Electrostrictive effect for active control of surface plasmon signals

Lucas Karperien; Ribal Georges Sabat

doi:10.1364/OE.24.013264

1. Introduction

Tunable optical elements include micro-electro-mechanical and nano-electro-mechanical systems capable of adapting and changing their function or form either automatically or at the user’s command. These systems are important in applications because they can allow for active compensation of thermal fluctuations in optical instruments, light wavelength tunability and beam steering in display systems and optical cross-connects and switches. Examples of such elements include tunable diffraction gratings based on piezoelectrically-driven [1–3] and viscoelastic [4] actuators, deformable grating optical modulators based on micromachined gratings [5], wavelength-tunable lasers [6,7], tunable Fabry-Pérot filters for optical communications [8] and beam steering in photonic crystals [9].

Surface plasmons (SPs) are light-induced collective and coherent surface electron density fluctuations at the interface between a thin layer of metal and a dielectric material. When a SP occurs, the free electrons within the metal collectively oscillate at the surface in resonance with the incident light, resulting in surface-bound light waves. These waves can propagate several micrometers along a flat interface until their energy is eventually attenuated due to absorption in the metal or radiation into free-space. In contrast, the electric field induced by the electron density oscillations during a SP resonance becomes perpendicularly evanescent in the adjacent mediums and decays to zero in the dielectric material within a few hundred nanometers from the interface. The excitation of surface plasmons can only be achieved by matching the incident light wave vector to that of the plasmon along the direction of propagation. Several SP excitation methods exist [10,11], however a diffraction grating is the easiest and most predictable method of exciting SPs. Interestingly, if the diffraction grating is deep enough, surface plasmon photonic energy gap can be observed in the light spectrum since the flat interface assumption between the metal and dielectric layers is no longer valid [12].

Surface plasmons have been used in a large number of applications ranging from enhancements in the properties of solar cells [13] and biosensors [14] to studying film growth and interface characteristics [15]. Tuning the incident light wavelength at which a SP occurs can offer several advantages to practical applications. Localized surface plasmon resonance can be tuned by varying either the size of the metallic nanostructures [16,17] or the dielectric layer’s nanotopography [18]. In situ tunable localized surface plasmons have been observed by photoinducing SP wavelength shifts in Ag@TiO₂ composite clusters by increasing the electron storage in TiO₂ shells [19]. A recent review [20] outlines the work done thus far in the literature on electrically controlled plasmonic switches and modulators. Most of the reviewed work was based on the thermal effect, the free carrier dispersion effect, the Pockels electro-optic effect, phase change materials and switching caused by electrochemical metallization, notably real-time plasmonic modulation to enhance camouflage using bimetallic nanodot arrays and electrochemical bias [21]. None of the reviewed work reports on electrically tuning the SP wavelength using a tunable diffraction grating.

Azobenzene-containing molecular glasses [22] can reversibly photoisomerize between the trans and cis isomers upon irradiation at an absorbing laser wavelength. Upon exposure to a sinusoidal laser interference pattern, surface relief diffraction gratings can be inscribed onto thin films of azo materials deposited on a rigid substrate [23]. The grating pitch can be controlled upon inscription by varying the laser incidence angle, while the depth is dependent on the exposure time. In this work, an electrostritive Lead Lanthanum Zirconate Titanate (PLZT) ceramic substrate was used to enable electrically varying the azo grating pitch, hence allowing for real-time modulation of SP signals.

PLZT ceramics have the following chemical formula Pb_1-x La_x (Zr_y, Ti_1-y)_1-0.25x V^B_0.25x O₃ and are known as PLZT (100x/100y/100(1-y)). PLZT compositions (a/65/35) with 7<a<12, are known as relaxor ferroelectrics, since they exhibit a frequency-dependent diffuse ferroelectric-paraelectric phase transition in their complex dielectric permittivity. These compositions show strong potential for transducer applications because they exhibit a large electrostrictive strain with a very slim ferroelectric hysteresis. PLZT (9.5/65/35) has one of the highest electrostriction coefficients in the series $(γ_{333} = 6.14 \times 10^{- 16} m^{2} . V^{- 2})$ [24], and therefore was the chosen composition in this work. A literature review indicates that it was primarily the electro-optic properties of PLZT ceramics that have contributed to their use in tunable optics applications, such as optical switching [25] and variable focal-length lenses [26]. In this work, we report that the electromechanical properties of PLZT (9.5/65/35) arising from the application of a combination of AC and DC bias electric fields result in extremely accurate control over the SP excitation wavelength.

2. Experimental overview

2.1 Sample preparation

Several substrates of PLZT (9.5/65/35), each having a thickness of 0.64 mm, were cut to rectangular dimensions of 10 x 17 mm². After cleaning, a Baltec SCD-050 sputter coater was used to deposit 100 nm-thick layers of platinum on the edges of both upper and lower surfaces of each PLZT sample to ensure the subsequent application of a uniform electric field and avoid non-linear distortion of the substrate. If only a top platinum electrode is deposited on the PLZT, the ceramic would then strain only at the upper surface and not the bottom surface causing an undesirable clamped condition and a reduction in the total strain. Electric wires were attached to the PLZT ceramic using silver paste, as illustrated in Fig. 1(a).

Fig. 1 (a) A 3-dimensional model showing the PLZT test sample with the electrical attachment points, the half-disc grating location and the top silver coating. (b) An Atomic Force Microscope image of the top layer of silver-coated grating.

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Azobenzene Disperse Red 1 molecular glass powders were dissolved in CH₂Cl₂ to yield a solution with a concentration of 3 wt%. The solution was then mechanically stirred for one hour before being filtered through a 0.45-micron syringe filter. Thin film deposition on the PLZT substrates was performed using a Headway Research spin-coater. After deposition, each slide was spun at a rate of 1250 rpm for 20 seconds to ensure a uniform spread. The films were then dried in a Yamato ADP-21 oven at 95°C for 30 minutes. The final product was a uniform thin film with an average thickness of approximately 400 nm, as measured using a Sloan Dektak II profilometer.

A diffraction grating was then inscribed on the azobenzene layer using a 532-nm Coherent Verdi V5 diode-pumped laser and a Lloyd mirror setup [13]. Gratings with pitches $Λ = 615 nm and 635 nm$ were inscribed on different PLZT substrates with a laser irradiance of 870 mW/cm² for an exposure time of 375 seconds, which yielded grating depths of approximately 150 nm, as measured with the Atomic Force Miscroscope (AFM). The grating vector was oriented along the 3-axis or the direction of the electric field, as depicted in Fig. 1(a). Finally, a 60 nm layer of silver was sputter coated in the center of the PLZT sample, on top of the grating, with a narrow width of only 2 mm. The silver layer took the same shape as the grating below it. Figure 1(b) shows an AFM image of the surface of the grating coated with silver. A nominal grating depth of around 80 nm was measured after the silver layer deposition.

For this experiment, surface plasmon resonance was intended to be excited at the silver/air interface and by probing the SP spectrum in reflection, SP signal modulation would occur only due to the electrostrictive effect and not the electro-optic effect of the PLZT ceramic, since almost no incident light is transmitted past the silver layer (the transmittance of a 60-nm silver film at a wavelength of 600 nm is 1.13% [27]).

2.2 Experimental set-up

Once a test sample was fabricated, it was placed vertically on a fixture where light from a ScienceTech Model 9040 scanning spectrometer was passed through a mechanical chopper, a linear polarizer set at 45 degrees, followed by a second polarizer with its transmission axis set either vertically (TE polarization) or horizontally (TM polarization). The light was then collimated and reflected off of a concave mirror before being normally incident upon the test sample, which was angled slightly off-vertical. Light reflected from the test sample was directed to a second mirror in front of the sample, before finally being incident onto a silicon photo detector. The signal from the photo detector was amplified using a Stanford Research Systems Model SR830 DSP lock-in amplifier and recorded on a computer. This allowed for spectral scans in reflection. The PLZT ceramic was electrically driven using an Agilent 33220A function generator connected to a Trek Model 610D voltage amplifier. To acquire the modulation signal of the test sample, the mechanical chopper was removed and the lock-in amplifier signal was referenced directly to the function generator during the spectral scans.

3. Theory

For a flat metal/dielectric interface, the SP wavelength $λ_{S P}$ is given by the following equation [13]:

λ_{S P} = n_{d} (\sqrt{\frac{{\tilde{ε}}_{r, m}^{'}}{n_{d}^{2} + {\tilde{ε}}_{r, m}^{'}}} \mp \sin θ_{i}) Λ,

where n_d is the refractive index of the dielectric medium,

{\tilde{ε}}_{r, m}

is the real part of the dielectric permittivity of the metal,

θ_{i}

is the light incidence angle and

Λ

is the grating pitch. For a non-flat metal/dielectric interface, such as a deep diffraction grating, Eq. (1) can be used to approximate the center of the SP photonic energy gap wavelength. For a silver/air interface and for normally incident light with a wavelength of 650 nm, Eq. (1) simplifies to the following [13]:

λ_{S P} \approx 1.027 Λ .

Therefore, a pitch variation caused by the PLZT ceramic should also affect the SP wavelength. When an electric field E₃ is applied onto the PLZT ceramic, the corresponding strain S₃ in the same direction as the field is given by [24]:

S_{3} = \frac{Δ Λ}{Λ} = γ_{333} E_{3}^{2} .

Therefore, combining Eqs. (2) and (3), we obtain that:

Δ λ_{S P} \approx 1.027 Λ γ_{333} E_{3}^{2} .

For example, when applying a DC electric field of 0.35 MV/m and knowing the electrostriction coefficient of PLZT (9.5/65/35)

(γ_{333} = 6.14 \times 10^{- 16} m^{2} . V^{- 2})

, the calculated maximum strain is

7.52 \times 10^{- 5}

and the maximum SP wavelength shift for a grating with a pitch around 600 nm is only about 0.05 nm. Clearly, this wavelength shift is too small to measure using a scanning spectrometer, but experimental measurements of the grating pitch variations under AC fields are possible using signal modulation, since it provides an amplification of the expected grating pitch change dependent on the slope of the reflected SP scan. Theoretically, a small sinusoidal oscillation of

λ_{S P}

at twice the electric field frequency would yield a modulation signal that is nearly identical to the localized slope of the SP spectrum scan. The steeper the slope in the reflected SP scans, the larger the measured modulation signal. When a combined AC and DC bias electric field is applied on the PLZT ceramic, both first order piezoelectric and second order electrostrictive strain is expected in the material’s response at the first and second harmonic frequency of the electric field respectively [24]. For an applied sinusoidal electric field in the form of

E_{3} = E_{d c} + E_{0} \cos (ω t)

, the strain at different harmonics can be approximated as:

\begin{array}{l} S_{3} ≃ [...] + [\begin{array}{l} d_{33} E_{0} + 3 ψ_{3333} E_{D C}^{2} E_{0} + \frac{3}{4} ψ_{3333} E_{0}^{3} \\ + 2 γ_{333} E_{D C} E_{0} + 4 χ_{33333} E_{D C}^{3} E_{0} + 3 χ_{33333} E_{D C} E_{0}^{3} + ... \end{array}] \cos (ω t) \\ + [\begin{array}{l} \frac{3}{2} ψ_{3333} E_{D C} E_{0}^{2} + \frac{1}{2} γ_{333} E_{0}^{2} \\ + 3 χ_{33333} E_{D C}^{2} E_{0}^{2} + \frac{1}{2} χ_{33333} E_{0}^{4} + ... \end{array}] \cos (2 ω t) + [...] \cos (3 ω t) + ... \end{array}

where

d_{i j}

is the piezoelectric coefficient,

γ_{i j k}

is the electrostriction coefficient,

ψ_{i j k l} and χ_{i j k l m}

are coefficients relating the change of third and fourth powers respectively of the electric field to the strain tensor [24]. For the PLZT ceramic used in this experiment, the dominant electromechanical coefficient is

γ_{i j k}

, which is the electrostriction coefficient.

4. Results and analysis

Surface plasmon resonance on a diffraction grating will only occur when the incident light polarization is along the grating vector or perpendicular to the grating’s peaks and troughs [28]. In a spectral scan, a SP is seen as a positive peak in transmission and a negative peak in reflection. The latter is due to the fact that light emitted by the resonant electrons in the metal will be 180 degrees out of phase with the incident light, creating destructive interference, while transmitted SP light will interfere constructively with the incident light. The easiest way to observe a SP excited with a linear diffraction grating is to normalize one incident light polarization spectrum over another spectrum obtained using the light’s orthogonal polarization. For instance, for a grating oriented with its vector horizontal, SP will only be excited using TM polarization, and a TE polarization scan can be used as the normalization scan.

Figure 2 shows the SP spectra of two gratings having pitches of $Λ = 615 and 635 nm$ for normally incident light. The theoretical SP wavelengths obtained using Eq. (2) were calculated to be 631 and 652 nm respectively and are indicated by the vertical dotted lines in Fig. 2. Furthermore, two other wavelengths, 630 and 640 nm, are indicated with arrows and these correspond to the wavelengths at which maximum modulation signals were subsequently measured in this experiment. The SP resonance plots, seen in Fig. 2, are the result of a SP standing wave that occurs when the first forward and backward diffracted orders from the grating are coupled to the SP simultaneously. At off-normal incidence, two $λ_{S P}$ values are possible according to Eq. (1); as the wavelength is increased, the forward diffracted order couples to the SP first, followed by the backward diffracted order. Typically, the SP standing wave, observed at normal incidence, yields a plasmon that is twice as strong as those plasmons observed at off-normal incidence.

Fig. 2 Normalized reflected intensity as a function of wavelength for grating pitches of 615 nm and 635 nm.

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As seen in Fig. 2, very strong SP excitation occurred for both gratings, each associated with a large plasmonic energy gap extending over a wavelength range of nearly 150 nm. This indicates that the gratings are too deep for the flat interface assumption. From experiments previously done in our lab [29], we have observed that the deeper the gratings, the stronger the SP signals at normal incidence, but also the wider the wavelength range of the SP photonic energy gap at normal incidence. The spectrum scans in Fig. 2 were taken with the lock-in amplifier set to the reference frequency of the mechanical light chopper and no voltage was applied on the PLZT substrates. The chopper was subsequently removed and a sinusoidal electric field having peak-to-peak amplitudes of 0.6 and 0.7 MV/m and a randomly-chosen frequency of 158 Hz were applied onto the PLZT samples with those gratings having pitches of 615 and 635 nm respectively. The lock-in amplifier was then referenced to twice the function generator frequency and modulation scans were obtained for both gratings as a function of wavelength.

As seen in Fig. 3, very sharp and narrow peaks are present in the modulation scans for normally incident TM polarized light at the second harmonic of the electric field. Since the grating vector was oriented along the horizontal, no modulation occurred for TE polarized light. This indicates a successful grating pitch variation due to the electrostritive effect of the PLZT substrates. Other spectral scans, not shown here, were taken at incidence angles of 2, 4 and 6 degrees, and it was observed that the central modulation peak at normal incidence would split into two symmetrical peaks at off-normal incidence, with each peak having half the maximum signal strength as the one observed at normal incidence. This behavior is easily explained as an indirect consequence of having two different $λ_{S P}$ values as explained earlier.

Fig. 3 Reflected modulation signals for TE and TM polarizations at the second harmonic for gratings with pitch (a) 615 nm and (b) 635 nm.

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The shallow wide-band modulation signal between 500 and 550 nm and the slight peak at 625 nm in the TE polarization plot in Fig. 3(a) are likely due to a low signal-to-noise ratio or a slight misalignment of the polarizers in the experimental setup. Since the modulation signal was only observed for TM polarized light, this means that only the SP resonance was affected by the grating pitch variation. The maximum modulation signal wavelengths were 630 and 640 nm for those gratings with pitches of 615 and 635 nm respectively. These wavelengths are also marked in their respective SP plot in Fig. 2. It is highly likely that the maximum modulation signal wavelengths are associated with the highest localized slope of the plots in Fig. 2. Theoretically, a small variation in the grating pitch should affect the central SP wavelength and would yield a modulation plot similar to the absolute value of the first order derivative of the SP plots in Fig. 2. The theoretical first order smoothed derivatives of the plots in Fig. 2 were calculated using Origin Pro software and the results are presented in Fig. 4.

Fig. 4 Absolute value of the theoretical first order smoothed derivative of the SP plots in Fig. 2 for gratings with pitch (a) 615 nm and (b) 635 nm.

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For the grating with a 615 nm pitch, a maximum theoretical slope was calculated to be at a wavelength of 630 nm, corresponding exactly to the experimentally measured maximum modulation wavelength in Fig. 3. For the other grating having a 635 nm pitch, the maximum theoretical slope is at 645 nm, while the measured maximum modulation wavelength was 640 nm. This difference could be associated with the resolution of our scanning spectrometer, a measurement uncertainty or fabrication defects in this particular sample. Also, it is apparent that the general shapes of the theoretical plots in Fig. 4 don’t correspond to the actual measured modulation signals in Fig. 3. It appears that electrically varying the grating pitch only affects a fairly narrow region in the SP spectrum. One can assume that electrically increasing the grating pitch should also affect the grating depth due to Poisson’s ratio; it could also indirectly decrease the width of the SP photonic energy gap. However, this doesn’t seem to be the case since most of the secondary peaks in the theoretical modulation plots are missing in the measured modulation plots. It’s also noteworthy that the widths of the experimental modulation peaks are narrower than those in the theoretical plots in Fig. 4. This also points to the fact that even with a large SP photonic energy gap, only a small portion of the SP plot is actually oscillating. This might offer clues for explaining the origin of plasmonic photonic energy gaps.

For the 615 nm pitch grating, the peak-to-peak amplitude of the electric field was varied between 0.3 and 0.6 MV/m and the reflected modulation signals for TM polarized light were plotted as a function of wavelength. As seen in Fig. 5, the maximum modulation signal increased with the electric field amplitude. Interestingly, the electric field frequency was increased from 158 Hz to almost 1000 Hz on the same sample at an amplitude of 0.6 MV/m and it was found that the maximum modulation signal strength and wavelength remained nearly unchanged.

Fig. 5 Reflected modulation signal as a function of wavelength for various electric field amplitudes.

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According to Eq. (5), the application of a DC bias electric field in addition to the sinusoidal electric field will affect the total strain exhibited by the PLZT ceramic at various harmonics of the AC field frequency. As seen in Fig. 6(a), the maximum modulation signal at twice the electric field frequency increases almost linearly with the AC field peak-to-peak amplitude for the PLZT sample with the 615 nm pitch grating. This is unexpected since the dominant electrostrictive effect corresponds to a quadratic strain relationship with the field. Perhaps, the electric field didn’t reach values high enough to show the quadratic behavior. The maximum modulation signal was enhanced upon the application of a DC bias electric field, with a best overall modulation enhancement occurring at 0.3 MV/m DC bias. This enhancement occurs since the application of a DC bias creates stronger electric dipoles in the PLZT ceramic and enhances its total strain response by means of the harmonic electromechanical coefficients up to the fourth order, as discussed elsewhere [24]. However, if the DC bias field is too strong, it hinders the PLZT dipoles rotation at the AC field frequency and a reduction of the total strain is observed [30], as seen in Fig. 6(a) for an AC field peak-to-peak amplitude of 0.4 MV/m.

Fig. 6 (a) The maximum reflected modulation signal at 316 Hz as a function of AC electric field peak-to-peak amplitude in addition to various DC bias fields, (b) the maximum reflected modulation signal at 316 Hz as a function of DC bias electric field in addition to various AC field and (c) the maximum reflected modulation signal at 158 Hz as a function of DC bias electric fields at a peak-to-peak AC field amplitude of 0.1 MV/m.

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Figure 6(b) is complimentary to Fig. 6(a) and it shows that the sign of the DC bias field has no effect on the maximum modulation signal enhancement. Furthermore, Eq. (5) predicts a first order piezoelectric strain with the application of a DC bias. As seen in Fig. 6(c), a small 0.1 MV/m peak-to-peak AC field was applied onto the sample and the DC bias was varied from −0.25 MV/m to 0.25 MV/m. Modulation signals were measured at the first harmonic, but clearly not as high as those measured at the second harmonic. Finally, the goal of Fig. 6 is to illustrate that it is possible to electrically tune the SP wavelength, although in a narrow wavelength band but with extreme precision, by applying a combination of DC bias and alternating electric fields.

5. Conclusion

Surface relief diffraction gratings were inscribed on azobenzene thin films spin coated on a PLZT (9.5/65/35) ceramic substrate. The gratings were coated with a layer of silver in order to excite surface plasmons at the interface between the silver and air. Light spectra were taken in reflection and wide bandwidth plasmonic signals were measured. Upon the application of longitudinal DC bias and AC electric fields on the PLZT substrate, a change in the grating’s pitch occurred that led to a variation in the measured SP wavelength. The applied electric fields allowed the measurement of modulation signals at the first and second harmonic frequencies of the field, indicating SP wavelength shifts. It was found that DC bias fields enhanced the modulation signals and that it was possible to accurately shift the SP wavelength within a narrow range.

Acknowledgment

The corresponding author would like to acknowledge research funding from the National Science Research Council of Canada Discovery Grants (RGPIN-2015-05743).

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Electrostrictive effect for active control of surface plasmon signals

Abstract

1. Introduction

2. Experimental overview

2.1 Sample preparation

2.2 Experimental set-up

3. Theory

4. Results and analysis

5. Conclusion

Acknowledgment

References and links

Cited By

Figures (6)

Equations (5)

Optics Express