Chapter 5 Modulation of Light

7/25/2019 Chapter 5 Modulation of Light

1/27

5 Modulation of Light

Modulation is needed in communication systems

Intensity, Phase and Frequency modulation

Internal and External modulation

Electro-optic, Magneto-optic and Acousto-opticmodulation

5.0 General comments


2/27

5.1 Electro-optic Modulation

Fig. 5.1: A steady electric field applied to an electro-optic material

changes its refractive index. This, in turn, changes the effect of

the material on light traveling through it. The electric field

therefore controls the light.


3/27

The refractive index changes in proportion to the applied

electr ic f ield, in which case the effect is known as thelinear electro-optic effect or the Pockels effect.

The refractive index changes in proportion to the square

of the applied electr ic f ield, in which case the effect is

known as the quadratic electro-optic effect or the Kerreffect.

The dependence of the refractive index on the applied

electr ic f ield takes one of two forms:


4/27

A. Pockels and Kerr Effects

n(E) can be expanded in a Taylors series aboutE = 0,

( ) ...,2

1 221 +++= EaEanEn (5-1)

r = 2a1 / n3 and= a2/n3 are known as the electro-opticcoefficients,

( ) ...,2

1

2

1 233 ++= EnErnnEn (5-2)


5/27

Pockels Effects

For 0, ( ) ErnnEn 32

1 (5-3)

r :Pockels coefficient or the linear electro-optic coefficient

Typical values ofr :

Range 10-12 to 10-10 m/V, very small

Common crystals used as Pockels cells:

NH4H2PO4 (ADP), KH2PO4 (KDP), LiNbO3, LiTaO3, and CdTe.

Kerr Ef fect

For r0, ( ) 232

1EnnEn (5-4)

:

Kerr coefficient or the quadratic electro-optic coefficient

Typical Values of

:

10-18 to 10-14 m2/V2 in crystals and 10-22 to 10-19 m2/V2 in liquids

Kerr cell (or medium):centrosymmetric, materials such as gases, liquids, and certain

crystals


6/27

B. Electro-Optic Modulators

Phased Modulators

When a beam of light traverse a Pockels cell of lengthL to which an electric fieldEis applied, it undergoes a phase shift = n(E)k0L = 2n(E)L/0, where 0 is thefree-space wavelength.

0

3

0

ELrn

= (5-5)

where 0=2nL/0. If the electric field is obtained by applying a voltage Vacrosstwo faces of the cell separated by distance d (Fig. 5.3b), then E=V/d, and (5-5)

gives

,0

V

V=

Phased Modulation

(5-6)

where3

0

xnL

dV

=

Half-Wave Voltage

(5-7)


7/27

Transverse and Longitudinal modulators

is proportional to

Modulation bandwidth limited by transit time is

L

d

T

1

Fig. 5.3: (a) Longitudinal modulator. The electrodes may take the shape of

washers or bands, or may be transparent conductors. (b)

Transverse modulator. (c) Traveling-wave transverse modulator.


8/27

I ntegrated optic phase modulator

Smaller half-wave voltage (~ 102)

Higher speed ( > 100 GHz demonstrated)

Fig. 5.4: An integrated-optical phase modulator using the electro-optic effect.


9/27

Dynamic Wave Retarders

For anisotropic medium that exhibits the Pockels effect.

( ) ,2

1 31111 EnrnEn

(5-8a)

( ) ,

2

1 32222 EnrnEn (5-8b)

where r1 and r2 are respectively the Pockels coefficients for two polarization states.

Phase retardation after traveling a distance L,

( ) ( )[ ] ( ) ( )ELnrnrkLnnkLEnEnk 32231102102102

1== (5-9)

( ) ( ) LdV

nrnrkLnnk

3

22

3

110210 2

1

=

V

V= 0

3

22

3

11

0

nrnrL

dV

= with

(5-10)

(5-11)

Retardation


10/27

I ntensity Modulators: Use of a Phase Modulator in an I nterferometer

Fig. 5.5: A phase modulator placed in one branch pf a Mach-Zehnder interferometer can serve

as an intensity modulator. The transmittance of the interferometer T(V) =I0/Ii varies

periodically with the applied voltage V. By operating in a limited region near pointB,the device acts as a linear intensity modulator. If Vis switched betweenA and C, the

device serves as an optical switch.

( ) 2coscos1

2

1 20

ii

III =+= (5-12)

V

V== 021

( )

==

V

V

I

IVT

i 22cos 020


11/27

The I ntensity shown in F ig. 5.5 can be used as a switch, how?

A Integrated optic Intensity Modulator

Fig. 5.6: An integrated-optical intensity modular (or optical switch). A Mach-

Zehnder interferometer and an electro-optic phase modulator are

implemented using optical waveguides fabricated from a material such asLiNbO3.

Modulation speeds exceeding 25 GHz have been achieved


12/27

I ntensity Modulators: Use of a Retarder Between Crossed Polarizers

Fig. 5.7:(a) An optical intensity modulator using a Pockels cell placed between crossed

polarizers at 45 degree with respect to the retarders axes.

(b) Optical transmittance versus applied voltage for and arbitrary value 0 forlinear operation the cell is biased near the pointB.


13/27

( )

=

V

VVT

22sin 02 (5-14)

as shown in Fig. 5.7(b). By changing V, the transmittance can be varied

between 0 (shutter closed) and 1 (shutter open). The device can also be

used as a linear modulator if the system is operated in the region near T(V)

= 0.5. By selecting 0 = / 2 and V


14/27

5.2 Magneto-optic ModulationFaraday Effect

=VB (5-16)

Vis known as the Verdet constant.

Fig. 5.8: Polarization rotation in a medium exhibiting the Faraday effect. The sense rotation is invariantto the direction of travel of the wave

The sense of rotation is governed by the direction of the magnetic field: only and does not

reverse with the reversal of the direction of propagation of the wave (Fig. 5.8). The

Verdet constant is a function of the wavelength 0.

Materials that exhibit the Faraday effect include glasses, yttrium-iron-garnet (YIG),

terbium-gallium-garnet (TGG), and terbium-aluminum garnet (TbAIG).

A polarization rotator rotates the plane of polarization of linearly polarized light by afixed angle, maintaining its linearly polarized nature. Materials exhibiting the Faraday

effect acts as polarization rotators.


15/27

Optical I solators

Fig. 5.9: An optical isolator using a Faraday rotator transmits light in one direction, as in (a), and

blocks light in the opposite direction, as in (b).

Faraday-rotator isolators made of yttrium-iron-garnet (YIG) or terbium-

gallium-garnet (TGG), for example, can offer an attenuation of the backwardwave up to 90 dB, over a relatively wide wavelength range.

5 3 A t ti M d l ti


16/27

5.3 Acousto-optic Modulation

Acousto-optic effect

The refractive index of an optical medium is altered by the presence of sound.Sound therefore modifies the effect of the medium on light; i.e., sound can

control light (Fig. 5.10)

Fig. 5.10: Sound modifies the effect of an optical medium on light


17/27

Fig. 5.11: Variation of the refractive index accompanying a harmonic sound wave. The pattern

has a period , the wavelength of sound, and travels with the velocity of sound.

The variations of the refractive index in a medium perturbed by sound areusually very slow in comparison with an optical period.

The material can be regarded as quasi-stationary, and acousto-optics becomes

the optics of an inhomogeneous medium (usually periodic) that is controlled bysound.

Basics of l ight-sound interaction


18/27

Basics of l ight sound interaction

Fig. 7.12: Bragg diffraction: an acoustic plane wave acts as a partial reflector of light (a beamsplitter)

when the angle of incidence satisfies the Bragg condition.

=

2sin

B

(5-17)

where is the wavelength of light in the medium.

Bragg Condition

Reflectance

sIL

nR

4

0

22222

= (5-19)

The reflectance is therefore proportional to the intensity of the acoustic wave Is,

to the parameter that depends on the acoustic property of the material. Thereflectance is inversely proportional to 4 (or directly proportional to 4).L is theinteraction length and n is the refractive index of the material.


19/27

Example: Bragg Angle

An acousto-optic cell is made of flint glass in which the sound

velocity is s = 3 km/s and the refractive index is n = 1.95. The

Bragg angle for reflection of an optical wave of free-spacewavelength 0 = 633 nm ( = 0 /n = 325 nm) from a soundwave of frequencyf= 100 MHz ( = s /f= 30m) is B = 5.4

mrad = 0.31 degree. This angle is internal (i.e., inside themedium). If the cell is placed in air, B corresponds to anexternal angle B = nB = 0.61 degree. A sound wave of 10

times greater frequency (f = 1GHz) corresponds to a Braggangle B = 3.1 degree.

Acouto Optic Devices


20/27

Acouto-Optic Devices

Modulators

The intensity of the reflected light in a Bragg cell is proportional to the intensity of

sound and can be used as a linear analog modulator of light (5.13(a)).

As the acoustic power increases, however, saturation occurs and almost total reflectioncan be achieved. The modulator then serves as an optical switch (Fig. 5.14 (b)).

Fig. 5.14: (a) An acousto-optic modulator. The intensity of the reflected light is

proportional to the intensity of sound. (b) An acousto-optic switch.

Modulation Bandwidth


21/27

Modulation Bandwidth

ffss

22sin

2sin 11 ==

(5-20)

Fig. 5.15: The waveform of an amplitude-modulated acoustic signal and its spectrum.


22/27

( )B

B

s

s

=

/2

/2(5-21)

(5-22)

As the bandwidth of the modulator is thereforeD

=

DB s

s

==

Fig. 5.17: Interaction of an optical beam of angular divergence with an acoustic plane waveof frequency in the bandf0 B. There are many parallel q vectors of different lengths

each matching a direction of the incident light.


23/27

5 Problems

Response Time of a Phase Modu lator

A GaAs crystal with refractive index n = 3.6 and electro-optic coefficient

r = 1.6 pm/V is used as an electro-optic phase modulator operating at 0 =1.3 m in the longitudinal configuration. The crystal is 3 cm long and hasa 1 cm2 cross-sectional area. Determine the half-eave voltage V, the

transit time of light through the crystal, and the electric capacitance of the

device (the dielectric constant of GaAs is / 0 =13.5). The voltage isapplied using a source with 50 resistance. Which factor limits the speedof the device, the transit time of the light through the crystal or the

response time of the electric circuit?


24/27

5 Problems

Sens i t iv i ty o f an Inter ferometr ic Electro-Opt ic Intensi ty Modulator

An integrated-optic intensity modulator using the Mach-Zehnder configuration,illustrated in Fig. 5.6, is used as a linear analog modulator. If the half-wave

voltage is V = 10 V, what is the sensitivity of the device (the incremental

change of the intensity transmittance per unit incremental change of theapplied voltage)?


25/27

5 Problems

An Elasto -Optic Strain Senso r

An elasto-optic material exhibits a change of the refractive index proportional to

the strain. Design a strain sensor based on this effect. Consider an integrated-optic implementation. If the material is also electro-optic, consider a design

based on compensating the elasto-optic and the electro-optic refractive index

change, and measuring the electric field that nulls the reading of the

photodetector in a Mach-Zehnder interferometer.


26/27

5 Problems

Magneto-Opt ic Modulator

Describes how a Faraday rotator may be used as an optical intensity modulator.

5 Problems


27/27

Parameters o f Acousto-Opt ic Modu lators

Determine the Bragg angle and the maxi-mum bandwidth of the following

acousto-optic modulators:

Modulator 1

He-Ne laser, wavelength 0 = 633 nm, angulardivergence = 1 mradLight:

Frequencyf= 50MHzSound:

Fused quartz (n = 1.46, s = 6 km/s)Material:

Modulator 2

CO2 laser, wavelength 0 = 10.6 m, and beamwidthD = 1 mm

Light:

Frequencyf= 100MHzSound:

Tellurium (n = 4.8, s = 2.2 km/s)Material:

Date post:	26-Feb-2018
Category:	Documents
Upload:	rio354
View:	215 times
Download:	0 times

Chapter 5 Modulation of Light

Documents