Transverse modes of light have been widely exploited in both classical and quantum optics in recent years. Among the devices to manipulate the transverse modes of light, a π/2 converter is a fundamental and important one that analogs to the quarter-wave plate in the polarization degree of freedom. While a π/2 converter is typically achieved by a pair of well-adjusted cylindrical lenses, it suffers from complexity in its installation and adjustment, which strongly limits its practical applications. In this paper an integrated design of a π/2 converter is reported. We compute the necessary parameters for manufacturing according to refractive theory of a cylindrical surface. Based on the change of refractive indices, we simulate the response of Gouy phase versus wavelengths. We also implement an experiment to verify the conversion between Laguerre-Gaussian modes and Hermite-Gaussian modes by using our compact π/2 converter to confirm its simple adjustment and reliable performance in practice.