Effect of higher-order diffraction on the interference formed by Bragg scattering for large size optical surfaces

Novel Approach to Improve the Optical Performance by Machining Process Without Surface Finishing

“…In addition, two theoretical calculations-an analytical calculation based on the interference equation, and a numerical simulation based on Fourier optics-were conducted for all the diffracted beam modes to reflect the effects of higherorder diffraction. On the other hand, this study presents the first experimental result of maximizing the effectiveness of Bragg scattering caused by a periodic structure on the optical surface, confirmed through [22,23] to improve the performance of the optical surface. In this study, we provide a new perspective on improving the laser beam profile by avoiding interference between the diffracted beam modes caused by Bragg scattering without attempting to eliminate the waviness through additional surface finishing processes.…”

“…Thus, the overall periods and amplitudes on both sample surfaces were appropriately fabricated through the mechanical DTM process. It was predicted that a planar sample with a waviness of 7 mm period and an amplitude of 50 nm (aspect ratio: 1.4 × 10 -5 ) would form interference fringes in the propagating laser beam profile by Bragg scattering [22,23]. The experimental configuration for measuring the laser beam profiles propagating after reflection from the two planar samples is described in detail in [22].…”

“…During mechanical processing with a DTM, periodic structures, such as roughness (with a period of several μm) and waviness (with a period of several mm) are commonly formed mainly due to the radius/speed of the cutting tool and environmental factors (like temperature/humidity), respectively [20,21]. It is important to minimize the roughness and waviness, because they will produce Bragg diffraction and Bragg scattering, respectively, [22,23] in the laser beam profile propagating in the optical system. In particular, the waviness can affect the shape of the laser beam profile reflected from the optical surface over a long propagation distance (see Fig.…”

“…Recent studies investigating the Bragg scattering produced by waviness on optical surfaces confirmed that it has a significant effect on the propagating beam profile due to the interference patterns caused by the Bragg scattering, even at extremely small aspect ratios (~ 10 -5 ) [22,23]. In [22], it was reported that the reflected light experiences Bragg scattering even on the optical surface, which has a periodic…”

“…Under this condition, the beam intensity changes periodically due to the interference between the 0th, 1st, and − 1st order diffracted beam modes, as the beam propagates after reflection from the optical surface. In [23], a generalized equation was presented for two diffracted beam modes represented by the arbitrary m-th and n-th order, which determines the period of constructive interference formed by Bragg scattering observed in [22]. In addition, two theoretical calculations-an analytical calculation based on the interference equation, and a numerical simulation based on Fourier optics-were conducted for all the diffracted beam modes to reflect the effects of higherorder diffraction.…”