Introduction
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The mechanism of the pulsed emission from pulsars has been an important unsolved problem for more than forty years. The recent observations of the $\textit{Fermi}$ Gamma-ray Space Telescope has promoted an understanding of the emission from gamma-ray pulsars. The pulse shapes show substantial diversity, but roughly 75$\%$ of the gamma-ray profiles have two peaks, separated by $\gtrsim 0.2$ of rotation phase [@b1]. Additionally, most of the radio-loud gamma-ray pulsars have the first gamma-ray peak lagging the main radio component. This indicates that radio and gamma-ray beams are coming from different emitting regions. Also, the high-confidence gamma-ray from a millisecond pulsar is detected first by $\textit{Fermi}$. After that, it was found that most of the millisecond pulsars have the features of the gamma-ray light curves and spectra like normal pulsars.

Polar cap (PC) (eg, [@b2]), slot gap (SG) (eg, [@b3; @b4]) and outer gap (OG) (eg, [@b5; @b6]) models are promising particle acceleration models to explain pulsed emission from pulsars. In PC models, particle acceleration and resultant gamma-ray emission takes place in the open field line region above the magnetic poles. The gamma-rays undergo the magnetic pair production, which leads to super-exponential spectral cutoff. Then, the produced pairs screen 