A volume phase holographic (VPH) grating achieves high angular dispersion and very high diffraction efficiency for the first diffraction order and for S or P polarization. However the VPH grating could not achieve high diffraction efficiency for non-polarized light at a large diffraction angle because properties of diffraction efficiencies for S and P polarizations are different. Furthermore diffraction efficiency of the VPH grating extinguishes toward a higher diffraction order. A birefringence binary Bragg (3B) grating is a thick transmission grating with optically anisotropic material such as lithium niobate or liquid crystal. The 3B grating achieves diffraction efficiency up to 100% for non-polarized light by tuning of refractive indices for S and P polarizations, even in higher diffraction orders. We fabricated 3B grating with liquid crystal and evaluated the performance of the liquid crystal grating. A quasi-Bragg (QB) grating, which consists long rectangle mirrors aligned in parallel precisely such as a window shade, also achieves high diffraction efficiency toward higher orders. We fabricated QB grating by laminating of silica glass substrates and glued by pressure fusion of gold films. A quasi-Bragg immersion (QBI) grating has smooth mirror hypotenuse and reflector array inside the hypotenuse, instead of step-like grooves of a conventional immersion grating. An incident beam of the QBI grating reflects obliquely at a reflector, then reflects vertically at the mirror surface and reflects again at the same reflector. We are going to fabricate QBI gratings by laminating of mirror plates as similar to fabrication of the QB grating. We will also fabricate silicon and germanium immersion gratings with conventional step-like grooves by means of the latest diamond machining methods. We introduce characteristics and performance of these gratings.