Long-period fiber gratings (LPFG’s) find applications in optical fiber communication systems and fiber sensor systems. Among others, it can be used as gain flattening filters (GFF’s) in the communication systems. Depend on the amplifier design, the GFF’s need to be either athermal, or have specific temperature sensitivities. The temperature sensitivity requiement sometimes can be very stringent. It has been known that the temperature and strain sensitivity are dependent on the fiber parameters and the order of the cladding modes it is used. In this paper we will describe the general method for finding suitable cladding mode in a specific fiber for specific requirements. We found that the polarization dependent losses (PDL) in high sensitivity modes are remarkably higher than the ones in common LPFG’s. In those high sensitivity filters achieved by the UV-beam side illuminating, the birefringence-related resonant wavelength separation (RWS), which is the central wavelength separation corresponding the slow and fast axis state of polarizations (SOP), can be in the range of 5 nm, which is remarkably larger than the reported values in other LPFG’s. There are two sources of birefringence which lead to PDL: fiber core ovality induced birefringence, which is intrinsic, and the anisotropic UV-beam exposure induced birefringence. We proposed methods to deal with those birefringence sources. The leads to almost complete remove of the RWS in the high sensitivity LPFG’s.