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We develop an efficient numerical method for analyzing second harmonic generation (SHG) in two-dimensional photonic crystals composed of nonlinear circular cylinders embedded in a linear background medium. Instead of solving the governing inhomogeneous Helmholtz equation for the second harmonic wave in the entire structure directly, we define and solve a locally generated second harmonic field in each cylinder (independent of all other cylinders), then merge the field together usingdoi:10.1364/josab.26.000587 fatcat:txsjd3yh25hyzcfg64mvzzdnhi