ENE 423

Lecture IV

Integrated Optic Components

We may distinguish the integrated optic devices into two kinds in passive and

active components.

Passive devices: directional couplers, beam splitters, isolators, lenses, and

prisms. An example of passive integrated optic directional coupler is shown in the

figure below. Ideally, relative output powers are given by

Where Lc is called the coupling length. It is the length which there is complete

transfer from the upper to the lower waveguide.

Directional coupler

Beam splitter

Active devices: modulators, switches, light sources, and light detectors.

An integrated-optic modulator called Mach-Zehnder interferometer consists of

parallel Ti:LiNbO3 indiffused waveguide. An external modulator like this is very

2a2b

cladding, n2

cladding, n2

core, n1

important for high speed network. Modulation could be externally produced at higher

frequencies than that of direct modulation. Also, direct modulation of a light source

might cause a change in output wavelength and spectral width while external

modulation does not.

Mach-Zehnder Interferometer

Optical Fiber Waveguides

If we consider index profile in fibers, we may categorize them into 2 types:

step-index fiber and graded-index fiber.

Step-Index Fiber (SI fiber)

The critical angle of SI fiber is the same as in slab waveguide that is

2

Graded-Index Fiber (GRIN fiber)

where = parameter describing the refractive index profile variation

n(r)

= n1

= 1

= 2

r a

n(r)

= n1

= 1

= 2

r a

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Butted coupling from the light source to a GRIN fiber is more efficient near

the axis than further out. Unlike the SI fiber for which NA remains the same

regardless the entry point. Therefore, coupling efficiency is generally higher for SI

fibers than for GRIN fibers.

Advantages of GRIN fiber is that several modes can be lumped together and

cause the effective number of modes to decrease. NA of GRIN fiber may be written as

As seen above, NA of GRIN decreases from to zero as r moves from

the fiber axis to the core-cladding boundary.

Attenuation

The length of fiber is limited by dispersion and attenuation. Attenuation or

loss in fiber may be classified as absorption, scattering, geometric effects, connectors,

or splicing.

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Bending loss

When fiber is bent, fields break away and radiate into cladding. This bending

loss can be reduced by increasing radius of curvature R.

Attenuation can be measured by a cut-back method and OTDR (optical time

domain reflectometer).

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Ex. Consider a fiber whose core index is 1.5 and whose cladding index is 1.485. The

core radius is 100 micron. At what bending radius does a ray traveling along the fiber

axis strike the cladding at the critical angle in the bend?

Soln

Cut back method

OTDR

This method requires only one end of the fiber to be measured. This OTDR

transmits an optical pulse down the fiber and measures the reflections. Reflections

occur owing to discontinuities due to splices, connectors, and fiber breaks and to

scattering. The Rayleigh scattering gives a continuous return signal. The time delay of

reflections is a measure of their location along the fiber.

Pin P02

P01

l

1 2

Pin P02

P01

l

1 2

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Ex. A 50 km fiber link between transmitter and receiver consists of 3 km segments

that are spliced together. Losses are fiber attenuation at 0.5 dB/km, 0.3 dB/splice loss,

1 dB/connector. Calculate

(a) Total loss in the link

(b) Calculate output power when Pin = 1 mW

Sol n

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Ex. A fiber has n1 = 1.5 and n2 = 1.49 and core diameter 50 micron. Consider the

guided ray traveling at the steepest angle with respect to the fiber axis. How many

reflections are there per meter for this ray?

Soln

Modes in SI fibers

The geometry of fiber causes modes like the case of slab waveguide. The fiber

mode chart is normalized by plotting neff vs. normalized frequency V (famously

known as V-number).

where a = core radius

Conventional fibers do not preserve the polarization of the wave due to some

external forces to the fibers (such as bending, twisting, or splicing). The polarization

of light in fiber is random. To preserve polarization, impurities are added to the core

and core geometry is adjusted. This can produce “polarization maintaining”(PM)

fiber. Another special fiber called “polarizing”(PZ) fiber is done by designing the

asymmetry in the fiber such that the undesired polarization state has a higher

attenuation than that of the desired state.

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Some light propagation in the fiber is similar to that in the slab. We have

and . At a fixed value of V, several modes may propagate, each

having a different neff. This V-number can determine the number of modes (N) for

V>10 by

For single mode fibers, it needs all modes expect HE11 to be cut off. This

occurs at V 2.405 and this yields

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Because of 2-D con confinements, modes in fibers are designated by 2

subscripts, e.g. TE01 or TM01. There are still some modes called “hybrid” that are HE

and EH. The hybrid mode is the mode that contains components of both electric and

magnetic field.

Modes in GRIN fiber

Generally, the expression for neff is presented instead of producing a mode

chart in case of GRIN fibers. The effective refractive index of GRIN is expressed as

where p, q are numbers to describe a mode. The lowest mode can be

obtained with p = q = 0.

Again, the allowed modes of light propagation have the range of neff as

In this case, cutoff occurs at neff = n2. If we want only single mode to guide in

GRIN fiber, we substitute p = 1, q = 0 along with neff = n2 into the equation

, it yields

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If we use V-number and it is large, the number of modes in GRIN fiber can be

approximated by . Some predict the number of modes using -profile as

Ex. Consider an SI fiber with n1 = 1.5 and n2 = 1.485 at 0.82 μm. If the core radius is

50 μm, how many modes can propagate?

Soln

Distortion in fibers

Fiber links are limited in path length by attenuation and pulse distortion.

Distortion in signal due to fiber includes

1. Material dispersion

2. Waveguide dispersion

3. Multimode dispersion

Waveguide dispersion in a silica fiber

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Total dispersion for various kinds of fibers

Distortion in SI fibers

Total pulse spreading could be expressed as

where m, g, and mm are the same expression as in slab

waveguide.

If n1 n2

m and g are much less than mm in SI fiber. Especially, g can be

neglected for the short wavelength such as < 1.2 μm.

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Distortion in GRIN fibers

GRIN fiber have effective number of modes less than in SI fiber since rays

travel in shorter routes and faster. This minimizes multimode pulse spreading. The

multimode distortion can be expressed as

By using the same expression of m and g as in slab waveguide for the

GRIN fiber, the total pulse spreading can be written as

Length dependence of the pulse spread in multimode fibers

Pulse spreading increases linearly with fiber length for short distance of the

link. For longer link, pulse broadening is proportional to the square root of the length.

This is caused by the mode mixing in multimode fiber. In short path, this

mixing is still incomplete. After traveling further, an equilibrium modal power

distribution is reached. The length in which equilibrium is reached called “equilibrium

length (le)” or some call it “critical length (lc). Therefore, we can write the multimode

distortion as

where (/l) is the spread per unit length in linear region.

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Ex. The equilibrium length of a multimode fiber is 2 km. The modal spread is 25

ns/km. The light source emits at 800 nm and has a spectral width of 50 nm. Compute

the optical 3-dB bandwidth of a 5-km length of this fiber.

Soln

Ex. Calculate the multimode dispersion for the fiber with n1 = 1.48 and n2 = 1.46 if

(a) the fiber is a SI fiber.

(b) the fiber is a GRIN fiber.

Soln

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