### >> What is AWG?

A remarkable device that has been made using several planar-waveguide technologies and has found a variety of applications in WDM lightwave systems is the arrayed-waveguide grating, or AWG.

Arrayed-waveguide gratings (AWG) are based on the principles of diffractions. An AWG device is sometimes called an optical waveguide, a waveguide grating router, a phase array, or a phasar. An AWG device consists of an array of curved-channel waveguides with a fixed difference in the length of optical path between the adjacent channels.

An arrayed waveguide grating (AWG) is a generalization of the Mach-Zehnder interferometer. This device is illustrated in the following figure.

It combines two NxM star couplers through an array of M waveguides whose lengths are chosen in such a way that the length difference δl between any two neighboring waveguides is constant. As a result, the phase difference between two neighboring waveguides is also constant as an input signal propagates through it.

The Mach-Zehnder interferometer can be viewed as a device where two copies of the same signal, but shifted in phase by different amounts, are added together. The AWG is a device where several copies of the same signal, but shifted in phase by different amounts, are added together. It is this constant phase difference that creates the grating-like behavior.

When light enters the input cavity, it is diffracted and enters the waveguide array. There the optical path difference of each waveguide creates phase delays in the output cavity, where an array of fibers is coupled. The process results in different wavelengths having constructive interference at different locations, where the output ports are aligned.

__>> How does AWG work?__

The wavelength dependence of an AWG can be understood in simple physical terms as follows. Consider a WDM signal consisting of multiple channels at different wavelengths with a constant channel spacing Δν. When this signal is launched into one of the input waveguides, the first star coupler splits its power into many parts and directs them into the waveguides forming the grating. At the output end of the grating array, the wavefront is tilted because of linearly varying phase shifts in waveguides of different lengths. The tilt is wavelength-dependent and it forces each channel to focus on a different output waveguide of the second coupler. This behavior is similar to a bulk grating that also directs different wavelengths to different locations.

To fully understand the principles of operation. Let’s consider the AWG shown above. Let the number of inputs and outputs of the AWG be denoted by n. Let the couplers at the input and output be n × m and m × n in size, respectively. Thus the couplers are interconnected by m waveguides. We will call these waveguides * arrayed waveguides* to distinguish them from the input and output waveguides. The lengths of these waveguides are chosen such that the difference in length between consecutive waveguides is a constant denoted by L.

The MZI is a special case of the AWG, where n = m = 2. We will now determine which wavelengths will be transmitted from a given input to a given output. The first coupler splits the signal into m parts. The relative phases of these parts are determined by the distances traveled in the coupler from the input waveguides to the arrayed waveguides. Denote the differences in the distances traveled (relative to any one of the input waveguides and any one of the arrayed waveguides) between input waveguide i and arrayed waveguide k by d_{ik}^{in}.

Assume that arrayed waveguide k has a path length larger than arrayed waveguide k −1 by ΔL. Similarly, denote the differences in the distances traveled (relative to any one of the arrayed waveguides and any one of the output waveguides) between arrayed waveguide k and output waveguide j by d_{kj}^{out}

. Then, the relative phases of the signals from input i to output j traversing the m different paths between them are given by

Here, n_{1} is the refractive index in the input and output directional couplers, and n_{2} is the refractive index in the arrayed waveguides. From input i, those wavelengths λ, for which φ_{ijk} , k = 1, . . . ,m, differ by a multiple of 2π will add in phase at output j . The question is, Are there any such wavelengths?

If the input and output couplers are designed such that and , then the above equation can be written as

Such a construction is possible and is called the Rowland circle construction. It is illustrated in the following figure. Thus wavelengths λ that are present at input i and that satisfy for some integer p add in phase at output j.

The Rowland circle construction for the couplers used in the AWG. The arrayed waveguides are located on the arc of a circle, called the grating circle, whose center is at the end of the central input (output) waveguide.

Let the radius of this circle be denoted by R. The other input (output) waveguides are located on the arc of a circle whose diameter is equal to R; this circle is called the Rowland circle. The vertical spacing between the arrayed waveguides is chosen to be constant.

For use as a demultiplexer, all the wavelengths are present at the same input, say, input i. Therefore, if the wavelengths, λ_{1}, λ_{2}, . . . ,λ_{n} in the WDM system satisfy for some integer p, we infer from the previous equation that these wavelengths are demultiplexed by the AWG.

Note that though δ_{i}^{in} and L are necessary to define the precise set of wavelengths that are demultiplexed, the (minimum) spacing between them is independent of δ_{i}^{in} and L, and determined primarily by δ_{j}^{out} .

__>> AWG Applications__

For most arrayed-waveguide gratings, the diffraction orders are very large. This is an advantage of arrayed-waveguide gratings over conventional gratings that typically operate with low diffraction orders. The wavelength resolution of AWG varies inversely with mN. Since arrayed-waveguide gratings can resolve small wavelength differences, they are used extensively in WDM communications.

The above figure shows schematically the used of 4 × 4 AWG devices as multiplexers, demultiplexers, drop/add multiplexers, and full interconnections.

In Figure (a), signals having four different wavelengths and impinging upon the four input ports are combined and “multiplexed” in an output port. In a demultiplexer, Figure (b), an input signal containing four wavelengths λ_{1}, λ_{2}, λ_{3} and λ_{4} is sorted and routed to ports 1, 2, 3, and 4, respectively. In a drop–add multiplexer [Figure (c)], information contained in a light beam of wavelength λ_{2}, for example, is dropped and replaced by new and different data before the beam exiting from the output port. In a full interconnect [Figure (d)], a signal arriving at input port 1 with different spectral components is distributed to the output ports according to the signal wavelengths. A signal of wavelength λ_{1} goes to output port 1, wavelength λ_{2} to output port 2, and so forth. For signals impinging upon input port 2 with wavelengths λ_{1}, λ_{2}, λ_{3}, and λ_{4} going to output ports 2, 3, 4, and 1, respectively. In short, arrayed-waveguide gratings can perform many functions and are capable of resolving fine wavelength differences. As a result, they find applications in many WDM communications.

Since the path lengths of different grating elements are different, and the difference are defined and determined lithographically. Arrayed-waveguide gratings are also useful in generating and shaping femtosecond pulses.

__>> More Discussion__

The AWG has several uses. It can be used as an n × 1 wavelength multiplexer. In this capacity, it is an n-input, 1-output device where the n inputs are signals at different wavelengths that are combined onto the single output. The inverse of this function, namely, 1 × n wavelength demultiplexing, can also be performed using an AWG. Although these wavelength multiplexers and demultiplexers can also be built using MZIs interconnected in a suitable fashion, it is preferable to use an AWG. Relative to an MZI chain, an AWG has lower loss and flatter passband, and is easier to realize on an integrated-optic substrate. The input and output waveguides, the multiport couplers, and the arrayed waveguides are all fabricated on a single substrate. The substrate material is usually silicon, and the waveguides are silica, Ge-doped silica, or SiO2-Ta2O5. Thirty-two–channel AWGs are commercially available, and smaller AWGs are being used in WDM transmission systems. Their temperature coefficient (0.01 nm/◦C) is not as low as those of some other competing technologies such as fiber gratings and multilayer thin-film filters. So we will need to use active temperature control for these devices.

Another way to understand the working of the AWG as a demultiplexer is to think of the multiport couplers as lenses and the array of waveguides as a prism. The input coupler collimates the light from an input waveguide to the array of waveguides. The array of waveguides acts like a prism, providing a wavelength-dependent phase shift, and the output coupler focuses different wavelengths on different output waveguides.

The AWG can also be used as a static wavelength crossconnect. However, this wavelength crossconnect is not capable of achieving an arbitrary routing pattern. Although several interconnection patterns can be achieved by a suitable choice of the wavelengths and the FSR of the device, the most useful one is illustrated in the following figure. This figure shows a 4 × 4 static wavelength crossconnect using four wavelengths with one wavelength routed from each of the inputs to each of the outputs.

In order to achieve this interconnection pattern, the operating wavelengths and the FSR(Free Spectral Range) of the AWG must be chosen suitably.