In this article, dielectric photonic crystals (PhC) with finite dimensions and exposed in air is analyzed for its potential value in traveling wave tubes (TWTs). The modes existing in finite dielectric PhC are EH and HE, and also E if the finite PhC is two-dimensiond. The E1 mode is the E polarization in infinite dielectric PhC. Calculation shows that only the existence of gaps of pass-bands is necessary for PhC in TWTs, while the complete photonic crystal band gaps are superfluous.