Modal analysis of high-efficiency wideband reflective gratings

Abstract

Modal analysis of the reflective wideband grating with high efficiency of the negative first order in Littrow mounting is presented. The reflective grating consists of a highly reflective mirror and a transmission grating on the top. The modal analysis is carried out for TE polarization and it reveals that two modes are excited in the transmission grating. Using the two modes and ignoring the absorption of the mirror, a simple expression of diffraction efficiency of the reflective grating is derived and thus the grating depth to achieve high efficiency of the negative first order is obtained. The influence of duty cycle on the difference of effective indices of the two modes for different wavelengths is analyzed, which can explain the wideband behavior of reflective gratings. The modal analysis should be a useful tool for the design of high-efficiency wideband reflective gratings

Polarization-independent wideband mixed metal dielectric reflective gratings

“…Ignoring the evanescent modes, the diffraction efficiency of the −1st order can be expressed as [12] …”

“…(3), we can see that when the phase difference between mode 0 and mode 1, Δφ 2l 1π ∕ 2 with l 0; 1; 2; …, the diffraction efficiency of the −1st order reaches its maximum. Therefore, the grating depth to achieve high efficiency of the −1st order can be express as [12] h r 2l 1 4 λ n 0eff − n 1eff :…”

“…However, to our knowledge, polarization-independent mixed metal dielectric reflective gratings have not been reported before. Although simplified modal analysis has been presented for a wideband mixed metal dielectric grating for TE polarization [12], no one has pointed out before that there still exist 1559-128X/12/204902-05$15.00/0 © 2012 Optical Society of America simple equations to govern polarization-independent wideband mixed metal dielectric gratings.…”

Modal analysis of 1 × 3 reflective triangular gratings under normal incidence

“…The modal method was first developed by Rytov and Collin [13,14] , and it was Botten et al [15] who first applied it to dielectric gratings. The simplified modal method has been used to clarify the mechanisms of different gratings [16][17][18][19][20][21][22] . Zheng et al analyzed the transmission of triangular-groove gratings by the simplified modal method [17] .…”

“…But this expression is not suitable for reflective gratings. Reflective gratings have only been analyzed in a Littrow mounting [21,22] with the simplified modal method by Hu et al In addition, as we know, this method has already been applied to analyze beam splitting gratings under the second Bragg incidence [20] . However, a simplified modal analysis of reflective triangular gratings under normal incidence has not been done before to the best of our knowledge.…”