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OPTICS LETTERS / Vol. 39, No. 16 / August 15, 2014
All-optical modulation and switching by a metamaterial of plasmonic circuits Timothy J. Davis,1,2,* Daniel E. Gómez,1,2 and Fatima Eftekhari2 1
2
CSIRO Materials Science and Engineering, Private Bag 33 Clayton, Victoria 3168, Australia Melbourne Centre for Nanofabrication, ANFF, 151 Wellington Road Clayton, Victoria 3168, Australia *Corresponding author: [email protected] Received June 30, 2014; accepted July 17, 2014; posted July 21, 2014 (Doc. ID 214598); published August 15, 2014
We demonstrate experimentally the modulation and switching of one light beam by a second beam using metamaterials constructed from arrays of plasmonic circuits. Each circuit consists of three gold nanorods that mix together two coherent but orthogonally polarized light beams leading to modulation by an interference effect. By adjusting the phase and the amplitude of one of the beams, the amplitude and spectral composition of the second beam is altered. The plasmonic circuits display an asymmetry that enables an angle-dependent modulation, which we demonstrate with a diffraction grating where the energy directed into two diffraction orders is controlled by a second light beam. This effect appears like an optically controlled blaze that we use to switch a light beam between two different directions. © 2014 Optical Society of America OCIS codes: (230.1150) All-optical devices; (250.5403) Plasmonics; (050.6624) Subwavelength structures; (230.4110) Modulators; (230.1950) Diffraction gratings. http://dx.doi.org/10.1364/OL.39.004938
All-optical modulation is the control of the phase or intensity of one light beam by another. Although modulation can be achieved using nonlinear optical materials, with optical properties that change with the intensity of light, such nonlinear interactions are very weak. Optical metamaterials based on subwavelength arrays of plasmonic structures have improved the modulation efficiencies of some nonlinear materials [1–5], but these devices still require high optical energy densities to function. As an alternative, modulation can be obtained using constructive or destructive interference when two coherent beams overlap. Plasmonic waveguide devices based on this principle have been demonstrated (for example [6,7]), as well as a modulator that exploits the dependence of absorption on the field strength in an optical standing wave [8]. In this Letter, we take a different approach to create a metamaterial (an artificial optical material) using subwavelength arrays of plasmonic circuits that demonstrates all-optical modulation by interference. This device has the advantage of being compact, fast, and intrinsically low power while demonstrating large modulations. More generally, the plasmonic circuit concept can be extended to more complex devices that use interference for all-optical control. We demonstrate this with a diffraction grating of plasmonic circuits that acts like an all-optical switch. The plasmonic circuit concept uses nanoscale metal structures that support localized surface plasmon (LSP) resonances and behave like an electrical circuit [9–12]. The evanescent electric fields from the LSPs mix optical energy in a similar way that an electrical circuit mixes electrical signals [13], and this effect enables two orthogonally polarized light beams to interfere resulting in modulation by destructive or constructive interference. We construct our metamaterial from subwavelength arrays of plasmonic circuits that are analogous to the Wheatstone bridge in electronics [11]. The circuit (Fig. 1) is made from three metal nano-scale rods that generate sums and differences between the optical inputs [13]. The two input channels are separated using 0146-9592/14/164938-04$15.00/0
polarization: the input beams are orthogonally polarized, one of which we call the “signal” beam and the other the “control’ beam.” As indicated in Fig. 1(b), the signal beam excites LSPs in the two “arms” of the circuit that oscillate in phase (a dipole LSP mode), whereas the control beam excites a single LSP in the “bridge” that induces two LSPs in the arms that oscillate out of phase (a quadrupole LSP mode). All-optical amplitude modulation is achieved by illuminating the metamaterial simultaneously with both signal and control beams. The two LSP modes interfere leading to constructive or destructive interference depending on the relative phases of the signal and control beams. The interference alters the optical energy flow through the metamaterial resulting in amplitude modulation. This scheme does not rely on changes of the refractive index of a medium, such as in nonlinear materials, and it operates solely by the imbalance in the arms of the optical Wheatstone bridge. The metamaterial was analyzed using our wellestablished theory of LSP coupling [14,15]. Assuming the two arms are identical, the amplitude of the light radiated from them is proportional to ψ a~ 1 expiks · d∕2 a~ 2 exp−iks · d∕2, where a~ 1;2 a1;2 f a ωGab are the
Fig. 1. Optical modulation concept. (a) Metamaterial is created from arrayed plasmonic circuits each consisting of three gold nanorods where the signal and control beams are orthogonally polarized. (b) The signal beam S excites LSPs (solid arrows) in phase in the two arms. The control beam C excites the LSP in the bridge, which induces LSPs out of phase (dashed arrows) and leads to interference. (c) Experimental configuration for testing the metamaterial. © 2014 Optical Society of America
August 15, 2014 / Vol. 39, No. 16 / OPTICS LETTERS
amplitudes of the LSP excitations and we include phase terms relating to their spatial separation d and the wavevector ks in the direction of scattering. The “uncoupled” LSP excitations in each arm a1;2 f a ωpa · E1;2 depend on a complex resonance term f a ω Ra expiϕa represented by a magnitude Ra and a phase ϕa . The dipole moments of the LSP modes pa are aligned parallel to the long axis of each nanorod and are excited by the electric field E1;2 of the light incident on each arm. The incident fields are E1;2 E0 exp∓ikI · d∕2, where kI is the incident wavevector and we take the −sign for arm 1 and sign for arm 2. The LSP resonances in the circuit arms depend on the coupling f a ωG of the evanescent fields from the bridge nanorod, where G is the strength of the coupling and the resonance term f a controls the degree by which the arms resonate with the evanescent fields from the bridge. The LSP excitation of the bridge nanorod ab f b ωpb · Ec expiϕc depends on a different component of the electric field Ec that we assume is shifted in phase ϕc relative to E0 . Here, f b Rb expiϕb is the resonance factor of the LSP in the bridge. Note that the LSP dipole moment pb of the bridge rod is perpendicular to the dipole moments pa of the arms— the arms and the bridge nanorods are excited by orthogonally polarized light components. Under the condition that the coupling G is relatively weak, we derive an approximate expression for the wave scattered from the arms ψ ≈ expiϕa S cosq · d∕2 iRb GC sinks · d∕2 expiϕc ϕb ;
(1)
where S 2Ra pa · E0 and C 2Ra pb · Ec represent the amplitudes of the signal and control beams, respectively, and q ks − kI is the scattering vector. For subwavelength arrays of plasmonic circuits, there is no diffraction so that ks kI and q 0. The intensity I jψj2 scattered in the direction of propagation is then I S 2 1–2C∕SRb GΘ sinϕc ϕb Rb GΘ2 C∕S2 : (2) Note that the intensity depends on the ratio C∕S of the amplitudes of the control beam and the signal beam. The first term in Eq. (2) is the direct scattering associated with the signal beam S incident on the two arms of the circuit. The second term is the interference between the signal beam and the control beam C that depends on both the phase ϕc of the control beam and the phase ϕb of the LSP oscillation in the bridge nanorod. This interference term is responsible for the modulation effect. It depends on the angle of incidence θ, through the function Θ sinkd∕2 sin θ. Since Θ is zero at normal incidence θ 0, the modulation is only observed for nonnormal incidence. The third term is the intensity from the control beam that has coupled into the two arms of the circuit and then is radiated by them. This represents the unwanted “crosstalk” between the control channel and the signal channel. Figure 2 shows a series of images of the modulation of light transmitted at θ 25° through a metamaterial as the
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Fig. 2. Transmitted intensity through the metamaterial with different control beam phases ϕc and amplitudes C expressed as a ratio to the signal amplitude S. A patch of parallel gold rods was included as a control. The scanning electron microscope (SEM) image shows the resist pattern of a circuit during fabrication.
control beam amplitude C and phase ϕc were changed relative to the signal beam amplitude S. The images were formed by passing 695 nm light through a linear polarizer and a quarter-wave plate, thereby creating polarized light that can be decomposed into two coherent, orthogonal components, one representing the signal beam and the other the control beam [Fig. 1(c)]. This decomposition is similar to polarization encoding in interferometric logic gates [16]. The orientations of the polarizer and wave plate set the relative amplitudes and phases of these beams while maintaining coherence, which is important for the plasmonic circuits to generate interference. The signal and control beams are orthogonally polarized and cannot directly interfere. However, the control beam adds a background offset at the detector that reduces image contrast. The linear polarizer placed after the metamaterial and aligned with the circuit arms [Fig. 1(c)] removes this unwanted component so that the constant background illumination in Fig. 2 arises solely from the incident signal beam. The metamaterial was fabricated on a borosilicate glass substrate using electron beam lithography to define an array of plasmonic circuits, each one made from gold rods 40 nm wide, 100 nm long, and 30 nm thick. The center-to-center spacing of the two arms was d 200 nm and the array period was 400 nm in both directions. The bottom edge of the bridge nanorod was aligned with the tops of the arms. For comparison, a metamaterial with the bridge nanorod missing from each metaatom was also fabricated on the same substrate, as shown in Fig. 2. This metamaterial shows no modulation. The optical properties were measured by passing white light through the linear polarizer and a broadband quarter-wave plate. The signal beam was collected by a 40× microscope objective and directed to a spectrometer. The extinction spectra in Fig. 3(a) show the fraction of the incident signal beam that is blocked by the metamaterial. The resonance peaks are characteristic of LSPs, but the maxima depend on the control beam ratio C∕S and phase ϕc , which is switched between 0° and 180° relative to the signal beam. The effect of switching the control beam phase between −90° and 90° is shown in Fig. 3(b). Remarkably, in this case the control beam shifts the maxima of the spectral peaks by almost 50 nm, which is due to a frequency-dependent interference arising from the phase change of the LSP as the incident frequency passes through the resonance. Such plasmon resonance shifts are usually associated with the refractive index
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Fig. 3. Experimental extinction and modulation spectra measured from the metamaterial. (a) Extinction spectra with two different control amplitudes and with phases ϕc switched between 0° (solid) and 180° (dashed) for an incidence angle of 25°; (b) as per (a) but with different control amplitudes and phases ϕc switched between −90° (dashed) and 90° (solid). (c) Modulation spectra derived from the data in (a); the crosstalk measures how much of the control beam is transmitted through the optical system. (d) Modulation spectra derived from the data in (b).
change in a nonlinear material. This is not the situation here because the metamaterial contains only linear optical materials and the incident light intensity is very low, being derived from a quartz–halogen globe. We also note that the spectral peaks in Fig. 3(a) shift with the control signal. This shift arises from small resonance differences between the dipole and quadrupole modes of the circuit, which we measured to be at 680 and 690 nm, respectively. From Eq. (2), we derive two useful measures that quantify the properties of the metamaterial. The first is the modulation strength M 4 GRb Θ sinϕc ϕb C∕S, which is defined by the difference in the transmitted light, when the control beam phase is shifted from ϕc to ϕc 180°, divided by the signal beam intensity S 2 . The modulation depends on the initial choice of the phase ϕc ϕb with a maximum when ϕc ϕb 90°, which we call M max . Examples of the modulation are given in Figs. 3(c) and 3(d) for ϕc 0 and ϕc 90°, respectively. The modulations appear quite different and represent parts of the curve sinϕc ϕb as the bridge nanorod phase ϕb changes with frequency about the LSP resonance. Below resonance ϕb → 0° and it passes through ϕb 90° at resonance and then ϕb → 180° above resonance. In Fig. 3(c), where ϕc 0°, the modulation follows sin ϕb , which is the maximum on resonance since ϕb 90° there, and it drops to zero away from resonance. In Fig. 3(d), where ϕc 90°, the modulation follows sinπ∕2 ϕb cos ϕb . It is positive away from the resonance (long wavelengths), where ϕb ≈ 0, and it changes sign above the resonance (short wavelengths), where ϕb ≈ 180°. We observe in Fig. 3(c) that a
modulation of 100% is obtained, which represents a change of the transmitted intensity from S 2 ∕2 to 3S 2 ∕2. The second measure of performance is the crosstalk ratio C tlk , which is defined as the ratio of the third term in Eq. (2) to the first term C tlk Rb GΘ2 C∕S2 M 2max ∕16. Ideally, none of the control beam should pass through the metamaterial in the absence of a signal beam. The crosstalk ratio measures the departure from this ideal situation and quantifies the “contamination” of the signal by the control beam. The crosstalk is proportional to the square of the maximum modulation, which implies the crosstalk is much smaller than the modulated signal unless the modulation becomes very large. For example, a modulation of 100% (M max 1) has a crosstalk C tlk 1∕16, or about 6%. This is verified experimentally in Fig. 3(c), which shows the crosstalk ratio with a maximum of about 8% at resonance despite the control signal creating a 100% modulation. We have demonstrated a metamaterial made from a subwavelength array of plasmonic circuits that mix two light beams together to generate interference, which leads to all-optical modulation. However, the plasmonic circuit concept is quite general and different configurations of metal nanostructures will create meta-atoms with different signal-mixing characteristics. Moreover, redistributing the circuits over the substrate in different ways results in a large variety of modulating devices. For example, a grating with optically modulated diffraction orders is created from lines of plasmonic circuits [Fig. 4(a)] that form one-dimensional metamaterial strips. This device exploits the dependence of the modulation on the direction of scattering, given by sinks · d∕2 in
Fig. 4. All-optical switch created from a diffracting metamaterial. (a) The metamaterial consists of vertical lines of plasmonic circuits on a glass substrate with each line separated by P 1 micrometers. The inset shows the SEM image of the structure. A polarizer filters out the control beam, with an orientation as shown by the arrow. Only the transmitted signal beam and the two diffracting orders pass through. (b) Two images taken with a camera that show the intensity change in the two diffraction orders with the change in the phase of the control beam, which results in a switching effect. The zero order (transmitted beam) is not shown in the image. The incident light wavelength was 700 nm.
August 15, 2014 / Vol. 39, No. 16 / OPTICS LETTERS
Eq. (1). For light of wavelength λ at normal incidence on a grating of period P, we have q · d ks · d kd sin θ , where the scattering direction θ of the two diffracting orders is found from the grating equation sin θ λ∕P. These two orders labeled 1 propagate in different directions and are therefore modulated with opposite signs: that is, one order suffers destructive interference and the other constructive interference depending on the amplitude and phase of the control signal. Since the energy directed into the two diffracting orders is modulated by the control beam, this device behaves like a grating with an optically controlled blaze. By carefully choosing the amplitude ratio C∕S, we can arrange for complete destructive interference of one diffraction order and constructive interference of the other order. Flipping the phase of the control beam from 0° to 180° reverses their intensities, and this leads to the switching effect in Fig. 4(b). In our examples, the metamaterials function without intense coherent laser sources—the data in Fig. 3 were collected with incoherent white light from an incandescent source. However, the modulation is sensitive to the phase difference between the signal and the control beams, which therefore must be coherent with one another. In principle, the signal and control beams can be derived from light sources with different frequencies, which results in modulations at extremely high rates determined by their frequency difference δω. In this case, the phase of the control signal varies rapidly with time according to ϕc t δωt. The maximum modulation rate from the metamaterial is determined by the rate at which the surface plasmons can be driven into oscillation. This rate is related to the full width at half-maximum of the LSP resonance, which we estimate to be 50 THz. Such modulations would also lead to exceptionally fast switching devices, which could switch the direction of a light beam within 20 fs.
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The devices were fabricated at the Melbourne Centre for Nanofabrication (MCN) in the Victorian Node of the Australian National Fabrication Facility (ANFF). References 1. K. Dani, Z. Ku, P. Upadhya, R. Prasankumar, S. Brueck, and A. Taylor, Nano Lett. 9, 3565 (2009). 2. D. Cho, W. Wu, E. Ponizovskaya, P. Chaturvedi, A. Bratkovsky, S. Wang, X. Zhang, F. Wang, and Y. Shen, Opt. Express 17, 17652 (2009). 3. A. Nikolaenko, D. A. Francesco, S. Boden, N. Papasimakis, P. Ashburn, D. F. Enzo, and N. Zheludev, Phys. Rev. Lett. 104, 153902 (2010). 4. M. Ren, B. Jia, J. Ou, E. Plum, J. Zhang, K. MacDonald, A. Nikolaenko, J. Xu, M. Gu, and N. Zheludev, Adv. Mater. 23, 5540 (2011). 5. B. Gholipour, J. Zhang, K. MacDonald, D. Hewak, and N. Zheludev, Adv. Mater. 25, 3050 (2013). 6. H. Wei, Z. Wang, X. Tian, M. Kall, and H. Xu, Nat. Commun. 2, 387 (2011). 7. Y. Fu, X. Hu, C. Lu, S. Yue, H. Yang, and Q. Gong, Nano Lett. 12, 5784 (2012). 8. J. Zhang, K. MacDonald, and N. Zheludev, Light Sci. Appl. 1, e18 (2012). 9. N. Engheta, A. Salandrino, and A. Alù, Phys. Rev. Lett. 95, 95504 (2005). 10. N. Engheta, Science 317, 1698 (2007). 11. T. Davis, K. Vernon, and D. Gómez, J. Appl. Phys. 106, 043502 (2009). 12. B. Abasahl, C. Santschi, and O. Martin, ACS Photon. 1, 403 (2014). 13. F. Eftekhari, D. E. Gómez, and T. Davis, Opt. Lett. 39, 2994 (2014). 14. T. J. Davis, K. C. Vernon, and D. E. Gómez, Phys. Rev. B 79, 155423 (2009). 15. T. J. Davis, D. E. Gómez, and K. C. Vernon, Nano Lett. 10, 2618 (2010). 16. A. Zavalin, J. Shamir, C. Vikram, and H. Caulfield, Appl. Opt. 45, 360 (2006).
OPTICS LETTERS / Vol. 39, No. 16 / August 15, 2014
All-optical modulation and switching by a metamaterial of plasmonic circuits Timothy J. Davis,1,2,* Daniel E. Gómez,1,2 and Fatima Eftekhari2 1
2
CSIRO Materials Science and Engineering, Private Bag 33 Clayton, Victoria 3168, Australia Melbourne Centre for Nanofabrication, ANFF, 151 Wellington Road Clayton, Victoria 3168, Australia *Corresponding author: [email protected] Received June 30, 2014; accepted July 17, 2014; posted July 21, 2014 (Doc. ID 214598); published August 15, 2014
We demonstrate experimentally the modulation and switching of one light beam by a second beam using metamaterials constructed from arrays of plasmonic circuits. Each circuit consists of three gold nanorods that mix together two coherent but orthogonally polarized light beams leading to modulation by an interference effect. By adjusting the phase and the amplitude of one of the beams, the amplitude and spectral composition of the second beam is altered. The plasmonic circuits display an asymmetry that enables an angle-dependent modulation, which we demonstrate with a diffraction grating where the energy directed into two diffraction orders is controlled by a second light beam. This effect appears like an optically controlled blaze that we use to switch a light beam between two different directions. © 2014 Optical Society of America OCIS codes: (230.1150) All-optical devices; (250.5403) Plasmonics; (050.6624) Subwavelength structures; (230.4110) Modulators; (230.1950) Diffraction gratings. http://dx.doi.org/10.1364/OL.39.004938
All-optical modulation is the control of the phase or intensity of one light beam by another. Although modulation can be achieved using nonlinear optical materials, with optical properties that change with the intensity of light, such nonlinear interactions are very weak. Optical metamaterials based on subwavelength arrays of plasmonic structures have improved the modulation efficiencies of some nonlinear materials [1–5], but these devices still require high optical energy densities to function. As an alternative, modulation can be obtained using constructive or destructive interference when two coherent beams overlap. Plasmonic waveguide devices based on this principle have been demonstrated (for example [6,7]), as well as a modulator that exploits the dependence of absorption on the field strength in an optical standing wave [8]. In this Letter, we take a different approach to create a metamaterial (an artificial optical material) using subwavelength arrays of plasmonic circuits that demonstrates all-optical modulation by interference. This device has the advantage of being compact, fast, and intrinsically low power while demonstrating large modulations. More generally, the plasmonic circuit concept can be extended to more complex devices that use interference for all-optical control. We demonstrate this with a diffraction grating of plasmonic circuits that acts like an all-optical switch. The plasmonic circuit concept uses nanoscale metal structures that support localized surface plasmon (LSP) resonances and behave like an electrical circuit [9–12]. The evanescent electric fields from the LSPs mix optical energy in a similar way that an electrical circuit mixes electrical signals [13], and this effect enables two orthogonally polarized light beams to interfere resulting in modulation by destructive or constructive interference. We construct our metamaterial from subwavelength arrays of plasmonic circuits that are analogous to the Wheatstone bridge in electronics [11]. The circuit (Fig. 1) is made from three metal nano-scale rods that generate sums and differences between the optical inputs [13]. The two input channels are separated using 0146-9592/14/164938-04$15.00/0
polarization: the input beams are orthogonally polarized, one of which we call the “signal” beam and the other the “control’ beam.” As indicated in Fig. 1(b), the signal beam excites LSPs in the two “arms” of the circuit that oscillate in phase (a dipole LSP mode), whereas the control beam excites a single LSP in the “bridge” that induces two LSPs in the arms that oscillate out of phase (a quadrupole LSP mode). All-optical amplitude modulation is achieved by illuminating the metamaterial simultaneously with both signal and control beams. The two LSP modes interfere leading to constructive or destructive interference depending on the relative phases of the signal and control beams. The interference alters the optical energy flow through the metamaterial resulting in amplitude modulation. This scheme does not rely on changes of the refractive index of a medium, such as in nonlinear materials, and it operates solely by the imbalance in the arms of the optical Wheatstone bridge. The metamaterial was analyzed using our wellestablished theory of LSP coupling [14,15]. Assuming the two arms are identical, the amplitude of the light radiated from them is proportional to ψ a~ 1 expiks · d∕2 a~ 2 exp−iks · d∕2, where a~ 1;2 a1;2 f a ωGab are the
Fig. 1. Optical modulation concept. (a) Metamaterial is created from arrayed plasmonic circuits each consisting of three gold nanorods where the signal and control beams are orthogonally polarized. (b) The signal beam S excites LSPs (solid arrows) in phase in the two arms. The control beam C excites the LSP in the bridge, which induces LSPs out of phase (dashed arrows) and leads to interference. (c) Experimental configuration for testing the metamaterial. © 2014 Optical Society of America
August 15, 2014 / Vol. 39, No. 16 / OPTICS LETTERS
amplitudes of the LSP excitations and we include phase terms relating to their spatial separation d and the wavevector ks in the direction of scattering. The “uncoupled” LSP excitations in each arm a1;2 f a ωpa · E1;2 depend on a complex resonance term f a ω Ra expiϕa represented by a magnitude Ra and a phase ϕa . The dipole moments of the LSP modes pa are aligned parallel to the long axis of each nanorod and are excited by the electric field E1;2 of the light incident on each arm. The incident fields are E1;2 E0 exp∓ikI · d∕2, where kI is the incident wavevector and we take the −sign for arm 1 and sign for arm 2. The LSP resonances in the circuit arms depend on the coupling f a ωG of the evanescent fields from the bridge nanorod, where G is the strength of the coupling and the resonance term f a controls the degree by which the arms resonate with the evanescent fields from the bridge. The LSP excitation of the bridge nanorod ab f b ωpb · Ec expiϕc depends on a different component of the electric field Ec that we assume is shifted in phase ϕc relative to E0 . Here, f b Rb expiϕb is the resonance factor of the LSP in the bridge. Note that the LSP dipole moment pb of the bridge rod is perpendicular to the dipole moments pa of the arms— the arms and the bridge nanorods are excited by orthogonally polarized light components. Under the condition that the coupling G is relatively weak, we derive an approximate expression for the wave scattered from the arms ψ ≈ expiϕa S cosq · d∕2 iRb GC sinks · d∕2 expiϕc ϕb ;
(1)
where S 2Ra pa · E0 and C 2Ra pb · Ec represent the amplitudes of the signal and control beams, respectively, and q ks − kI is the scattering vector. For subwavelength arrays of plasmonic circuits, there is no diffraction so that ks kI and q 0. The intensity I jψj2 scattered in the direction of propagation is then I S 2 1–2C∕SRb GΘ sinϕc ϕb Rb GΘ2 C∕S2 : (2) Note that the intensity depends on the ratio C∕S of the amplitudes of the control beam and the signal beam. The first term in Eq. (2) is the direct scattering associated with the signal beam S incident on the two arms of the circuit. The second term is the interference between the signal beam and the control beam C that depends on both the phase ϕc of the control beam and the phase ϕb of the LSP oscillation in the bridge nanorod. This interference term is responsible for the modulation effect. It depends on the angle of incidence θ, through the function Θ sinkd∕2 sin θ. Since Θ is zero at normal incidence θ 0, the modulation is only observed for nonnormal incidence. The third term is the intensity from the control beam that has coupled into the two arms of the circuit and then is radiated by them. This represents the unwanted “crosstalk” between the control channel and the signal channel. Figure 2 shows a series of images of the modulation of light transmitted at θ 25° through a metamaterial as the
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Fig. 2. Transmitted intensity through the metamaterial with different control beam phases ϕc and amplitudes C expressed as a ratio to the signal amplitude S. A patch of parallel gold rods was included as a control. The scanning electron microscope (SEM) image shows the resist pattern of a circuit during fabrication.
control beam amplitude C and phase ϕc were changed relative to the signal beam amplitude S. The images were formed by passing 695 nm light through a linear polarizer and a quarter-wave plate, thereby creating polarized light that can be decomposed into two coherent, orthogonal components, one representing the signal beam and the other the control beam [Fig. 1(c)]. This decomposition is similar to polarization encoding in interferometric logic gates [16]. The orientations of the polarizer and wave plate set the relative amplitudes and phases of these beams while maintaining coherence, which is important for the plasmonic circuits to generate interference. The signal and control beams are orthogonally polarized and cannot directly interfere. However, the control beam adds a background offset at the detector that reduces image contrast. The linear polarizer placed after the metamaterial and aligned with the circuit arms [Fig. 1(c)] removes this unwanted component so that the constant background illumination in Fig. 2 arises solely from the incident signal beam. The metamaterial was fabricated on a borosilicate glass substrate using electron beam lithography to define an array of plasmonic circuits, each one made from gold rods 40 nm wide, 100 nm long, and 30 nm thick. The center-to-center spacing of the two arms was d 200 nm and the array period was 400 nm in both directions. The bottom edge of the bridge nanorod was aligned with the tops of the arms. For comparison, a metamaterial with the bridge nanorod missing from each metaatom was also fabricated on the same substrate, as shown in Fig. 2. This metamaterial shows no modulation. The optical properties were measured by passing white light through the linear polarizer and a broadband quarter-wave plate. The signal beam was collected by a 40× microscope objective and directed to a spectrometer. The extinction spectra in Fig. 3(a) show the fraction of the incident signal beam that is blocked by the metamaterial. The resonance peaks are characteristic of LSPs, but the maxima depend on the control beam ratio C∕S and phase ϕc , which is switched between 0° and 180° relative to the signal beam. The effect of switching the control beam phase between −90° and 90° is shown in Fig. 3(b). Remarkably, in this case the control beam shifts the maxima of the spectral peaks by almost 50 nm, which is due to a frequency-dependent interference arising from the phase change of the LSP as the incident frequency passes through the resonance. Such plasmon resonance shifts are usually associated with the refractive index
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Fig. 3. Experimental extinction and modulation spectra measured from the metamaterial. (a) Extinction spectra with two different control amplitudes and with phases ϕc switched between 0° (solid) and 180° (dashed) for an incidence angle of 25°; (b) as per (a) but with different control amplitudes and phases ϕc switched between −90° (dashed) and 90° (solid). (c) Modulation spectra derived from the data in (a); the crosstalk measures how much of the control beam is transmitted through the optical system. (d) Modulation spectra derived from the data in (b).
change in a nonlinear material. This is not the situation here because the metamaterial contains only linear optical materials and the incident light intensity is very low, being derived from a quartz–halogen globe. We also note that the spectral peaks in Fig. 3(a) shift with the control signal. This shift arises from small resonance differences between the dipole and quadrupole modes of the circuit, which we measured to be at 680 and 690 nm, respectively. From Eq. (2), we derive two useful measures that quantify the properties of the metamaterial. The first is the modulation strength M 4 GRb Θ sinϕc ϕb C∕S, which is defined by the difference in the transmitted light, when the control beam phase is shifted from ϕc to ϕc 180°, divided by the signal beam intensity S 2 . The modulation depends on the initial choice of the phase ϕc ϕb with a maximum when ϕc ϕb 90°, which we call M max . Examples of the modulation are given in Figs. 3(c) and 3(d) for ϕc 0 and ϕc 90°, respectively. The modulations appear quite different and represent parts of the curve sinϕc ϕb as the bridge nanorod phase ϕb changes with frequency about the LSP resonance. Below resonance ϕb → 0° and it passes through ϕb 90° at resonance and then ϕb → 180° above resonance. In Fig. 3(c), where ϕc 0°, the modulation follows sin ϕb , which is the maximum on resonance since ϕb 90° there, and it drops to zero away from resonance. In Fig. 3(d), where ϕc 90°, the modulation follows sinπ∕2 ϕb cos ϕb . It is positive away from the resonance (long wavelengths), where ϕb ≈ 0, and it changes sign above the resonance (short wavelengths), where ϕb ≈ 180°. We observe in Fig. 3(c) that a
modulation of 100% is obtained, which represents a change of the transmitted intensity from S 2 ∕2 to 3S 2 ∕2. The second measure of performance is the crosstalk ratio C tlk , which is defined as the ratio of the third term in Eq. (2) to the first term C tlk Rb GΘ2 C∕S2 M 2max ∕16. Ideally, none of the control beam should pass through the metamaterial in the absence of a signal beam. The crosstalk ratio measures the departure from this ideal situation and quantifies the “contamination” of the signal by the control beam. The crosstalk is proportional to the square of the maximum modulation, which implies the crosstalk is much smaller than the modulated signal unless the modulation becomes very large. For example, a modulation of 100% (M max 1) has a crosstalk C tlk 1∕16, or about 6%. This is verified experimentally in Fig. 3(c), which shows the crosstalk ratio with a maximum of about 8% at resonance despite the control signal creating a 100% modulation. We have demonstrated a metamaterial made from a subwavelength array of plasmonic circuits that mix two light beams together to generate interference, which leads to all-optical modulation. However, the plasmonic circuit concept is quite general and different configurations of metal nanostructures will create meta-atoms with different signal-mixing characteristics. Moreover, redistributing the circuits over the substrate in different ways results in a large variety of modulating devices. For example, a grating with optically modulated diffraction orders is created from lines of plasmonic circuits [Fig. 4(a)] that form one-dimensional metamaterial strips. This device exploits the dependence of the modulation on the direction of scattering, given by sinks · d∕2 in
Fig. 4. All-optical switch created from a diffracting metamaterial. (a) The metamaterial consists of vertical lines of plasmonic circuits on a glass substrate with each line separated by P 1 micrometers. The inset shows the SEM image of the structure. A polarizer filters out the control beam, with an orientation as shown by the arrow. Only the transmitted signal beam and the two diffracting orders pass through. (b) Two images taken with a camera that show the intensity change in the two diffraction orders with the change in the phase of the control beam, which results in a switching effect. The zero order (transmitted beam) is not shown in the image. The incident light wavelength was 700 nm.
August 15, 2014 / Vol. 39, No. 16 / OPTICS LETTERS
Eq. (1). For light of wavelength λ at normal incidence on a grating of period P, we have q · d ks · d kd sin θ , where the scattering direction θ of the two diffracting orders is found from the grating equation sin θ λ∕P. These two orders labeled 1 propagate in different directions and are therefore modulated with opposite signs: that is, one order suffers destructive interference and the other constructive interference depending on the amplitude and phase of the control signal. Since the energy directed into the two diffracting orders is modulated by the control beam, this device behaves like a grating with an optically controlled blaze. By carefully choosing the amplitude ratio C∕S, we can arrange for complete destructive interference of one diffraction order and constructive interference of the other order. Flipping the phase of the control beam from 0° to 180° reverses their intensities, and this leads to the switching effect in Fig. 4(b). In our examples, the metamaterials function without intense coherent laser sources—the data in Fig. 3 were collected with incoherent white light from an incandescent source. However, the modulation is sensitive to the phase difference between the signal and the control beams, which therefore must be coherent with one another. In principle, the signal and control beams can be derived from light sources with different frequencies, which results in modulations at extremely high rates determined by their frequency difference δω. In this case, the phase of the control signal varies rapidly with time according to ϕc t δωt. The maximum modulation rate from the metamaterial is determined by the rate at which the surface plasmons can be driven into oscillation. This rate is related to the full width at half-maximum of the LSP resonance, which we estimate to be 50 THz. Such modulations would also lead to exceptionally fast switching devices, which could switch the direction of a light beam within 20 fs.
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