1. Introduction

Propelled by advances in nanoscience and nanofabrication technology, plasmonics is expanding its application scope and bearing fruit [1–4]. Once surface plasmon polaritons (SPPs) are excited in some ways, the electromagnetic fields can be confined in subwavelength scale and hence intensified greatly. Consequently, nonlinear response of optical materials under the influence of the strengthened electromagnetic fields can be enhanced accordingly [1,2,5]. In the past years, by pumping more electrons into the skin layer of transparent indium tin oxide (ITO) films with an external (or internal) electric field, the plasma frequency of the ITO skin layer was shifted successfully towards shorter wave [6–10]. These techniques could be used in designing plasmonics based photonic devices especially in near-IR and visible regimes, such as epsilon-near-zero metamaterials [11], by which electrooptic modulators were designed and implemented successfully [12,13]. Along the line in electrostatic modification of ferroelectric materials by ITO coating [14], this work aims at studying monomolecular layer charge accumulation in ferroelectric crystals with nonlinearity. Without ITO coating, the air/crystal interface of true nanolayer was swarmed with charge carriers and SPP excitation is possible. From another aspect, although attenuated total internal reflection offers standard ways in exciting nonradiative SPPs, it is rather difficult to miniaturize the configurations for small size requirement in most applications. To circumvent this inconvenience, alternative ways in exciting SPPs are often sought and used in plasmonics [1,2,15]. Metallic gratings were employed to supply a quasi-wavevector of m(2π/Λ) to the x component of the incident light wavevector k_xin to reach the nonradiative region (right-hand side of the air light line) [1,2,15]. However, metallic gratings are not updatable and hence unsuitable for reconfigurable applications. Recently, using updatable phase grating to make up the deficiency in phase matching condition for SPP excitation, we have demonstrated excitation of SPPs in ITO coated Fe doped lithium niobate slabs [8,9]. It was evidenced that the nonlinear response of the lithium niobate was raised remarkably within subwavelength scale [8,9], including unity refractive index change. This work offers opportunity in designing tuneable plasmonics based devices. Meanwhile, photorefractivity enhancement of polymer through surface plasmon effects was investigated using proper methods [16], which could be used in three-dimensional (3D) image processing and displays. Along this line, it will be highly desirable to excite SPPs on nonlinear optical materials with faster response. Of all promising nonlinear optical materials, (Sr_0.75Ba_0.25)Nb₂O₆ (SBN) [17] and (K_0.5Na_0.5)_0.2 (Sr_0.75Ba_0.25)_0.9Nb₂O₆ (KNSBN) [13–19] have many advantages in growth and processing over their counterparts, barium titanate or potassium niobate, i.e. without 90° domains and low-temperature ferroelectric phase transition. Moreover, several crystallographic sites are empty, which makes it possible to tailor crystal properties [18–20]. Excellent photorefractive performances of KNSBN crystals can be seen from high reflectivity of self-pumped phase conjugation [21–23] and microsecond holographic recording times. In this work, Cu:KNSBN was chosen in place of lithium niobate. We studied electrostrictive and photoinduced field driven charge carrier accumulation on the sample faces. Upon applying electric field, evident surface grating can be written on one of the a-faces with two incident p-polarized laser beams. This surface grating was so strong that it stole all energy away from the bulk fanning light. At the same time, a 2D diffraction pattern emerged around the two transmitted light beams. To delve into the origin of the surface grating formation, we measured photoinduced and electrostrictive currents. The experimental results revealed that the charge accumulation on the c-faces accompanies the charge accumulation on the a-faces. Therefore, the surface grating originated from surface charge accumulation on the a-faces. In addition, the substantial variation of reflectivity on the first surface upon application of external electric field and its evident energy coupling with other laser beams within the sample suggested the physical processes was in the subwavelength scale. The SPPs involvement was proposed to elucidate all these observations. We report our work as follows.

2. Experiment

The KNSBN sample used throughout this work was single-domain crystal with 0.05 wt.% Cu doping and size 8.5 mm × 8.0 mm × 5.0 mm. The c-axis is parallel to the 8.5 mm edge. The sample was cut from a slug grown by conventional Czochralski technique. Firstly, all reagent grade Nb₂O₅, K₂CO₃, Na₂CO₃, SrCO₃, BaCO₃ and CuO were mixed in stoichiometry and were ball milled. Secondly, the materials were pressed into pellets and sintered at 1300 °C for 24 hours. Thirdly, these pellets were put into a platinum crucible and were molten at 1500 °C. Finally, the sample was grown with seed rotation speed of 25 rpm and pulling seed of 1.5 mm/hr. All six faces of the sample were optically polished, and the opposite c-faces (8.0 × 5.0 mm²) were coated with 150 nm thick ITO films with magneto-sputtering methodology (refer to Fig. 1(a)).

 

Fig. 1 (a) Schematic of surface grating recording in a bulk KNSBN sample and high diffraction orders casting on a viewing screen; (b) a photograph taken prior to applying voltage; (c) a typical 2D diffraction pattern taken after applying external voltage 5s (left side are the light spots of 561 nm laser beams, right side are the diffraction spots of reading beam at 532 nm).

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The photoinduced current intensity in the KNSBN sample was measured in a closed loop with a picoammeter (Keithley, 6485). To realize this objective, the voltage source in Fig. 1(a) was replaced by the picoammeter and the laser (532 nm) illuminating the ITO coated surface in the normal direction.

3.Results and discussion

Fig. 1(a) illustrates the structure of the Cu:KNSBN sample, the prime and diffraction light beams. The main phase grating was written with two light beams from a continuous laser at 561 nm (Cobolt Samba 100). The prime and diffraction beams along the central row were marked with −4,-3, −2, −1, 0A, 0B, + 1, + 2, + 3, + 4, and so on. Two p-polarized laser beams were incident into the sample at incident angle 20° between the beam bisector and surface normal (Fig. 1(a)), equal both in diameter (2.5 mm) and in power (17.0 mW). The full cross angle between the two beams was set at θ = 0.61°. Upon applying 5.0 kV voltage on the sample along its c-axis, a diffraction pattern emerged after 1s and expanded in high order numbers. Fig. 1(b) exhibits a photograph taken before applying external voltage. Fig. 1(c) exhibits a photograph taken after applying external voltage about 5s. The polarization of the diffraction dots was all the same to the directly transmitted laser beams, i.e. p-polarized light. There were 14 orders emerging from the 5.0 mm-thick sample.

Considering the phase grating spacing Λ = 23.2 μm, one sees that the grating behind the 34 orders diffraction pattern shown in Fig. 1(b) must be a surface one, based on the criterion given in [24]. If a volume grating dictates the diffraction, it should be in rigorous Bragg condition and thus only two transmitted dots would be seen, since the ratio d/Λ = 215.5 is far above criterion for a thick grating d/Λ >10 [24]. To prove the surface grating, we used another laser beam at 532 nm incident to the grating region and got 2D diffraction patterns at arbitrary incidence angle (not shown).

After being convinced about the surface dominating gratings written in the KNSBN sample, one can understand that something must happen near the surfaces leading to such a 2D diffraction pattern. It is well known that Cu:KNSBN was electostrictive, strong in pyroelectric (PY) effect and also with photovoltaic (PV) effect. Upon applying electric field along c-faces, the electostrictive, PV and PV effects will result in charge accumulation near the air/KNSBN interfaces, which will change its optical properties accordingly.

To see how much the photoinduced charge could be accumulated near the air/KNSBN interfaces (a-faces), the photoinduced current intensity in the KNSBN sample was measured. The current dynamic curves during turning on (off) light (at 532 nm in power 350 mW) were shown in Fig. 2(a) and the peak current was plotted against illumination power in Fig. 2(b). When applying 5 kV voltage across the c-faces, there are about 40 times higher current density measured with two 2.0 mm² silver paint electrodes on the a-faces (as shown in Fig. 2(c)). From the current intensity obtained from the closed loop case, the rough calculated electron density that was accumulated near a mono-molecular layer [25,26] reached 10²⁰ cm⁻³ magnitude.

 

Fig. 2 (a) Photoinduced current dynamic curve upon turning on illuminating laser light (the inset is the shutting down current dynamic curve); (b) Photoinduced peak current intensity versus illuminating light power; (c) Electrostrictive current dynamic curve upon turning on voltage source with no light illuminating (the inset is the turning off current dynamic curve); (d) Plasmonic band structure of the air/KNSBN interface with the adjacent curves with order increment ∆m = 3, the red line corresponding to k_xin, the green line represents light line in the KNSBN sample (k_x), the bold black line is the original SPP dispersion curve.

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When an air/KNSBN interface was flooded with electrons, the effective electron density of the interface was raised significantly. This kind of alteration was referred to as electrostatic modification, which was employed widely in designing electronic devices. Here, the collective electrons and positive ions form the basis in supporting SPPs. In view of plasmonics, the plasma frequency (ω_p) of the collective electrons and ions could be calculated by expression as [27]

The dispersion relation of a SPPs propagation on the interface can be written in the form

It is known that a thin phase grating diffracts an incident light into various high orders. Similar to the metal gratings used in most reported works [15], the role of the phase grating in this work is to supply a quasi-wavevector of m(2π/Λ) to the x-component of incident light wavevector k_xin [1], where Λ is spatial period of the phase grating. The condition for SPP excitation by the phase grating is expressed as

Based on the expressions given above, we computed the plasmonic band structure in the air/KNSBN interface, exhibited in Fig. 2(d). Some orders of quasi-wavevector supplied by the phase grating were not drawn to make the illustration easier to read. Since the diffraction orders are symmetrical, we consider that the SPPs propagate in both positive and negative directions of the x-axis. Therefore, both the positive and negative k_x should be considered. Note that the manifold dispersion curves have various crossed points with the laser light frequency within the radiation zone demarcated with the light lines, implying that some diffracted waves could couple with SPPs.

When we studied the electrostrictive and photoinduced surface grating, it was found there were distinctly a bulk grating and a surface grating which compete each other in energy coupling. To see clearly the energy coupling competition, the incident angle was set at 10°. Without external electric field applied on the sample, the bulk gratings resulted in obvious fanning effect (Fig. 3(a)). It was noticed that the scattering light and diffraction rings formed on the right side of the photograph (Fig. 3(a)). It should be pointed out that the scattering light emerged within one second. However, upon applying 5.0 kV voltage on the two c-faces of KNSBN sample, the fanning pattern and diffraction rings disappeared rapidly (Fig. 3(b)). At the same time, the diffraction pattern around two directly transmitted dots expanded in rows and orders and became quite bright (Fig. 3(b)). It was zoomed in (Fig. 3(c)) to see the details of the central part. At first glance, one may think these dots were formed from four wave mixing processes discussed systematically by Sturman et al. [28] Since all the dots are mainly extraordinary to the slab, thus the process should be of ee→ee processes if the dots indeed originated from four wave mixing. However, after carefully checking the scattering angle based on KNSBN birefringence data, it was found that the dots cannot be explained with simple four-wave mixing processes alone [28].

 

Fig. 3 (a) Transmitted diffraction dots when two laser beams were incident onto the KNSBN sample; (b) exhibits a typical diffraction pattern when 5.0 kV voltage was applied on the KNSBN sample after 5 seconds waiting time; (c) schematic diagram shows the reflection beam on the first face of the Cu:KNSBN sample and its beam coupling with another incident laser beam I₂₀ within the subwavelength modified layer.

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From Fig. 2(d), it is seen that for a smaller crossing angle, the grating period is getting larger, and hence the two SPP dispersion curves are getting closer for the same ∆m. Therefore, there are more curves packed in radiation zone between the two light lines. In a PR sample, a phase grating tend to self-adjust automatically. Consequently, the smaller angular distance can be easily amplified. This can elucidate why the scattering light with large angle (fanning light) lose power while the diffraction and scattering light with smaller angle was gaining power over time, surrounding the two transmitted dots (refer to Fig. 3(a) and (b)).

Up to this point, the high diffraction orders affirmatively rooted in surface phase grating which was enhanced by SPP. We may emphasize that the KNSBN crystal used in this work was intrinsically anisotropic and this actually eases the SPP excitation along horizontal and vertical direction [29]. And this should contribute to the strong 2D diffraction patterns observed (Refer to Figs. 1 and 3).

In addition, we performed a simple experiment to directly verify the photoinduced modification of the air/KNSBN interface by PY effect. When a p-polarized laser beam at 561 nm was incident onto the -a face at an incident angle 25° and 5.0 kV voltage was applied on the sample, the reflectivity from the very first interface grew from 15.08% to 15.28% (Fig. 3(c)), equivalent to refractive index change from 2.270 to 2.283. That is, the photoinduced refractive index change was 0.023. This refractive index change is much larger than the typical refractive change 10⁻³ to 10⁻⁴ in photorefractive effect. Moreover, when the KNSBN was illuminated by another coherent laser beam I₂₀ at the same time, a dynamic change in the reflection power on the first surface was observed. The maximum reflectivity was 15.61%. This hinted that the energy coupling within subwavelength scale was undergoing, since the reflectivity on the first surface was determined by the molecular layer of less than half a wavelength (Fig. 3(c)). As shown in Fig. 3(c), the intensity increasing in I₁’ must result from the coupling with I₂₀ in the subwavelength modified layer. To emphasize the increasing was caused by the coupling from the transmitted portion of I₂₀ at the first interface, all other nonrelated beams are drawn in dashed lines and many other reflection and high order diffraction beams are omitted in the drawing. The thickness of the subwavelength modified layer was exaggerated purposely in the drawing for clarity. I₁ and I₂ are the transmitted beams after penetrating the modified layer. These two simple straightforward experiments provided solid support to the SPP involvement picture.

4. Conclusion

In summary, 2D diffraction patterns from a bulk Cu:KNSBN sample was explained with surface dominant grating written due to charge accumulation on the air/KNSBN interface, which originates from electrostrictive, PY and PV effects. Based on photoinduced current measurement, a theoretical consideration was given in understanding the excitation of SPPs via phase grating in electrostatically modified air/KNSBN interface. As high as 0.013 refractive index change on the very first interface upon applying electric field and 0.023 dynamic change owing to energy coupling with another laser beam served as solid support to the picture of the SPP excitation. This subwavelength energy coupling might be useful in designing photonics circuits.