Optical Networks - _Problems2_45

# Optical Networks - _Problems2_45 - Problems 231 Input 3 dB...

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Problems 231 Input 3 dB coupler Figure 3.80 A 3 dB coupler with the two outputs connected by a piece of ﬁber. An overview of optical detectors and receivers can be found in [Per08]. The tutorial article by Spanke [Spa87] is a good review of large switch architec- tures for optical switches. See also [MS88] for a good collection of papers on optical switching and [Clo53] for the original paper on the Clos switch architecture. The classic book by Beneˇs [Ben65] is the authoritative reference for the mathematical theory of large switch architectures developed for telephony applications. A very accessible survey of mechanical switches can be found in [Kas95, Chap- ter 13]. Several papers [NR01, LGT98, Nei00, Ryf01, Lao99, WSF06] describe MEMS-based switches. The inkjet-based waveguide switch is described in [Fou00]. See [WL96, PS95] for some early papers on liquid crystal switches. Surveys and comparisons of different types of wavelength converters appear in [Stu00, EM00, NKM98, Yoo96, ISSV96, DMJ + 96, Chi97]. Problems 3.1 Consider the 3 dB 2 × 2 coupler shown in Figure 3.80. Suppose we connect the two outputs with a piece of ﬁber. Assume that the polarizations are preserved through the device. A light signal is sent in on the ﬁrst input. What happens? Derive the ﬁeld transfer function for the device. Assume the coupler used is a reciprocal device so that it works exactly the same way if its inputs and outputs are reversed. Hint: This device is called a loop mirror. 3.2 Consider a device with three ports where it is desired to send all the energy input at ports 1 and 2 to port 3. We assume, for generality, that all ports can be used as inputs and outputs. The scattering matrix of such a device can be written as S = 00 s 13 s 23 s 31 s 32 s 33 .

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232 Components Show that a scattering matrix of this form cannot satisfy the conservation of energy condition, (3.4). Thus it is impossible to build a device that combines all the power from two input ports to a third port, without loss. 3.3 Consider an isolator that is a two-port device where power must be transferred from port 1 to port 2, but no power must be transferred from port 2 to port 1. The scattering matrix of such a device can be written as S = ± s 11 s 12 0 s 22 ² . Show that a scattering matrix of this form cannot satisfy the conservation of energy condition, (3.4). Thus the loss occurs in the isolator because the power input at port 2 must be absorbed by it. However, the power input at port 1 can be transferred to port 2 without loss. 3.4 In Figure 3.10, show that the path length difference between the rays diffracted at angle θ d and traversing through adjacent slits is approximately a [sin i ) sin d ) ] when the grating pitch a is small compared to the distance of the source and the imaging plane from the grating plane.
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## This note was uploaded on 01/15/2011 for the course ECE 6543 taught by Professor Boussert during the Spring '09 term at Georgia Tech.

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Optical Networks - _Problems2_45 - Problems 231 Input 3 dB...

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