TFC设计实例.doc

Two Ramp Filters Contents Index Home As an interesting design exercise, we decided to create two ramp filters. The goal is to create filters in which the transmittance increases (or decreases) linearly over some wavelength range. Too make it slightly more difficult, we also require the transmittance to be 0% and 100% on either side of the ramp. Here are the specific requirements for the normal-incidence increasing-transmittance ramp filter: 400 to 500 nm, T 2% 500 to 700 nm, T increases linearly from 98% 700 to 800 nm, T 98% The substrate has index 1.52 and is assumed to have an AR coating on its backside. The incident medium is air. The coating materials are SIO2 and TIO2. We use the three continuous optimization targets. To find the thinnest possible design, we start with a single thin layer of TIO2 and use TFCalcs needle/tunneling optimization to design the filter from scratch. Optimizing this design takes only a minute or two on a 2.8 GHz Pentium computer. The performance of the 23-layer design is shown here. For the second design, we just replace transmittance by reflectance in the requirements. The performance of the filter, which also has 23 layers, is shown here. If you want a copy of the design files, which will work in the demo version of TFCalc, please send e-mail to . Anti-Reflection Filters Contents Index Home Also called AR coatings. Probably the most common type of coating, an anti-reflection coating reduces the reflection (increases the transmission) of the surface on which it is applied. AR coatings may be designed for any part of the spectrum. It is possible to create high efficiency AR coatings (which reduce the reflectance very close to zero for a narrow band of wavelengths), broadband AR coatings, multiband AR coatings, etc. The graphic below shows the performance of a 4-layer design that reduces the reflectance of glass from its usual value of about 4% down to less than 0.1%. Broadband Antireflection Graded-Index Coating Contents Index Home In an important 1962 paper, Peter H. Berning, Use of Equivalent films in the design of infrared multilayer antireflection coatings, Journal of the Optical Society of America, Vol. 52(4), pp. 431-436 (April 1962).one of the coatings discussed by the author is a step-graded-index antireflection coating for germanium. This coating consists of 20 quarter-wave layers whose indices vary linearly from 1.35 (the lowest practical index available) to 4 (the index of germanium), as illustrated below. The coating has a very broad wavelength range over which the reflectance is low. The question arises: is the linear profile the best possible? We can use optimization to explore this problem. Here we use a feature unique to TFCalc - the capability of optimizing the reflective index while keeping the optical thickness fixed. We use one continuous optimization target: R=0 for 3-20 microns. To make the reflectance as flat as possible, we set the power in the merit function to 16. Surprisingly, the resulting index profile looks like part of a sine curve: The performance of the optimized design is significantly better. The reflectances of the two designs are shown below. Here is the list of refractive indices in the optimized design, starting with the layer closest to the germanium substrate: 1 3.9356 2 3.7482 3 3.3986 4 2.9121 5 2.3790 6 1.9044 7 1.5598 8 1.3726 9 1.3500 10 1.5042 11 1.8606 12 2.4315 13 3.1456 14 3.7738 15 4.0000 16 3.6871 17 3.0181 18 2.3016 19 1.7310 20 1.3500The reference wavelength for the quarter-wave optical thickness is 5.217 microns, which is the midpoint, in the frequency scale, between 3 and 20 microns. Note: by using more layers, designs with more cycles of the sine curve can be found. However, the additional cycles do not improve the performance as dramatically as above. Download DesignYou may download the Berning design and watch how TFCalc optimizes it. You will need a real copy (i.e., not a demo) of TFCalc. Click here for the Windows or Macintosh file. This design assumes that you have a substrate called G whose index is 4. The G substrate was installed with the TFCalc software. Windows users, when they download this file, will have Bandpass Filters Contents Index Home This type of filter transmits a band of wavelengths (the passband) and rejects wavelengths outside of that band. The passband can be narrow or wide. The transition from transmitting to rejection can be gradual or sharp. Filters having multiple passbands are also possible. The graphic below shows a fairly narrow bandpass filter. Wide Infrared Bandpass Filter Contents Index Home This coating is for light at normal incidence on a germanium substrate (index 4). The requirements are:A. Transmittance 99% for wavelengths 3300-5000 nmC. Transmittance 99.9% for wavelengths 400-700 nm at angles 65,66,.,75 P Optical Density 3.0 for wavelengths 400-700 nm at angles 65,66,.,75 There are many ways to design this coating. One simple method is to start with a stack such as (0.5H L 0.5H)n that reflects the P polarization for the wavelengths and angles given above, and then use optimization to force the coating to transmit S polarization. Here H and L represent quarter-wave layers of index 2.35 and 1.45, respectively. Some tests show that if we start with the 21-layer design created by setting n=10, then the optimization targets given above will be met. The performance is shown below, with the left scale for the optical density of P reflectance and the right scale for S transmittance. The extinction ratio is greater than 1000 for all design angles and wavelengths. Here is the design, with the first layer closest to the substrate and thickness given in nm: H 11.16 L 48.87 H 35.94 L 68.58 H 39.50 L 79.77 H 46.20 L 96.61 H 49.71 L 102.74 H 50.49 L 102.74 H 49.71 L 96.61 H 46.20 L 79.77 H 39.50 L 68.58 H 35.94 L 48.87 H 11.16Note, curiously, that optimization preserved the symmetry of the original design (i.e., layers 1 and 21, 2 and 20, 3 and 19, etc., have the same thickness). The authors are commended for this ingenious polarizer, which is the subject of a patent application. However, it seems that this polarizer has two drawbacks: (1) the dimensions of the prisms may prevent its use in some applications and (2) the prisms seem to require a high-index glass, which presents other problems. *Recently, a paper was published that gives much more detail about this polarizer. See Li Li and J.A. Dobrowolski, High-performance thin-film polarizing beam splitter operating at angles greater than the critical angle, Applied Optics, Vol. 39, No. 16, pp. 2754-71.Immersed Wideband Nonpolarizing Beamsplitter Contents Index Home This coating is immersed in glass (index 1.52) and light is incident at 45 degrees. As shown below, it divides the incident light so that the reflectance (and transmittance) of the S and P polarizations are between 45% and 55% for wavelengths from 420 nm to 680 nm - a very wide bandwidth for this type of coating. Three materials are used: L (1.35), M (1.9), and H (2.35). Starting with a thin, one-layer design, TFCalcs needle/tunneling method produced a sequence of designs of increasing