杏吧原创

MOST of us learnt at school that light is an electromagnetic wave. It
can travel through a vacuum and also through some substances, air, water
or glass, for example. When a light wave passes from one medium to another,
it changes direction. We use this fact to manipulate light waves by designing
lenses and other optical devices. Although the frequency of light remains
the same, its velocity and, therefore, wavelength changes. Light travels
fastest in a vacuum, and ratio of this velocity to that in a transparent
substance is called the refractive index. Normally, the refractive index
is a constant for a particular substance at a certain temperature and pressure.

Applying an electric field to some substances, however, can change the
velocity of light passing through them, which changes their refractive index,
and their optical properties. The field may originate from the light wave
itself or from an external electrical voltage. Such materials are said to
be 鈥榥onlinear鈥�. They show a whole range of curious optical effects that
physicists and electronic engineers are very interested in. The reason is
that nonlinear optics provides a rapid and sensitive way of manipulating
beams of light. This means that light can be used instead of electricity
as a means of communication and storing information. The advantage is that
photons of light travel much faster than electrons, so optical signals can
be processed more quickly than electrical ones. A whole new technology 鈥�
that of optoelectronics 鈥� is being developed, starting with optical fibres
to carry the light, compact discs on which lasers store information optically,
optical devices to process signals, and, finally, logic circuits for optical
computing.

In the past, the main obstacle in optoelectronics has been that many
nonlinear effects are quite weak. But now the laser can provide intense
beams of light at a particular wavelength, allowing engineers selectively
to amplify the nonlinear effect that they have chosen to exploit. How quickly
this technology advances depends on what nonlinear materials are available
and how we manipulate them. Chemists are now looking for new materials that
show much stronger nonlinear effects, and are cheaper and easier to fabricate.

To find the optimum nonlinear material, researchers need to look at
what happens when light passes though a material. Light has associated with
it an oscillating electric (and magnetic) field. When the oscillating field
passes through a material, it disturbs the electrically charged particles
within that material (the electrons, ions and nuclei). This field causes
the charges to move, so inducing an oscillating dipole moment, or polarisation,
which in turn radiates a secondary oscillating electrical field (in the
same way as a small antenna). This secondary field interferes with field
due to the original, or incident light, and produces the optical properties.

The oscillating charges tend to move in a simple way, rather like a
pendulum swinging symmetrically from side to side about a central point
of equilibrium. The electrical force pulling the charges to and fro is directly
proportional to the displacement of the charges. If we were to draw a graph
of the displacement against the force, it would be a straight line, so this
kind of motion is said to be linear. The displacement is symmetrical about
the central equilibrium points of the charges, and is called harmonic. In
this case, the secondary field has the same frequency as the applied field.

In real materials, however, when an applied oscillating field is strong
(such as from a laser), the induced oscillations of the charges are no longer
proportional to the applied field 鈥� they are anharmonic. The equation describing
their motion becomes much more complicated 鈥� the resulting graph is no longer
a straight line, so is said to be nonlinear. The secondary field is not
just made up of one frequency but a series of frequencies that differ from
that of the incident light. These are analogous to the series of frequencies
鈥� the 鈥榟armonics鈥� 鈥� that make up the note of a violin string. The second
harmonic would be twice the original frequency. The equation describing
these effects can split up into a series of terms with increasing powers,
called first order, second order, third order terms and so on .

Today, all commercial applications of nonlinear optics use second order
effects. These include the first nonlinear optical process to be discovered
鈥� the electrooptic effect discovered by Agnes Pockels as long ago as 1906.
Here, the refractive index of a material changes, not as a result of passing
light through it, but as a result of applying a direct voltage. This provides
a way of converting the modulations in an electrical signal into an optical
wave. The electrooptic effect can also be used to form fast-switching shutters,
called Q-switches, within the cavities of high power lasers, to obtain short
pulses and to modulate the amplitude of light, so that it can carry information
in the same way that the radio wave does. The rapid growth in using optical
fibres for communications is leading to a demand for materials that are
more nonlinear to allow faster modulations at lower voltages. Engineers
also want better nonlinear materials to make more efficient 鈥榳aveguides鈥�
for switching optical signals between alternative routes in optical fibres
.

Another important nonlinear effect is 鈥榮econd harmonic generation鈥�,
in which light incident on a substance at one frequency, in the near infrared,
for example, then emerges from the material at twice the frequency in the
green part of the visible spectrum. Some lasers work on this system to produce
sources of light at new wavelengths. There is a great deal of interest in
doubling the frequency of lasers from the near infrared into the visible.
Using a frequency doubled laser in compact disc players or optical data
storage would quadruple the amount of data you could put on a disc.

There is also a third order process called the optical Kerr effect in
which the refractive index depends on the intensity of light passing through
a substance. Nobody is applying it practically yet because its use requires
advanced technology. But it is extremely fast and could be suitable for
optical computing. There are also a number of other nonlinear optical effects
that may eventually be exploited.

The size of nonlinear effects in different materials depends on the
chemical nature of the material. First, it depends on how readily the electrically
charged particles 鈥� usually positive ions or electrons 鈥� can interact with
light energy and be displaced from their equilibrium positions, and secondly,
on the distribution of the charges within the material. For there to be
second-order nonlinear effects, the distribution of charge within each molecule
needs to be asymmetrical, and the molecules of the material must align so
that when they interact with light, all the charges are equally pulled more
in one direction than in the other. This means that the material needs to
be a pure crystal or a film with a highly ordered array of molecules or
atoms.

The main materials used at the moment are two inorganic substances,
lithium niobate and potassium dihydrogen phosphate. In these compounds,
the positive ions of lithium or potassium are rather loosely bound within
the crystal, providing an asymmetrical field. Semiconductors, such as gallium
arsenide, also possess nonlinear properties because they have free electrons
and, therefore, asymmetrical fields, but the nonlinear properties are not
as great as in other materials. But they have an advantage in that they
can act as lasers, generating intense sources of light, and they can also
detect light. This means that engineers can make the light source, wave
guides and other devices all out of the same material on one chip.

Unfortunately, semiconductors do not have big enough nonlinearities
to exploit them for second harmonic generation. Chemists have developed
several new inorganic materials that have higher nonlinear properties, the
most notable being potassium titanyl phosphate and barium borate. Much work
is now going on, particularly in the US, to improve the quality and size
of the crystals.

A more interesting prospect is to look at the nonlinear optical properties
of organic materials, particularly those with long chains of carbon atoms
鈥� polymers. Because this work requires the collaboration of chemists and
materials scientists as well as physicists and device engineers, Britain鈥檚
Science and Engineering Research Council has sponsored several consortia
involving companies and universities under the Joint Opto-Electronic Research
Scheme (JOERS).

Organic molecules do it better

Organic materials have several advantages over the inorganic compounds.
They have much higher nonlinearities. Crystals of the organic compound 2-methyl-4-nitroaniline
are 59 times as effective as lithium niobate in second harmonic generation.
Chemists are developing a number of compounds that are even better at generating
second harmonic light. At ICI, working within one of the JOERS consortia,
we have recently developed a new organic electrooptic crystal that operates
at voltages a tenth as low as that achieved with lithium niobate. This means
that we can use a much smaller, and therefore cheaper, crystal as a laser
modulator, for example. Reducing the operating voltage also means that we
can apply electrical signals of much higher frequencies to the crystal.

One problem encountered is that the high intensity of laser light readily
damages many inorganic materials used in nonlinear optical devices (in particular,
those made with lithium niobate). They have a low 鈥榦ptical damage threshold鈥�.
Some of the organic materials have much higher damage thresholds than lithium
niobate. Another advantage of polymeric materials is that they are much
cheaper and easier to make than inorganic materials. It is difficult to
make perfect crystals of lithium niobate and there is a lot of wastage.
The process of growing, cutting and polishing crystals takes a long time.
Semiconductors, such as gallium arsenide, require expensive techniques 鈥�
molecular beam epitaxy or chemical vapour deposition 鈥� to lay down thin,
well-ordered films.

The arrangement of molecules within the material is extremely important,
whether in a single crystal or a thin film. The molecules have to be arranged
so that nonlinear properties of the individual molecules do not cancel each
other out. To obtain the highest nonlinear property of a material, the constituent
molecules must have high nonlinearities. This requires a highly asymmetrical
distribution of electrons. In other words, the molecules must be 鈥榥oncentrosymmetric鈥�.
Some organic compounds, for example, are made up of chains and rings of
carbon atoms which have alternating single and double bonds between them.
Two simple examples are polydiacetylenes, or polyenes, which are straight
chains of carbon atoms, and benzene, which is a ring of six carbon atoms.
The electrons involved in bonding tend to be loosely bound to their atoms.
They cannot make up their minds whether to form part of a single or double
bond, so become 鈥榙elocalised鈥�, spreading over the whole molecule.

We can create a high degree of asymmetry by putting groups of atoms
at one end of the molecule that either attract the delocalised electrons
(acceptors) or push some of their own electrons into these systems (donors).
To obtain the highest nonlinearities we put donor groups, such as methoxy
group -(OCH₃), the amino group (-NH₂) and the dimethylamino
group (-N(CH₃)₂) at one end of the molecule, and acceptor groups,
such as the cyanide group (C鈮�N) and the nitro group (-NO₃), at
the other end to create a push-pull effect (see Figure 1).

We can increase the molecular nonlinearity by either increasing the
number of alternating single and double bonds in the carbon chain, thereby
increasing the electron delocalisation, or increasing the strength and number
of donor and acceptor groups. In ICI, and in other companies, researchers
have been developing computer programs that will predict molecular nonlinearities
accurately. These programs help us to study the effect of adding or substituting
different chemical groups within the molecule, and varying their positions.

Continuously increasing the molecular nonlinearity may not produce the
best material, however. In the solid state, it is the nonlinearity per unit
volume that is important. Lengthening the number of alternating single and
double bonds can produce a larger increase in molecular volume than in nonlinearity.
Here again, the computer progams have been useful, predicting, for example,
that in a material made up of chains of benzene rings, there is nothing
to be gained from making chains very long, whereas lengthening simple straight
chains creates a large rise in nonlinearity (see Figure 2).

Another problem is that altering the chemical structure of a molecule
to improve its nonlinearity can also change its colour. For instance, crystals
of methyl nitroaniline, which is simply methyl benzene with an amino donor
group on one side of the benzene ring and a nitro acceptor group on the
other, are yellow. But those of the larger, more nonlinear stilbene molecule,
which has two benzene rings joined to two carbon atoms connected by a double
bond, are red. This turns out to be a problem if we are using second harmonic
generation to double the frequency of a laser diode 鈥� a small laser on a
chip. In the case of the stilbene crystal, the wavelength of the second
harmonic light is about 400 nanometres. It so happens that the crystal also
absorbs light at this wavelength, which means that the laser produces less
light and the crystal also tends to heat up. One of the major chemical challenges
is to make molecules that have a high nonlinearity but absorb very little
light over the visible range of wavelengths from 350 to 850 nanometres.
Organic molecules containing metals may be the answer.

We now know of many molecules having high nonlinearities. There remains,
however, the problem of making materials in which the molecules all line
up in the same direction so that their nonlinearities add up to a maximum.
Until recently, most work has concentrated on producing the right material
by growing perfect crystals from solutions, in much the same way as children
grow crystals of copper sulphate at school. Unfortunately, because nonlinear
molecules have one end that is positively charged and one that is negatively
charged, in other words a high dipole moment, they tend to arrange themselves
so that the positive and negative ends are next to each other in an antiparallel
fashion. This means that their nonlinearities cancel each other.

To stop this from happening, chemists have tried substituting various
groups of atoms to disrupt the antiparallel pairing and make the molecules
lie in a particular way. They have, for example, substituted groups that
prefer to have a particular arrangement in space, groups that encourage
hydrogen bonding between the molecules to hold them in place, and groups
that decrease the inherent molecular dipole moment. Unfortunately, we cannot
predict how molecules arrange themselves in a crystal. In fact, we get different
crystal structures using different methods of crystallisation with different
solvents. The result of this work, so far, is that the return has been small
from the number of compounds crystallised and tested.

An alternative to growing crystals is to use a polymer to hold the nonlinear
optical molecules in place. We can either just mix the molecules into it,
or actually graft the molecules onto the polymer. The mixture is heated
up to a temperature at which the polymer becomes rubbery so that the chains
of polymer molecules can move about. We then apply an electrical field across
the material, which causes the dipoles of the nonlinear molecules to line
up in the direction of the field. As the mixture cools, the polymer chains
stop moving about and lock the nonlinear molecules into their aligned positions.
The electric field can then be removed.

The advantage of this technique is that polymers are easy to process,
especially in the form of thin films suitable for making waveguides. We
can use any nonlinear molecule because the way it crystallises is no longer
important. But there are other problems. The polymer dilutes the effective
nonlinearity of the material, and it is sometimes difficult to dissolve
more than between 10 and 20 per cent of the nonlinear molecules in the polymer.
Even when using extremely high electric fields, it may be difficult to persuade
the molecules to stop jiggling around and settle down with their dipole
moments lined up.

Often after a certain time, their alignments tend to revert to what
they would have been without the electric field.

What is the future for these materials? Inorganic compounds, such as
gallium arsenide and lithium niobate, are already well-established optoelectronic
materials. Device manufacturers are extremely conservative, so we will have
to do a lot more work on alternative materials to persuade them to change
from the technologies they have now mastered to the new techniques required
to make organic and polymeric optical components. Nevertheless, researchers
at Hoechst-Celanese in Summit, New Jersey, and Lockheed in Palo Alto, California,
have made compounds mixed in polymers with nonlinearities that compare favourably
with lithium niobate, and they have used made waveguide switches in thin
films of these materials. These companies should have some devices on the
market within the next 12 months. European consortia, such as the one that
ICI is part of, will not be far behind. The work that these companies and
our consortium have done so far shows the huge potential of the new materials.

Simon Allen is a research scientist at the Wilton Materials Research
Centre, ICI.

* * *

A MATHEMATICAL DESCRIPTION OF NONLINEAR OPTICS

IN a linear optical material, the polarisation (P) induced in a unit
volume by an optical electric field E is directly proportional to this field:

P = &egr;₀&khgr;E

where &egr;₀ is the permittivity of free space (a fundamental constant)
and the constant of proportionality &khgr; is the susceptibility of the material.
It is related to the refractive index n of the material by:

n² = 1 + &khgr;

In a nonlinear optical material, this strict proportionality no longer
holds, and the polarisation can be described by the more complicated equation:

P = &egr;₀(&khgr;⁽¹⁾E + &khgr;⁽²⁾E² + &khgr;⁽³⁾E³ + . . .)

The higher order terms, in E² and E³ become important only at high electric
field strengths, and are the origins of the nonlinear optical effects. The
physical effects are generally classified as 鈥榮econd-order鈥�, 鈥榯hird-order鈥�
and so on, if they originate from the &khgr;⁽²⁾, &khgr;⁽³⁾ term in this equation.
This description is, in fact, an oversimplification, because it does not
take into account the anisotropy of the material properties. The fields
E and P are vectors and the coefficients &khgr; are tensors. The third-order
nonlinear optical susceptibility, &khgr;⁽³⁾ can be finite in all materials, but
in order to obtain a nonzero second-order susceptibility &khgr;⁽²⁾, there must
be a noncentrosymmetric arrangement of atoms or molecules within the material.

As an example of how the above relationship between P and E gives rise
to nonlinear optical effects, we can write the oscillating electric field
of a light wave in the form:

E = E₀sin(2&pgr;ft)

where f is its frequency. For a linear medium:

P = &egr;₀&khgr;E₀sin(2ft) = P₀sin(2&pgr;ft)

and P oscillates at the same frequency f. For a nonlinear medium:

P = &egr;₀&khgr;⁽¹⁾E₀sin(2&pgr;ft) + &egr;₀&khgr;⁽²⁾(E₀sin(2&khgr;ft))² + . . .,

which can be written, using the well-known trigonometrical relationship
(sin(x))² = (1-cos(2x))/2, because:

P = &egr;₀&khgr;⁽¹⁾E₀sin(2&pgr;ft) + &egr;₀&khgr;⁽²⁾(E₀²)/2-&egr;₀&khgr;⁽²⁾E₀2cos(4&pgr;ft)
= P₀ + P₀^鈥�sin(2&pgr;ft) + P₀^鈥�cos(2&pgr;>(2f)t)

showing that the polarisation P has a component oscillating at the frequency
2f, which gives rise to second harmonic generation.

* * *

OPTICAL WAVEGUIDES

WAVEGUIDES are thin films or channels formed in an optical material
and used to guide light in particular directions. The waveguide itself is
thin (a few millionths of a metre thick) and must have a higher refractive
index than the surrounding materials (the 鈥榮ubstrate鈥� and the 鈥榗ladding鈥�).
The light is then confined by total internal reflection at the boundaries
of the waveguide. The light can be confined laterally as well as vertically
by defining a 鈥榮tripe鈥� of high refractive index within the medium. If the
stripe is bent, the light can be directed round the corner without leaking
out of the waveguide.

An example of a simple waveguide device is the 鈥楳ach-Zender interferometer鈥�
shown below. A single waveguide is split into two arms of equal length,
which then recombine into a single guide. The waveguide is fabricated in
an electrooptic material, and electrodes are formed so as to be able to
apply an electric field across one arm of the device. When no field is applied,
half the incoming light travels down each arm. Because both arms have identical
path lengths, the two beams recombine at the output junction in phase with
each other, and maximum output is achieved. If an electric field is applied
to one arm, the refractive index of the material in this arm is changed
via the electrooptic effect. The light now travels at different speeds in
the two arms of the device. When the beams recombine, they are no longer
in phase with each other, and some destructive interference will occur.
The total intensity of light in the output channel is thus reduced. By changing
the voltage applied to the device, any output intensity between zero and
the maximum can be achieved.