Middleton W.M. (ed.) Reference Data for Engineers: Radio, Electronics, Computer and Communications

41-10

REFERENCE

DATA

FOR

ENGINEERS

(A)

Coaxla1

flash

lomp pumped dyes (Condelo Corp.)

WAVELENGTH IN NANOMETERS

(Bj

Nd:

YAG

pumped dyes

(Quonto-Ray)

so

that the normal index of refraction is given by

n2

=

If the symmetry property of the material is such that

a

reversal of the sign of all coordinates causes no change

in the spatial arrangement of the atoms, the material is

said to be centrosymmetric. Applying the reversal to

P

and

E,

one sees that the

x(~)

coefficient must be zero in

centrosymmetric systems but that

x(I)

and

x(3)

are not.

Accordingly, the lowest order or quadratic nonlinearity

is seen in noncentrosymmetric systems which comprise

21

of the

32

known crystal classes.

1

+

x(1'.

Fig.

10.

Typical

tuning

curves

for

various

dyes

when

In general,

x(')

has nine components. If one chooses

a natural coordinate system that reflects the symmetry

axis

of

the material,

x(')

becomes diagonal with three

components only. This is referred to as the principal

axis frame. In the princi a1

axis

frame

x(~)

has at most

components are separately distinguishable,

so

it is

possible to reduce the independent number down

to

18

for

x(~).

This

is

done by noting that the ith component

of the quadratic

part

of

the polarization is

4

=

2 2

27

components while

,y(

P

)

has

34

components.

Not

all

ki

LASERS

41-11

WAVELENGTH IN NANOMETERS

(C)

Nz

pumped

dyer

(Molectron)

WAVELENGTH IN NANOMETERS

(D)

Art

and

Kr*

CW

pumped dyes

(Spectra-Physics)

excited

by

the

indicated

sources.

(Courtesy

Exciton

Corp.)

q,x$2)

E,E,

,

so

a new parameter is accordingly defined

as

di,

=

~~xif)~)

where

q

is a contracted index for the

jk

combination in parentheses (the Voight notation). Prin-

cipal axes along

x,

y,

and

z

are labeled

1,

2,

and

3

so

that

q

ranges from 1 to

6

according to the

jk

combina-

tions 11, 22,

33,

23, or 32;

13

or 31; and 12 or 21,

respectively.

So,

for example,

x$iz)

=

x\&)

contributes

to

did.

With this,

d

is a

3

X

6

matrix with at most

18

elements.

The symmetry

of

the individual system is then used

to deduce which elements are nonzero. Since

x(')

is the

same order tensor as that used to describe the piezoelec-

tric effect, the nonzero elements are well known and are

compiled in Chapter

4.

Similarly, the individual values

ford,, for various materials and optical frequencies are

tabulated elsewhere. The same kind of symmetry-based

reductions can be applied

to

x'~'

for crystals, but none

are used

for

amorphous materials.

A

specific example is for the crystal class

52m,

which

is appropriate to the common nonlinear material po-

tassium dihydrogen phosphate

(KDP).

For

this class,

xi(')

=

xii)

#

x3('),

and

41-12

REFERENCE

DATA

FOR ENGINEERS

TABLE

2.

PULSED

LASERS-HIGH

POWER

A*

157

193

222

249

282

308

35

1

266

337

347

355

502

532

510.6

578.2

694.3

850.0

1.06

pm

1.06

2.64-3.01

pm

5-6

pm

9'4

10.6

pm

1

12-13

pm

385

pm

496.1

Atom

or

Molecule

s

4rF

KICl

KrF

XeBr

XeCl

XeF

Nd: YAG,

Glass

N2

Cr:AI203

Nd:YAG

HgBr

Nd

:

YAG,

Glass

cu

Cr:A1,03

GaAs

Nd:YAG

Nd:Glass

HF

co

CO2

NH3

D20

CH,F

Materials

*Nanometers unless noted otherwise.

-

Pulse

Width

(ns)

6

14

9

16

8

6

14

4

6

25

5

50

I

30

20

100

15

20

500

1000

100

-

Energy

(mJ)

10

200

30

250

17

150

400

50

16

100

200

2.5

1-10

J

0.01

0.1-1

J

1-20

J

300

85

IOz

J

0.1

J

0.1

J

10

50

3.02-20

100

0.1

0.1-20

5-100

20

6

kHz

0.02

1

kHz

10

0.03

2

5

0.1-102

1-10

Comments

RGH

excimers: mixtures

of

rare gas

and halide donors;

105-106

laser

pulses per gas

fill.

Can also be

used with

N2,

HF, C02 in a typical

laser system.

mrth harmonic

of

1.06

pn

Nd

econd harmonic

of

694.3

nm (ruby)

hird harmonic

of

1.06

pm

Nd

[igh temperature

(>

150'C)

req.

econd harmonic

of

1.06

pm

Nd

Iigh temperature, high average power

?

Switched

iemiconductor diode array

Ither transitions are possible.

:hemica1 lasers, discrete line

,pectra associated with VR bands

liscrete

-

50

line spectra

issociated with VR structure

Discrete

-

50

line spectra

issociated with VR structure

Dptically pumped with C02

Optically pumped with COz

SECOND-HARMONIC

0%

49)

GENERATION

0000

0

d36

With the presence

of

an

intense optical field, the

quadratic nonlinearity leads

to

a polarization at twice

with

d14

=

d25.

41-13

TABLE

3.

COMMON CW

LASERS

~

A

(nm)

325.0

441.6

290-305

351.1, 363.8

454.5

457.9

476.5

488

O*

496.5

501.7

514.5*

528.7

405-805

413.1

468.0

476.2

482.5

520.8

530.9%

568.2'

647.1*

676.4'

752.5

799.0*

632.8

670-

1

I30

1152.3

3391.3

750-900

864-904

1.06

pm

1.1-1.3

pm

2.3-3.3

pm

2.6-3

pm

3.6-4.1

pm

Atom

or

Molecule

Cdt

Dye

Arf+

Ar'

Kr+

Ne

Ti3+(AI203)

Ne

A1,Gal-,As

GaAs

Nd3' (YAG)

In,-,Ga,P,-,

F-center

HF

DF

Materials

Power

8

mW

40

mW

50

mW

2.5

W

1.1

w

1.35

W

2.7

W

6.5

W

2.5

W

1.5 W

7.5

w

1.0

w

0.05-2.0

W

0.5

W

0.3

W

0.40

W

0.40

W

0.7

W

1.5 W

1.1

w

3.5

w

0.9

W

1.2

w

0.3

W

1-50

mW

100

mW

10

mW

10

mW

10

mW

1-1000

mW

1-10

w

0.1-10

mW

1-10 mW

1-50

W

Comments

Small compact

SHG

of

R6G

dye

1.

Many other lines

possible

2. Very intense discharge

3.

Dominant lines

denoted by

*

4.

Water cooling usually

required

Optically pumped by

Ar'

or

K+

lasers (See Fig.

10

for

more

detail.)

1.

Many other lines

possible

2.

Very intense

discharge

3.

Dominant lines

denoted by

*

4.

Water cooling required

Common "red" laser

Optically pumped by Art

First gas laser

Frequency standard

Typical drive current

=

150

mA

A

is temperature dependent.

Optically pumped (flash lamp)

Color center

Chemical laser, gas flow

required

Continued on next page.

41-14

Atom

or

Molecule

co

COZ

co2

H20

CH,OH

HCN

CH,F

REFERENCE

DATA

FOR ENGINEERS

Materials

g

h

(nm)

5-6.5

pm

9.2-11.2

pm

10.6

pm

28, 78, 118

pm

118.1

pm

311, 377

pm

496.1

un

1.4

-

12

-

g

1.0

-

?

3

’

0.8

-

2

0.6

-

+

2

0.4

-

0

0.2

-

TABLE

3

(CONT).

COMMON

CW

LASERS

Power

10-20

w

4w

50 W-8.5

kW

10 mW

100

mW

100

mW

25

mW

Comments

Line

selectable

Line selectable, sealed

Flowing gas

Electrically excited

Optically pumped

(See

Fig.

12.)

Electrically excited

Optically pumped with COz

650

700 800

900

1000

1100

1200

WAVELENGTH IN NANOMETERS

Fig. 11. Output power versus wavelength for

a

titatium-doped sapphire laser pumped with an argon laser. The curves refer to

different mirror sets with a 5-watt pump laser, except for the far right curve which

is

for a 7.5-watt pump.

(SchwurrzElectro-Optics,

Inc.)

i=

WAVE

NUMBER

(l/cm)

Fig.

12.

Optically pumped far-infrared laser lines.

the optical frequency, which may act as a driving term

for a new field component at

2w.

Since the growth tends

to occur

on

spatial scales long compared with the

wavelengths, the

full

set

of

Maxwell’s

equations

can

be

reduced to a first-order equation for the evolution

of

the

field amplitude. The growth of the harmonic is gov-

erned

by

d(E,,)/dz

=

A

E;

exp

(iAkz)

(Eq.

50)

where,

Ak

=

k(2w)

-

2k(w)

=

2k0[n(20)

-

n(w)],

k,(o)

=

wtc,

A

=

a constant proportional to the

d,

elements,

the exact

form

of

which depends on the field

orientations and the

d

matrix.

LASERS

I

d

41-15

I

(A)

Bands at zero bras.

(5) Bands wlth forward

blas

(C)

Representatiw field configuratlon

of

(i

mode

In

the

laser.

Fig.

13.

Semiconductor injection laser.

(From

J.

T.

Verdeyen,

Laser Electronics,

Englewood

Clifs,

N.J.:

Prentice-Hull,

Inc.,

1981;

Fig.

10-19.)

METAL CONTACT

(A)

Dlagram

1

METAL CONTACT

n-(GaAI)As

I

n-GaAs

I

p-GaAs

1

p-(GaAI)As

I

(0

Dlstrlbutlon perpendlcular to lunctlon

of

refractlue Index

LIGHT

I

-I

I

INTENSITY

(0)

Dlstrlbutlon perpendlcular to junctlon

of

lfght lntenslty.

Fig.

14.

Four-layer separate confinement heterostructure.

(From

G.

H.

E.

Thompson,

Physics

of

Semiconductor Laser Devices.

New

York:

John

Wiley

&

Sons,

Inc.,

1980;

Figs.

3.16

and

3.17.)

41-16

REFERENCE

DATA

FOR

ENGINEERS

300

K

<

100

K

IIIII

f

I

I I I I,,, I I

,

,I,

,

PbSe

SALTSPbSe

1.0

10

WAVELENGTH

IN

NANOMEl€RS

Fig.

15.

Common

CW

compound semiconductor lasers grouped according to the active-layer material

and

substrate material. The

wavelength range refers

to

different chemical compositions.

If

E,

is approximately constant,

E2w

is seen to be

harmonic in

z

if

Ak

#

0.

If

Ak

=

0,

then

E2@

=

z,

and

the growth increases with distance. This latter case is

clearly favorable and requires

Ak

=

0;

it

is

referred to as

a phase-matched condition.

Since

most

materials are normally dispersive,

420)

>

n(o),

the phase-matched condition is not automatic.

It can be achieved by using the anisotropic properties of

the index of refraction.

An

important linear optical

class of materials used as harmonic generators is

uniaxial, for which

nl

=

n2

#

n3.

Other classes are

isotropic,

nl

=

n2

=

n3,

and biaxial,

nl

<

n2

<

n3.

For

the uniaxial class,

n,

=

n2

=

no,

the

ordinary

index of

refraction, and

n3

=

ne,

the

extraordinary

index of

refraction. If

ne

>

(<)no,

the material is said to be

positive (negative) uniaxial.

A

wave polarized in the

x-y

or

1-2

plane (ordinary

ray) has an index of refraction equal to

no.

A wave

polarized with a field component along the

z

or

3

axis

(optic axis)

is

an extraordinary ray and has an effective

index of refraction,

neff,

given by

lln,;

=

cos2

Oh:

+

sin2

Oh$

(Eq.

51)

where

0

is the angle between the optic axis and the

direction of propagation. A common representation of

these is a polar plot of

n(O),

which is referred to as an

index surface. Fig. 16A shows the index surface for a

negative uniaxial crystal.

Phase matching may be achieved if the index-surface

curves at

o

and

20

cross as shown in Fig. 16B. For

n,(2o)

<

n,(w),

there is an angle

e,,,

for which

neff(20)

=

no(@).

Since the angular width of the phase matching

(AkL

=

?r)

is comparable

to

the divergence angle of a

laser, the phase matching

of

this type

is

referred to as

critical phase matching.

In

some cases, the temperature

dependence

of

no

and

n,

is sufficiently different that

phase matching can be achieved at elevated tempera-

tures.

Under fully phase-matched conditions, the harmonic

intensity is given by

which shows the full conversion capability of the

process, which has an initial growth of

LASERS

41-17

z

AXIS

(A)

Negotlue

unioxlai

crystal.

3

i=l

j=

1

(B)

Phase

rnntchlng.

Fig.

16.

Wave vectors in

a

uniaxial crystal.

The term

AEJO)

represents an inverse conversion

distance,

l,,,,.,

such that at

z

=

lc0,,~

58%

of the

fundamental has been converted to a harmonic. For

practically all materials with large

d

values,

Z,,,,

on the

order

of

centimeters requires initial pumping intensities

of 10-100 MW/cm2. Although the

di,

values tend to be

larger at lower frequencies, the equivalent

A

terms tend

to be numerically about the same. Hence, harmonic

generation by this method tends to be efficient,

50-

80%,

but requires large powers. Representative nonline-

ar materials and coefficients are listed in Table

4.

Pockels

Effect

A

second effect associated with

is the Pockels, or

linear electro-optic, effect used to amplitude modulate

light. Here, the nonlinear polarization is at the

o

tical

nonoptical field. The effect, which has the same basic

d

matrix as for the case of second-harmonic generation,

leads only

to

a shift in the index of refraction caused by

Eo.

The effect is described by a three-dimensional

version of the index surface called the index ellipsoid,

which relates

nefi

to

the displacement vector rather than

to the direction of propagation. With no applied field,

the index ellipsoid is

of

the general form

frequency and is proportional to

E,,,Eo,

where E

!.

IS

a

where

Di

are the normalized displacement vectors along

the principal axis. The effective index of refraction

is

simply the length

of

this vector.

The effect of

Eo

is to distort the index ellipsoid. The

distortion

is

expressed in terms

of

a new matrix,

r,

which structurally is the transpose of the

d

matrix. The

generalized index ellipsoid is then

where

bB(ij,k

=

r(v)kF!,

and the indices in parentheses

are contracted according to-the Voight notation. Contin-

uing with the example

of

42m

crystals,

and

r41

=

r5*.

The resulting index elipsoid is

TABLE

4.

NONLINEAR OPTICAL

COEFFICIENTS

Material Class

h

(pm)

rqk

(10-'~miV)

diqlq,

(IO-12miV)

Class

-

KDP

42m

1

r63

=

-9

d14

=

0.49

Uniaxial

r4]

=

8.6

d,,

=

0.47

-

GaAs

43m

10

r41

=

1.6

d,,

=

134

Isotropic

CdTe

Z3m

10

~41

=

6.8

dI4

=

16.7

Isotropic

41-18

REFERENCE

DATA

FOR ENGINEERS

The problem then reduces to finding a new principal

axis frame for which the index elipsoid is diagonal.

Two special cases exist. For longitudinal modulators,

the optical field is perpendicular to

Eo,

whereas for

transverse modulators, it is parallel to

Eo.

Fig. 17A

illustrates the former, for which the index ellipsoid is

diagonal in the indicated primed axis for

42m.

The

index ellipsoid is then

1

=

Di2[l/n;

-

r63Eg]

f

D;’[l/n:

+

r63E!]

+

D:ln?

=

Di2/ni2

+

D;2/ni2

+

D32/n?

(Eq.

57)

For all materials, the product

rqkE:

is

small compared

with the indices of refraction,

so

in the primed axis the

new indices of refraction

are

approximately

n

’

(112) n:r6,E;

and

n2’

=

no

-

(112) n2r63E3.

A wave

originally polarized along the

1

axis will have equal

field components along the

1’

and

2’

axes, each

of

which propagates with a different phase velocity. After

exiting from the crystal, the net optical polarization will

be rotated from the incident polarization by an amount

proportional to

n,‘

-

n2‘

=

nar~~E2.

Amplitude

modulation is accomplished by placing a polarizer after

the crystal. For this orientation, the transmission,

T,

through the crystal-polarizer combination is given by

T

=

sin2

(r12)

(Eq.

58)

b

=no+

In practice,

tlL

<<

1,

so

the half-wave voltage in the

transverse case is considerably smaller than in the

longitudinal case.

Half-wave voltages of

1

-

10

kV

are not uncommon

so

that for high-frequency modulation, operational volt-

ages are typically less than Because of the sin2

dependence, small modulating voltages lead to a distor-

tion, since sin2@

=

0’

for small

t?.

This can be

eliminated by optically biasing the system to the

50%

transmission point by using a quarter-wave plate be-

tween the polarizer and crystal as shown in Fig.

17C.

With this arrangement, the transmission becomes

T

=

(1

+

sinr)/2

(Eq.

60)

and results in a change in transmission linear in

V(r)

for

small modulation. Hence, the standard amplitude mod-

ulator is a three-element device. For certain types of

crystals, a reduction

of

the half-wave voltage can be

achieved by using multiple crystals connected optically

in series but electrically in parallel.

The intrinsic material response is almost instantane-

ous,

so

the system response time tends to be determined

simply by circuit effects. If these are made small, a

second frequency limitation occurs because of the finite

optical transit time through the crystal. Operation above

1

GHz generally requires a traveling-wave modulation

wherein a certain type of phase matching is used.

POLARIZER

(A)

Longftudlnol

modulator

where,

r

is the retardation given by

o(nII

-

n’2)L/c

VI,,

=

riIon:rs3,

the half-wave voltage.

The half-wave voltage is the most important parameter

in specifying electro-optic modulators.

For the transverse case shown in Fig.

17B,

the

retardation becomes

r

=

(o/c)

(no

-

n,

-

$

n:r6&)~

(~q.

59a)

(Eq.

59b)

=

rm

-

rvlv,,,

where,

V

=

E;t,

v,,,

=

2~ct/onjr~~~,

Tm

=

a fixed retardation due to the natural

birefringence.

3

1’

J.

2’ f40

(B)

Transverse

rnodulotor

(CJ

Blas

with

U4

plate.

Fig.

17.

Configurations

for

amplitude modulation

of

light.

41-19

If the incident optical field is oriented along the

primed principal axis,

no

rotation of the polarization

occurs, but modulation of the phase velocity exists. By

this method, phase modulation may be achieved.

Stimulated Raman Emission

There are many other different effects associated with

x@)

and

x(3)

nonlinearities depending

on

the number of

different fields present. Frequency tripling into the dee

is significant. Similarly, another third-order effect leads

to a self-induced index of refraction change and causes

focusing and defocusing

of

a beam by virtue of its radial

intensity variation.

One important

x(~)

effect used to frequency shift light

is the stimulated Raman effect. Here, a polarization and

hence a gain is created at frequency

o'

due to a strong

field at

o

where

fio

-

fid

=

AE,

a characteristic

atomic or molecular energy, typically a vibrational

energy in a molecule. The interaction can also be

viewed as an inelastic scattering process wherein the

shift is determined by the characteristic energy. It is

possible to have stimulated rotational, vibrational, and

electronic Raman scattering with shifts ranging from a

few to a few thousand wave numbers. Representative

Raman materials and shifts are listed in Table

5.

In

the usual Raman situation, the gain is large,

so

the

conversion can be very efficient in terms

of

photons. In

terms of power, the conversion efficiency is limited by

the Manley-Rowe limit of

fiw'lho.

Typically, the

requirements for pump intensities lie in the range

10-

100

kW/cm3.

The normal Raman effect occurs when

w'

<

o

and

is

called a Stokes wave. The growing first Stokes can reach

a sufficient intensity to act as a pump for a second

Stokes, and

so

on.

With the presence of astrong pump

ultraviolet is commonly done with gases for which

,y(

s

)

and first Stokes, an anti-Stokes wave may be generated

at

o"

=

o

+

AElfi.

Hence, under normal conditions a

number of Stokes and anti-Stokes waves may be creat-

ed. A Raman cell is usually constructed locally because

of

its simplicity.

REFERENCES

General Laser Theory

Elementary Laser Theory

Siegman,

A.

An Introduction to Lasers and Masers.

New York: McGraw-Hill Book

Co.,

1976.

Verdeyen,

J.

T.

Laser Electronics.

2nd ed. Englewood

Cliffs, N.J.: Prentice-Hall, Inc., 1989.

Yariv, A.

Optical Electronics.

4th ed. New York: Holt,

Rinehart

&

Winston, Inc., 1991.

Advanced Laser Theory

Pantell, R., and Puthoff,

H.

Fundamentals

of

Quantum

Electronics.

New York John Wiley

&

Sons, Inc.,

1969.

Sargent,

M.

111,

Scully, M.

O.,

and Lamb, W.

E.,

Jr.

Laser Physics.

Reading, Mass

.:

Addison-Wesley

Publishing Co., Inc., 1974.

Yariv, A.

Quantum Electronic.:.

3rd ed. New York:

John Wiley

&

Sons, Inc., 1989.

Specific

Lasers

Solid State and Gas Lasers

Brown,

D.

C., ed.

High-Peak-Power

ND:

Glass Laser

Systems.

Springer Series

in

Optical Sciences. Ber-

lin: Springer-Verlag, 1979.

TABLE

5.

RAMAN MATERIALS

AND

SHIFTS

~ ~~

Stokes

Shift

Substance

States

(cm-')

H2 Vibrational 4155

*2

Vibrational 2331

D2 Vibrational 2991

Carbon Tetrachloride

Vibrational 460

Carbon Disulfide

Vibrational 656

Benzene

Vibrational

992

Nitrobenzene Vibrational

1344

Acetone

Vibrational 292

1

Water

Vibrational 365

1

H2

Rotational 365

Lead Electronic

10

600

Middleton W.M. (ed.) Reference Data for Engineers: Radio, Electronics, Computer and Communications

Подождите немного. Документ загружается.