Optical Thin Films Design Using Digital Filters Method

Applications of optical thin film involve various aspects of modern optical systems. The main task of designing the optical thin film is to calculate the structure parameters by required target spectrum. Generally, it is completed by various optimization algorithms. These algorithms always take the required spectrum partly and point by point as the target value and then search for the structure parameters of the thin film. Now, the Fourier transform is the main method to design the thin film with global description of the target spectrum. But, it just can be achieved through approximation calculation for the discrete refraction index structure of multilayer optical film. Currently, the designers can not see the physical processes by usually optimization algorithms. Design of the optical film is mainly based on comparing the input and the output point by point. If the points become more and more, the film system will get complicated and the film coating will be more difficulty.The layer structure of optical film has the same structure with the lattice structure of digital filter, which the phase difference of each layer corresponds to the time delay of digital filter. The theory system and the design of digital filter are very mature, which has a wide range of applications in the circuit system. In this thesis, we transplant the method of digital filter to the optical thin film and use the method of digital filter to design the optical thin film, obtain the structure parameters of optical thin film by the transfer function of the needed spectrum. In the design of digital filter, numerical feature of the transfer function, such as zero point and pole point, directly show the spectrum characteristics. This method can display the physical process, and overcome the flaws of the current optimization algorithm that can't show the physical process of film system by using transfer function of digital filter pre-evaluate film system structure. This method which comparing with the previous design, is expected to reduce the number of the layers and can effectively reduce the coating difficulty of special multilayer optical film.The main content of this paper is as follows:First, a brief introduction to the electromagnetic field theory and common optical thin film system structure. The matrix of multilayer dielectric films are expressed in another way, which is adventaged to use the recursive algorithm and layer-peeling method. Then give the commonly multilayer optical film optimization design, and the advantages and disadvantages of them.Second, introduced the basic principle of digital filter design and several classic digital filters and its corresponding Matlab function. Then, display the design of the IIR digital filter with low/band pass and the lattice structure with FIR and IIR digital filters.Third, elaborated how to design the optical thin film by digital filter. Like the approach of lattice digital filter, the transfer matrix of the optical film is displayed into a mathematical form of transfer function, calculate the refraction index of each layer by using the recursive algorithm and layer-peeling method, and then obtain the target spectrum transfer function of film system structure. Two examples of four layers anti-reflective and eight layers reflective films design with equal optical thickness are given by this method, and this method is compared with the result of film design software.Finally, summarize the method of the film design by digital filter.