Simulation and Optimization of Gradient-Index (GRIN) Lenses in Quadoa® Optical CAD

Introduction Gradient-Index (GRIN) lenses represent a class of optical elements in which the refractive index varies continuously within the material. Unlike conventional lenses where the optical power is introduced by refraction at the curved surfaces, GRIN lenses utilize a gradient index profile to bend the light in the desired direction. Quadoa® provides advanced tools for simulating, optimizing, and analyzing GRIN lenses, making it a powerful tool for optical designers. This article aims to highlight the features of Quadoa® that are particularly beneficial for working with GRIN lenses, such as the ease of assigning GRIN profiles, simulating inhomogeneities on arbitrary optical elements or performing tolerance analysis.

GRIN Lens Simulation

Assigning GRIN Profiles In Quadoa®, the process of simulating a GRIN lens begins with the assignment of a GRIN profile to a lens material within the Optical Design Editor. Users can assign a specific GRIN profile by right-clicking on the desired material and selecting from different profile types. The GRIN profile always describes the local deviation of the refractive index from the base material refractive index and is defined inside the local lens element coordinate system. Any material type (e.g. a catalog material or a model material) can be used as base material. As an example we add a radial GRIN profile to a cylindrical substrate to simulate the refractive index variation within the material. For our demonstration, we used a GRIN profile defined by a second-order polynomial with coefficients A1= -0.00036 and A2 = -0.0029 to simulate the refractive index variation within the material. These coefficients are typically provided by the lens manufacturer and are critical for accurate simulation. Visualization and Analysis Once the GRIN profile is applied, the 3D view in Quadoa® visually demonstrates the curved propagation of rays within the GRIN media. The software also offers a range of analysis tools under the Analysis Tab, allowing users to assess the impact of the GRIN profile on system performance. Accuracy Control The software solves the Eikonal equation, which governs ray propagation in GRIN media, using an interactive algorithm based on the Runge-Kutta method. The iteration step size, controlled by the "Z Step" parameter, is adjustable to balance accuracy and computational time. Reducing the step size leads to higher accuracy but simultaneously slows down the ray tracing. A good way to find the optimal setting for the step size it is recommended to start with a larger value and then reduce it step by step until there is no significant change to the system any more. Optimization Quadoa® allows for the optimization of GRIN parameters, similar to other optical design parameters. By activating the variable icon for optimization, users can fine-tune the GRIN profile to achieve desired optical characteristics.

Tolerancing

Coordinate System Independence The GRIN profile in Quadoa® is always defined inside the lens-material coordinate system and therefore independent of the shape, tilt or decenter of the surfaces surrounding it. This allows to manipulate the surface independently from the orientation of the GRIN profile which is crucial when it comes to tolerancing, as it allows the GRIN profile to adapt to changes in lens orientation or shape without being constrained by the surface geometry. Versatility in Surface Design Quadoa® does not limit the surfaces of GRIN lenses to specific shapes or phase types. This means that designers can apply GRIN profiles to various surface types, including free-form lenses and diffractive optics. Such versatility is particularly valuable when simulating index inhomogeneities in complex lenses, such as free-form designs.

Advanced Applications: Thermal Lensing and Index Inhomogeneity

Quadoa®'s ability to simulate GRIN lenses can be applied to the simulation of thermal lensing or index inhomogeneities of lens materials. Especially the 3D GRIN profile type can be utilized to import refractive index data from FEM software as it is obtained when performing STOP analysis.

Watch GRIN Video Tutorial