An optimization procedure for the design of all-optical switches based on metal-dielectric nanocomposites

Albert S. Reyna; Cid B. de Araújo

doi:10.1364/OE.23.007659

1. Introduction

Ultrafast all-optical switches (AOS) are essential components of high-speed photonic networks and the efficient control of light-by-light by using nonlinear (NL) media is of great interest nowadays [1–5]. For selection of materials with proper third-order susceptibility, $χ^{(3)}$ , for AOS, two figures-of-merit are considered: $T = | α_{2} λ {(n_{2})}^{- 1} |$ and $W = | Δ n {(α_{0} λ)}^{- 1} |$ , where $λ$ is the laser wavelength, $α_{0}$ is the linear absorption coefficient, $α_{2} \propto Im χ^{(3)}$ is the two-photon absorption coefficient, $n_{2} \propto Re χ^{(3)}$ is the third-order refractive index and $Δ n$ is the maximum variation of the refractive index that can be induced in the material. $T < 1$ and $W > 1$ are required to obtain efficient AOS; hence, NL materials should present fast response, high transmittance, large NL refractive index and small NL absorption coefficient. Unfortunately, large $n_{2}$ normally corresponds to large $α_{2}$ [6], and therefore it becomes difficult to find proper materials for efficient AOS [7]. Also, one should pay attention that the highly NL materials available present high-order nonlinearities (HON) that may affect the evaluation based on the third-order susceptibility only.

Among the physical systems considered for AOS the metal-dielectric nanocomposites (MDNCs) with metallic nanoparticles (NPs) deserve special attention due to their high optical susceptibility, ultrafast response and the possibility of changing their NL susceptibility by changing the NPs volume fraction, f – the ratio between the volume occupied by the NPs and the host [8–12]. For instance, it was reported that gold NPs embedded inside an oxide glass film improved T by more than one-order of magnitude at 800 nm [10]. Limitations for use of MDNCs are the large linear optical absorption at the localized surface plasmons (LSP) resonance frequency and strong NL absorption [13–16]. In principle the optical response of MDNCs varies with f [14], the NPs environment [17, 18], the size and shape of NPs [19, 20], and the laser wavelength [20]. The NL response of MDNCs is described by effective susceptibilities that contain information on the NPs and the host material. Enhancement, decrease and even suppression of specific NL susceptibilities of MDNCs can be obtained varying f and the incident laser intensity [21–23].

In this work we applied the nonlinearity management procedure of [21–23] in order to demonstrate the optimization of AOS in proof-of-principle experiments with metal-colloids. Section 2 describes the samples preparation with silver (Ag) NPs suspended in acetone and experimental details. Section 3 presents the NL characterization of samples with various NPs volume fractions for different laser intensities. Considering the measured NL parameters it is shown that the nonlinearity of MDNCs can be controlled to obtain figures-of-merit for all-optical switching that may be enhanced by about two-orders of magnitude. Section 4 presents a summary of the results.

2. Experimental details

Initially colloids containing Ag NPs suspended in water were prepared following the method presented in [24]. 90 mg of AgNO₃ were diluted in 500 ml of water at 100°C; 10 ml of 1% sodium citrate solution was added for reduction the Ag⁺ ions, and later was boiled and strongly stirred for 1 h. A colloid with Ag NPs of various shapes was obtained. Subsequently, photofragmentation of the NPs was performed by irradiation of the pristine colloid, under slow stirring, using the second harmonic beam at 532 nm obtained from a Nd: YAG laser (8 ns, 85 mJ/pulse, 10 Hz) for 1 h, according to [25]. The photofragmentation of the NPs is due to their melting and vaporization because of the large absorption of the laser energy by the particles and low heat-transfer for the hosting medium [26, 27]. After photofragmentation metal-colloids with $0.5 \times 10^{- 5} \leq f \leq 2.5 \times 10^{- 4}$ were obtained by adding 20 µl to 300 µl of the Ag-water suspension in 1 ml of acetone. The Ag NPs do not aggregate due to the sodium citrate molecules attached to their surface; the shape and size of the NPs remained unchanged for at least 3 months.

The linear absorption spectra were measured using a commercial spectrophotometer. The light source for the NL measurements was the second harmonic beam at 532 nm of a Q-switched and mode-locked Nd: YAG laser that delivers selected single pulses of 80 ps with repetition rate of 10 Hz.

Z-scan [28] and Kerr shutter [29] experiments were performed to characterize the samples. In the Z-scan setup the laser beam was focused by a 10 cm focal length lens (beam waist: 20 µm) on a sample with thickness of 1 mm, contained in a quartz cell. Photodetectors placed in the far-field region, with adjustable apertures in front of them, were used to measure the intensity transmitted by the sample in different Z positions along the beam propagation direction. Closed-aperture (CA) and open-aperture (OA) Z-scan schemes were used. A reference channel was used to improve the signal-to-noise ratio as in [30]. For the Kerr shutter setup the laser beam was split into probe and pump beams with relative intensities: $I_{p r o b e} = 0.1 (I_{p u m p})$ . The angle between the beams was 2.3° and the angle between their electric fields was 45°. Both beams were focused inside the sample by a 10 cm focal length lens. When the two beams overlap spatially and temporally inside the sample, the pump beam induces a NL birefringence that induces rotation of the probe beam electric field. Then, a fraction of the transmitted $I_{p r o b e}$ by the sample passes through a polarizer crossed to the input probe beam electric field. A detector was used to record the transmitted $I_{p r o b e}$ versus the delay time, τ, between the pump and probe pulses. Liquid carbon disulfide (CS₂) with $n_{2} = + 3.1 \times 10^{- 14} c m^{2} / W$ [28] was the reference standard for calibration of the measurements.

All NL experiments were repeated more than one time with each sample and the results were reproduced.

3. Results and discussion

Figure 1(a) shows the linear absorbance spectra of the metal-colloids before (dotted line) and after (solid line) photofragmentation of the original NPs synthesized. The smaller LSP resonance linewidth exhibited by the laser-ablated colloid indicates a homogeneous distribution of Ag NPs sizes. The absorbance spectrum of pure acetone (dashed line) presents large transparency window, corroborating that the resonance at ~400 nm is due to the LSP in the Ag NPs. Figure 1(b) shows the size distribution histogram of the spherical NPs with average diameter of 9 nm, obtained using a Transmission Electron Microscope (TEM).

Fig. 1 (a) Linear absorption spectra of the metal-colloid with $f = 4.0 \times 10^{- 5}$ and acetone (cell thickness: 1 mm). (b) Size distribution histogram of the NPs after photofragmentation. A TEM image of the silver NPs is shown in the inset.

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Figure 2 shows the normalized Z-scan profiles for $f = 2.0 \times 10^{- 5}$ , $3.7 \times 10^{- 5}$ , $5.9 \times 10^{- 5}$ and $8.0 \times 10^{- 5}$ , with the intensity in the focus adjusted to be $I_{0} = 9.5 G W / c m^{2}$ . The Z-scan profiles in Fig. 2(a) display a defocusing nonlinearity with small features on the third-order profiles due to HON [21, 22]. Figure 2(b) shows profiles that indicate saturated absorption due to the small detuning between the laser and the LSP frequencies.

Fig. 2 Normalized (a) closed-aperture and (b) open-aperture Z-scan profiles obtained for different NPs volume fractions. Laser peak intensity: $9.5 G W / c m^{2}$ .

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The NL response of the metal-colloid is described by effective susceptibilities, $χ_{e f f}^{(2 N + 1)},$ $N = 1, 2, 3, \dots$ , that contain information on the NL susceptibilities of the host liquid and the NPs. The total NL susceptibility with contributions up to the seventh-order is given by $χ_{N L} (| E |) = \frac{3}{4} χ_{e f f}^{(3)} {| E |}^{2} + \frac{5}{8} χ_{e f f}^{(5)} {| E |}^{4} + \frac{35}{64} χ_{e f f}^{(7)} {| E |}^{6}$ [31], where E is the amplitude of the laser electric field. $χ_{e f f}^{(2 N + 1)}$ , $N = 1 - 3$ , were calculated in [22] assuming that the NPs diameters are smaller than their relative distances that are smaller than λ. The NL measurements allow to determine $n_{2 N} \propto Re χ_{e f f}^{(2 N + 1)}$ and $α_{2 N} \propto Im χ_{e f f}^{(2 N + 1)}$ as in [21, 22].

The NL refractive indices were obtained from the CA Z-scan data, plotting the normalized peak-to-valley transmittance change per incident intensity, $| Δ T_{P - V} | / I$ , versus $I$ and making a polynomial fit using the expression

\frac{Δ T_{P - V}}{I} ≅ 0.396 k L_{e f f}^{(1)} n_{2} + 0.198 k L_{e f f}^{(2)} n_{4} I + 0.102 k L_{e f f}^{(3)} n_{6} I^{2},

where

k = 2 π n_{0} / λ

,

L_{e f f}^{(N)} = (1 - e^{- N α_{0} L}) / (N α_{0})

and

L

is the sample length.

The NL absorption coefficients were obtained from the OA Z-scan experiments fitting the expression

\frac{Δ T}{I} ≅ {(2)}^{- \frac{3}{2}} L_{e f f}^{(1)} (α_{2} + α_{4} I + α_{6} I^{2}) .

The solid lines in Fig. 2 correspond to the normalized laser transmittance in the far-field as a function of the sample's position given by

T (z, Δ Φ_{0}) ≅ 1 + \sum_{N = 1}^{3} \frac{(4 N) Δ Φ_{0}^{(2 N + 1)} z / z_{0}}{[{(z / z_{0})}^{2} + {(2 N + 1)}^{2}] {[{(z / z_{0})}^{2} + 1]}^{N}},

in the CA Z-scan scheme. The lines corresponding to the OA scheme were obtained using the expression

T (z, q_{0}) ≅ \frac{1}{\sqrt{π} q_{0}} \int_{- \infty}^{\infty} \ln [1 + q_{0} \exp (- τ^{2})] d τ .

The on-axis phase-shift at the beam focus is given by

Δ Φ_{0}^{(2 N + 1)} = k n_{2 N} I^{N} [1 - \exp (- N α_{0} L)] / (N α_{0})

;

q_{0} = α_{N L} I L_{e f f}^{(1)} / (1 + z^{2} / z_{0}^{2})

[28] and

z_{0}

is the Rayleigh length of the focused beam.

Figures 3(a) and 3(b) show the linear dependence of the NL refractive indices and the NL absorption coefficients with f for $I_{0} = 9.5 G W / c m^{2}$ . The linear dependence with f was also measured for $I_{0} = 5.0$ , $8.6$ , and $10 G W / c m^{2}$ but is not presented. Therefore, the total effective NL refractive index $n_{N L} (I) = n_{2} + n_{4} I + n_{6} I^{2}$ and the total effective NL absorption coefficient $α_{N L} (I) = α_{2} + α_{4} I + α_{6} I^{2}$ also vary linearly with f as shown in Fig. 3(c) and Fig. 3(d). The solid lines were obtained using the generalized Maxwell-Garnett (GMG) model [22] as discussed below.

Fig. 3 Dependence with the NPs volume fraction of: (a) NL refractive indices, (b) NL absorption coefficients, (c) total effective NL refractive index and (d) total effective NL absorption coefficient. In (a) and (b) the laser peak intensity was $9.5 G W / c m^{2}$ . Normalized (e) Closed-aperture and (f) Open-aperture Z-scan profiles for $f = 5.9 \times 10^{- 5}$ , obtained for different laser peak intensities. The solid lines were obtained from Eqs. (3) and (4).

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Figures 3(e) and 3(f) show the Z-scan profiles for the same intensities as in Figs. 3(c) and 3(d) with $f = 5.9 \times 10^{- 5}$ . The solid curves were obtained from Eqs. (3) and (4) using the NL coefficients found in Figs. 3(a) and 3(b). Notice that $| n_{N L} (I) |$ increases while increasing the laser intensity; on the other hand $| α_{N L} (I) |$ reaches a minimum value for $I_{0} = 8.6 G W / c m^{2}$ . Therefore, the results of Fig. (3)-(5) show that using the nonlinearity management procedure of [21–23], which consists in controlling the NL response of a MDNC by selecting appropriate values of f and I, it is possible to obtain large $n_{N L} (I)$ and small $α_{N L} (I)$ simultaneously.

Fig. 4 (a) Transmitted Kerr signal in 532 nm for silver colloid for pump intensities of: $I_{1} = 10 G W / c m^{2}$ , $I_{2} = 8.6 G W / c m^{2}$ , $I_{3} = 8.0 G W / c m^{2}$ and $I_{4} = 7.0 G W / c m^{2}$ and $I_{p r o b e} = 0.1 (I_{p u m p})$ . The inset is the Kerr signal for CS₂. (b) Dependence of $| Δ T | / I_{p u m p}$ as a function of the pump intensity. Volume fraction: $5.9 \times 10^{- 5}$ .

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Fig. 5 Figures-of-merit for all-optical switching.

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The origin of the effective NL susceptibilities of the metal-colloid was discussed in [13–18, 32, 33]. For the laser wavelength and pulse duration used the NL response is mainly due to the free electrons in the NPs. The influence of thermal effects is negligible due to the low pulses repetition rate. The dependence of the effective NL parameters with f and with the materials susceptibilities is understood using the GMG model [22] which describes the total NL susceptibility of the colloid in terms of the host third-order susceptibility, $χ_{h}^{(3)}$ , and the NPs susceptibilities, $χ_{n p}^{(2 N + 1)}$ , $N = 1 - 3$ .

Expressions for the effective third-, fifth- and seventh-order susceptibilities are obtained as

χ_{e f f}^{(3)} = f L^{2} {| L |}^{2} χ_{n p}^{(3)} + χ_{h}^{(3)},

χ_{e f f}^{(5)} = f L^{2} {| L |}^{4} χ_{n p}^{(5)} - \frac{6}{10} f L^{3} {| L |}^{4} {(χ_{n p}^{(3)})}^{2} - \frac{3}{10} f L {| L |}^{6} {| χ_{n p}^{(3)} |}^{2},

\begin{array}{l} χ_{e f f}^{(7)} = f L^{2} {| L |}^{6} χ_{n p}^{(7)} + \frac{12}{35} f L^{4} {| L |}^{6} {(χ_{n p}^{(3)})}^{3} + \frac{3}{35} f {| L |}^{8} [4 L^{2} χ_{n p}^{(3)} + {| L |}^{2} {(χ_{n p}^{(3)})}^{*}] {| χ_{n p}^{(3)} |}^{2} \\ - \frac{4}{7} f L {| L |}^{6} [2 L^{2} χ_{n p}^{(3)} + {| L |}^{2} {(χ_{n p}^{(3)})}^{*}] χ_{n p}^{(5)}, \end{array}

where

L = 3 ε_{h}^{(L)} / (ε_{n p}^{(L)} + 2 ε_{h}^{(L)})

and

ε_{n p}^{(L)}

(ε_{h}^{(L)})

is the linear dielectric function of the NPs (host).

The value of $χ_{e f f}^{(3)}$ is affected by the competition between $χ_{n p}^{(3)}$ and $χ_{h}^{(3)}$ , that have opposite signs; as a result $χ_{e f f}^{(3)}$ changes sign as a function of f [22]. On the other hand, the contributions of L and $χ_{n p}^{(2 N + 1)}$ , $N = 1 - 3$ , for the susceptibilities $χ_{e f f}^{(5)}$ and $χ_{e f f}^{(7)}$ are more complex as can be observed from Eqs. (6)-(7).

Figure 4(a) shows the Kerr shutter signals for $f = 5.9 \times 10^{- 5}$ with pump intensities equal to $10$ , $8.6$ , $8.0$ , and $7.0 G W / c m^{2}$ . The symmetric profiles are due to the fast NL response of the free electrons in the NPs. Similar behavior was observed for other values of f. The inset of Fig. 4(a) shows the CS₂ signal that exhibits asymmetry with respect to τ due to molecular reorientation. The result for CS₂ is shown to illustrate the fast temporal response of the apparatus. The signal for pure acetone is smaller than our detection limit.

Figure 4(b) shows a polynomial dependence of $Δ T / I_{p u m p}$ versus $I_{p u m p}$ (red line) due to HON. For $I_{p u m p} \leq 4 G W / c m^{2}$ the ratio $Δ T / I_{p u m p}$ is constant and the signal is properly described by $n_{2}$ . For $4 G W / c m^{2} < I_{p u m p} \leq 7 G W / c m^{2}$ the ratio $Δ T / I_{p u m p}$ presents linear dependence with $I_{p u m p}$ and the slope of the straight line is related to $n_{4}$ . For $I_{p u m p} > 7 G W / c m^{2}$ the contribution of $n_{6}$ becomes relevant as already observed in [22].

Figure 5 summarizes the results for W and T but, for better visualization of the results we plotted $T^{- 1}$ instead of T. In the present case $n_{2}$ should be replaced by $n_{N L} (I)$ and instead of $α_{2}$ we consider $α_{N L} (I)$ . Figure 5(a) shows W versus f for intensities between 7.0 and $10 G W / c m^{2}$ . The dependence of $Δ n$ and $α_{0}$ with f was considered. For example for $f = 5.9 \times 10^{- 5}$ the values of $Δ n$ ≈10⁻⁴ and $α_{0} = 0.06 m m^{- 1}$ were used. Then, $W > 1$ was obtained for intensities larger than $7.0 G W / c m^{2}$ . Figure 5(b) shows $T^{- 1}$ versus f. Notice, for instance, that for 10 GW/cm² we obtained $T^{- 1} \approx 3$ corresponding to $f > 2 \times 10^{- 5}$ , while for 8.6 GW/cm² the value of $T^{- 1}$ increases by about two orders of magnitude.

For a more detailed evaluation, Table 1 gives the values of the NL parameters for particular choices of f, laser intensity and the corresponding figures-of-merit for all-optical switching. Notice that the values of $n_{N L}$ increase by approximately a factor of 3 for an increase of f from $3.0 \times 10^{- 5}$ to $8.0 \times 10^{- 5}$ , for a constant intensity. However, a dramatic variation of $α_{N L}$ , which produces a significant reduction of the figure of merit $T$ , is observed for small variations in intensity and fixed value of f. The very small values of $α_{N L}$ , for $I_{0} = 8.6 G W / c m^{2}$ , were obtained due to the destructive interference between the contributions of negative $α_{2}$ and $α_{6}$ with positive $α_{4}$ . Therefore, metal-colloids with appropriate values of f and laser intensity may present optimal figures-of-merit for all-optical switching.

Table 1. NPs volume fraction, f, laser intensity, I, and the corresponding total NL refractive indices, n_NL(I), total NL absorption coefficients, α_NL(I), and figures-of-merit (T and W)

View Table

Clearly the results of Fig. 5 and Table 1 indicate that the nonlinearity management procedure applied here can be much useful for the fabrication of efficient AOS.

4. Conclusions

In summary, we reported a procedure to fabricate appropriate MDNCs for AOS by managing the effective NL susceptibility. Fast NL response and optimized values of the figures-of-merit for all-optical switching were obtained by adjusting the NPs volume fraction and the incident laser intensity. The present results will be useful for the design of AOS based on MDNCs if proper manipulation of host material and metal NPs is made.

Acknowledgments

We acknowledge financial support from the Conselho Nacional de Desenvolvimento Cientifico e Tecnológico (CNPq) and the Fundação de Amparo à Ciência e Tecnologia do Estado de Pernambuco (FACEPE). The work was performed in the framework of the National Institute of Photonics (INCT de Fotônica) project and PRONEX/CNPq/FACEPE.

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f ( × 10⁻⁵)	$I_{0}$ (GW/cm²)	$n_{N L}$ ( × 10⁻¹⁵ cm²/W)	$α_{N L}$ ( × 10⁻¹¹ cm²/W)	W	T
3.0	7.0	−2.04	−1.16	0.91	0.30
	8.6	−4.28	−1.75 × 10⁻³	1.87	3.07 × 10⁻³
	10.0	−6.85	−3.27	3.39	0.28
3.8	7.0	−3.56	−1.33	0.95	0.20
	8.6	−5.98	−3.75 × 10⁻³	2.32	2.87 × 10⁻³
	10.0	−8.84	−3.81	3.79	0.25
5.9	7.0	−4.94	−0.91	1.45	0.13
	8.6	−8.19	−3.72 × 10⁻³	2.45	2.80 × 10⁻³
	10.0	−13.30	−6.92	4.34	0.24
8.0	7.0	−7.47	−1.61	1.56	0.12
	8.6	−14.68	−3.68 × 10⁻³	2.83	2.58 × 10⁻³
	10.0	−20.68	−9.72	4.62	0.25

An optimization procedure for the design of all-optical switches based on metal-dielectric nanocomposites

Abstract

1. Introduction

2. Experimental details

3. Results and discussion

4. Conclusions

Acknowledgments

References and links

Cited By

Figures (5)

Tables (1)

Equations (7)

Optics Express