ECE 4332 ELECTR OOPTIC DEVICES AND SYSTEMS - Assignment Example

Fiber Bragg gratings have emerged as important components in a variety of lightwave applications. They are used in wavelength-stabilized lasers, Raman amplifiers, phase conjugators, fiber lasers, wavelength converters, passive optical networks, wavelength division multiplexers, and gain equalizers.IntroductionLightwave networks enable high capacity interconnections of information on many parts of earth. What has stimulated their development is the demand for increased bandwidth. Commercial point-to-point wavelength division multiplexers operating in the 1550nm wavelength region may have 8, 16, and more connections, each carrying 2.

5 or10 Gb/s traffic and proposals for finer granularity.Accompanying the evolution from copper wire or wireless connection to lightwave networks is the proliferation of new optical devices. Discoveries in optical transmitters, amplifiers, frequency converters, filters and multiplexers enable ways to generate, condition, and detect light.The study of wave interactions with periodic structures has yielded convenient methods of analysis and the results have been extended to gratings in wavelengths such as those in distributed feedback lasers, acousto-optic modulators and filters, and other diffracted waveguide devices.

The fiber Bragg gratings is readily analyzed by coupled mode and transfer matrixes analysis. the two modes of the waveguide Bragg grating are the counter propagating waves in the fiber which are coupled through the grating reflection. In the absence of the grating, the spatial dependence of the polarization currents for the forward wave are proportional to. Perturbations by a grating having spatial period ٨ create new sidebands that result in wave coupling i.e. exp( jβz)cos(2πz/٨) = ½{exp[j(β-2π/٨)z]+exp[j(β+2π/٨)z]} and mode coupling to the backward coupling wave.

Exp[-jβz] described by the first term on the right-hand side, occurs when -β~(β-2π/٨). Then the forward propagating wave is reflected (coupled) into the backward propagating wave.Coupled mode equations are readily derived upon substitution by the grating refractive index function into the wave equation +[]2E(٤)=0 where ٤=koz is the normalized axial dimension and n(٤)/no=1+σ(٤)+2h(٤)cos[2٤+2ǿ(٤)]. Here, no is the effective index of the propagating waves, and k0=٤onok is the nominal Bragg wave number, for constant ǿ, the Bragg wavelength is λbragg=2πn0/k0.

Change in the local average refractive index is defined by σ, the peak-to-peak index variation is 4h and corresponds to grating chirp; linear chirp has ǿα٤2. Defining a detuning parameter about the nominal Bragg wavelength, Δ= (w-w0)/w0=λbragg/( λ-1) and expanding ( βn/k0no)2 to first orders +[1+2(α+Δ)+2hexp(iχ)+2hexp(-iχ)]E(ﯕ)=0 where χ=2ﯕ +2ǿ. Assuming slowly varying field amplitudes and expressing the field as the sum forward and backward propagating waves E(ﯕ)= a +(ﯕ)exp(iﯕ)+a-(ﯕ)exp(-iﯕ) is substituted and only first derivatives retained.

Grouping yields the coupled mode equations for the field amplitudes in the forward and backward-propagating waves. Therefore coupling between waves is directly proportional to the grating amplitude and change in the average refractive index has a similar effect as grating chirp.APPLICATIONSFiber gratings are of interest to lightwave communications as either auxiliary components or as network elementsFiber lasersThese can be constructed using fiber Bragg gratings as wavelength selective resonator mirrors and erbium-doped fiber as the gain medium.

These fiber lasers are optically pumped, often directly without the use of pump wavelength division multiplexers.The output behavior is described by a simple above threshold two mirror model of the erbium fiber laser derived from rate equations. For an undepleted pump, the laser’s output power PL as a function of pump power PP isPL= .{.[ where α, g and ﯕ designate fiber parameter R is the reflectivity of the fiber Bragg grating cavity mirrors and n2=(αl-ln )/(αl+gl) is the normalized metastable population.

The laser threshold and slope efficiency are easily calculated whether pumped at 650, 980, or 1480nm wavelength.Reflectors in fiber amplifiersPlacing a single broadband reflector at the output of an erbium-doped fiber amplifier double-passes the input signal, increasing the small-signal gain and recycles remnant pump light. The equation for reflected wavelengths is obtained. = Exp[ ()-2αiL].Raman-shifted lasers and Raman amplifiers These enable efficient conversion of short-wavelength light into longer wavelengths suitable for long-distance fiber transmission.

Pump reflector in a phase conjugator- Blocking filter in a programmable wavelength converterThe phase conjugator compensates chromatic dispersion in optical fiber. Dispersion-induced signal distortion from the first half of the span is cancelled by dispersion in the second half. Efficient phase conjugation may be obtained through 4-wave mixing in semiconductor lasers or optical fibers, though the efficiency must be independent of the input signal polarization for its practical use in a lightwave system.

Isolation filters in bidirectional lightwave transmissionThese are used in long-distance systems where fiber is scarce. There are 1300/1550nm bidirectional systems. Having a minimum fiber count requirement for bidirectional systems may allow improved path diversity, smoother upgrade transitions and marginal growth in congested routes.WDM demultipliersThe channels in a wavelength division multiplexer are combined in a multiplier, traverse the fiber link and then are separated with a demultiplier to direct each channel to its receiver.

REFERENCES1. R Kashysp, ‘Photosensitive optical fibers: Devices and applications,’ Optic Fiber Technol.vol1 pp.17-34, 1994.2. M. Yamada and K. Sakuda, ‘Analysis of almost-periodic distributed feedback slab waveguides via a fundamental matrix approach,’ Appl. Opt. vol. 26, no. 16, pp 3474-3478, 1987.3. H.A. Haus: Waves in optoelectronics: Englewood cliffs, NJ: Prentice Hall, 1984 Ch. 8.4. A. Hamakawa, T. Kato, G. Sasaki, and M. Higehara, ‘wavelength stabilization of 1.

48μm pump laser by fiber grating,’ in Proc. ECOC ’96, Oslo, Norway, 1996, paper MoC3.6.