GratingMaster^{®} is an optical software tool for designing optical gratings. The gratings in target are mostly in small dimensions with grating period within or less than optical wavelength.

The algorithm behind GratingMaster^{®} is Rigorous Coupled Wave Analysis (RCWA), which is one popular algorithm to accurately analyze the diffraction of electromagnetic waves by periodic structures, like gratings. Rigorous diffraction algorithms are mostly applied for gratings with feature size comparable to the optical wavelength. RCWA has been successfully applied to the analysis of holographic gratings and surface-relief grating.

RCWA was first formulated by Moharam and Gaylord for planar gratings and then extended to surface relief gratings and crossed-gratings. In RCWA, the vector nature of the electromagnetic field is considered by exactly solving Maxwell’s Equations or vector wave equations without any deliberate approximations. The field inside the grating medium is expanded in terms of the space harmonic components of the field in the periodic structure. These space harmonics inside the grating are phase matched to diffracted orders outside of the grating. The individual space-harmonic fields do not satisfy the vector wave equation (and thus Maxwell’s Equations). But the sum of all space harmonic fields satisfies the wave equations. RCWA gives diffraction results in terms of the diffraction efficiency of each order.

Compared to RCWA, Scalar diffraction theory, an alternative theory of analyzing diffractive optical elements with relatively larger dimensions, treats the vector characteristic of electromagnetic field as a scalar field with approximations. Scalar theory is valid and mathematically efficient for variety of diffractive elements, especially with feature size way greater than optical wavelength.

The grating period or feature size of today’s DOE’s has been continually decreasing with advances in micro-fabrication technologies and computer modeling techniques. When the feature size of DOE’s is of the order of or less than the optical wavelength, the classical scalar diffraction theory is no longer valid and cannot be applied to the analysis and design of such elements. Rigorous electromagnetic diffraction models must be used to accurately predict the performance of such DOE’s. Rigorous diffraction models solve Maxwell’s Equations without arbitrary approximations.

**A general design procedure of Grating/DOE’s, in three basic stages,**

**Analyze DOE design problem**

The designer first needs to understand the physics of the DOE function and select the required fabrication process. The choice of diffraction design model is related to the algorithm complexity, such as rigorous analysis or scalar theory. Fabrication model needs to address the process details with consideration of the smallest feature size.**Translate the physical understanding of the problem to optimization definition**

Secondly the designer casts the design problem into an optimization problem. Based on the physical parameters that determine the performance of the DOE, some design metric (a measure of the performance of DOE) is defined, and some grating geometry parameters are set as variables for optimization. The design metric may be expressed in terms of physical parameters such as diffraction efficiency in each of the grating orders.**DOE design implementation**

Finally design is carried out and the optimized DOE is fabricated. Iterative processes may happen in real applications.