Polymeric and Dendritic Electro-Optic Materials: Materials Issues

1
Polymeric and Dendritic Electro-Optic Materials
Materials Issues Larry R. Dalton Department of
Chemistry University of Washington Seattle, WA
98195-1700 E-mail dalton_at_chem.washington.edu Loke
r Hydrocarbon Research Institute University of
Southern California Los Angeles, CA
90089-1661 E-mail dalton_at_usc.edu Acknowl
edgements This work has been supported by the
National Science Foundation, the Air Force Office
of Scientific Research and by the Ballistic
Missile Defense Organization.
2
Why Organic Electro-Optic Materials? BANDWIDTH.
Device bandwidths of 113 GHz have been
demonstrated and intrinsic materials bandwidths
are on the order of 365 GHz. Response defined
phase relaxation time which is on the order of
femtoseconds. Pi electron system defines both
dielectric permittivity and index of
refraction--electrical and optical fields
propagate at the same velocity thus long
interaction lengths possible. ELECTRO-OPTIC
ACTIVITY. Electro-optic coefficients of 60-100
pm/V (at telecommunication wavelengths of 1.3 and
1.55 microns) are now routinely realized. These
have lead to Vp voltages of less than 1 volt.
Such values are critical for lossless
telecommunication links. PROCESSABILITY.
Excellent processability has led to 3-dimensional
active/passive optical circuitry that can be
effectivlye integrated with VLSI semiconductor
electronics and silica fiber optics.
Electro-optic materials are inherently conformal
and capable of being designed for compatibility
with virtually any surface. LOW PERTURBATION.
The low dielectric permittivity of organic
materials affords minimum perturbation of
radiofrequency fields of relevance to
applications such as sensing. Power dissipation
is minimal as are problems with crosstalk between
electro-optic circuit elements.
3
Potential Problems? OPTICAL LOSS. Optical loss
of organic electro-optic waveguides are typically
on the order of 1-2 dB/cm which is marginal.
Optical loss values as low as 0.2 dB/cm
(comparable to lithium niobate) have been
obtained. This issue has not been the focus of
much attention. With attention from the
synthetic community, it will likely not be a
problem. THERMAL STABILITY. Thermal
decomposition of materials is not a problem.
Chromophores are typically stable to more than
300C (which is more than adequate). Rotational
relaxation of poling-induced order is an on-going
concern. Composite materials generally are not
adequate unless the host has a very high glass
transition temperature. Chemical lattice
hardening a viable answer to improved stability
with stability to 200C realized in some
instances. Unfortunately, lattice hardening is
typically achieved at the price of some
attenuation in electro-optic activity. PHOTOCHEMI
CAL STABILITY. Singlet oxygen mechanisms are a
problem. Simple packaging leads to viable
stability (ability to withstand 50 mW power input
into EO waveguides for periods of months).
Elimination of oxygen would certainly lead to
viable materials as other mechanisms, such as two
photon absorption, appear to be ineffective. O2
forms strong VDW complexes with chromophores
simple degassing not effective in eliminating
oxygen. Exclusion of oxygen must start during
chromophore synthesis. Lattice hardening and
incorporation of scavengers also helpful.
4
Organic Electro-Optic Materials Issues and Status
of Synthesis of Materials -Chromophores Issues
Optimization of hyperpolarizability
minimization of optical absorption optimization
of thermal stability control of solubility and
processability optimization of chemical and
photochemical stability Status m? values of
greater than 10-44 esu are now routine,
absorption typically 0.8 dB/cm but values as low
as 0.2 dB/cm have been obtained thermal
stability to 300C is routine adequate
processability is routinely realized. -Bulk
Materials Issues Optimization of macroscopic
electro-optic activity minimization of material
optical loss from both absorption and scattering
mechanisms optimization of thermal stability of
electro-optic activity optimization of
photochemical stability. Status Electro-optic
coefficients in the range 60-100 pm/V (at
1.3-1.55 mm) routinely obtained optical loss of
1-2 dB/cm typical but values as low as 0.2 dB/cm
have been realized in composite materials
thermal stability is less than 100C but with
lattice hardening values of 120-150C are easily
realized photochemical stability in the presence
of atmospheric oxygen is not acceptable but
simple packaging appears to lead to adequate
stability. Materials are clearly adequate for
prototype device development but all necessary
properties have not been realized in a single
material as is required for commercialization.
Realization of a commercial material appears very
likely.
5
Organic Electro-Optic Materials Issues and Status
of Materials Processing -Wavguide Fabrication
Issues Fabrication of buried channel waveguides
exhibiting minimum optical loss fabrication of
sophisticated three dimensional circuitry.
Status Reactive ion etching and
photolithographic methods have been optimized to
the point of yielding waveguides with excess loss
on the order of 0.01 dB/cm. Use of gray scale,
offset, and shadow ion mask lithographic
techniques has permitted the fabrication of
sophisticated 3-D circuits with insignificant
excess loss. Post fabrication photochemical
trimming of circuit performance has been
demonstrated. -Integration of EO Waveguides
Issues Minimization of mode mismatch coupling
losses for integration with silica fiber optics
maximization of bandwidth and minimization of
loss for integration with drive
electronics. Status Several schemes (up
coupling into EO wedges and use of spherical
lens) have been employed to demonstrate low loss
optical of silica and polymeric EO waveguides.
The use of such schemes in a commercial structure
remains to be demonstrated. Several high
bandwidth integrated structures have been
explored. Device operation to 113 GHz has been
demonstrated and 220 GHz operation may be
possible in the near future. Integration of
polymeric EO circuitry with VLSI semiconductor
electronics for low bandwidth operation has been
convincingly demonstrated. Commercially-relevant
integration for high bandwidth operation not yet
demonstrated but likely viable.
6
Organic Electro-Optic Materials Cladding
Materials -Issues The cladding material must
prevent the propagating optical wave from seeing
the lossy metal electrodes. The cladding
material should have a higher electrical
conductivity so that poling and drive fields are
dropped across the cladding layer(s) to permit
the electro-optic chromophores to see the largest
possible effective field. Cladding materials
must be photochemically and thermally stable.
Cladding materials must not be subject to
photoconductivity effects that could cause
instability in device operation. Cladding must
not themselves contribution to optical loss. In
short many of the same issues that apply to the
active core materials apply to cladding
materials. -Status Very little attention has
been paid to the performance of cladding
materials. Almost all prototype devices have
been fabricated with off the shelf commercial
epoxy materials (thermally and UV-curable
epoxies). The only attention paid to
conductivity issues is the work carried out at
AFRL-Wright Patterson AFB and at Lockheed Martin.
These researchers have demonstrated that
improvement in device Vp performance can be
achieved with attention to cladding conductivity.
More research is required to demonstrate the
commercial relevance of development of custom
cladding materials. General conclusion An
important but neglected area of research.
7
Organic Electro-Optic Materials A Historical
Perspective Quantum mechanics has guided the
systematic improvement of molecular
hyperpolarizability shown below. Chromophore
dipole moment-molecular hyperpolarizability
product (mb) values of greater than 10-44 esu are
now routinely achieved This improvement has be
achieved without sacrifice of thermal and
chemical stability (e.g, the decomposition
temperature of the FTC chromophore is
approximately 325C)..
8
Organic Electro-Optic Materials A Historical
Perspective Improved molecular
hyperpolarizability has been exploited with the
development of statistical mechanical
calculations to guide the transitioning of
molecular second order optical nonlinearity into
macroscopic electro-optic activity leading to
improvements shown below
9
Organic Electro-Optic Materials A Historical
Perspective In 1996 it was realized that
intermolecular electrostatic interactions were
inhibiting the efficient translation of molecular
EO activity to macroscopic EO activity. These
interactions resulted in a maximum in the plot of
EO activity reverse chromophore loading in the
host polymer matrix. The position of this
maximum shifts to lower loading with increasing
chromophore dipole moment and hence dipole
moment-hyperpolarizability product. The
attenuation of electro-optic activity is most
severe for prolate ellispsoidal chromophores and
less severe for more spherical chromophores.
Statistical mechanical calculations predicted
that intermolecular electrostatic interactions
would lead to this behavior and motivated the
experimental investigations shown below
10
Organic Electro-Optic Materials A Historical
Perspective Statistical mechanical calculations
suggested a new paradigm optimization of
electro-optic activity Control chromophore
shape!
CLD-2
CLD-3
Disperse Red (1995)
11
Organic Electro-Optic Materials A Historical
Perspective
12
Organic Electro-Optic Materials A Historical
Perspective
Materials with improved electro-optic activity
have been used to used to fabricate a number of
prototype devices including (1) phased array
radars (2) spatial light modulators/laser beam
steering devices (3) broadband high stability
oscillators (4) acoustic spectrum analyzers (5)
polarization-insensitive signal transducers
(modulators) (6) time stretchers and compressors
(ultrafast A/D converters) (7) optical
gyroscopes and (8) high bandwidth optical
switches. Some selected references are given
below Acoustic Spectrum Analyzer IEEE Selected
Topics in Quantum Electronics, Vol. 6, pp. 810-6
(2000). Photonically Controlled RF Phase Shifter
IEEE Microwave and Guided Wave Letters, Vol. 9,
pp. 357-9 (1999). 102 GHz Time Stretching IEEE
Photonics Technology Letters, Vol. 12, pp. 537-9
(2000). Spatial Light Modulators Proceedings
SPIE, Vol. 3950, pp. 98-107 (2000). Sub 1 Volt
modulation (Science, Vol. 288, pp. 119-22 (2000))
is shown below
13
Organic Electro-Optic Materials What Is Required
For Further Material Improvements And What Can Be
Expected In the Near Term? The improvements of
the past four years have been realized exploiting
a theoretically derived paradigm. Current theory
suggests that further improvements are clearly
possible. Indeed, electro-optic values in the
range of 100-200 pm/V are a realistic target.
Improved theory is the first step toward this
target. Two theoretical advances are required
(1) Development of simple theory that is easily
utilized by those synthesizing chromophores.
This development would be analogous to the
development of the simple two state quantum
mechanical model of molecular hyperpolarizabilitie
s by Marder and Perry. (2) Development of
theory, such as atomistic Monte Carlo methods,
capable of treating complex electro-optic
materials structures such as multi-chromophore-con
taining dendrimers such as shown in the text
slide. Crosslinked versions of such
multi-choromophore dendrimers have yielded
electro-optic activities two to three times that
of lithium niobate at 1.55 microns while
exhibiting material optical loss of 1 dB/cm or
less. The electro-optic activity for such
materials has been observed to be stable for 1000
hours at 85C. All preliminary studies point to
continued dramatic improvements however,
dendrimer structures are very complex and the
folding of dendrimer structures is critical in
determining observed materials properties.
Dendrimer structures also appear optimum for
improving intrinsic photochemical stability both
by restricting diffusion of reactive species and
by judiciously positioning scavenging agents.
Dendrimers appear to lead to improved poling
dynamics potentially because chain entanglements
of linear polymers are avoided. Segmental
flexibility of dendrimers can be controlled to be
less problematic for chromophore rotational
relaxation.
14
Organic Electro-Optic Materials The Future A
Multi-Chromophore Dendrimer
Ma, Chen, Takafumi, Dalton, and Jen, Journal of
the American Chemical Society, 123, 986 (2001).
15
Recent Advances in Analytical Theory Comparison
With Monte Carlo Calculations
We explore the development of both analytical and
numerical results and will discuss the
relationship between these. The principal
electro-optic coefficient tensor element, r33, is
related to the acentric order parameter,
ltcos3(?)gt the first molecular hyperpolarizability
, ? the chromophore number density in an inert
host, N the index of refraction, n and the
local field arising from the host dielectric
permittivity, f(?), by r33 Nltcos3(?)gt2???f(?)/
n4 (1) For a homogeneous, single-phase
material, the number density is related to the
mean distance between chromophores, r, as N
1/r3. Consider an ensemble of M chromophores.
Statistical mechanics provides a method of
computing the mean order from the M particle
energy, U(r(M),?(M),Ep), including the effect of
a uniform electric poling field, Ep. ?(M) are
the two (or three) Euler angles that define the
directions of the M chromophores. The order
parameter can be computed from a consideration of
all interactions contributing to the total energy
according to ltcos3(?)gt ??? cos3(?)G(r,?(M),Ep)d
rMd?M/??? G(r,?(M),Ep)drMd?M (2) where
G(r,?(M),Ep) exp(-(U(r(M),?(M),Ep)/kT) is the
M-particle partition function and kT is the
thermal energy. From an analytic perspective
this is a difficult problem. To make progress,
we suggest that a single chromophore (designated
as 1) be the one for which averaging is done.
We then average over all other chromophores. The
non-normalized probability distribution around
the first chromophore is then PM(?1), where
PM(?1) ?G(r,?,Ep) drMd?M-1. The average order
is then cos3(??)gt ??? cos3(??)PM(?1) d?1 /???
PM(?1) d?1 (3)
16
Here we deviate from the standard statistical
mechanical treatment of the pairwise interaction
of particles and follow Piekaras treatment of a
many body interaction among particles. Piekara
suggested that the bulk material consists of many
solidus regions that cannot interconvert. The
orientation ?1 is composed of two rotations ?1
? ?M, which is rigorously true when the minor
angles are equal. More generally, the Euler
angles are related formally as ?1 ???M. Thus,
the angle ?1 is related to the other Euler angles
by cos(?1) cos(?)cos(?M) sin(?)sin(?M)cos(?-?M
). PM(?1) is the product of two terms (1) the
distribution of chromophore 1 with respect to the
center of symmetry of the local solidus and (2)
the interaction of chromophore 1 with the poling
field. Therefore, the averaging over the
orientations of 1 must be done in two steps. The
first is the averaging over the effective field
around chromophore 1 due to the other M-1
chromophores. Hence, ltcos3(?)gtM ???
cos3(??)PM(?1) d?1 /??? PM(?1) d?1 (4) This
average must then be averaged over all ?
according to ltcos3(?)gt (1/8?2)?? ltcos3(?)gtM
d? (5) Piekara suggested a specific form for
PM(?1) as PM(?1) (1/4?)exp(-fcos?)exp(-wcos?M)
(6) Where w is an undetermined constant
independent of the poling field. f ?Ep/?kT.
Here ? is the chromophore dipole moment and ? is
the dielectric permittivity. The first
exponential of Eq. 6 is due to the poling field
on chromophore 1 and the second term is the
leading term in an expansion of the effect of all
other chromophores in the vicinity of chromophore
1 on 1. With this definition of the single
particle probability distribution, we can
evaluate the following integral G(z) sinh(z)/z
(1/4?) ?cos?? ???? exp(-fcos?)exp(-wcos?M)
dcos?Md?M ??? PM(?1) d?M (7) G(z) is the
generating function for the rest of the
integration. Moreover, z is the magnitude of the
vector sum of the poling field and the local
crystal field z2 f2 w2 2fwcos(?) (8)
17
This result demonstrates the vectorial nature of
the interaction of the local crystal field with
the poling field. The poling field-dipole
interaction energy of the simple Langevin theory
is now replaced with the interaction energy of
the vector sum of the local interaction field
with the poling field. The final averaged
quantity of interest can then be determined using
the generating function. ltcos3(?)gt
(1/2)?cos??(1/G(z))?3G(z)/?3fdcos? (9) The
integrand can be evaluated and written as an
analytic function of z. The integrand can be
written in terms of the first Langevin function,
L(z), with z as the argument. L(z) coth(z)
(1/z) (10) Explicitly, the order parameter
can be expressed as ltcos3(?)gt (1/2)?cos????(f
wcos(?))A Bdcos? (11) A 3(3/z)L(z)
1/z2 (11a) B (f wcos(?))25 (z2
15)(L(z)/z)z4 (11b) Here the two groupings of
L(z) make the functional forms numerically stable
at small z. This integrated may be numerically
evaluated in this form. The integrand is
analytic and finite everywhere. A reasonable
form for w is suggested by London namely, w
(?2/r3kT)2 (N?2/kT)2 (12) Two approximate
solutions of Eq. 11 are easily written. For f lt
kT, Eq. 12 becomes ltcos3(?)gt (f/(5)1
L1(w)2 (13a) For w lt kT, Eq. 12
becomes ltcos3(?)gt L3(f)1 L1(w)2 (13b)
18
The two approximations are bounded everywhere by
the exact solution of Eq. 12. The term in
brackets is referred to as the attenuation
factor. The first factor is independent of N
while the attenuation term decreases with
increasing concentration as 1-L1(N)2. Since r33
varies as ?f(?)Nltcos3?gt/n4, a maximum is
predicted in the plot of electro-optic
coefficient versus N. The value of N leading to
maximum EO activity is given (for normal poling
field strengths) by Nmax (v1.91)/(?2/kT) (14
) illustrating the simple scaling with
chromophore dipole moment, ?. Eq. 14 works
surprising well for experiments employing typical
poling fields. However, analytical expressions
can also be derived that explicitly include the
poling field, f, dependence. The effect of
chromophore shape may be approximately treated as
the interaction of two hard sphere ellipsoids
separated by distance r. The mean intermolecular
distance is determined from the number density as
given above. However, if the ellipsoids are
prolate then they both cannot point along the
line joining their centers if the concentration
is in a regime where 2a gt r gt 2b. Here a and b
are the major and minor semi-axes of the prolate
ellipsoid. In this regime, there is a constraint
on the angles accessible to an ellipsoid before
colliding with a neighbor (at the same
orientation). The orientation of the molecular
is found from the x and y distances form the
center to the surface x2 y2 (r/2)2. The
equation for the surface of the ellipse is (x/b)2
(y/a)2 1. From these two equations and two
unknowns, the cutoff or the minimum angle that
can be obtained as a function of r c c(r)
cos(?min) 1 (2b/r)2/1 (b/a)2. A
similar expression is found ffor the oblate
ellipsoid case. The cutoff function, c(r), is a
continuous function of r or N because c(r) 1
for r gt 2a and c(r) 0 for 2b gt r. This minimum
angle can be incorporated into the evaluation of
the order parameters by restricting the limits of
integation so that c cos(?M) c. The
integral of the generating function, Eq. 7, is
then evaluated between these limits rather than
between 1 and 1. This integral can be
evaluated and shown to yield Gc(z) ccos
(?)G(cz cos(?))exp(zsin(?min)sin(?) (15) Therefo
re, this restriction on the integration over this
one angle just scales the value of z or the
vectors connecting the two terms. Hence, the
average quantities may be evaluated in a similar
manner as before. Application of this simple
approximate treatment to data obtained for the
CLD chromophore is shown in the accompanying
figure.
19
Comparison of experimental (solid diamonds) and
theoretical data for the CLD chromophore in
polymethylmethacrylate is shown. The dashed line
shows the result (discussed in the text) of
considering only electronic electrostatic
interactions. The dotted line shows the
influence of steric effects, the c(r) parameter
discussed in the text. The solid line shows the
combined effect of these two types of
interactions. Note that as expected, electronic
interactions are longer range (the maximum value
occurs at lower number density). Note that all
calculations are executed without adjustable
parameters. For the purposes of these
calculations, the chromophore shape was
approximated by a prolate ellipsoid. Improvement
in agreement between theory and experiment can be
achieved by self-consistent treatment of the
effect of chromophore concentration on material
(host polymer) dielectric permittivity.
Surprisingly good reproduction of experimental
data is obtained even with the simple model
discussed in the text.
20
This simple approximation works surprisingly well
for relatively stiff electro-optic chromophores
and yields essentially quantitative reproduction
of experimental data for many chromophores. The
approximate theory provides very valuable
guidance to the optimization of macroscopic
electro-optic activity. It provides a simple
expression for calculating the chromophore
loading that will lead to optimum electro-optic
activity. It also indicates that electro-optic
activity can be optimized by making prolate
ellipsoidal chromophores more spherical. We
have sought to test the approximations of simple
theory and to gain insight into the details of
the chromophore distributions by carrying out
Monte Carlo calculations. A variety of such
calculations have been carried out at different
levels of approximation. We briefly describe the
most simple variant here. In this treatment,
individual chromophores are placed at lattice
sites, one per site in an ordered array. For the
case of a simple cubic lattice, the dipoles are
placed M by M by M, where values of M from 10
through 13 are typically examined. The lattice
is then embedded in images of itself to avoid end
effects (i.e., re-entrant boundary conditions).
The statistical effective field is then found
around each dipole from the histogram of all
relative orientations, ?, due to the nearest
neighbor dipoles, j, around each and every
individual dipole i. The histogram generated
from the Monte Carlo calculations is well fit to
the functional form P(?) Aexp(-0.3wcos(?)
Bexp(0.3wcos(?) (16) where B is approximately
1/3. This expression is nearly in quantitative
agreement with the potential function proposed by
Piekara. The value of 0.3 in the exponential of
Eq. 16 accounts for the 26 nearest neighbors
weighed by those diagonally related to the
central one. Monte Carlo calculations also
establish that w follows a fourth power
dependence on chromophore dipole moment. The
theoretical results presented here clearly
provide motivation for pursuing development of
approximately spherical chromophore by synthetic
approaches such as dendritic methods. The
segmental flexibility of dendrimers argues for
atomistic kinetic Monte Carlo methods to assure
that chromophores are held in an appropriate
nanostructured array. In the course of using
statistical mechanical methods to optimize
electro-optic activity, it became clear that
control over molecular structure could be used to
control processability (solubility in spin
casting solvents), optical loss, chemical
stability, thermal stability, and photochemical
stability.