### Needle Optimization

 Needle optimization is a unique feature of OptiLayer. Using Needle optimization you can solve almost all mutilayer design problems. Needle Optimization is available through: Synthesis --> Needle Optimization AUTO. Needle Optimization steps are performed in many other algorithms (Gradual Evolution,  Sensitivity-Directed Refinement, Deep Search versions, Robust algorithms). You need the needle optimization algorithm if: You do not have a good starting design and cannot apply Refinement algorithms. You do not know the number of layers. You design a multilayer from scratch. You solve a complicated design problem. As design total thickness is a very important and conservative parameter, an estimation of the total design thickness is necessary. You can start with any starting design, also with a single layer of enough thickness. Fig. 1. Demonstration of designing a RAMP coating using needle optimization algorithm. Put the mouse on and out of the plot to see the animation. Fig. 2. Refractive index profile, $$P$$-function and needle variation. Mathematically, any refractive index profiles can be represented as a function $$n(z)$$, which is a dependence of the refractive index on the coating coordinate (Fig. 2). Needle optimization algorithm introduces into consideration some new physical effects in multilayers by insertion new design layers, which are equivalent to variations of the refractive index profile (Fig. 2). These variations are referred to as needle variations. If new layers are inserted in proper places, then new interference effects associated with these layers improve the correspondence between actual and target spectral characteristics. The determination of proper places for needle variations is based on rigorous complicated mathematical considerations (if you are interested, you can find the details in the book that can be free downloaded from our website). OptiLayer calculates the proper places automatically and then optimizes the layer thicknesses in the most effective way. Due to some reasons, it may be required to define such places manually. This can be done through Needle Optimization (manual mode). In a simplified representation, a so-called $$P$$-function is calculated (Fig. 2). The merit function can be presented as: $\delta MF=P(n_k,z)\cdot\delta z+o(\delta z) \qquad\; (1)$ An appropriate place for a needle variation corresponds to $$z-$$ point where $$P$$-function takes its most negative value. After insertion of the new layer(s), the structure is optimized with respect to layer thicknesses (Refinement). General schematic of the needle optimization algorithm is shown in Fig. 3. When the number of coating materials exceeds two, an optimal material is chosen among all materials automatically in the most optimal way. At the Refinement step, the same optimization methods are used (Fig. 4). Unparalleled computation capability and outstanding efficiency of the Needle Optimization algorithm is due to unique know-how of OptiLayer. Fig. 3. Schematic of the needle optimization algorithm. Fig. 4. Settings of parameters of optimization algorithms. Advanced fine tuning of the needle optimization settings can be performed in Synthesis --> Options --> Method tab These settings allows you to choose: Optimization method at the Refinement step Termination criteria Needle sensitivity (for complicated problems Strict is recommended, for non-complicated problems Standard or relaxed) Number of needle variations in one iteration, power in the merit function (2 is a default value, the most typical one, recommended). Two more animations are shown in Figs. 5 and 6: a broadband beamsplitter and a two-line filter. Fig. 5. Design of a broadband bemsplitter (put the mouse on and out of the picture) Fig. 6. Design of a two-line filter (put the mouse on and out of the picture) You may be also interested in following articles: Refinement Gradual evolution Robust synthesis Deep Search See also our videos at YourTube : References: Sh. Furman and A.V.Tikhonravov, "Basics of optics of multilayer systems", Editions Frontiers, Gif-sur Yvette, 1992, 242 p. This book can be free downloaded here. A. V. Tikhonravov, M. K. Trubetskov, and G. W. DeBell, "Optical coating design approaches based on the needle optimization technique," Appl. Opt. 46, 704-710 (2007). A. V. Tikhonravov and M. K. Trubetskov, "Modern status and prospects of the development of methods of designing multilayer optical coatings," J. Opt. Technol. 74, 845-850 (2007). A. Tikhonravov and M. Trubetskov, "Modern design tools and a new paradigm in optical coating design," Appl. Opt. 51, 7319-7332 (2012). A. V. Tikhonravov, M. K. Trubetskov, and G. W. DeBell, "Application of the needle optimization technique to the design of optical coatings," Appl. Opt. 35, 5493-5508 (1996).