Ultrafast control of third-order optical nonlinearities in fishnet metamaterials

Abstract

Nonlinear photonic nanostructures that allow efficient all-optical switching are considered to be a prospective platform for novel building blocks in photonics. We performed time-resolved measurements of the photoinduced transient third-order nonlinear optical response of a fishnet metamaterial. The mutual influence of two non-collinear pulses exciting the magnetic resonance of the metamaterial was probed by detecting the third-harmonic radiation as a function of the time delay between pulses. Subpicosecond-scale dynamics of the metamaterial's χ⁽³⁾ was observed; the all-optical χ⁽³⁾ modulation depth was found to be approximately 70% at a pump fluence of only 20 μJ/cm² .

Ultrafast control of third-order metamaterials

OPEN

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Alexander S. Shorokhov, Kirill I. Okhlopkov, Jrg Reinhold, Christian Helgert, Maxim R. Shcherbakov, Thomas Pertsch & Andrey A. Fedyanin

prospective platform for novel building blocks in photonics. We performed time-resolved measurements was probed by detecting the third-harmonic radiation as a function of the time delay between pulses. Subpicosecond-scale dynamics of the metamaterials was observed; the all-optical modulation J/cm.

Articially nanostructured materials with novel electromagnetic properties, currently referred to as metamaterials, were originally introduced to enable the on-demand tailoring of their constitutive parameters. Negative refractive indices1,2, epsilon-near-zero phenomena3, form birefringence4, chirality5,6, and other properties of metamaterials have been reported. Because the constitutive relations for these materials consist of both linear and nonlinear terms, enabling articial control over electromagnetic nonlinearities is a very feasible task. Nonlinear metamaterials have constituted their own research eld for over a decade7, and experimental results vary, for example, from self-action nonlinearities in varactor-loaded magnetic metamaterials8,9 and magnetoelastic self-action10 to inverse phase-matching11 and light-controlled metamaterials12, together with novel low-loss all-dielectric nonlinear metamaterials1316.

In contrast to the case of macroscopic microwave and terahertz metamaterials, the natural obstacles imposed by nanofabrication limitations impede the possibility of scaling nonlinear metamaterials to the optical regime. The development of new nonlinear media for optical radiation is therefore crucial for applications in all-optical switching, and metallic metamaterials may represent a potential source of large plasmonic nonlinearities. Following the basic concepts of local-eld-enhanced metal nonlinearities17,18, plasmon-enhanced harmonic generation and wave mixing1922 have been observed in metamaterials and plasmonic nanosystems. Most importantly, the symmetry of nanostructured metamaterial may give rise to new nonlinear contributions because of its specic geometry23,24 or the specic symmetry of the currents of magnetic resonances2528.

The use of optical metamaterials and plasmonic nanosystems for all-optical switching has been extensively discussed27,29. The photoinduced modulation of linear dielectric constants in metamaterials via free-carrier generation in silicon30, graphene31 or aluminum29; the reorientation of liquid crystals32; and coherent control33,34 have been demonstrated. Notably, the shortest switching times have been achieved by utilising ultrafast free-electron gas heating and thermalization in plain metallic lms35,36, nanoparticles37, and nanorod metamaterials27; one drawback of these mechanisms lies in the necessity of high-power laser pumping with regenerative-amplier-scale intensities. Nevertheless, nonlinear susceptibilities are well known to be more highly sensitive to external stimuli than are linear susceptibilities, and femtosecond control over the optical nonlinearities in metamaterials has not been reported to date.

In this contribution, we report an experimental demonstration of the ultrafast modulation of the third-order optical nonlinearities of a shnet metamaterial excited at its magnetic resonance by femtosecond laser pulses. By observing the third-harmonic radiation generated as a function of the time delay between two consecutive pulses, we probed the photoinduced third-order nonlinear susceptibility dynamics. The experimental results reveal (3)

modulation on the subpicosecond time scale and relaxation times with a modulation depth of 70% under a very

Friedrich Schiller University

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Figure 1. (a) Schematic illustration of the studied shnet metamaterial. (b) Scanning electron micrograph of the sample. (c) Absorption spectrum of the sample acquired at 10 incidence. The dashed line indicates the carrier wavelength of the pump laser. (d) Schematic illustration of the experimental setup: HWP representsa half-wave plate, GT represents a laser-grade Glan-Taylor polarizer, the beams were chopped at frequencies of f1 and f2, BG indicates a 4mm thick Schott BG39 lter glass, PMT represents a photomultiplier tube, FCU represents a frequency-conditioning unit, and A represents an iris aperture. (e) Calculated at 1550nm E-eld distribution plotted in the horizontal plane sliced through the center of the MgO slab. White dashed line represents the borders of the hole perforated through the structure. (f) Calculated at 1550nm E-eld distribution superimposed with the normalized eld vectors plotted in the vertical plane sliced through the center of the unit cell depicted in (e). For both (e,f), scale bars denote 100nm.

modest pump peak intensity of 90MW/cm2 and a uence of 20J/cm2. The underlying microscopic picture of

nonlinear control based on free-electron gas heating and thermalization explains the ultrashort (3) relaxation times.

Results and Discussion

A shnet metamaterial of the same type studied in ref. 25 was used to demonstrate the all-optical control of its third-order optical nonlinearities. The sample consisted of a three-layer Au/MgO/Au heterostructure patterned with an array of rectangular holes and situated on a fused silica substrate. The dimensions, a scanning electron micrograph and the absorption spectrum of the sample are shown in Fig.1(ac), respectively. Careful experimental and numerical analyses revealed a magnetic resonance at a wavelength of 1.55m and polarization along the lesser of the hole sides. This resonance sustains the antisymmetric movement of free-electron currents in the two gold layers and causes the oscillation of a nonzero magnetic moment at the external electromagnetic eld frequency. Calculated E-eld proles excited inside the structure at 1550nm are provided in Fig.1(ef) and clearly illustrate this statement. Electric elds are in the reversed phase in top and bottom layers of the shnet metamaterial (Fig.1(f)) forming two plasmon waves propagating oppositely along top and bottom interfaces between gold and MgO layers. It leads to the formation of standing waves in the dielectric slab of the structure (Fig.1(e)). Based on the spectral full width at half maximum of the resonance, the lifetime of the mode can be estimated to be approximately 50fs.

Local eld enhancement has previously been observed in shnet metamaterials see, e.g. ref. 38resulting in enhanced nonlinearities. The third-order optical nonlinearities are of particular interest because of the large reported (3) values of bulk gold39 and the retardation peculiarities observed in metamaterials25. To probe the photoinduced modulation of (3), a setup based on an Er3+-doped ber femtosecond laser was built to observe

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Figure 2. Filled black dots: THG of the sample as a function of the time delay between pulses, as detected at the f1+f2 frequency of the chopper. Blue solid curve and dots: THG of the silica substrate as a function of the time delay between pulses, as detected at f1+f2. Inset: THG signal of the sample measured at f1 when the second beam was blocked as a function of the power of the rst beam. The solid red line represents a t to the power function f(x)=axb, indicating a power of b=2.90.1.

time-dependent third-harmonic generation (THG). The basic design of the setup is depicted in Fig.1(d). A train of 220fs pulses with a central wavelength of = 1560nm was split into two beams with an approximately equal power; the rst and second beams were focused by an objective lens with a numerical aperture of NA= 0.5 and a working distance of WD = 14 mm onto the sample surface at a mutual angle of approximately 20 aer passing through a polarization conditioner and a delay line, respectively. The horizontally polarized beams, corresponding to the resonant excitation of the sample, were brought together to a waist with a diameter of 25 m, leading to a maximum single-beam peak intensity of 90 MW/cm2 and a uence of 20 J/cm2 in the plane of the sample. Based on the reproducibility of the THG values obtained from the same sample area at the same pump powers, it was concluded that the sample suered no irreversible damage. A double-frequency 1:1 optical chopper was installed before the objective lens to chop the rst and second beams at frequencies of f1 =500 Hz and f2 = 600 Hz, respectively. This enabled the measurement of both THG contributions originating from each beam independently, locked in at either f1 or f2, and the THG resulting from the interaction of the beams, locked in at a frequency of f1 + f2. The use of two types of long-pass color lters revealed that the detected signal arose from light with a spectrum lying between 510 nm and 530 nm. This range includes the THG wavelength of = 520nm, demonstrating that the detected signal can be attributed to the THG and not to any other source, e.g., three-photon luminescence.

The THG from either of the beams was measured by analyzing the PMT signal at the frequencies of f1 and f2 separately, with the aperture removed. Blocking one of the beams yielded the same THG signal from the other. As expected, a cubic (curved slope equal to 2.9 0.1) dependence of the single-beam THG intensity on the pump power was observed (see the inset of Fig.2).

However, a complicated picture of the mutual modulation of the THG signal was observed upon bringing the two beams together at the sample site. The normalized time-resolved THG dependence measured by locking in the PMT signal at f1+ f2 is shown by the lled dots in Fig.2. Here, the abscissa values indicate the time delay between pulses. Superimposed on the samples THG dependence is the normalized THG dependence measured in the silica substrate. The maximum THG signal from the sample measured at the lock-in reference frequency of f1+f2 was approximately 10 times higher than the signal from the substrate and approximately 3 times higher than the THG signal from the sample measured at f1 with the second beam blocked. On the one hand, the THG of the sample at close-to-zero time delay values resembled the shape of the cross-correlation function, indicating a coherent process of THG enhancement. On the other hand, there existed time delay values, e.g., from 0.5 ps to 1.5 ps, at which the cross-correlation function was nearly zero and the pump beam was seen to exert a signicant inuence on the THG from the probe beam. The observed eect can be explained in terms of modication of the electron plasma nonlinear susceptibility under the strong impact of the pump laser beam with the following relaxation of the electronic subsystem through the interaction with the lattice. Such processes will be considered in more details further in the manuscript.

When a powerful laser pulse impinges on a gold lm, it modies the linear dielectric constants of the medium, as many authors have previously shown35,36. This implies that in a pump-probe experiment, when the stronger of the two pulses drives the (electronic) system out of its thermal equilibrium state and the weaker of the two probes this transient state, the weaker pulse is modulated by the stronger one. The specic form of the temporal dependence of the dielectric permittivity, (t), is dened by the microscopic dynamics of the electron gas evolution under laser pulse stimulation. In the case of gold and the pump photon energy used in this study,

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Figure 3. The relative change in the eective third-order nonlinear susceptibility of the shnet metamaterial as a function of the time delay between the pump and probe pulses (black dots) and its t to Eq. (7) (red curve). The gray dashed area represents the normalized cross-correlation function of the laser pulses. Inset: illustration of the photoinduced relaxation processes occurring in the structure.

the following processes aect the linear optical properties of the sample: (a) the intraband photoexcitation of electrons and the formation of a non-equilibrium electron distribution, (b) electron thermalization and the establishment of a new electron gas temperature, (c) electron-phonon relaxation, and (d) energy transfer from the gold to the environment; see the inset of Fig.3. Process (a) has been shown to occur in the sub-100 fs regime37; hence, it is regarded as instantaneous with respect to the pulse length used in this paper. Process (d) is slow, with a relaxation time of hundreds of picoseconds. This process is minimally important with regard to the present research because both the linear and nonlinear susceptibilities of noble metals can be reasonably described based on the properties of the electronic subsystem40. Finally, the characteristic relaxation times of processes (b) and (c) are in the subpicosecond range, and thus, these processes explain the observed THG dynamics.

The effects on the electronic subsystem can contribute to the transient nonlinear response of a meta-material in three different ways: (i) changes in the linear transmittance coefficient at both the fundamental and third-harmonic wavelengths, (ii) modulation of the local field factor of the structure at both the fundamental and third-harmonic wavelengths, and (iii) modification of the effective nonlinear susceptibility of the sample. Using the finite-difference time-domain (FDTD) method, we theoretically and numerically calculated the relative contributions of the terms related to (i) and (ii), which are equal to 103104 and thus cannot explain the observed modulation in the third-harmonic generation signal. Therefore, these contributions will be neglected.

The general expression for nonlinear third-order polarization in the isotropic response approximation can be written as follows41:

(3) 3

+ +

p t L E t E t

(3) ( , ) ( ) ( ) ( ) (1)

1 2

Here, E1 and E2 are the electric elds that correspond to the pump and probe pulses, respectively; is the time delay between them; and L is the local eld factor at the fundamental frequency. The local eld factor of the sample at the third-harmonic frequency is on the order of unity; therefore, we neglect it. Moreover, for simplicity, we will assume that the eective nonlinear susceptibility of the sample, (3), is a real scalar value. It can be represented as

(3) = + ( )

0

(3) (3) , where 0(3) is the non-disturbed static nonlinear susceptibility of the metamaterial and

(3)() is the time-dependent contribution. The overall time-averaged THG signal from the sample can then be written as follows:

+ + + + .

(3) (3) 2 6

I L E t t E t t dt

samp ( ) ( ( )) ( )cos ( )cos ( ) (2)

01 02

+ =

E t A

( ) exp t

02 2

2 2 and

3

^

6

0

+ 2 are dened as Gaussian. Aer the phase-averaging procedure42, we can deduce (3)() as a function of the measured dependences (see the

Supplementary Information):

Here, the envelopes =

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E t A

( ) exp t

01 1

( )

( )

( )2

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(3) ( ) 1 ( )( ) 1 (3)

I I

samp

norm

sub

norm

( ) ( )

+

=

.

(3)

The norm superscript denotes the fact that both I() dependences should be normalized with respect to unity before being substituted into the equation. Here, () is a function of the pulse parameters:

= ++

( ) 1 1 9 9

,

I I

2

4 2

3 2 01

02

01 e e

I I

4 2

3 2

2

(4)

where

I A

01 1

2 and

I A

02 2

2; can be obtained from the normalized cross-correlation function of the pulses.

Generally, Eq.(3) is valid for all delay times . However, in the case of large , the relative error of the experimental Isub dependence data is too high to achieve valid results. When is larger than a couple of , we can neglect the coherent eects and deduce the relaxation of (3)() by measuring the mixed signal Isam(f1+f2) and normalizing it with respect to the single-beam signal Isam(f1) (see the Supplementary Information):

(3) = +

( )

I f f

I f

(3)

2

( )( )

( ) , (5)

3 1 2

3 2

where is the proportionality coefficient between the lock-in signal values detected at the frequencies of f2 and f1 + f2; in our case, = 2.3. By stitching together Eqs(3) and (5) at = 800 fs, one can obtain the overall relative photoinduced third-order nonlinear susceptibility dynamics of the sample, as shown in Fig.3 by means of data points and their corresponding error bars. The dependence corresponds to a standard transient process that involves free-electron plasma; however, this is the rst observation of the transient photoinduced dynamics of the nonlinear susceptibility of a material.

Here, we quantify the excitation and relaxation times of

/

(3) (3). For a weak perturbation of the electron gas, the response function of the system can be presented in the following form35:

=

0

S t H t e e

( ) ( ) 1 , (6)

t t 0 1 2

( )

where H(t) is the step function. The rst term introduces a delayed rise of the response function with a time constant 1, which characterizes the energy transfer between nonthermal electrons via electron-electron interactions.

The exponential decay with a characteristic time of 2 describes the relaxation of the excited electrons to the lattice temperature. Because the pulse duration is comparable to the characteristic electron gas relaxation times, the response function must be convolved with the pulse shape. Upon accounting for the nite pulse length, one can nally obtain the following expression for t0:

=

S t A e e t

( ) 1 erf ,

(7)

( )

1 2

t t

p

where p is the pulse width, A is the normalization factor, and erf(x) is the error function. Eq.(7) is in good agreement with the experimental data; the t parameters are A =2.10.4, 1=28070fs, and2=50040fs, and the pulse width is xed at p = 220 fs. These values are in good qualitative agreement with those reported previously35,36, further supporting our initial hypothesis regarding the origin of the observed (3) modulation.

Figure3 explicitly illustrates how the nonlinear susceptibility of a shnet metamaterial evolves over time once free electrons are being excited via intraband transitions. Please note that the relative (3) modulation reaches 70% at a very modest pump uence of 20J/cm2. A similar modulation depth of the linear response of shnet metamaterials has been achieved at much higher pump levels of approximately 1 mJ/cm2 30,43. Further increase of the modulation can be envisioned in other plasmonic geometries with larger Qs of the resonance4,44,45. We have, therefore, successfully utilized the fact that the nonlinear response of a medium is much more sensitive than the linear response to the microscopic processes to establish a novel and efficient platform for all-optical switching.

Conclusions

The subpicosecond all-optical modulation of third-order nonlinearities in a shnet metamaterial was demonstrated via the third-harmonic generation pump-probe technique. The observed modulation, with a characteristic time scale of less than 1ps, can be ascribed to the ultrafast relaxation processes occurring inside the metal portions of the structure. The demonstrated nonlinear susceptibility modulation of approximately 70% for low pump uences of 20J/cm2 is much higher than that of the linear susceptibility, which could be a useful feature in modern all-optical telecommunication technologies.

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Acknowledgements

This work was supported by the Russian Science Foundation (Grant 14-12-01144, experimental part) and the Russian Foundation of Basic Research (modeling results).

Author Contributions

C.H. fabricated the sample; J.R. provided linear spectroscopic measurements, SEM measurements and helped to develop the nonlinear measurements; A.S.S., K.I.O. and M.R.S. constructed and aligned the pump-probe optical instrumentation, performed the experiments, A.S.S. and M.R.S. developed the theoretical description; A.A.F. and T.P. initiated the project and coordinated the work; all authors participated in the discussion of the results and contributed to the preparation of the nal manuscript.

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Additional Information

Supplementary information accompanies this paper at http://www.nature.com/srep

Competing nancial interests: The authors declare no competing nancial interests.

How to cite this article: Shorokhov, A. S. et al. Ultrafast control of third-order optical nonlinearities in shnet metamaterials. Sci. Rep. 6, 28440; doi: 10.1038/srep28440 (2016).

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