Optical systems have carrier frequencies of ~100 THz. This corresponds to wavelengths from µm.

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Lucas Aldous Simpson
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1 Introduction A communication system transmits information form one place to another. This could be from one building to another or across the ocean(s). Many systems use an EM carrier wave to transmit information. The carrier frequency can vary from a few Megahertz to hundreds of terahertz. Optical systems have carrier frequencies of ~00 THz. This corresponds to wavelengths from µm. Fiber optic communication systems are lightwave systems that use light guiding optical materials to transmit optical signals. Fiber optic systems have been deployed worldwide since 980. Fiber optic systems are one of two major factors affecting the advent of the `information age (the other being microelectronics). This class will investigate the physical and information theory issues related to the design and implementation of these systems. The physical characteristics of fiber optic components will be studied as well as the basic elements of communication theory. Once this ground work is set we will look at the design of a complete fiber optic system and the problems associated with existing photonic components and fiber. Specific modulation and multiplexing schemes will also be studied. Historical Perspective The earliest optical communications systems consisted of fire or smoke signals, signaling lamps, and semaphore flags to convey a single piece of information. The bit rate of these systems is much less than b/s. Relay or regeneration systems were proposed by Claude Chappe in 79 to transmit coded messages over distance of 00 km.

2 In the 830 s electrical communication came into being with the use of Morse Code keying techniques. This increased the bit rate to ~ 0 b/s. Intermediate relay stations increased the transmission distances to ~000 km. In 866 the first transatlantic cable was laid. These coding techniques were essentially a digital code. In 876 the telephone was invented that primarily used analog signals. These electrical techniques dominated communication transmission for nearly a century. The development of worldwide telephone networks led to many advances in electrical communications systems. Coaxial cable used in place of wire pairs greatly increased system capacity. The first coax cable was placed in service in 940 was a 3 MHz system capable of carrying 300 voice channels or one television channel. This type of transmission medium is limited by frequency dependent cable losses that increase rapidly with frequencies above 0 MHz. Microwave systems extended the carrier frequency to about 4GHz and systems of this type were first placed into service in 948. The carrier frequency and attenuation limit the performance of both microwave and coax systems. A common figure of merit for transmission systems of this type is the bit ratedistance product (B-L). The large improvement offered by the high carrier frequency of optical transmission fibers is the motivation for optical communications system development.

3 During the 960 s the main drawback of optical fibers were their loss. During the 960 s the loss was ~ 000 db/km. In 970 losses were reduced to 0 db/km by using refined fiber fabrication techniques. At about the same time GaAs semiconductor lasers were able to operate at room temperature. This combination of developments led to development of a world-wide fiber optic systems.

4 Five Generations of Lightwave Systems First Generation 980 operating at 0.8 µm wavelength and 45 Mb/s data rate. Repeater spacing was 0 km and was much greater than for comparable coax systems. Lower installation and maintenance costs resulted from fewer repeaters. Second Generation Deployed during the early 80 s. This generation was focused on using a transmission wavelength near.3 µm to take advantage of the low attenuation (< db/km) and low dispersion. Sources and detectors were developed that use InGaAsP semiconductor sources and detectors. The bit rate of these systems were limited to <00Mb/s due to dispersion in multi mode fibers. Single mode fiber was then incorporated. In 98 a demonstration system was capable of transmitting Gb/s signals over 44 km of fiber without a repeater. By 987 second generation systems were operating at.7 Gb/s at.3 µm with repeater spacing of 50 km. Third Generation these systems were based on the use of.55µm sources and detectors. At this wavelength the attenuation of fused silica fiber is minimal. The deployment of these systems was delayed however due to the relatively large dispersion at this wavelength. Two approaches were taken to solve the dispersion problem. The first approach was to develop single mode lasers and the second was to develop dispersion shifted fiber at.55 µm. In µm systems operating at.5 Gb/s were commercially available and were capable of operating at 0 Gb/s for distances of 00 km. Best performance was achieved with dispersion shifted fibers in conjunction with single mode lasers. A drawback of these systems was the need for electronic regeneration with repeaters typically spaced every km. Coherent detection methods were investigated to increase receiver sensitivity however this approach was superceded by the development of the optical amplifier. Fourth Generation These systems are based on the use of optical amplifiers to increase repeater spacing and wavelength division multiplexing (WDM) to increase aggergatebit rate. Erbium doped fiber amplifiers were developed to amplify signals

5 without electronic regeneration during the 980 s. In 99 signals could be transmitted 4,300 km at 5 Gb/s without electronic regeneration. The first transpacific commercial system went into operation sending signals over,300 km at 5 Gb/s and other systems are being deployed. System capacity is increased through use of WDM. Multiple wavelengths can be amplified with the same optical amplifier. In Gb/s signals were transmitted over 900 km providing a total bit rate of 00 Gb/s and a B-L product of 90 (Tb/s)-km. In these broad band systems dispersion becomes more of an issue. Fifth Generation This effort is primarily concerned with the fiber dispersion problem. Optical amplifiers solve the loss problem but increase the dispersion problem since dispersion effects accumulate over multiple amplification stages. An ultimate solution is based on the novel concept of optical solitons. These are pulses that preserve their shape during propagation in a loss less fiber by counteracting the effect of dispersion through fiber nonlinearity. Experiments using stimulated Raman scattering as the nonlinearity to compensate for both loss and dispersion were effective in transmitting signals over 4000 km. EDFAs were first used to amplify solitons in 989. By 994 a demonstration of soliton transmission over 9400 km was performed at a bit rate of 70 Gb/s by multiplexing 7, 0 Gb/s channels. Sixth Generation- Recently efforts have been directed toward realizing greater capacity of fiber systems by multiplexing a large number of wavelengths. These systems are referred to as dense wavelength division multiplexing (DWDM) systems. Systems with wavelength separation of 0.8 nm are currently in operation and efforts are pushing to reduce this to < 0.5 nm. Controlling wavelength stability and the development of wavelength demultiplexing devices are critical to this effort. Systems are currently operating at 0 Gb/s. Future Systems `All optical 3R regeneration systems. 3R re-amplifying, reshaping, and re-timing operations. Combinations of DWDM, optical time division multiplexing (OTDM), and optical code division multiple access (OCDMA) systems are emerging that will operate at 40 Gb/s and higher bit rates.

6 index index ANATOMY of OPTICAL FIBERS Step Index Fiber Graded-index fiber a b n n n n no no r r Core radius (a); cladding thickness (b-a) Step index profile Graded index profile There are two approaches to analyzing the propagation of light through fibers a.) Field propagation using exact solutions to Maxwell s equations. b.) Ray tracing When the core radius is much larger than the wavelength λ (i.e. a 0λ), can use geometrical optics description with high accuracy. Geometrical optics is very insightful for many situations.

7 Geometrical Description of Beam Propagation in Optical Fibers: The geometrical description of light propagation in fibers is based on the phenomena of total internal reflection. When a beam is incident to an interface from a medium with higher refractive index a critical angle occurs at which light is refracted at 90 o to the surface normal between to dielectrics. Beyond this angle light is no longer transmitted into the second medium (appreciably). Interface Beam Division Refl. n Trans. n > n < c n Inc Critical n Angle Condition c 90 o n n > c n

8 Snell s Law: n sin n sin n sin sin n Since n > n there is a limit to (i.e. 90 o ) and this limit is the critical angle c. It occurs when n sin n Surrounding a medium with refractive index n with a medium of lower index n will form a trap for light that is incident at angles > c. This is the basis for an optical waveguide. c. Optical Waveguide n > c n Fresnel Reflection Coefficients: TE Polarized Fields: r t n n n + n n n + n

9 TE Intensity Coefficients: R T r n n t TM Polarized Fields: r t n n n + n n n + n TM Intensity Coefficients: R T r n t n Can also consider that for angles of incidence that are equal and greater than the critical angle c : sin n n sin When > c,sin > n / n, and becomes completely imaginary. In this case we can write: /

10 cos jb,( > ) B n sin n c / A n/ n Letting ( ) coefficients as we can re-write the Fresnel reflection (amplitude) r TE A+ jb A jb cos Ψ + jsin Ψ exp( jψ) cos Ψ j sin Ψ exp( jψ) exp( jψ) with ( ) n B n/ n sin tan Ψ A n Similarly for TM reflection: with ( n n ) sin / rtm / exp( jδ ) ( n n ) tan δ / tan Ψ. Therefore for each case there is a phase change upon reflection that leads the phase of the incident field. (i.e. the phase of the reflected field is advanced relative to the incident field.) /

11 Example: Consider light incident from a glass with n.53 to a glass with n.50 at an angle of 85 o. Determine the phase difference between the TE and the TM fields. Out of interest the critical angle is: c sin (.50 /.53) o For the TE reflection coefficient the phase of the reflected field is: ( ) n B n/ n sin tan Ψ A n ψ o ( n n ) sin / / / Similarly for the TM reflection coefficient the phase of the reflected field is ( n n ) tan δ / tan Ψ δ o The resultant phase difference is φ ( δ ψ).7785 o. These parameters are typical of what will be encountered for optical waveguides and fibers.

12 Fiber Numerical Aperture: The acceptance angle for a fiber defines its numerical aperture (NA). It is an important parameter for determining the beam propagation and coupling characteristics of optical waveguides. n n i α α i Not Guided n The NA is defined as: NA n sinα i i where α i is the largest acceptance angle that is coupled into the waveguide. This can be determined from the TIR condition at the interface between n and n. n min( ) sin n max ( α ) 90 o

13 i i o ( ) n sinα n sin 90 n n sin n n n This leads to the simple result: NA n sinα n n. Example: n.50; n.49; NA 0.79 and α I 9.96 o. i i An important parameter based on the numerical aperture is the normalized frequency or V#. This parameter is used to determine mode characteristics of the fiber structure. The V# is defined as: V a π n n λ a π NA λ. Notice that a fiber with a particular radius and NA can change simply by using a different wavelength.

14 Approximate Method for Modes: Consider the optical waveguide shown in the figure below with n > n. n A n a C k π n /λ B A ray propagates from A to B to C reflecting at interfaces between n and n at locations A and B. In order for a wavefront to be stable within the waveguide the wavefront must be continuous at all locations within the guide. The total phase delay between the wave front at points A and C: ϕ ϕ + ϕ tot ϕ is the phase change upon reflection (there are two reflections), and ϕ is the phase change due to path length difference over path ABC.

15 The geometrical path ABC: L ABC a a + a [ + ] a + ( cos ) cos L ABC 4a cos 4a Converting to an optical phase difference: ϕ π n λ 4a. Therefore a stable mode will exist when: 8π n ϕtot ϕ + a π m, cos λ with m 0,,,

16 Example: n.50 n.40 a d/ 5 µm; λ.0 µm Assume that ϕ 0 o In this case c o ; α I o and 4 λ n a cos c M M max 54 rounded to the next lowest integer. There will also be one mode for M 0 making the total estimated modes equal to 55. max It should be noted that this is only an approximate expression to provide an intuitive concept of modes. The actual number of modes is determined from solution to the field equations and boundary conditions for the specific waveguide. Birefringence Effects in Fibers: In an ideal SMF there will be two orthogonally polarized degenerate modes. However, this only holds true if the fiber is perfectly cylindrical. Real fibers have considerable shape and stress variations that break the symmetry. These factors remove the degeneracy and result in birefringence.

17 The degree of birefringence is defined as: B n n where nx, ny are the average refractive indices in the x and y directions respectively. This aspect makes the fiber appear as a retardation plate with extended phase difference between the two polarization states. The state of polarization will vary with propagation length through the fiber. Linearly polarized light will remain linear only when the polarization coincides with one of the orthogonal axes. When linearly polarized light is oriented at other angles a phase difference is introduced between the two components and the state of polarization also changes. Associated with this birefringence is a beat length L B where L λ / B. B x y Fast Axis L B Slow Axis

18 The beat length indicates the distance along the fiber at which the polarization of the field will return to its original state. In typical SMF B is not constant but changes randomly due to variations during fiber drawing and processing. Fiber Attenuation: One of the most important limiting parameters of fiber systems is loss or attenuation within the fiber medium. Fiber optic transmission systems became competitive with electrical transmission lines only when losses were sufficiently reduced to allow signal transmission over distances greater than 0 km. Fiber attenuation reduces the average power that reaches a receiver. Fiber attenuation can be described by the general relation: dp dz αp where α is the power attenuation coefficient per unit length. The coefficient α includes scattering as well as band-band mechanisms. If P in is the power launched into the fiber, the power remaining after propagating a length L within the fiber P out is P P exp( αl). out An expression for α in terms of db/km in 0 P out α( db / km) log α. L Pin The absorption coefficient varies with wavelength as many of the absorption and scattering mechanisms vary with λ.

19 For instance Rayleigh scattering in fiber is due to microscopic variations in the density of glass and varies as 4 α R C / λ, with C a constant that varies from (db/km)-µm depending on the type of glass. For Rayleigh scattering the density fluctuation sites < λ. It is one of the dominant loss mechanisms in fiber as can be seen from the figure. Imperfections in the core-cladding interface also form a loss mechanism. Here the scattering sites are larger than λ and the scattering mechanism can be described by Mie scattering. Losses due to Mie scattering can be kept to ~0.03 db/km with proper design. Other sources of loss such as fiber bends and microbends can also be controlled with proper design SMF Loss (db/km).0 Rayleigh scattering UV Absorption IR Abs 0.05 Waveguide imperfections Wavelength (um)

University of Arizona ECE 430/530: Optical Communication Systems Spring 2010, Ivan B. Djordjevic Introduction to Fiber-Optics Communications

University of Arizona ECE 430/530: Optical Communication Systems Spring 2010, Ivan B. Djordjevic Introduction to Fiber-Optics Communications University of Arizona : Optical Communication Systems Spring 2010, Ivan B. Djordjevic Introduction to Fiber-Optics Communications 1 INTRODUCTION TO FIBER-OPTICS COMMUNICATIONS Optical communication systems