Periodical energy oscillation and pulse splitting in sinusoidal volume holographic grating

This paper presents dynamical diffraction properties of a femtosecond pulse in a sinusoidal volume holographic grating (VHG). By the modified coupled-wave equations of Kogelnik, we show that the diffraction of a femtosecond pulse on the VHG gives rise to periodical energy oscillation and pulse splitting. In the initial stage of diffraction, one diffracted pulse and one transmitted pulse emerge, and energy of the transmitted pulse periodically transfers to the diffracted pulse and vice versa. In the latter stage, both the diffracted and transmitted pulses split into two spatially separated pulses. One pair of transmitted and diffracted pulses propagates in the same direction and forms the output diffracted dual pulses of the VHG, and the other pair of pulses forms the output transmitted dual pulses. The pulse interval between each pair of dual pulses is in linearly proportional to the refractive index modulation and grating thickness. By the interference effect and group velocity difference we give explanations on the periodical energy oscillation and pulse splitting respectively.