# OPTICAL FIBER COMMUNICATIONS JOHN M SENIOR PDF

The right of John M. Senior to be identified as author of this work has Optical fiber communications: principles and practice / John M. Senior, assisted by myavr.info, with permission from Fujikura Limited; Figure (a) from Optical. Optical Fibre Communications myavr.info - Free ebook download as PDF File .pdf), Text File .txt) or read book online for free. E-Book Optical Fibre. This Digital Download PDF eBook edition and related web site are NOT.. dependable philosophy of individual achievement.

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This is a trusted location to have Optical Fiber Communication By John M Senior 2nd Edition. Pdf by myavr.info Study You allow to download and. Download Optical Fiber Communications: Principles and Practice By John M. Senior – Senior is an established core text in a field that is growing fast, and in. [PDF] Optical Fiber Communications: Principles and. Optical Fiber Communications by John M. Senior is one of the important book for Electronics and.

Installation of optical fiber communication systems is progressing within both national telecommunication networks and more localized data communication and telemetry environments. Furthermore, optical fiber communication has become synonymous with the current worldwide revolution in information techno1ogy..

The relentless onslaught will undoubtedly continue over the next decade and the further predicted developments will ensure even wider application of optical fiber communication technology in this 'infermation age'..

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The practical realization of wide-scale optical fiber communications requires suitable education and training for engineers and scientists within the technology. In this context the book has been developed from both teaching the subject to final year undergraduates and from a successful series of short courses on optical fiber communications conducted for professional engineers at Manchester Polytechnic.

This book has therefore been written as a comprehensive introductory textbook for use by undergraduate and postgraduate engineers and scientists to provide them with a firm grounding in the major aspects of this new technology whilst giving an insight into the possible future developments within the field.

The reader should therefore be in a position to appreciate developments as they occur. With these aims in mind the book has been produced in the form of a teaching text enabling the reader to progress onto the growing number of specialist texts concerned with optical fiber waveguides, optoelectronics, integrated optics, etc. In keeping with the status of an introductory text the fundamentals are included where necessary and there has been no attempt to cover the entire field in full mathematical rigor.

However, selected proofs are developed in important areas throughout the text. It is assumed that the reader is conversant with differential and integral calcu1us and differential equations. In this context the book has been developed from both teaching the subject to final year undergraduates and from a successful series of short courses on optical fiber communications conducted for professional engineers at Manchester Polytechnic.

This book has therefore been written as a comprehensive introductory textbook for use by undergraduate and postgraduate engineers and scientists to provide them with a firm grounding in the major aspects of this new technology whilst giving an insight into the possible future developments within the field.

The reader should therefore be in a position to appreciate developments as they occur. With these aims in mind the book has been produced in the form of a teaching text enabling the reader to progress onto the growing number of specialist texts concerned with optical fiber waveguides, optoelectronics, integrated optics, etc. In keeping with the status of an introductory text the fundamentals are included where necessary and there has been no attempt to cover the entire field in full mathematical rigor.

However, selected proofs are developed in important areas throughout the text. It is assumed that the reader is conversant with differential and integral calcu1us and differential equations. In addition, the reader will find it useful to have a grounding in optics as well as a reasonable familiarity with the fundamentals of , solid state physics.

Chapter 1 gives a short introduction to optical fiber communications by considering the historical development, the general system and the major advantages provided by this new technology. Chapter 2 the concept of the optical fiber as a transmission medium is introduced using a simple ray theory approach.

This is followed by discuslion of electromagnetic wave theory applied to optical fibers prior to consideration of Ii,htwave transmission within the various fiber types, The major transmission cha r acteris tics of optical fi bers are th en di sCU ssed in so me detail in C h a pter 3.

When the total This situation is illustrated in Fig.. However, it may he observed from Fig. Nevertheless the optical wave is etTectively confined within the guide and the electric fiel d distribution in the x direction docs not chan gc as the wa vc propagates in the z di rection. The sin usoidally vary ing electric field 1 n the z direction is also shown in Fig. In effect Eq 54 2. It should be noted that there is a phase shift on reflection of the plane wave at the interface a.

## [PDF] Optical Fiber Communications: Principles and Practice By John M. Senior Book Free Download

The phase shift on reflection at a dielectric interflce til dc. Hence the light propagating within the guide is fanned into discrete "modes each typified by a distinct value of 9. These modes have a periodic z dependence of the form exp -J! If we now assume a time dependence for the monochromatic electromagnetic 1ight field with angular frequency OJ of cxp Urnt '!

To visualize the dominant modes propagating in the z direction we may consider plane w aves correspond ing to rays at different specific angles in the planar guide.. These plane waves give constructive interference to form standing wave patterns across the guide following a sine or cosine formula.

It may be observed that m denotes the number of zeros in this tran s verse field pat tern. I n this way m signifies the order of the mode and is known as the mode number. When light is described as an electromagnetic wave it consists of a periodically varying electric field E and magnetic fie1d H wh i ch are orientated "' Claduuig penet For plane waves these constant phase points form a surface which is referred to as a wavefront.

As a monochrornati c I ight wave propagates along a waveguide in the z direction these points of constant phase tr a vel at a phase velocity Pp given by: Often the situation exists where a group of waves with closely similar frequencies propagate so that their resultant forms a packet of waves. The envelope of the wave packet or group 01 waves travels at a grou p velocitv Vg.

Equation 2. Using Eq.. In order to appreciate these p hcnomena it is necessary to use the wave theory model for total internal reflection at a planar interface.

This is illustrated in Fig. As the guide-cladding interface lies in the y-z plane and the wave is incident in the. Since the phase fronts must match at all points along the interface in the z direction, the three waves shown in Fig.

When the components are resolved in this plane: The wave vectors of the incident. Thus the three waves in the waveguide indicated in Fig. Initially let us consider the TE field at the boundary.

When Eqs.. The expressions obtained in Eqs, 2. Under the conditions of tota] internal reflection Eq4 2. This is signified by OE which is given by: The curves of the amplitude reflection coefficient I rER I and phase shift on reflection, against angle of incidence 4t l' for TE waves incident on a glass-a ir interface are displayed in Fig" 2. These curves illustrate the above results, where under the condition s of tota] in ternal reflection the reflected wave h as an equal amplitude to the incident wave, but undergoes a phase shift corresponding to OE degrees.

Again the expressions given in Eqs, 2. The second phenomenon of interest under conditions of total internal reflection is the form of the electric field in the ciaddi ng of the g uidc, Before the cri tical angle for total intern al reflection is reached and hen ce when there is only partial reflection, the field in the cladding is of the form given by Eq. A field of th is type stores energy and tran sports it in the directi on of propagation z but docs not tr ansport energy in the transverse di rection x , Nevertheless the existence of an evanescent field beyond the plane of reflection in the lower index medium indicates that optical energy is transmitted into the cladding.

The penetration of energy into the cladding underlines the importance of the choice of cladding mat eri al.

It gives rise to the follow in g rcq uirernen ts: These effects degrade the reflection process by in tern cti on wi th the evanescent Held. Therefore the most widely used optical fibers consist of a core and cladding both made of gl ass.

## Optical Fibre Communications JOHN.M.seniOR

The cl adding refractive index is thus hig her than would be the case with liquid or gaseous cladding giving a lower numerical aperture [or the fiber. Careful examination shows that the reflected beam is shifted laterally from the trajectory predicted by simple ray theory analysis as illustrated in Fig. This lateral displacement is known as the Goos-Haenchen shift after its first observers..

The geometric reflection appears to take place at a virtual reflecting plane which is parallel to the dielectric interface in the lower index medium as indicated in Fig. However, this concept provides an important insight into the guidance mechanism of d ielectric optical waveguides.

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In common with the planar guide Section 2. For the cylindrical waveguide we therefore refer to TE1m and TM1m modes. These modes correspond to meridional rays see Section 2. DES 35 modes where E, and Hz are nonzero also occur within the cylindrical waveguide, These modes which result from skew ray propagation see Section 2.

Fort un ately the analy sis may be simplified when considering optical fibers for communication purposes. This corresponds to small grazing angles a in Eq, These linearly polarized L.

P modes are not exact modes of the fiber except for the fundamental lowest order mode. However, as 6. Such modes are said to be degenerate. This linear combination of degenerate modes obtained from the exact solution produces a u sefu 1 sirnpl ification in the analysis of weakly guiding fibers. The mode subscripts I and m are related to the electric field intensity profile for a particul ar LP mode see Fig. T here are in general 21 field maxim a around the circumference of the fiber core and m field maxima along a radius vector.

Furthermore, it may be observed from Table 2. The electric field intensity profile for the lowest three LP modes, together with the electric field distribution of thci r constituent exact modes, are shown in Fig. Hence the origin of the term 'linearly polarized'. Sol ution s of the wa vc equation for the cyl i ndrical fiber are separable, having the form: Hence the fiber supports a finite number of guided modes of the form of Eq, 2.

In the core region the solutions are Bes sel function s denoted by J t: A graph of these grad u ally dam ped oscillatory functions with respect to r is shown in Fig. The electric field may therefore be given by: U and W which are the eigenvalues in the core and cladding respectively, are defined as: However, within this chapter there should be no confusion over this point.

Furthermore, using Eqs.. V is sometimes known as the normalized f lm thi c knes s as it re] ares to the thick ness 0 f the i u i de layer see Section J 1. It is also possible to define the normalized propagation constant b for a fiber in term s of the parameters of Eq, 2.

Nevertheless, wave propagation does not cease abruptly below cutoff. I llEu 1[t:: Reproduced with permission from D. Glope, Appl.

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The lower order modes obtained in a cylindrical homogeneous core waveguide are shown in Fig. In addition, the Bessel functions Jo and J1 arc plotted against the normalized frequency and where they cross the zero gives the cutoff point for the various modes. However, the first zero crossing for J 0 is when the normalized frcq ucncy is 2. The electric field distribution of different modes gives similar distributions of light intensity within the fiber core.

These waveguide patterns often called mode pattern s may give an indication of t he predominant modes propagating in the fiber. The field intensity distributions for the three lower order L P modes were shown in Fig. I n Fig. Reproduced with permission from D, Gloge, Appl. These will have the effect of coupling energy tra velling in one mode to another depcndin g on th e specific pertu rba tion.. Ray theory aids the u nderstan ding of th i s phenomenon as shown in Fig. In electromagnetic wave theory this corresponds to a change in the propagating mode for the 1 ight.

Thu s individ u al modes do not norm all y propagate throughout the length of the fiber without large energy transfers to adjacent modes even when the fiber is exceptionally good quality and not strained or bent by its surroundings.

This mode conversion is known as mode coupling or mixing. It is usually ana1yzed using coupled mode equations which can be obtained direct1y from Maxwell's equations. However, the theory is beyond the scope of this text and the reader is directed to Ref.

Mode coupling affects the transmission properties of fibers in several important ways; a major one being in relation to the dispersive properties of fibers over long distances.

This is pursued further in Sections 3. This is because the refractive index profi1e for this type of fiber makes a step change at the core-cladding interrace as indicated in F ig.

The refrac '" Live index profile may be defined as: This i s illustrated in Fig. The propagation of a single mode is illustrated in Fig. However, for lower bandwidth applications multirnodc fibers have several advantages over single mode fibers, These arc: It was indicated in Section 2.

However, moue propagation does not entirely cease below cutoff. Modes may propagate as unguided or leaky modes which can travel con sider able distances along the fiber.

Nevertheless it is the guided modes wh i ch are of para mou nt importance in opti cal fiber com munication s as these are confined to the fiber over its full length" It can be shown I Ref. Ji viriq nca rly t] LJ i dod modes. Therefore as ill u str ated in examp1e 2. Also the majority of these guided modes opera te far from cutoff, and are well confined to the fiber core l Ref.

The properties of the cladd ing e.. Multimode step index fibers do not lend themselves to the propagation of a single mode due to the difficulties of maintaining single mode operation within the fiber when mode conversion i.

Hence for the transmission of a single mode the fiber must be designed to allow propagation of only one mode.. For single mode operation.. Hence the limit of single mode operation depends on the lower limit of guided propagation for the LP II mode. The cutoff norma1ized frequency for the L. It must be noted that there are in fact two modes with orthogonal polarization over this range, and the term s Ingle mode applies to propagation of Ugh t of a parti cu lar polarizati on.

Also, it is apparent that the normalized frequency for the fiber may be adjusted to within the range given in Eq, Consideri ng th e re I ationship 9 ivan in Eq. Hence from Eq. It is clear from example 2. Both these factors create difficulties with single mode fibers. Thus the exponentially decaying evanescent field may extend significan t distances into the cl adding, 11 is therefore essen ti al t ha t the cladding is of a s uitable thick ness, a nd has low absorption and scattering losses in order to reduce attenuation of the mode.

Estimates [Ref. Conseq uently these modes will lose power by radiation into the lossy surroundings.

Thi s design can provide single mode fibers with J arger core di am ctcrs than the conventional single cladding approach which proves useful for easing jointing difficulties, W fibers also tend to give reduced losses at bends in comparison with conventional single mode fibers.

Equa tion 2. This range of refractive index profiles is illustrated in Fig" 2. For this reason in this section we consider the wavcguiding properties of graded index tiber with a parabo1ic refractive index profile core. Using the concepts of: I CMe a: S Fig.

Although many different modes are excited in the graded. Again considering ray theory, the rays travelling close to the fiber axis have shorter paths when compared with rays which travel into the outer regions of the core. However, the near axial rays are transmitted through a region of higher refractive index and therefore tra vel with a lower velocity than the more extreme rays.

This compensates for the shorter path lengths and red uces dispersion in the fiber. A similar situation exists for skew rays which follow longer helical paths as illustrated in Fig. Hence multirnode graded index fibers with parabolic or near parabolic index profile cores ha vc tran smission bandwidths which may be orders of magnitude greater than multirnode step index fiber bandwidths, Consequently, although they are not capable of the bandwidths attainable with single mode fibers, such multimode graded index fibers have the advantage of la rge core diameters greater th an 30 11m coupled with bandwidths suitable for long distance communication.

The parameters defined for step index fibers i. However, it must be noted that for graded index fibers the situation is more complicated since the numerical aperture is a function of the radial distance from the tiber axis.

Graded index fibers, therefore, accept less light than corresponding step ind ex fibers with t he same relative refractive index difference. Electromagnetic mode theory may also be utilized with the graded profiles, Approximate field solutions of the same order as geometric optics are often obtained employing the WKB method from quantum mechanics after Wentzel, Kramcrs and Brillouin I Ref Using the WK B method modal solutions of the guided w ave arc ac h ieved by ex pressing the field in the form: Substitution of Eq..

The ray is contained within two cylindrical caustic surfaces and for most rays a caustic does not coincide. I,' -t: Hence the caustics define the classical turning points of the light ray within the graded fiber core. These turning points defined by the two caustics may be designated as occurring at r:: Fortunately this may be amended by replacing the actual refractive index profile by a li near approxim ation at the location of the caustics.

The solutions at the turning points can then be expressed in terms of Hankel functions of the first and second kind of order f I Ref. This eigenvalue equation can only be solved in a closed analytical form for a few simple refractive index profiles. Hence, in most cases it must be solved approximately or with the use of n u m ericai techniq ucs, Finally the amplitude coefficient D may be expressed in terms of the total optical power PG within the guided mode.

Considering the power carried between the turning points rl and r2 gives a geometric optics approximation of I Ref. Th is iss hown in Fig. Th is corr,.

Substitution of Eq, 2. Furthermore" practical parabolic refractive index profile core fibers exhibit a tru nc ated par abolic distribution which merges into a con stant refractive index at the cladding.. Hence Eq. The tnode number plane contains guided, leaky and radiation modes. The mode boundary which separates the guided modes from the leaky and radiation modes is indicated by the solid line in Fig.

It depicts a constant value of P following Eq. It can be shown l Ref. The fiber has a n U me rica I a pertu re of 0,2. E 5t1 m ale the total number of guided modes propagating in the ffber whe n it is ope rating at a wavel ength of m.

Using Eq, 2,69 , the normalized frequency for the fiber is: It may be noted that the critical val ue of normal i zed frequency for the parabolic profile graded index fiber is increased by a factor of y2 on the step index case. This gives a core diameter increased by a similar factor for the graded index fiber over a step index fiber with the eq uiv a1ent core refractive index equivalent to the core axis index , and the same relative refractive index d iffcrence, The maximum V number which permits single mode operation can be increased still further when a graded index tiber with a triangular profile is employed.

It is apparent from Eq. Hence significantly larger core diameter single mode fibers may be produced utilizing this index profile.

## Optical Fiber Communications-3rd Edition

Briefly discuss with the aid of a suitable diagram what is meant by the acceptance angle for an optical fiber. Show how this is related to the fiber numerical aperture and the refractive indices for the fiber core and cladding. An optical fiber has a numerical aperture of 0. Comment on any assumptions made about the fiber. Determine the numerical aperture and the acceptance angle for the fiber in air, assuming it has a core diameter suitable for consideration by ray analysis.

Estimate the speed of Jight in the fiber core. Derive an expression for the acceptance angle for a skew ray which changes direction by an angle 3y at each reflection in a step index fiber in terms of the fiber NA and y. It may be assumed that ray theory holds for the fiber. A step index fiber with a suitably large core diameter for ray theory considerations has core and cladding refractive indices of L44 and 1.

Determine the acceptance angle for meridional rays for the fiber in air. Determine the normalized frequency for the fiber when light at a wavelength of 0. Compare the advantages and disadvantages of these two types of fiber for use as an opti c al chan nel, 2. The number of modes propagating at a wavelength of Esti mate the dia meter of the fiber core.

Estimate the maximum possible relative refractive index difference for the fiber. Indicate the major advantage of this type of fiber with regard to multirnode propagation. Estimate values for the numerical aperature of the fiber when: Comment on the results.

Determine the wavelength of the light propagating in the fiber. Further estimate the maximum diameter of the fiber which gives single mode operation at the same wavelength.

Estimate the number of guided modes propagating in the fiber when the transrn itted light has a wa velength of 1. Anlwers to Numerical Problems 2. Hondros and P. Debye 'Electromagnetic waves along long cylinders of dieiectric', Annal.

Schriever, 'Blectromagnetic waves in dielectric wires', Annal. Kao and O. Proc IE R. Fiber Commun. O'Con nor, F. W r Di M arcel1 o, J. Miya, Y. Tcrunuma, T.

Hosaka and T.This corresponds to small grazing angles a in Eq, TSi I II puru. More recently this wavelength range has been extended to include the 1. Baqar Rizvi. Debye 'Electromagnetic waves along long cylinders of dieiectric', Annal. This produces an opti cal frcq uency shi ft which varies with the sea ttcri ng angle because the f req ucn c y of t he sound wave varies with acoustic w a vclcngth, The frcq ucncy shirt is a maxim urn in the back ward direction reducing to zero in the forward direction making Brillou in scattering a mainly back w ard proces s.

Linear scattering may be categorized into two major types: A similar situation exists for skew rays which follow longer helical paths as illustrated in Fig.

These modes correspond to meridional rays see Section 2.