научная статья по теме FEMTOSECOND PULSE SHAPING WITH PLASMONIC CRYSTALS Физика

Текст научной статьи на тему «FEMTOSECOND PULSE SHAPING WITH PLASMONIC CRYSTALS»

Pis'ma v ZhETF, vol. 101, iss. 12, pp. 885-890 © 2015 June 25

Femtosecond pulse shaping with plasmonic crystals

P. P. Vabishchevich, M. R. Shcherbakov, V. O. Bessonov, T. V. Dolgova, A. A. Fedyanin^ Faculty of Physics, Lornonosov MSU, 119991 Moscow, Russia Submitted 18 May 2015

The temporal shaping of femtosecond laser pulses reflected from a one-dimensional plasmonic crystal using a commercially available polymer grating coated with a silver film is experimentally demonstrated by time-resolved measurements of the intensity correlation function. Shaping is achieved by the excitation of surface plasmon-polaritons with a lifetime comparable to the 130 fs laser pulse duration. The variety of data obtained demonstrate the flexible shaping of fs-pulses by delaying, advancing, splitting, broadening, compressing, and changing the topological properties of the pulse with the plasmonic crystals under study.

DOI: 10.7868/S0370274X15120036

1. Introduction. Femtosecond laser pulse shaping technology [1,2] has found many applications in fundamental science and applied research, e.g., in studies of light-matter interaction [3], the coherent control of quantum states [4,5], all-optical switching [6], biome-chanical and biomedical applications [7,8], and optical communications [9-11]. All these applications require maximal flexibility in the design of femtosecond pulse electric fields. The Fourier transform pulse shaping technique [12,13] involves a spatial light modulator placed in the plane of symmetry of a 4/-zero-dispersion compressor, which modifies the individual frequency components of the spectrally dispersed pulse. The direct space-to-time pulse shaping is also propitious for communication applications [14-16]. Another approach is pulse reshaping by light-matter interactions [17-18]. The main idea behind this approach is the use of ultrafast processes with durations of a few hundreds of femtoseconds, which can be temporally mixed with femtosecond laser pulses. The use of surface waves in the temporal reshaping of femtosecond pulses was theoretically suggested in Ref. [19]. The earliest experimental works reported a femtosecond pulse delay induced by resonant surface plasmon-polariton (SPP) excitation [20,21]. Later on, temporal pulse reshaping was demonstrated experimentally [22-25]. These pulse modifications strongly depend on the interplay between the parameters of the fs-pulse and SPP resonance. For example, in plasmonic crystals [26, 27], the SPP lifetime varies from several tens of femtoseconds to several picoseconds in the spectral vicinity of a plasmonic band gap (PBG). Significant differences in the nature of the fs-pulse distortion were found for the SPP states at two PBG edges, resulting in a

-^e-mail: fedyanin@nanolab.phys.msu.ru

sharp contrast in their lifetimes [28, 29] .In this paper, the controllable reshaping of a femtosecond laser pulse reflected from a digital versatile disc (DVD)-based plasmonic crystal is reported. The reshaping of fs-pulses is demonstrated by time-resolved measurements of the intensity correlation functions. Various pulse-shaping options, namely, broadening, compression, delaying, advancing, and splitting, are achieved by the spectral tuning of the pulse carrier wavelength in the vicinity of surface plasmon resonances.

A DVD comprises a multilayer grating consisting of a polycarbonate substrate, a set of thin active layers, an intermediate reflective silver layer with a thickness of 50-100 nm, and a polycarbonate superstrate. Commercial discs have been proven to be a convenient medium for observing SPP resonances [30,31]. The polycarbonate top layer was mechanically removed to observe SPPs at the air-metal interface. Studies of the remaining layers show that the DVD-based plasmonic crystal has a period of 750 nm and a modulation depth of 60 nm, as depicted in Fig. la.

The reflection spectra of the sample were measured for s- and p-polarized light. While no resonant features were detected for the s-polarized light, the reflection spectra, measured for the p-polarized light for different angles of incidence 0 shown in Fig. lb have pronounced resonances related to the SPP excitation at the air-metal interface; their angular spectral position is associated with the SPP dispersion. Intersections of the dispersion curves achieved at normal light incidence and at 0 = 21° lead to the formation of PBGs. The dispersion curves of the SPP excitation define the operating spectral range of the plasmon-based pulse shaper.

Two experimental configurations (described in Sec. 3) were considered for ultrafast studies. The first

d = 60 mil

p = 750 nm

h = 50-100 mil Polymer substrate 6 (deg)

0 10 20 30 40 50 60 70

1.0 0.5 0

<*! 0.6 0.2

"I

:(c) A

11 M i

|(d)

...... ........

650 700 750

X (nm)

800

Fig. 1. (a) - Scanning electron microscopy image and scheme of the DVD-based plasmonic crystal sample, (b) -Reflection coefficient of the plasmonic crystal as a function of wavelength A and angle of incidence 6 measured for p-polarized incident light. Data within the grey rectangle are not available, (c) - Reflection spectrum for 6 = 67". (d) - Reflection spectrum for 6 = 1"

configuration is the case of 9 = 67° with the single surface plasmon resonance located far from the PBGs, as shown in Fig. lc. This configuration produces a Fano line shape caused by the interference of directly reflected light and the light reradiated by SPPs [32-34]. The reflectance R(oj) = |r(w)|2 is represented by a complex sum of the nonresonant reflection of the incident radiation and the resonance profile of the SPP with a Lorentzian line shape:

r(w) = C0 +

/IV

1(f)

OJ -0JR-\- iV

(1)

where Co is the nonresonant reflection amplitude, which is considered independent of uj because the nonresonant contribution varies insignificantly relative to the SPP-induced reflection modifications; fe'1^ is the oscillator strength; lur is the resonance frequency, and V is the SPP resonance width.

Another case comprises a PBG observed at the near-normal incidence found for A = 750 nm. The reflection spectrum shown in Fig. id is a superposition of two resonances with Fano-type line shapes. The bi-resonant shape of the spectrum makes it futile to attempt to determine the actual width of the PBG: the resonant frequencies cjr1 2for the PBG edges lie somewhere between the reflection maxima and minimum. Such a complex reflection spectra of the plasmonic crystal should lead to the pulse shaping of the reflected femtosecond laser pulses, which can be controlled by tuning the carrier wavelength or the angle of incidence.

2. Correlation function measurements. The time-resolved response of the plasmonic crystal was studied using an intensity correlation function measurement setup based on a Ti:sapphire laser generating a train of 130 fs pulses; for details of the experimental setup, see Ref. [22]. The intensity correlation functions (CFs), Icf(t), were measured to determine the effect of the surface plasmons on the femtosecond pulse shape. Here, r is the time delay between the laser pulse reflected from the sample and the reference laser pulse. The measured correlation functions were compared using the autocorrelation functions (ACFs) obtained after azimuthally rotating the sample by 90°. Both the CFs and the ACFs were then fitted to the Gaussian function if possible, and the broadening and shifts of the CFs and ACFs were acquired. For the single resonance case, the electric fields were numerically reconstructed based on the Fano resonance model using the procedure described below.

The electric field amplitude of the laser pulse E\(uj) is modeled by a Gaussian function with the carrier frequency wo, amplitude Au, and pulse duration to- The electric field amplitude is described in the spectral domain as

E1(uj) = Aue

and in the time domain as

o)2/2

E1(t)=Ae-t2/2t »e-

icoot

(2)

(3)

Eqs. (1) and (2) determine the electric field Eo{uj) of the pulse reflected from the sample:

En (w) = Ei{ui)r{ui A^e-'o("-"»)2/2 (C0 +

jVei4

UJ — ojr + «r

(4)

According to the convolution theorem, this pulse has the following shape in the time domain:

E2(t) = J Ae-f'2^ x

— OO

e-iu0t' _ t')+C06(t - t'fjdt', (5)

where H(t) is the Heaviside function. In the experiment, pulse Eo{t) was spatially combined at the nonlinear crystal with the reference laser pulse E\(t) and the former was controllably delayed by r with respect to the latter. The measured intensity of the second-harmonic radiation is proportional to the second-order intensity correlation function:

/cf(t)~ J |£i(r-i')|2|£2(r')|A'. (6)

The fitting parameter set (</>, A, /, T, ojr, Co) can be adjusted to numerically evaluate Eq. (6) and fit it to the experimentally obtained correlation functions.

The spectral dependence of the CF measured for the carrier wavelength of fs-pulses, An = 2-kc/luo, tuned from 720 to 780 nm in 1 mil increments for the near-band-gap case is shown in Fig. 2b. Only a slight modification of the

720 730 740 750 760 770 780 A, (nm)

Fig. 2. (a) - Reflection coefficient for the plasmonic crystal sample as a function of wavelength A measured for 0 = 1". (b) - Experimental spectral dependence of the normalized correlation function in the spectral range of the plasmonic band gap

CF within the experimental uncertainties is observed for the long-wavelength resonance. This result means that the lifetime and/or amplitude of the SPP excitation are small relative to the lionresonant contribution. For the short-wavelength band-gap edge at An = 740nm, the CF is significantly modified, and the plasmonic impact becomes obvious. Broadening of the CF is detected in

the spectral range from An = 733 nm to An = 745 nm, which is accompanied by a temporal shift of the CF maximum by up to 100 fs for An = 740 nm. A series of CFs measured for six carrier wavelengths in the vicinity of the PBG edge as shown in Fig. 3 reveals a clear double-peaked pulse structure.

737 nm

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