Chirality - ACS Publications - American Chemical Society

Chapter 11

Downloaded by PENNSYLVANIA STATE UNIV on September 13, 2012 | http://pubs.acs.org Publication Date: March 1, 2002 | doi: 10.1021/bk-2002-0810.ch011

Application of Chiral Symmetries in Even-Order Nonlinear Optics André Persoons , Thierry Verbiest , Sven Van Elshocht , 1

1

and Martti Kauranen 1

1

2

Laboratory of Chemical and Biological Dynamics, University of Leuven, Celestijnenlaan 200 D, B-3001 Heverlee, Belgium Institute of Physics, Tampere University of Technology, P.O. Box 692, FIN-33101, Tampere, Finland 2

We give an overview of the role of chirality in second-order nonlinear optics. In particular, we describe the use of chiral materials to create highly symmetric materials and thin films for second-order nonlinear optics. We discuss the role of magnetic-dipole contributions to the second-order nonlinearity and the possible applications of chiral nonlinear optical materials.

Introduction Even-order nonlinear optics (NLO) has several applications in the field of opto-electronics (1,2). Several of these nonlinear processes are straightforward to experimentally demonstrate but their application in devices has been hampered by the lack of appropriate materials. Necessary requirements for second-order nonlinear optical materials include the absence of centrosymmetry, stability (thermal and mechanical), low optical loss and large and fast nonlinearities (1). Perhaps the most stringent requirement for second-order N L O is the absence of centrosymmetry. On a molecular level, this has been achieved by connecting electron donor and acceptor groups by a highly polarizable π-conjugated system, yielding strongly dipolar molecules (3). On a macroscopic level the centrosymmetry must be broken artificially by techniques such as aligning molecular dipoles in an external electric field (poling) or by depositing Langmuir-Blodgett films or selfassembled films (1). These techniques result in noncentrosymmetric media with polar order.

© 2002 American Chemical Society

In Chirality: Physical Chemistry; Hicks, J.; ACS Symposium Series; American Chemical Society: Washington, DC, 2002.

145


146 However, polar order is not required for a material to be noncentrosymmetric (4). For example, chiral materials comprised of enantiomerically pure chiral molecules are inherently noncentrosymmetric. Accordingly they give rise to second-order nonlinear optical effects even in the absence of polar order. In fact, frequency mixing has been observed in isotropic solutions of chiral sugar molecules and the electro-optic effect has been predicted to occur in isotropic media (5,6). A significant advantage of chiral isotropic media as compared to traditional polar materials is their inherent thermodynamic stability. Furthermore, we have recently shown that the susceptibility coefficients related to chirality can be quite large (7). In addition, the nonlinear optical properties of chiral molecules and polymers can be significantly enhanced by optimizing magnetic-dipole contributions to the nonlinearity, as was recently demonstrated for thin films of chiral poly(isocyanide)s (8). Therefore, we believe that chirality can be a valuable alternative in the search for new second-order N L O materials. In this paper, we give an overview of the role of chirality in the field of second-order nonlinear optics and the potential applications of chiral materials in this field.

Theoretical Background Consider the situation where several optical fields at different frequencies are incident on a nonlinear medium. In general, electric-dipole interactions as well as magnetic-dipole and electric-quadrupole interactions will contribute to the nonlinear response (9). However, in the remainder of this paper, we will only consider electric-dipole and magnetic-dipole contributions to the nonlinearity of the medium. One reason for this is that the magnetic-dipole interaction is actually somewhat stronger than the quadrupole interaction (10). Furthermore, the importance of magnetic interactions in chiral media is well established and one can argue that chirality favours the magnetic interactions (11-13). Furthermore, the general symmetry properties of magnetic-dipole and electric-quadrupole interactions are very similar in second-order nonlinear optics, and separation of the two is difficult. Hence, the quadrupole interaction can be implicitly included in the magnetic-dipole interaction. Then, up to first order in the magnetic-dipole contributions, the nonlinear polarization is given by (2) Pi ( ω + co ) = Σ Σ Xijk (ω + ω ;ω , o> )Εj ( ω )E (co ) + jfc (pq) ρ

q

e

ρ

ς

ρ

q

ρ

k

q

(l) η

Σ Σχ^ (ω +ω ;ωρ,ω )Β (ω )Β^ω ) jk(pq) ρ

ς

α

ί

ρ

ς


147 where the subscripts refer to Cartesian coordinates in the laboratory (macroscopic) frame. In addition, the materials develops a nonlinear magnetization Mi(co + t o ) = X I X Î j f ( ω jk(pq) p

q

q

p

q

p

k

q

In eqs (1) and (2), the notation (pq) indicates that, in performing the summation over ρ and q, the sum ω 4- co is to be held fixed, although ω and co are each allowed to vary. The superscripts in the susceptibility components associate the respective subscripts with electric-dipole (e) or magnetic-dipole (m) interactions. Both nonlinear polarization and magnetization act as sources of second-harmonic generation. The number of nonvanishing susceptibility components depends on the symmetry of the materials system. In the following paragraphs we will explicitly consider second-order nonlinear optical processes in several specific cases of materials symmetry. ρ


(2)

+ œ ;œ ,œ )Ej(œ )E (co )

ρ

q

ρ

q

Second-order Nonlinear Optical Processes in Centrosymmetric Isotropic Media For a centrosymmetric isotropic medium, all electric tensor components χ-jjf vanish. However, because of the different symmetry properties of magnetic quantities the tensors % eem Λ v

eem

and x

have one independent component (13) :

m e e

eem _ eem _ eem _ A x y z ~~ A y z x Λ zxy "~

eem _ Λ xzy ~"

mee _ mee _ mee _ A x y z ~" A/yzx ~ Azxy

mee _ Axzy

eem _ &yxz

eem λ zyx

mee _ /Cyxz

mee Azyx

and Λ

mee

—

—

Hence, we can rewrite eqs (1) and (2) as :

Ρ ( ω + co ) = x ρ

q

χ

e e m

66111

( ω + co ; ω , co ) Ε ( ω ) x Β ( ω ) + ρ

q

ρ

q

ρ

ς

(3)

( ω + co ; ω , ω )E(œ ) x Β ( ω ) ρ

q

ς

ρ

q

ρ

and

Μ ( ω + ω ) = 2x m e e ( ω + ω ; ω , œ )Ε(ω ) x E(œ ) ρ

ς

ρ

ς

ρ

q

ρ

q

(4)

The functional forms of eqs (3) and (4) imply that isotropic centrosymmetric materials cannot support nonlinear optical processes were the two input beams are copropagating. In that case, the polarization and magnetization would be directed


148 along the wavevectors of the incident beams and cannot give rise to coherent radiation. However, processes that rely on input beams that cross each other are possible. For example, second-harmonic generation with two noncoplanar input beams is possible through the tensor % (% is zero for second-harmonic generation). As for the magnitude of the effect, one could argue that magnetic contributions to the nonlinearity are weak and that the effect would be difficult to detect. However, it has been shown that chirality enhances the strength of magnetic interactions (12). Hence, combining equal amounts of both enantiomers in an isotropic medium (for example a racemic solution of chiral molecules, which is isotropic and centrosymmetric) could therefore still lead to a nonlinear optical response. To the best of our knowledge, second-harmonic generation through % in an isotropic medium has never been observed. However, second-harmonic generation in centrosymmetric crystals of chiral molecules has been observed and attributed to magnetic-dipole contributions (12).


eem

mee

ecm

Chiral Isotropic Media The highest possible symmetry that allows for a nonlinear optical process through the tensor % is an isotropic chiral medium. Such a medium is for example an isotropic solution of enantiomerically pure molecules. In that case, the nonvanishing tensor components are eee

_ e e e _. e e e _ e e e _ _ e e e A x y z ~~" A y z x "" A zxy *~ A x z y

x

eee

x

e e m

x

m e e

v

v

v

v

_

- v

- eem _ eem _ eem _ _ eem A y z x ~" Azxy ~" A x z y — — £ y v

v

X

v

v

Z

mee A x z y ~~

_ mee _ mee _ mee _ ~~ A x y z — A y z x ~~ A z x y ~~ v

v

v

_ . eee "Xzyx »

eee Ayxz

eem _ Ayxz ~

v

mee _ A y x z ~~

v

eem Azyx

v

mee Azyx

v

Hence, eqs (1) and (2) transform into Ρ(ω

+ω )=

ρ

ς

( ω + ω ; ω , ω )Ε(ω ) χ Ε(ω ) +

Ιχ™

ρ

ς

ρ

ς

ρ

ς

X

eem

(œ +œ ;œ œ )E(cû )xB(co )+

X

e e m

(œ

p

q

p

p>

q

p

q

(5)

+œ ;œ œ )E(ro )xB(ro ) q

q)

p

q

p

and

Μ ( ω + ω ) = 2x m e e ( ω + a> ; ω , co )Ε(ω ) χ Ε ( ω ) ρ

ς

ρ

q

ρ

q

ρ

ς

(6)

It is clear from eqs (5) and (6) that, in order to observe any nonlinear optical effect, the input beams must not be copropagating. Furthermore, nonlinear optical effects


149 through the tensor χ requires two different input frequencies. For example, sumfrequency generation in isotropic solutions of chiral molecules through the tensor χ ^ has been experimentally observed (5). Recently, this technique has been proposed as a new tool to study chiral molecules in solution (14). Another interesting effect is the possibility of the electro-optic effect in chiral isotropic media through the tensor χ (6,15). If we neglect the weaker magneticdipole contributions, the source polarization is given by : 666

6


εεε

Ρ(ω) = 2χ

666

(ω;ω,0)Ε(ω) x E(0)

(7)

The tensor χ (ω;ω,0) will be nonvanishing when material damping is properly accounted for. For a plane wave propagating in the z-direction and a static electric field (with amplitude E ) applied along z, the nonlinear polarization can be written as εεε

0

P ± ( œ ) = ±i2x E E±(co) eee

(8)

0

Where + and - refer to the left- and right-hand circular polarization of the optical field, Ε ( ω ) = Ε ± (x ± iy)/ V2 with E the scalar amplitude of the field. Important is that the overall imaginary factor in eq 8 reverses the role of the real and imaginary parts of the susceptibility. Therefore, in isotropic chiral media, index modulation is due to the imaginary part of χ, while electro-absorption is due to the real part of χ. A time-dependent perturbative density-matrix formalism (16) yields the following expression for the susceptibility (5): ±

χ

β66

±

ί2γ

(ω;ω,0) = - ^ Σ on , m Γ

ω

n

«

m

gn-( nm d

x d

mmg> ir)

- i yrng (vœm g - ω - i Ym g);( c "ng o + i'ng> y )

η β

i 2

d

nfi

w

m £

Ymg

mg

d

ne

gn-( nm d

x d

n g

mg)

- i Yi m g (vωn g + ω + iYnfi)(co ng/v mg - i y

g

m f i

w

η £

w

mg

m g

) (9)

+ iK

d

nmg ( œ

+ i Knmg

m g

gn( nm d

-œ-iY

d

x

mmg_> g )

d

)(œ

m g A n ngg

m E

gn-( nm d

w

x

d

ng

n g

mg)

(CO +CO + iY )(CD ng

+ i rYn g ;)

mg

-i7

m g

)_

Where g is the ground state and m and η are intermediate states. d are transition dipole moments, co = ω - co is the transition frequency and y the damping rate between states η and m, and n m

nm

η

m

nm


150


K

n

m

g

=

Y

m

n

^

Y

m

s

:

Y

n

do)

g

The first two terms in eq 9 are only nonvanishing in the presence of damping. The last two terms have to be considered in the presence of dephasing, which leads to incomplete destructive interference between the quantum-mechanical pathways. This factor becomes resonant whenever the optical frequency is close to the energy difference between two unpopulated intermediate excited states. A close inspection of eq 9 leads to several surprising results. When the optical frequency is detuned far from any material resonances, the damping rates can be neglected in the denominators of eqs 9 and 10 and the susceptibility becomes purely imaginary. Eq 8 then implies that index modulation is possible through nonresonant interactions. However, when the optical frequency is close to the energy difference between intermediate excited states the dephasing-induced terms become dominant and essentially real. Eq 8 then implies that the optical field can experience gain due to the electro-optic response. We must note however, that the existence of the electro-optic effect in chiral isotropic media depends critically on how damping is treated. Recently, the validity of the density-matrix formalism in treating quantummechanical damping and, as a consequence the existence of the electro-optic effect in chiral isotropic media, has been challenged (16). Therefore, experimental work in this particular field could be used to test various approaches to the quantummechanical description of nonlinear optical phenomena.

Chiral Thin Films With In-plane Isotropy We have observed significant magnetic contributions to second-harmonic generation of Langmuir-Blodgett (LB) films of chiral poly(isocyanides) (8). Such films belong to the C*. symmetry group and their nonlinearity can be described by four independent components of % , seven independent components of % and four independent components of % . To obtain an idea about the relative magnitude of the various susceptibilities, we performed an extensive analysis of the second-order nonlinearity of thin films of a chiral chromophore-functionalized poly(isocyanide) (Fig. 1), using a recently developed polarization technique based on secondharmonic generation (8, 17). The relative magnitudes of all components of % , % , and x are listed in Table I. The components that are nonvanishing for chiral surfaces only are referred to as chiral components. Susceptibility components that are non-vanishing for any isotropic (chiral or achiral) surface are called achiral components. From table 1 it is clear that the largest magnetic susceptibility component is of the order of 20 % of the largest electric susceptibility components. If we use an absolute value of 9 pm/V for the zzz components of % , the magnitude of the largest magnetic contribution would be on the order of 2 pm/V. This value certainly indicates that magnetic-dipole contributions to the nonlinearity can be useful for nonlinear optical applications. eee

eem

mee

eee

mee

eee


eem


151

Table I. Relative magnitudes of the chiral and achiral susceptibility components of Langmuir-BIodgett films of a chiral chromophore-functionalized poly(isocyanide) (8). Tensor

achiral components

X

zzz zxx=zyy xxz=xzx=yyz=yzy

eee

%

eem

chiral components

relative magnitude

xyz=xzy=-yxz=-yzx

1.00 0.62 0.60 0.08

zzz zxx=zyy xxz=yyz xzx=yzy

0.23 0.12 0.01 0.05 0.06 0.13 0.06

zzz zxx=zyy xxz=xzx=yyz=yzy

0.15 0.00 0.00 0.03

xyz=-yxz zxy=-zyx xzy=-yzx

%

mee

xyz=xzy=-yxz=-yzx SOURCE: data from Reference 8


152

Chiral Thin Films With Twofold Symmetry We have also investigated Langmuir-BIodgett films of the chiral helicenebisquinone derivative shown in Fig. 2 (7, 18). The enantiomerically pure material combines into large large helical stacks when incorporated into L B films. The large helical stacks further organize into bundles. Consequently, the samples have a C symmetry. In Langmuir-BIodgett films of the racemic material, such strong organization does not occur. The supramolecular organization in the nonracemic (i.e. prepared from enantiomerically pure material) L B films has a profound impact onto the second order nonlinear optical properties [7]. For example, a 30-layer thick LB-sample made from the pure enantiomer generates a second harmonic signal which is three orders of magnitude higher compared to the signal from a sample with the same number of layers but made from the racemic mixture. The reason is that the nonlinear optical response is dominated by the chiral (electric) tensor components. These components were found to be equal in magnitude for both enantiomers but opposite in sign. No evidence of magnetic contributions to the nonlinearity was found.


2

A n important property of this material is that the anisotropy (and the supramolecular organisation) of the L B samples can be manipulated by external factors (19). Because of the intimate connection between film structure and second-order nonlinear optical response it should therefore be possible to optimize and fine-tune the nonlinear optical response. We found that at least two experimentally controllable parameters have an influence on the anisotropy of the LB-samples. First, the dipping procedure (i.e. horizontal or vertical dipping) has a profound influence on the structure of the L B films (20). The symmetry of LB-films prepared by vertical and horizontal dipping was investigated by recording the S H intensity while rotating the samples around their surface normal. The rotation patterns obtained for a p-poiarized fundamental beam and a s-polarized second-harmonic beam are shown in Fig. 3. Both patterns clearly reveal a twofold symmetry, but the vertically dipped samples are clearly more anisotropic. Furthermore, the maximum signal intensity is about 50 percent higher for the vertically dipped sample. Second, we found that heating also influences the structure of the L B samples and consequently the SH-intensity generated by the film. To study the effect of heating, horizontally dipped LB-samples were heated to 220 "C (the melting point of the bulk material is 211 °C) at an average rate of 2 degrees/min. The material was kept at that temperature for 5 minutes and than cooled at an average rate of 4 degrees/min. Next, S H G rotation patterns were recorded before and after heating. From Fig. 3 it is clear that heating significantly increases the in-plane anisotropy. Furthermore, the maximum amount of SHG is more than a factor of two higher for the heated sample.



153

Rotation angle of the sample (degrees)

Rotation angle of the sample (degrees)

Figure 3, Second-harmonic generation versus the rotation angle of the sample for (a) horizontally (open circles) and vertically dipped (filled squares) sample, and (b) heated (filled squares) and unheated (open circles) horizontally dipped sample



154 The helicenebisquinone can also be used to achieve a new way of quasi-phase matching (21). Quasi-phase matching is important in frequency conversion processes, in which the phase relation between the nonlinear source polarization and the generated field can only be maintained over the distance of a coherence length. However, by reversing the sign of the nonlinearity after each coherence length, the phase relation between the source and the generated field will be restored, allowing the nonlinear signal to grow quasi continuously. In systems with polar order, for example electric field poled materials, this can be achieved by periodically poling the material. In chiral materials, the second-order nonlinear optical coefficients associated with chirality differ in sign for the two enantiomers. Therefore, quasiphase matched frequency conversion in periodically alternating stacks of the enantiomers of a chiral material should be possible. Since the nonlinearity in the L B - films of the helicenebisquinone is dominated by chirality, this material is an excellent candidate to demonstrate this new type of quasi-phase matching. We first tested the compatibility of both enantiomers by constructing films whose units were four layers of a single enantiomer, either (P)-(+)- or the (M)-(-). The films were composed of 32 layers comprised of eight identical (P/P/P...) or alternating (P/M/P...) units. Second-harmonic light generated in the samples was detected in transmission, where the coherence length is much larger than the thickness of the samples. In that case, the nonlinear response of each unit can be added. Hence, because of the chirality of the helicene, the second-harmonic intensity from films composed of a single enantiomer should increase quadratically with the total number of layers. On the hand, films composed of alternating stacks of the two enantiomers should exhibit no S H G . Such behaviour was experimentally observed. The results are shown in Table II.

Table II. SH-intensity in transmission of LB-films composed of stacks of the (P) (+)· and (MH-)-enantiomer of the chiral helicenebisquinone. Number of layers ^ 0 4 8 12 16 20 24 28 32

(P)-(+)-enantiomer SH-intensity (arb. u.) ^

(P)-(+)-enantiomer alternated With (M)-(-)-enantiomer SH-intensity (arb. u.)

0 1 3 7 9 21 22 35 46

0.1 0.3 0.1 0.5 0.1 0.6 0.1



155

Subsequently, the coherence length for the material was determined. Measurements were done in reflection, where the coherence length is much shorter, to avoid having to deposit a too large number of layers. Films were made consisting of two stacks (one for each enantiomer) with a varying number of layers. Such a procedure avoids possible interference of the SH-signal that is generated in transmission and reflected by the film/substrate and substrate/air interfaces. In addition, any interference of linear optical activity of the material is avoided. For an angle of incidence of 42.6°, the coherence length was determined to be approximately 48 layers (21). As a final step, LB-films were constructed with stacks of 48 layers, alternating both enantiomers. Table III clearly demonstrates that there is a continuous build-up of the second harmonic signal, thus demonstrating quasi-phase-matching in chiral materials. Table III. SH-intensity in reflection of LB-films composed of stacks of 48 layers of the (P)-(+)- and (M)-(-)-enantiomer of the chiral helicenebisquinone. Number of layers

SH-intensity (arb. u.)

stacks of 48 layers

48 96 144 192 288

1 4 9 14 32

Ρ P/M P/M/P P/M/P/M P/M/P/M/P/M

Conclusions We have given an overview of how chirality can be used to advantage in secondorder nonlinear optics. Since chiral materials are inherently noncentrosymmetric, second-order nonlinear optical effects can be observed in highly symmetric media. Furthermore, magnetic-dipole contributions are enhanced by chirality and can significantly increase the nonlinear optical response. A n important application of chiral materials in second-order nonlinear optics is the possibility of achieving quasiphase-matching in structures consisting of alternating stacks of the different enantiomers of the chiral material.

Acknowledgements We acknowledge the support of the Belgian Government (IUAP P4/11) and the Fund for Scientific Research-Flanders ( F W O V G.0338.98, 9.0407.98). T.V. is a postdoctoral fellow of the Fund for Scientific Research-Flanders.


156


References 1. Prasad, P.N.; Williams, D.J. Introduction to Nonlinear Optical Effects in Molecules & Polymers; Wiley Interscience: New York, 1990 2. Boyd, R.W. Nonlinear Optics; Academic, San Diego, 1992 3. Verbiest, T.; Houbrechts, S.; Kauranen, M . ; Clays, K.; Persoons, A . J. Mater. Chem. 1997, 7, 2175 4. Giordmaine, J.A. Phys. Rev. 1965, 138, A1599 5. Rentzepis, P.M.; Giordmaine, J.A.; Wecht, K.W. Phys. Rev. Lett. 1966,16,792 6. Kauranen, M . ; Persoons, A . Nonlinear Optics 1999, 19, 309 7. Verbiest, T.; Van Elshocht, S.; Kauranen, M . ; Hellemans, L.; Snauwaert, J.; Nuckolls, C.; Katz, T.J.; Persoons, A . Science 1998, 282, 913 8. Kauranen, M . ; Maki, J.J.; Verbiest, T.; Van Elshocht, S.; Persoons, A . Phys. Rev. Β 1997, 55, R1985 9. Wagniére, G. Linear and Nonlinear Optical Properties of Molecules; V C H , Weinheim, 1993 10. Louden, R. The Quantum Theory of Light, 2 ed.; Oxford, Oxford, 1983 11. Shuai, Z.; Brédas, J.L. Adv. Mater. 1994, 6, 486 12. Meijer, E.W.; Havinga, E.E. Phys. Rev. Lett. 1990, 65, 37 13. Kauranen, M . ; Verbiest, T.; Persoons, A. Journal of Nonlinear Optical Physics & Materials 1999, 8, 171 14. Yang, P.K.; Huang, J.Y. J. Opt. Soc. Am. Β 1998,15,1698 15. Beljonne, D.; Shuai, Z.; Brédas, J.L.; Kauranen, M . ; Verbiest, T.; Persoons, A. J. Chem. Phys. 1998, 108, 1301 16. Bloembergen, N . Nonlinear Optics 4 ed.; Benjamin, Reading, 1982 17. Maki, J.J.; Kauranen, M . ; Persoons, A . Phys. Rev. Β 1995, 51, 1425 18. Nuckolls, C.; Katz, T.J.; Van Elshocht, S.; Verbiest, T.; Kuball, H.-G.; Kiesewalter, S.; Lovinger, A.J.; Persoons, A. J. Am. Chem. Soc. 1999, 121, 3453 19. Van Elshocht, S.; Verbiest, T.; Katz, T.J.; Nuckolls, C.; Busson, B.; Kauranen, M . ; Persoons, A. accepted for publication in Nonlinear Optics 20. Van Elshocht, S.; Verbiest, T.; de Schaetzen, G.; Hellemans, L.; Phillips, K.E.S.; Nuckolls, C.; Katz, T.J.; Persoons, A. accepted for publication in Chem. Phys. Lett. 21. Busson, B.; Kauranen, M . ; Nuckolls, C.; Katz, T.J.; Persoons, A . Phys. Rev. Lett. 2000, 84, 79 nd

th


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