We suggest optimally designed one-dimensional metal/photonic crystal structures for the excitation of optical Tamm plasmon polaritons, which show strongly enhanced electromagnetic field intensities compared to those due to conventional surface plasmon excitations. We assume that the photonic crystal is made of weakly nonlinear optical materials and calculate the reflectance and the electromagnetic field distribution precisely, using the invariant imbedding method generalized to nonlinear media. We find field intensity enhancement factors as large as 3,000 at the metal/photonic crystal interface. We verify that due to this strong enhancement, nonlinear optical effects such as optical bistability can be observed for very small values of the incident wave power. Our results imply that using our structure, very strong surface enhanced Raman scattering signals can be achieved and optical switching devices can be operated in much lower threshold light intensities.