SEMBODAI RUKMANI VARATHARAJAN …gsundar.weebly.com/uploads/5/4/5/6/54560163/ec2402_unit_1.pdfSEMBODAI RUKMANI VARATHARAJAN ENGINEERING COLLEGE 1 ... UNIT 1 INTRODUCTION ... one around

SEMBODAI RUKMANI VARATHARAJAN ENGINEERING COLLEGE

1 | P a g e DEPT OF ECE EC2402 OPTICAL COMMUNICATION AND NETWORS NOTES

EC2402 OPTICAL COMMUNICATION AND NETWORS

UNIT 1 INTRODUCTION Optical Communication is the most modern mode of wired communication. Optical communication is also the youngest mode of communication. However its

capabilities supersede all other modes of communication. Before optical communication the most of the communication was in radio and

microwave domain which has frequency range orders of magnitude lower than the optical see Fig for the electromagnetic spectrum

For good communication a system needs to have following things.

Good signal to noise ratio (SNR) i.e. low loss Since the bandwidth of a system is more or less proportional to the frequency of operation, use of

higher frequency facilitates larger BW. The BW at optical frequencies is expected to be 3 to 4 orders of magnitude higher than that at the

microwave f frequencies (1GHz to 100GHz). Transmission media Alternative to the Optical Communication There are various wired and wireless media used for long and short distance communication.

Their broad characteristics are summarized in the following.

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The first two media have a very limited bandwidth.



Microwave links and Satellite communication has comparable bandwidths as in principle their mode of operation is same but the spatial reach of satellite is far greater.

Before Fiber optic communication became viable, satellite communication was the only choice for long distance communication. Hence Fiber optic communication may be achieved using an electromagnetic carrier which is selected from the optical range of frequency (1.76 x 1015 Hz to 3.75 x 1015 Hz). Therefore communication at optical wavelengths (0.8m to 1.7m or 850nm to 1700nm) offer an increase in bandwidth by a factor of 104 Advantages of Optical Communication

Ultra high bandwidth (THz) Low loss (0.2 dB/Km) Low EMI Security of transmission Low manufacturing cost Low weight, low volume Point to Point Communication

1.1 EVOLUTION OF OPTICAL COMMUNICATION SYSTEM Initially in early 1970s due to technology limitation, the optical fiber had a low loss

window around 800nm. Also the semiconductor optical sources were made of GaAs which emitted light at 800nm. Due to compatibility of the medium properties and the sources, the optical communication started in 800nm band so called the First window' .

As the glass purification technology improved, the true silica loss profile emerged in 1980s. The

loss profile shows two low loss windows, one around 1300nm and other around 1550nm. In 1980s the optical communication shifted to 1300nm band , so called the Second Window' . This window is attractive as it can support the highest data rate due to lowest dispersion.

In 1990s the communication was shifted to 1550nm window, so called Third Window' due to invention of the Erbium Doped Fiber Amplifier (EDFA). The EDFA can amplify light only in a narrow band around 1550nm. Also this window has intrinsically lowest loss of about 0.2 dB/Km . This band has higher dispersion, meaning lower bandwidth. However, this problem has been solved by use of so called dispersion shifted fibers'. To summarize: 1ST OPERATING WINDOW: centered at 850nm Fiber silica ( MM fiber) Sources LEDs, GaAlAs Photo detector silicon



Appln : Initial telephone field trials were carried out in USA in 1977 by GTE in Los Angeles and By AT & T in Chicago). Intercity applications ranged from 45 140 Mbps with repeater spacing of around 10Km. Long window 1300nm to 1700nm, attenuation



In 1998 a new ultrahigh purifying process patented by Lucent technologies eliminated virtually all water molecules from the glass fiber material. The resultant fiber produced, after reducing the OH content of silica is called All wave fiber. With these fibers the attenuation was reduced at 1550nm. 1.2 Elements of an optical fiber transmission link The key sections are transmitter consisting of a light source and its associated drive circuitry, fiber and a receiver consisting of a photo detector plus amplification & signal restoring circuitry. Additional components include optical amplifiers, connectors, splices, couplers and regenerators( for restoring the signal shape characteristics).The cabled fiber is one of the most important elements in an optical link.

Splice is permanent or semi-permanent joint b/w two fiber segments.



Let us now understand how information (voice, data and video) is transmitted on a light beam through

fiber cables. Once the fiber cable is installed, a source of light that is dimensionally compatible with the fiber core is

used to launch the optical power into the fiber. LEDS and LASERS are used for this purpose since; their output can be modulated rapidly at the desired

transmission rate, thereby producing an optical signal. The electric signals to the transmitter circuitry for the optical source can be either in analog or digital

form. For high rate systems (usually greater than 1 Gb/s), direct modulation of the source can lead to

unacceptable signal distortion. In this case, an external modulator is used the amplitude of a continuous light output from a laser diode source.

In the 800-900 nm region the light sources are generally alloys of GaAlAs. At longer wavelengths(1100-1600 nm) an InGaAsP alloy is the principal optical source material.

After the optical signal is launched into the fiber, it will become progressively attenuated and distorted with increasing distance because of scattering, absorption and dispersion mechanisms in the glass material.



At the receiver, a photodiode will detect the weakened optical signal and convert into an electrical current called as photocurrent. The design of an optical receiver is inherently more complex than that of the optical transmitter, since it has to interpret the content of weakened signal received by the photo detector. Wavelength Division Multiplexing(WDM)

The use of WDM offers a further boost in fiber transmission capacity. The basis of WDM is to use multiple sources operating at slightly different wavelengths,

to transmit several independent information streams over the same fiber. The longest link is SEA ME WE 3 cable system. It runs from Germany to

Singapore connecting many countries in between. 1.3 BASIC OPTICAL LAWS& DEFINITIONS: The fundamental parameter of a material is its refractive index n. The ratio of speed of light in vacuum to that in matter is the index of refraction n of the material given by n = c / v n = 1 for ain = 1.3 for water n = 1.55 for glass Representation of a critical angle and total internal reflection at a glass air interface. 1 angle of incidence 2 angle of refraction Using snells law n1 sin 1 = n2 sin 2, at 1 = c n1 sin c = n2 sin 90

sin c = n2 / n1 c = sin

-1(n2/n1) when 1> c min total internal reflection takes place. CRITICAL ANGLE OF INCIDENCE C: If the angle of incidence 1 is increased, a point will eventually be reached where the light ray in air is parallel to the glass surface. This point is known as critical angle of incidence c.



1.4 Optical fiber

Optical fiber is basically a solid glass rod. The diameter of rod is so small that it looks like a fiber.

Optical fiber is a dielectric waveguide. The light travels like an electromagnetic wave inside the waveguide.

The dielectric waveguide is different from a metallic waveguide which is used at microwave and millimeter wave frequencies.

In a metallic waveguide, there is a complete shielding of electromagnetic radiation but in an optical fiber the electromagnetic radiation is not just confined inside the fiber but also extends outside the fiber.

The light gets guided inside the structure, through the basic phenomenon of total internal reflection.

The optical fiber consists of two concentric cylinders; the inside solid cylinder is called the core and the surrounding shell is called the cladding. (See Fig 1)

Figure1: Schematic of an optical fiber

For the light to propagate inside the fiber through total internal reflections at core-cladding interface, the Refractive index of the core must be greater than the refractive index of the cladding. That is .

1.4.1 Different types of fibers: By refractive index profile

step-index fiber : the refractive index profile of fiber core is a step function graded-index fiber : the refractive index of fiber core depends on the radius distance.

By sustainable propagation mode single-mode fiber : support only single propagation mode. multi-mode fiber : support multiple propagation mode.

By dispersion characteristics non-dispersion-shifted fiber (NDSF) : standard single-mode fiber

with zero dispersion at 1.3m. [ITU-T G.652] dispersion-shifted fiber (DSF) : zero dispersion at 1.55m. [ITU-T G.653] non-zero dispersion

shifted fiber (NZDSF) : small but non-zero dispersion at 1.55m. [ITU-T G.655] By polarization characteristics

polarization maintaining fiber : polarization preserved fiber



1.4.1.1 STEP INDEX FIBER

Step Index Fiber (Refractive index profile)

For this fiber the refractive index of the core is constant (see Fig 5). Since refractive index profile looks like a pulse or step, this kind of fiber is called the STEP INDEX FIBER. This structure is useful for analyzing propagation of light inside an optical fiber. 1.4.1.2 GRADED INDEX FIBER In a step index fiber since the refractive index is constant inside the core, the velocity of all the rays is constant and hence there is travel time difference between different rays. If we develop a system where the rays which travel longer distances travel with higher velocities and the rays which travel shorter distances travel with lower velocities, the pulse spread on the fiber can be reduced and consequently the bandwidth can be increased. The ray which is at a higher angle, should speed up and the ray which is along the axis of the fiber should travel with the slowest possible velocity. Since velocity is inversely proportional to the refractive index, it can be manipulated by changing the refractive index of the core. The refractive index of outer layers of the core should be smaller compared to that of the inner layers, so the rays that go in the outer layers, travel faster. So we find that for reducing dispersion, the refractive index at the center should be maximum and it should gradually decrease from the center to the core-cladding interface. The rays that go at higher angles speed up and the dispersion gets reduced. In this fiber we grade the refractive index profile of the core and consequently it is called the graded index fiber.



A graded index fiber and the ray propagation is shown in the figure :

(Graded Index Profile) er the profile optimally, we get the dispersion reduction compared to that for a step index fiber,

factor of thousand. The data rate of a typical graded index fiber is typically 10 to 100 times higher compared to a step index fiber.

Therefore, in practice, even for LANs, we use GIF (Graded Index Fiber) instead of SIF \ (Step Index Fiber). Both the SI and GI fibers can be further divided into single mode and multimode fibers.

1.4.1.3 SINGLE MODE OPTICAL FIBER This fiber has one fundamental mode of propagation. It is a high capacity link used for long

distance communication. Having smaller radii, Lasers are used as optical sources which

is quiet expensive. The optical fiber in which only one ray travels along the axis of fiber is called the single mode optical fiber . Single mode optical fiber is the best amongst the three types of fibers, namely the step index fiber, GI fiber and the single mode fiber. In a long distance communication, we use single mode optical fiber, whereas in LANs we generally use graded index optical fiber.

Note: For single mode optical fiber however we have to use a source like laser because the diameter of the fiber is very small and without a highly collimated beam, sufficient light cannot be launched inside the fiber. The three types of fibers have typical diameters as follows: Core diameter: SM - 50-60 micrometre GI - 50-60 micrometre Single mode fiber-5-10 micrometre Cladding diameter (Standarised for all fibers)-125 micrometre



1.4.1.4 Multi-mode fiber : larger core area easier for power coupling between source and fiber or fiber to fiber. can use LEDs as the light source; LED are easy to make, Less expensive, require simpler circuitry, and have longer life time. This fiber has many modes of propagation. As the optical pulse is launched into this fiber, the optical power in the pulse is distributed over all of the modes of the fiber .Each of the modes that can propagate in a multimode fiber travels at a different velocity. This means that the modes arrive at different times, thus causing pulse broadening as it travels along the fiber. This effect is known as Intermodal dispersion. This is the main disadvantage of multimode fibers. This effect can be reduced by using Graded index profile in a fiber core. Comparison of single mode and multimode step index and graded index optical fibees.

1.5 Ray Optics Representation 1.5.1 Rays and Modes

The propagation of light along a waveguide can be described in terms of a set of guided electromagnetic waves called the modes of the waveguide.

These guided modes are confined to the core which is also referred as bound modes. Family of plane waves corresponding to a particular mode forms a set of rays called Ray Congruence.

The two types of rays that can propagate through a fiber are meridional rays and skew rays.

1.5.2 Meridional rays The Meridional rays are confined to the meridional planes of the fiber, the planes that has the axis of symmetry of the fiber (core axis). They are of two types of meridional rays:

o Bound Rays that propagate along the fiber axis and are trapped in the core. o Unbound Rays are refracted out of the core.



1.5.3 Skew Rays The Skew rays are not confined to a single plane, but tend to follow a helical type path along the fiber. These rays are more difficult to track as they travel along the fiber, since they do not lie in a single plane.

The Meridional ray is as shown in the fig for a step index fiber. The light ray enters the fiber core from a medium of refractive index n at an angle o with respect

to the fiber axis and strikes the core cladding interface at a normal angle . If it strikes the interface at such an angle that it is totally internally reflected, then the meridional ray allows a zigzag path along the core, passing through the axis after each reflection.



From snells law, the minimum angle that supports total internal reflection is given by sin Cmin = n2 / n1

At pt A, snells law is given as nsin0max = n1sinc ----(1) At pt B, snells law is given as n1sinc = n2 sin 90

----(2) c = sin

-1(n2/n1) From (1 ) nsin0max = n1sin (90 c)

nsin0max = n1cos c 2

= n11 sin c = n1 1 n22/n12

= n1 n12 n22/n12 nsin0max = n1

2 n2

2 Numerical aperture is defined as

Thus those rays having entrance angles c< 0max are said to be totally internally reflected at the core cladding interface. 1.6 Mode Theory of circular waveguides The different types of modes are

Guided (Or) Bound Modes Refracted (Or) Cladding Modes Leaky Modes

In optical fibers, the boundary condition at the core cladding interface lead to a coupling between electric and magnetic field component that results in hybrid modes designated as the HE or EH modes.

NA = nsin 0 max = n 1 2 n 2

2



Since n1 n2



the cladding, some of this radiation gets trapped in the cladding, thereby causing cladding modes to appear. In addition to guided and refracted modes, third category of modes are called leaky modes is present in fibers..These leaky modes are partially confined to the core region, and attenuate by continuously radiating their power out of the core as they propagate along the fiber. This power radiation out of the waveguide results from a quantum mechanical phenomenon known as the tunnel effect.

A mode remains guided as long as satisfies the condition n2k



cylindrical coordinate system used for analyzing EM wave propogation in an optical fiber.

For this fiber a cylindrical coordinate system(r, , z ) is defined with the x axis lying along the axis of the waveguide

If the EM waves are to propagate along the z axis they will have the functional dependence of the form

E = E0 ( r, ) ej(t-z) H = H0 ( r, ) ej(t-z)

where is the z component of the propagation constant k = 2/

These are harmonic in time t and coordinate z when these equations are substituted in maxwells equations, the wave equations in cylindrical coordinates is given as

2 Ez/ r2 + 1/r (Ez/ r) + 1/r

2 ( 2Ez/ 2)+ q2Ez = 0 (1)

|||ly 2 Hz/ r

2 + 1/r (Hz/ r) + 1/r2 (Hz/

2)+ q2Hz = 0 (2) where q2 = k2 2 where K free space propagation constant.

o If the boundary conditions do not lead to coupling between the field components, the modes are either TE or TM modes.

o If they are non zero ( Ez 0, Hz 0 ) that results in hybrid modes, HE (or) EH modes.

1.8.1 WAVE EQUATION FOR SI FIBERS: The above results are used to find the no of modes in SI fiber. The solution of (1) is of the form

Ez = AF1(r) F2 ( ) F3 (z) F4 (t) (3) A -arbitrary constant The time and the Z dependent factors are given by

F3 (z) F4 (t) = ej(t-z) (4) since the waves are

sinusoidal in time and propagates in the Z direction. Because of circular symmetry of the waveguide, each field component must not change when coordinate is increased by a factor of 2.

Assuming a periodic function of the form F2 () = e

jv (5)



where v can be positive or negative ,it should be an integer since the fields must be periodic with a period of 2 . sub (4) & (5) in (3) Ez = A F1 ( r ).e jv . ej (t-z) (6) Sub eqn (6) in (1) eqn (1 )becomes 2 F1/ r

2 + 1/r ( F1/ r) + (q2 v2 /r2 ) F1 = 0 (7)

This equation (7) is the differential equation for Bessel functions.

The reason for assuming an infinitely thick cladding is that the guided modes in the core have exponentially decaying fields outside the core which must have insignificant values at the outer boundary of the cladding.

The fields vary harmonically in the guiding region of refractive index n and decay exponentially outside of this region.

Equation (6) must be solved for regions inside and outside the core. Inside the core, the solutions must remain infinite as r 0. whereas , the solutions must decay to 0 as r .Thus for r 0. This in turn implies that K2 (since 2 = 2 K2

2 ) which represents the cutoff condition. A second condition of can be deduced from the behavior of Jv(ur). Inside the core, the parameter u should be real for F1 to be real from which it follows that k1 ( since u

2 = K12 2 )

Therefore the permissible range of for bound solutions is

where K = 2/ 1.8.2 MODES IN SI FIBERS:

To describe the modes, the behavior of J type Bessel functions Jv are examined and they are plotted for the first 3 orders. ( v = 0,1,2)

n 2 K = K 1 K 1 = n 1 K



As these functions are oscillatory in nature there will be m roots of modal equation for a given value of v. These roots are designated as vm

The modal equation is given as ( Jv +Kv) ( K1

2Jv + K22Kv) = ( v/ a)

2 ( 1/u2 + 1/ w2) 2 (8) where Jv = Jv(ua) / uJv (ua) or

JV+1 ( ua) / u Jv (ua) ( 9) Kv = kv

,(wa) / w Kv(wa) or Kv+1 (wa) / wKv (wa) (10) The different roots are designated as vm and the corresponding modes are represented as TEVM, TMVM, HEVM or EHVM For the dielectric fiber waveguide, all modes are hybrid modes expect for those for which v = 0. If v = 0 then the R.H.S of (8) becomes 0 and therefore two equations result which are

given as J0 + K0 = 0 (11) J1(ua ) / uJ0 (ua) + K1 (wa) / wK0 (wa) =0 (12)

which corresponds to TEOM mode K1

2J0 + K22K0 = 0 (13)

K12 J1 (ua ) / u (J0 wa) + K2

2 K1(wa) / wK0 (wa) =0 (14) which corresponds to TMOM mode

An important parameter connected with the cutoff condition is the normalized frequency V given as V2 =( u2 +2 ) a2 V2 = ( k12 2 + 2 k22 ) a2 V2 = ( k1

2 k22 ) a2

V2 = ( (2a/)2n12 (2/)2 n2

2) a2 V2 = (2a/)2 (n1

2 n22)

V2 = (2a/)2 (NA)2



The normalized propagation constant b = a2 2 / V2

substituting for and V, we get b= (/k)2 n2

2/ (n12-n2

2).

1.9 LINEARLY POLARISED MODES The exact analysis for the modes of a fiber is very complex. However a simpler approximation can be used based on this assumption. In SI fibers,



Each LP1m mode comes from TEom , TMom , & HE2m modes. Each LPvm mode (v 2) is from an HEv+1,m mode & on EHv-1,m mode. Table represent the composition of lower order linearly polarized modes

LP mode designation

Traditional mode designation and no of modes

No. of total degenerate modes

LP01 HE11 2

LP11 TE01, TM01, HE21 4

LP21 HE31, EH11 4

LP02 HE12 2

LP31 HE41, EH21 4

LP12 TE02, TM02, HE22 4

1.10 SINGLE MODE FIBERS: 1.10.1 MODE FIELD DIAMETER (MFD) For single mode fibers, the geometric distribution of light in the propagating mode( rather than core diameter and numerical aperture) is important in predicting the performance characteristics of these fibers.Thus a fundamental parameter of a single mode fiber called Mode Field Diameter (MFD )is defined. This can be determined from the mode field distribution of electric field of the fundamental mode LP01 mode.The main consideration in measuring the MFD is approximating the electric field distribution. let us assume that the electric field distribution is Gaussian in nature given as E( r) = Eo exp ( - r

2 / wo2)

Eo - electric field at zero radius r - radial distance wo - width of the electric field distribution Figure shows the distribution of light a SI fiber

, For Gaussian distribution MFD is given by 2 wo. Then MFD = 1/e2 of Eo (which is equivalent to the e

-2 radius of the optical power) 1.10.2 PROPOGATION MODES IN SM FIBERS: In any ordinary single mode fiber there are actually two independent, degenerate propagation modes.



These modes are very similar but their propagation planes are orthogonal. These are chosen as Horizontal (H) and vertical(V) polarizations as shown in the fig. Either one of these two polarization modes constitutes the fundamental HE11 mode .In general, the electric field of the light propagating along the fiber is a linear superposition of these polarization modes and depends on the polarization of the light at the launching point into the fiber. One of the mode have transverse electric field polarized along the x direction and the other to be polarized in the y direction. In the case of ideal fibers with perfect rotational symmetry, the two modes are degenerate With equal propagation constants(kx=ky), and any polarization state into the fiber will propagate Unchanged. In actual fibers, there are imperfections in practical fibers are such as

non circular cores asymmetrical lateral stresses variations in refractive index profiles.

These imperfections break the circular symmetry of the ideal fiber and lift the degeneracy of the two modes.so the two degenerate modes propagate with different phase velocities. Therefore the and the difference between the effective refractive indices is called fiber birefringence.

Bf = l ny nx l Defining the birefringence = Ko ( ny nx) , Where K0 = 2 / -free space propagation constant.

BEAT LENGTH: If light is injected into the fiber so that both the modes are excited, then one will be delayed in phase relative to the other as they propagate. When this phase difference is an integral multiple of 2, the two modes will beat at this point and the input polarization state will be reproduced. The length over which the beating occurs is called fiber beat length given as Lp = 2 /

1.11 GRADED INDEX FIBER STRUCTURE: In this fiber design, the core refractive index decreases continuously with increasing radial

distance r from the centre of the fiber, but is generally constant in the cladding. The most commonly used construction for the refractive index variation in the core is given by

the power law relation

n(r) = { n1 [1 2 (r/a) ] for 0 r a

{ n1 [1 2 ] = n1 (1 ) for r > a

~ n2 where is the shape of the refractive index profile = 1 if triangular profile = 2 if parabolic profile = for SI fiber for graded index fiber, the relative refractive index difference = (n1

2 n22 ) / n1

2 ~ n12 n2

2 / n1 For = n(r) = n1 that corresponds to a step index fiber The NA for GI fiber is a function of radial distance r given as NA( r) = { [ n2 (r) n2

2 ]1/2 ~ NA (0) 1 ( r/a) for r a 0 r > a



Where NA( 0) is the axial NA. o The number of bound modes in GI fiber is given by the expression o M = /+2 a2k2n12 1 o For

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SEMBODAI RUKMANI VARATHARAJAN …gsundar.weebly.com/uploads/5/4/5/6/54560163/ec2402_unit_1.pdfSEMBODAI RUKMANI VARATHARAJAN ENGINEERING COLLEGE 1 ... UNIT 1 INTRODUCTION ... one around