http://www.wiretechworld.com/the-future-of-optical-fibres/

EE 443 Optical Fiber Communications

Dr. Donald EstreichFall Semester

1

Lecture 5

2

https://www.slideshare.net/tossus/waveguiding-in-optical-fibers

Linearly Polarized (LP) ModesFrom Lecture 4:

3

LP01 Mode Distribution LP11 Mode Distribution

https://www.newport.com/t/fiber-optic-basics

When light is launched into a fiber, modes are excited to varying degrees depending on

the conditions of the launch — input cone angle, spot size, axial centration, etc. The

distribution of energy among the modes evolves with distance as energy is exchanged

between them. Energy can be coupled from guided to radiation modes by

perturbations such as microbending and twisting of the fiber.

LP01 and LP11 Modes in the Core of an Optical Fiber

4

The V Number (or Fiber Parameter)

The V number is an often-used dimensionless parameter in the context of

step-index fibers. V is given by

https://www.rp-photonics.com/v_number.html

2 2

1 2 1

2 2 22

a a aV n n NA n

= − = =

1

2

a

n

n

NA

Radius of fiber core within the claddingIndex of refraction of fiber coreIndex of refraction of claddingWavelength of optical signal in vacuumNumerical AperatureIndex difference between n1 and n2

2 2

1 2

2

12

n n

n

− =

5

http://www.invocom.et.put.poznan.pl/~invocom/C/P1-9/swiatlowody_en/p1-1_1_3.htm

Propagation Constant vs. V-number for Different Modes

V = 2.405

2 1n k n k

Single moderange

LP01

LP11

LP21

2n k

1n k

6

The V Number (or Normalized Frequency)

The V number is a dimensionless parameter which is often used in the context of

step-index fibers. It is defined as

where λ is the vacuum wavelength, a is the radius of the fiber core, and NA is the

numerical aperture. The V number can be interpreted as a kind of normalized optical frequency. (It is proportional to the optical frequency but rescaled depending upon waveguide properties.) It is relevant for various essential properties of a fiber:

2 2

1 2

2 2a aV n n NA

= − =

• For V values below ≈ 2.405, a fiber supports only one mode per polarization

direction (→ single-mode fibers).

• Multimode fibers can have much higher V numbers. For large values, the

number of supported modes of a step-index fiber (including polarization

multiplicity) can be calculated approximately as

2

2

VM

7

Cut-off wavelength can also be defined as the wavelength below which multimode transmission starts.

2 2

1 2

2

= −

C

lm

an n

V

Optical Fiber Cut-Off Wavelength

2

2.405

=

C

aNA

The cut-off frequency of an electromagnetic waveguide is the lowest frequency

for which a mode will propagate in it. In fiber optics, it is more common to

consider the cut-off wavelength, the maximum wavelength that will propagate in an optical fiber or waveguide. The cut-off wavelength is given by

https://en.wikipedia.org/wiki/Cutoff_frequency

8

https://physics.stackexchange.com/questions/106477/graded-index-fiber?rq=1

Single Mode Optical Fiber

Step Index Fiber

9

http://en.optipedia.info/lsource-index/fiberlaser-index/fiber/parameters/mode-field/

Mode Field Diameter (MFD)

For SMF, the diameter of the circular region for the light intensity of 1/e2 = 0.135 of

the core center light intensity is defined as mode field diameter (provided that the

light intensity distribution in SMF is approximated by the Gaussian function).

=MFD 2w

10

Mode Field Diameter (MFD)

From Figure 2.31 (page 61) in Senior.

Figure 2.31

A different definition ofMode Field Diameter

11https://www.slideshare.net/tossus/waveguiding-in-optical-fibers

Mode-Field Diameter is Dependent Upon Wavelength

Wavelength (nm)

Mo

de-

Fiel

d D

iam

eter

(

m)

12

Next Topic: Dispersion in Optical Fibers

Sections 3.8 to 3.12 in Senior (pages 105 to 140)Also Section 3.13.2.

13

Digital Bit Rate

For no overlapping light pulses within an optical fiber,the digital bit rate (BT) must be less than the reciprocalof the broadened pulse duration (2). Hence,

Note: Must distinguish between bit rate and bandwidth.

1(approximately)

2TB

14

Bit Rate (bps) and Bandwidth (Hz)

From: Figure 3.8 (page 107) in Senior.

Nonreturn-to-Zero

Return-to-Zero

Maximum rateof change inbit pattern

(b) 1 1 1 1

(a) 1 0 1 0

time

time

Conversion of bit rate BT (bps) to bandwidth BW (Hz) dependsupon the digital coding:

For Nonreturn-to-Zero: BT(max) = 2BWFor Return-to-Zero: BT(max) = BW

Two bits per period per Hz

One bit per period per Hz

15

Bandwidth-Length Product Is Most Useful Metric

The information carrying capability of an optical fiber is limited byThe amount of pulse distortion at the receiving end of the fiber.pulse broadening is proportional to the length of the fiber cable and thus bandwidth is inversely proportional to distance.

The Bandwidth-Length parameter is the most useful parameter tostate the information capability of a transmission line (optical fiber).

A more accurate estimate for maximum bit rate BT(max) is obtained ifWe assume a Gaussian pulse with standard deviation

TB L

0.2(max) [bits/sec]TB

=

See Appendix B (pp. 1052-1053)

of Senior

~

16

Example 3.5 (Page 109) of Senior

A multi-mode graded index fiber exhibits a pulse broadening of 0.1 microseconds (1 s) over a distance of 15 km.

(a) Estimate the maximum possible bandwidth of this fiber link assuming not ISI.

The maximum possible optical bandwidth which is equivalent to the maximumPossible bit rate (for to return-to-zero pulses) without ISI is

(b) The dispersion per unit length may be estimated using by dividing the totaldispersion by the total length of the fiber link.

6second

1 15 MHz

2 0.2 10opt TB B

−= = = =

6second0.1 10

Dispersion 6.667 ns/km15 km

−= =

17

Example 3.5 (continued)

(c) The bandwidth-length product can be determined in two ways. First, multiply the maximum bandwidth by its length.

The other way is to use the dispersion per unit length and applyit to BT 1/2.

5 MHz 15 km 75 MHz kmoptB L = =

9

1 175 MHz km

2 2 6.667 10 [sec/km]optB L

−= = =

18

Bit-Rate Distance Product Evolution

https://www.researchgate.net/figure/System-capacity-per-fiber-in-optical-communication-systems_fig2_309307654

19

https://fiberopticnetwork.wordpress.com/tag/fibre-optic-bandwidth/

Fiber

Size (m) Wavelength 850 nm 1300 nm 1550 nm

9/125 SM 2000 20,000 + 4000 – 20,000 +

50/125 MM 200 - 500 400 - 1500 300 - 1500

62.5/125 MM 100 - 400 200 - 1000 150 - 500

Bandwidth Distance Product (MHz km)

Bandwidth x Distance Product (MHz x km)Fiber

Some commonly cited numbers

20From: Figure 3.9 (page 108) in Senior.

Pulse Broadening From Intermodal Dispersion

20 MHz-km

1 GHz-km

100 GHz-km

Pulse Spreading & Attenuation Caused by Dispersion

https://www.researchgate.net/figure/Pulse-Spread-and-Attenuation-due-to-Dispersion_fig1_277014078

21

1 0 1

22

https://www.intechopen.com/books/current-developments-in-optical-fiber-technology/multimode-graded-index-optical-fibers-for-next-generation-broadband-access

Dispersion Mechanisms in Optical Fibers

MMF = Multi-Mode Fiber; SMF = Single Mode Fiber

23

Dispersion Mechanisms in Optical Fibers – I

Modal Dispersion is a distortion mechanism occurring in multimode fibers, where

signals spread in time because the propagation velocity of the signal is not the same

for all modes.

Modal Dispersion (also called Intermodal Dispersion)

Chromatic Dispersion is the result of the different colors, or wavelengths, in a light

beam arriving at their destination at slightly different times. Thus, the refractive index

is a function of wavelength.

Chromatic Dispersion

Waveguide Dispersion is a result of the different refractive indexes of the core and

cladding of an optical fiber. Some of the signal travels in the cladding, as well as the

core. Hence, the structure of the optical fiber enters into the dispersion.

Waveguide Dispersion

24

Dispersion Mechanisms in Optical Fibers – II

Polarization Mode Dispersion

Polarization Mode Dispersion (PMD) is a form of modal dispersion where two

different polarizations of light, which normally travel at the same speed, now travel

at different speeds due to their different polarizations.

Material Dispersion

Material Dispersion is one kind of Chromatic Dispersion. It is the variation of the

propagation velocity through a transparent material with wavelength. It is called

“material” dispersion to distinguish it from a similar effect called “waveguide”

dispersion, which is a consequence of the process by which light is guided in a

dielectric fiber.

25

Group Delay

❑ Group delay is the time required for a mode to travel down a fiber of length L.

❑ Total delay is the group delay per unit length along the fiber.❑ The collection of all frequencies constitutes the signal’s

waveform and the energy of the signal.❑ Each spectral component travel independently of the others.❑ Group velocity is the speed of the waveform (group of

frequencies) as it travels along the fiber.

21 1

2

distance traveled by the signal

2propagation constant;

gr

gr

d d

L v c dk c d

L

k

= = = −

=

= =

Ref. Section 2.3.3,pp. 28 to 30 in

Senior

26

Group Velocity

A packet of waves moves at the group velocity given by

where

The group velocity is the velocity of the energy transport of theoptical signal propagating on the fiber.

The phase velocity of a single frequency is

1 1

g gr

dv v c

dk

− −

= = = =

p phv v

= =

1 1

2n n

c

= =

Ref. Section 2.3.3,pp. 28 to 30 in

Senior

27

Group Velocity

1

1

1

1 1

2

11

2

1

2

gr

gr

d d dv n

d d d

dn n

d

c c

dn Nn

d

−

−

− = =

− = −

= =

−

where Ngr is known as the group index of the fiber.

Ref. Section 2.3.3,pp. 28 to 30 in

Senior

28

https://apps.lumerical.com/pic_circuits_optical_fiber.html

Modal Dispersion

Modes in fiber

Each mode has uniquevelocity of propagation

29

Modal Dispersion

The minimum time Tmin for a signal to travel distance L within the fiber is

The maximum time Tmax for a signal to travel distance L within the fiber is

Using Snell’s Law we can write

1min

1

distance

velocity ( / )

LnLT

c n c= = =

1max

distance

velocity cos( )

LnT

c = =

Ref. Section 3.10.1,pp. 114 to 119 in

Senior

1

2

max

2

LnT

c n=

30

Modal Dispersion (continued)

The delay difference between meridional ray and the axial ray by subtraction,

where delta is

And

What we want to know is the rms pulse broadening MD

1 1 11 1 2max min

2 2 2 2

2 2 2Ln Ln LnLn n nT T T

c n c c n n c n

−= − = − = =

1 2

1

n n

n

− =

2

1 1 2 1

2 1

( )or

2

Ln n n Ln L NAT T

c n c n c

−= = =

( )2

1

12 3 4 3MD s

L NALn

c n c

= = =

~

~

~

31

Example 3.8 (Modal Dispersion)Pages 117-118

Example 3.8. A six-kilometer (6 km) optical link with multi-mode step-index fiber withcore index of refraction = 1.500 and relative refractive index difference of 1% -- Find (a) The delay difference between the lowest and fastest modes of the fiber link.

Solution: The delay difference is given by

(b) Find the rms pulse broadening from modal dispersion over the fiber link of 6 km.

Solution:

(c) Next, find the maximum bit rate without errors on the fiber link.

3

1

8

(6 10 m) 1.500 0.01300 ns

3 10 m/sec

LnT

c

= = =

3

1

8

1 (6 10 m) 1.500 0.01 300ns 86.6 ns

3 10 m/sec 3.46412 3 2 3MD

Ln

c

= = = =

32

Example 3.8 (continued)Pages 117-118

Example 3.8. (c) Next, find the maximum bit rate without errors on the fiber link. (assume only

modal dispersion)

Solution: The maximum bit rate can be estimated in two ways. First, we may use the relationship between BT and the reciprocal of the delay , namely,

Or we can estimate it from the calculated rms pulse broadening from part (b).

(d) Find the bandwidth-length product corresponding to (c) above. Assume return-to-zero pulses.

9maximum

1 1 1( ) 1.67 Mbps

2 2 2 300 10 secTB

T −= = = =

9maximum

0.2 0.2( ) 2.31Mbps

86.6 10 secT

MD

B −

= = =

Bestestimate

2.31MHz 6 km 13.86 MHz kmoptB L = =

~

33