The study of the Cosmic Microwave Background (CMB) has advanced our understanding of the universe. CMB total intensity has been already characterized quite well and now most experiments are focusing on its polarization. One of the strong scientific motivations for measuring CMB polarization is to test the cosmic inflation theory. The CMB has a perfect blackbody spectrum while the foreground galactic emission has a different spectral behaviors. A broadband multi-chroic measurement allows us to distinguish the CMB from the foreground emissions. LiteBIRD, Lite(Light) satellite for the studies of B-mode polarization and Inflation from cosmic background Radiation Detection, is a satellite mission to detect signatures of primordial gravitational waves in the form of primordial B-mode polarization of the CMB. LiteBIRD will cover the frequency band between 34 GHz and 440 GHz with 3 telescopes (LFT, MFT, and HFT). LFT is developed by JAXA and will cover the frequency range between 34 and 161 GHz. In order to control the systematic uncertainty, we use sapphire-based rotating achromatic half-wave plate (AHWP) as the first optical element to modurate the signal. Sapphire is particularly attractive for CMB polarization experiments because of a high index of refraction of n 3, low-loss at millimeter-wave and a high thermal conductivity at cryogenic temperature. However, the high refractive index causes about 50 % reflection at the surface ofthe first optical element. This would result a significant reduction of the throughput of LFT, therefore we need a broadband anti-reflection (AR) coating on the surface of the AHWP. It is possible to achieve a broadband AR by employing sub-wavelength structures (SWS), also known as moth-eye structures. SWS method is not limited by the availability of the dielectric material since we simply manipulate the material itself. Also, this method is not subjected to a differential thermal shrinkage. Thus, it is more reliable at the cryogenic temperature. In this presentation we explore the fabrication of SWS through laser machining and we describe the method developed to machine SWS which can achieve >90% transmittance between 34 and 161 GHz. This is the broadest AR coverage that is achieved at millimeter wavelengths and possibly at any other wavelengths. By adding the parameter of curvature a, we discovered that the shape with a > 1.0 can cover a broader frequency band than the shape with a < 1.0 by the electromagnetic simulation. We developed the fabrication method to realize a shape with a > 1.0 in a practical time with ultra-short pulsed laser ablation. The transmittance measurement was in agreement with the prediction: > 90% transmittance in 40-161 GHz range. The fabrication time over a diameter of 34.5 mm is 11.5 h, and we expect that it will take 2.5 months to fabricate on a surface of a 450 mm diameter. It is drastically shorter time than our past estimate which was 4 years.