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Homework 2 2013

Fiber is bent the optical loss is given by the

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Unformatted text preview: t. The optical loss is given by the equation: Where R is the radius of curvature of the fiber (in cm). The loss is given in “decibels” (dB), which are related to the logarithm of the light intensity (a 20 dB loss is equivalent to a factor of 10 decrease in the light intensity, a 40 dB loss is a factor of 100 drop in intensity, etc). An acceptable loss for an optical component such as this might be 3 dB. The constraints are as follows: The fiber must enter vertically, and must leave vertically, at coordinates of (-1,0) and (+1,0), respectively. The fiber is exactly 25 cm long. The fiber path must fit into a box that is no taller than 10 cm. Here are your specific instructions: 1. Download the file Fiber Loss.xlsx from the canvas website. Here you will find a template for your solution, including some starting fiber coordinates and the associated curvature equations. 2. The easiest way to set this up (but not the only way, if you want to try something different) is to define the fiber path as a sequence of N straight line segments of equal length, s, and to allow the angle of each segment to be the parameter that you vary as you perform the optimization. With the segment length and the angle defined, the path of the curve is defined at each step along the fiber by: where s is the segment length, and the index i runs from 1 to N. The curvature of the plane curve given by its X-Y coordinates can be calculated from elementary calculus (or using wikipedia) using the formula: The derivatives have been calculated in the spreadsheet for you using “central finite differences”, and are indicated on the spreadsheet. (The radius of curvature is just R = 1/ ) 3. You need to define the objective function (by summing the loss over the entire length of the fiber), and define the constraints. 4. You can now vary the fiber path by adjusting the angles , (i = 1..N-1). Thus, you are optimizing the objective function, subject to these constraints to find the smallest possible intensity loss. 5. Lastly, you should plot the shape of the fiber in the box, using the graph in the template file. *You can either submit your homework in class (if your class meets on Thursday morning), or else turn it in to Ms. Stephanie Gesualdi on the north side of the 7th floor of Barus-Holley building....
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