ICTON 2014 Th.B5.1

978-1-4799-5601-2/14/$31.00 ©2014 IEEE 1

On Nonlinear Optical Properties of Chiral Materials

Concita Sibilia, Alessandro Belardini, and Fabio Antonio Bovino* Università di Roma La Sapienza- Dipartimento di Scienze di Base e Applicate per l’Ingegneria,

Via Scarpa 16,00161 Roma, Italy *Quantum Technologies Lab- Selex- Ex, Via Puccini 2,16154 Genova, Italy

e-mail:Concita.sibilia@uniroma1.it

ABSTRACT An overview of different nonlinear optical phenomena occurring in nanopatterned materials is presented. In particular a discussion about second order nonlinear effects is reported, for both natural and/or artificial chiral materials. Keywords: optics, plasmonics, nonlinear optics, chiral materials.

1. INTRODUCTION Chirality is equivalent to the absence of mirror plane symmetry and the medium exhibits optical activity, i.e. it rotates the state of polarization of light [1,2]. A microscopic model to describe the chirality is founded on the electron path in the molecule: as the electrons of chiral molecules are displaced from their equilibrium by the application of the electromagnetic field, they are forced to move along helical-like paths. This gives rise to an induced magnetic dipole moment of the molecules in addition to the electric dipole moment, therefore chiral molecules respond to both the electric and magnetic component of the field [1,2]. This simple model explains the role of magnetic effects in the optical activity. Optical activity recently has inspired a great effort in developing active photonic chiral metamaterials [3] i.e. artificial material designed to deliver an unusual electromagnetic response. However optical activity effect is a linear optical effect, i.e. it results from the linear response of the molecular medium to the electromagnetic field.

Optical second harmonic (SH) generation is a very sensitive method for the study of symmetry properties of surfaces and materials and thus was widely used for the characterisation of chemical and biological samples [4]. In this frame characterisation of the chirality by second harmonic generation assumes a large interest due to the great scientific importance of chiral molecules in life-science and pharmaceutical industries [5]. In fact among the different nonlinear optical processes, second harmonic generation (SHG) is one of the most investigated. Briefly, polarization in a dielectric material can be expanded in terms of applied electric field. Second harmonic generation corresponds to an optical process of coherent radiation from electric-dipoles forming in the nonlinear optical material. In particular, SHG is related to the second term of the polarization expansion, thus it can be obtained only in materials which are noncentrosymmetric i.e. possess no centre of inversion symmetry. From the experimental point of view, the frequency of the incoming – fundamental – beam, ω, is doubled by the second order optical susceptibility χ(2)

ijk of the material. The SHG processes, along with the structure of the nonlinear optical tensor, are strongly dependent on the crystalline structure of the material, thus by choosing the appropriate polarization state for the fundamental beam, different amplitude and polarization state of the nonlinear optical response can be selectively addressed.

Particularly interesting is the SHG of chiral materials [6,7,8]: several experimental results indicate that multipolar contributions are necessary to accurately explain the nonlinear optical activity [2]. In this case the second order nonlinear polarization (at 2ω) consists of a series of multipole terms [5,6,9]:

( ) ( ) ( ) ( )12 2 2 2eff DP P jkQ k Mω ω ω ω

ω= − − ×

where , ,DP Q M

represent the electric and magnetic-dipole polarization, electric-quadrupole polarization and nonlinear magnetization, respectively.

By means of SHG is possible to evidence the nonlinear optical activity ; it can be detected by using different techniques, such as the optical rotatory dispersion (SHG-ORD), the circular dichroism [2] (SHG-CD), or by detecting the SHG linear difference (SHG-LD). The above mentioned techniques have been recognized as tool to study the surface chirality, although with some limitation to discriminate the magnetic dipole or electric dipole interaction. Other methods, such as the continuous polarization method [2], reveal very sensitive to detect the nonlinear optical activity of materials in the form of films several wavelength tick: in practice the polarization state of the pump beam is varied and the linear polarization state of the SHG signal is detected.

In what follows we describe how chirality can be detected by using SHG in both natural and artificial structures. As natural material we describe SHG from Bacteriorhodopsin, and as artificial materials we describe gold nanowires and gold nanospheres.

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2. SECOND HARMONIC GENERATION FROM NATURAL CHIRAL MATERIALS

As also reported in the ref. [10], the transmembrane protein Bacteriorhodopsin (BR) is one of the simplest known active membrane transport system. It functions as a light driven proton pump converting light energy into a proton gradient across the bacterial cell membrane. BR has a well-established structure and the orientational averages connecting the retinal frame to the protein frame are also known with a high degree of accuracy. Trimers of BR proteins are placed in a hexagonal two dimension lattice within the purple membrane, forming thereby a real crystalline structure similar to a photonic crystal or to a natural optical chiral metamaterial. Each BR monomer contains a covalently bound retinal chromophore, presenting its own transition dipole, which is responsible for its outstanding quadratic nonlinear optical response enhanced by the protein environment, as well as for the light absorption in the visible range. The chromophore retinal axis is oriented at an angle of 23° ± 4° with respect to the plane of the purple membrane so to form an isotropic conical polar distribution around the normal. In the ref. [11] we studied the noncollinear SHG of an oriented BR film prepared by using the asymmetric electrostatic interaction of the surface charge of the membrane fragments with a charged support surface. The electrophoretic deposition technique allows to grow a 4 µm thick oriented film onto a substrate covered by a 60 nm thick ITO film. BR reveals a chiral behaviour with a SHG signal which contains a contribution from the second order nonlinear magnetization.

In order to study the full polarization content of the generated second harmonic signal, we have studied the evolution of the Stokes parameters as a function of the input linear polarization state of the two pump beams in a SHG noncollinear scheme. The experiment has been performed by means of a mode-locked femtosecond laser system tuned at λ = 830 nm. The polarization of both beams was varied with two identical rotating half wave plates in the range -90°-+90° degrees ( p

-polarized pump beam: 1ϕ =0°, and s

-polarized beam: 1ϕ = ± 90°).

The average input power of 125 mW was varied up to 350 mW, with 108 W/cm2 as maximum level of input intensity. The SHG was then split in two signals by a polarizer beam splitter (PBS). Polarization states of SHG signal ( s

and p

, +45°and -45°, left circular polarization (Lc) and right circular polarization (Rc)) were detected and mapped as a function of the linear polarization state of the two input beam. We have also measured the SHG under the application of a static magnetic field: the presence of a static magnetic field provide an interplay among chirality and magnetism, which result extremely interesting in particular considering the second order nonlinear effect. The polarization map is slightly modified by the presence of an applied static magnetic field of 0.1 T. An example of SHG polarization map is shown in the Fig. 1.

(a) (b)

Figure 1. Polarization map of SHG signal with a pump beam of 50 mW, under static magnetic field of 0.1 T (a) , and without magnetic field (b).

3. SECOND HARMONIC GENERATION FROM ARTIFICIAL CHIRAL MATERIALS

In order to enhance the SH conversion efficiency a large variety of metal nanopatterned surfaces was proposed as possible planar substrate such as nano-holes [12], nano-wires [13,14], nano-rods [15]. In these structures the electric field intensity can increase up to several order of magnitude due to the mutual effect of field localization near the sharp edges and localized surface plasmon excitation. During past years, lot of effort was devoted on the study of linear and nonlinear response of artificial surfaces that exploit together metal nano-patterning with a 3D- [16] or 2D-chiral [17] metamolecules. Also the possibility to obtain chirality (or its sign, optical activity) with non-chiral elements was studied in the past [18], but it is worth to note that only very recently this possibility has awaken a new interest as demonstrated in refs [19,20,21] where the phenomenon (that can be referred as extrinsic chirality) was characterised from the linear point of view. Here we report experimentally a nonlinear extrinsic chirality, or circular dichroism, of the second harmonic field (800 nm – 400 nm conversion, by means of a 150 fs source) generated by self-organized gold nanowires arrays with sub-wavelength periodicity (160 nm) [22]. Such circular dichroism is the evident signature of the sample morphology and in this material arises from the curvature of the self-assembled wires, producing a lack of symmetry at oblique incidence. High

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visibility (more than 50%) was obtained in the second harmonic generated field and the results were compared, both in the linear and nonlinear regime, with a reference sample with straight wires. The nonlinear circular dichroism is the difference between the generated second harmonic field intensity (at s- or p-polarization state) obtained from the left-handed circular polarized light and the right-handed one divided by the average total generated intensity

( )2 2

2 2 2L R

L R

I ISHG CD

I I

ω ω

ω ω

−− =

+.

The measurements highlight that extrinsic chirality arises when the wave vector direction k̂ , the normal to the

sample surface n̂ and the direction of the curvature R̂ do not lay on the same plane, the handedness of the

chirality can be expressed by the sign of the triple product of the formers three vectors (here called EXCH as

‘extrinsic chirality’): 1 ˆˆ ˆEXCH R k nR

= ⋅ × being R the radius of curvature of the wires and the R̂ is the average

direction of the radii of curvature. From the nonlinear point of view the second harmonic signal is generated

from the wires mainly by the magnetic dipole term or Lorentz term [23]

222

e iP J B

m iω ω ωωω ω γ

= × −

,

where e is the modulus of the electron charge, m is the electron effective mass, γ is a damping coefficient taking into account ohmic losses.

-2

-1

0

1

2

-40 -20 0 20 40

b08 400nm delta H downb08 400nm delta H up

(a) (b)

Figure 2: (a) Gold nanowires; (b) SHG-CD as a function of incidence angle.

Another artificial structure, is composed by self-ordered dielectric nanospheres partially covered by thin (10 nm) Au layer (see Fig. 3). Also for such as material we have studied the optical second harmonic signal generated by the structure under different polarization states excitation [24]. In particular SHG-CD reveals the presence of a geometrical induced chiral response of the nanospheres surface that depends on spheres radius and on the coupling of the electromagnetic field between the spheres. The effect of the plasmonic and optical resonances on the magnitude of the second harmonic signal has been also investigated. The results show a cooperative effect of localized plasmonic resonance of gold and collective resonant mode of the dielectric spheres.

-2

-1

0

1

2

-40 -20 0 20 40

260nm shg-cd p340nm shg-cd p426nm shg-cd p

Incidence angle (deg)

SH

G-C

D

(c) Figure 3. Scheme of the polystyrene spheres (a) and the one with Au on the top (b). SHG-CD on samples with

different diameters (c).

4. CONCLUSIONS

We presented the evidence of intrinsic and extrinsic optical activity in natural and artificial chiral materials. The SHG is an efficient tool to evidence the chiral response of materials.

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