogated grating, a unique reconstruction can be obtained. In weak long-period gratings, only the amplitude of the core-to-core transmission function is needed to reconstruct the grating. The results of our work can enable the experimental reconstruction of long-period gratings from their transmission function as well as the development of novel distributed sensors.Β [Read more…]
Fig. 1 Schematic description of the grating structure analyzed in the paper. Two cascaded LPGs with lengths πΏ1 and πΏ2 are separated by a gap with a length πΏπ . The fields of the core mode and cladding mode at the input end of the structure are denoted by π’2(π,π§=0) and π’1(π,π§=0) , respectively. The core-to-core and core-to-cladding transmission functions of the first grating are denoted by π1(π) and π1(π) , respectively, and the core-to-core and core-to-cladding transmission functions of the total structure are denoted by πtor(π) and πtot(π) , respectively.