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We designed and implemented periodic bar arrays metamaterials to select appropriate frequencies of terahertz (THz) waves propagating in a LiNbO3 sub-wavelength waveguide. The spatial and temporal electric field profiles of the THz waves were recorded using a time-resolved phase-contrast imaging system. The metamaterials can operate as a band-stop filter to realize blocking back THz waves in a band range of 0.6–1.0 THz, while transparent transmission for the fundamental mode of the slab over a range of 0.3–0.6 THz.
© 2015 Optical Society of America
1. Introduction
In recent years, THz-frequency phonon polariton generation, control and detection have received extensive attention due to their outstanding capabilities in THz spectroscopy, imaging and advanced signal processing [1–4 ]. Usually, phonon polariton can be generated in ferroelectric crystals such as LiNbO3 (LN) or LiTaO3 [5] via impulsive stimulated Raman scattering (ISRS) using femtosecond laser pulses [6]. Phonon polariton wave is the coupling of electromagnetic wave and lattice vibrational wave [7], and the electromagnetic component can be coupled into free space and acts as a source for intense THz pulses. At frequencies less than 2 THz, it behaves primarily like electromagnetic wave and performs as a THz wave in ferro-electric crystal. Due to the large index-mismatch with femtosecond laser, the THz wave does not propagate collinearly with the pump beam, instead in a Cherenkov radiation pattern. When generated in a thin slab LN crystal, the THz wave propagates almost perpendicular to the pump beam. Furthermore, when the sample thickness becomes less than the THz wavelength, the sample acts as a sub-wavelength waveguide, the strong field of the THz wave can interact with patterned structure such as interferometer structure [2] or 2D photonic crystal structures [8, 9] embedded in the slab waveguide. What’s more, the strong evanescent field of the THz wave can interact with patterned structure or materials deposited on the LN surface such as THz resonant antennas [10]. These capabilities make it possible to generate [11, 12], control, and detect the terahertz field in an integrated platform, the sub-wavelength LN waveguide.
When THz wave generates in a sub-wavelength slab crystal, it is broken up into discrete modes according to the waveguide size [13,14]. Selection of appropriate frequencies and modes is very important for the integrated platform of THz processing. The frequency distribution of generated THz wave can be controlled using appropriate beam shaping in space or time [11,12], or using frequency filtering. Metamaterials research has produced innumerable typical examples and applications such as negative index materials [15, 16], electromagnetic cloaking [17], perfect lensing [18, 19], sub-diffraction imaging [20], and perfect absorption [21, 22], to artificially manipulate refraction index and impedance utilizing randomly or periodically structured media. Metamaterials offer a possibility to control the linear as well as the nonlinear behavior for different frequencies of the electromagnetic spectrum, especially for THz frequencies [23, 24] because of the weak absorption and the ease of fabrication.
In this paper, we design and fabricate a band-stop filter using THz metamaterials composed of periodic bar arrays surfaced on a LN slab. The metamaterials can be tailored to select desired frequencies for THz waves propagating in the LN sub-wavelength waveguide. We use a time-resolved imaging method to visualize and quantitatively evaluate THz waves propagation. The method enables detection over a wide wavelength range and allows us to quantitatively resolve electric fields both spatially and temporally, exposing the details of frequency selection evolution. The behavior that the fundamental mode in a range of 0.3–0.6 THz transmits through the metamaterials structure and THz waves over a range of 0.6–1.0 THz are blocked back can be completely observed when the imageable propagation process is analyzed.
2. Experimental section
Metamaterials can be designed to yield a desired response at frequencies from the microwave through to the near visible. Importantly, suitable design flexibility is afforded by the judicious metamaterial elements to control THz frequency waves. For example, the frequency filtering has been achieved by means of band-stop filter embedding THz waveguide in a microstrip line [25], or notch filter using frequency-agile metamaterials [23]. However most metamaterials are designed in a plane perpendicular to the wave propagation direction. Here we try to introduce a type of through-plane metamaterials, 2D array of gold bars surfaced on a LN slab, to select appropriate frequencies and modes. One unit cell of the 2D bar array is shown in Fig. 1(a). The THz waves propagate through the metamaterials along −x direction. The resonance frequency range is designed to cover most frequencies of higher order modes of the LN slab waveguide, especially to cover the frequencies of the first-order mode. It should reflect back most of the higher order modes and transmit most of fundamental mode, whose frequencies are below the lower limit of the stop bandwidth. The bar length L, the gap g between bars (periodicity along z) and the gap d along the propagation direction (periodicity along x) will all affect the resonance frequencies.
Fig. 1 Metamaterials design and numerical calculation results of reflected spectrum. (a) An individual unit cell of metamaterials, gold bar (yellow) is deposited on the LN slab (grey) surface, the bar width is fixed to 5 μm, L is the bar length, d and g are the gaps between bars along x and z directions, −x direction is the propagation direction of THz waves, the thickness of LN slab is 53 μm along y direction; figures (b)–(d) shows reflected energy flow (Sr) vs frequency as a function of g, L, d, respectively.
We use FDTD method to simulate the reflected THz spectrums shown in Fig. 1. According to the experimental results in [14], the simulated THz source is set in a range of 0.3–1.0 THz and the polarization of electric field is parallel to z axis. When THz waves pass through the metamaterials along −x direction in LN slab plane, the reflected energy flow is calculated as a function of frequencies with different L, g and d parameters to show the filter ability. Firstly, we calculate the THz spectrum reflected by a 1D array of bars (long bars along z, g = 0) with d = 50 μm as shown in Fig. 1(b). The width of all the bars are fixed to 5 μm for convenient fabrication. The reflected spectrum is a narrow band centered at 0.7 THz. It can act as a notch filter to effectively reflect this narrow band of THz waves. However we need a relative broad band that can cover frequencies from 0.6 THz to higher frequency around 1.0 THz. As we calculate, a L = 50 μm gold bar is at resonance at around 0.5–0.75 THz, so we add gaps g between L = 50 μm bars along z direction. By this way, we acquire a relative broad reflected band via 2D array, shown in Fig. 1(b). By changing g = 30, 50, 70 μm respectively, the reflected frequency bands are almost the same in a range of 0.58–0.75 THz. Then, we fix the parameter g = 50 μm. In the further simulations we change the length of bars L = 30, 50, 70 μm respectively when g and d are fixed to 50 μm, and we also change the gap size d = 30, 50, 70 μm respectively when the other two parameters are fixed to 50 μm. The numerical calculation results are shown in Figs. 1(c) and 1(d). Comparing to the best result (red line in Fig. 1(c), L = d = g = 50 μm), two overlapped peaks are separated and shifted when L is changed. When d is changed, the band range of reflection dramatically changes as shown in Fig. 1(d). The bandwidth of reflection is mainly affected by the bar length and the gap between bars along the propagation direction. It is well known that photonic crystals have the ability to manipulate light comes from their unique dispersion relations and the presence of the photonic band gap, for example, a range of frequencies cannot propagate inside the photonic crystals. The periodic electric resonant gold bars along the propagation direction can act similar to the photonic crystal. The periodic spatial nature that the deposited resonant structures makes a periodic boundary condition for THz wave propagation, and the existence of the periodic boundary condition gives rise to a band gap. According to the experimental results, the most energy of higher order modes concentrate in a range of 0.6–0.8 THz. Referred to the simulation results shown in Fig. 1, parameters L, g, and d are all set to 50 μm to select appropriate frequency and mode.
As shown in Fig. 2, we utilized the phase contrast imaging method to observe the time-resolved imaging of THz wave propagating in bar arrays metamaterials structure, which was fabricated on LN substrate using ion-beam sputtering coating. The standard ultrafast pump-probe setup was achieved by separating a laser beam into a pump beam and a probe one (90% pump, 10% probe). The temporal resolution was 120 fs, which was determined by the probe pulse duration, and was about one-tenth of the THz wave duration. The imaging resolution can be achieved to 5 μm, which was about a few tenths of the THz wave wavelength in LN crystal. The THz wave was generated through ISRS by focusing an intense pump laser (800 nm central wavelength, 120 fs FWHM, 1 kHz repetition rate, 500 μJ/pulse) into a 53 μm thickness LN slab by using a cylindrical lens. The focusing line acted as a line source for THz radiation. The generated THz wave, which was also polarized along the optic axis of the sample, propagated along the slab crystal plane. The incident pump beam was tilted by θ =30° relative to the optical axis of the probe beam to avoid imaging disturbance of 400 nm light that was generated through second harmonic of the pump focusing light on the LN surface.
Fig. 2 Overview diagram of the main experimental setup. The sample, a 53 μm thickness LN slab, is imaged onto the CCD camera using three lenses, and the phase plate is placed in the Fourier plane of the first lens. Red beam represents the 800 nm pump beam and tightly focus in LN slab with an incident angle θ = 30°. Blue light represents the 400 nm probe beam and propagates perpendicular to the LN surface. In our setup, f1 = 10 cm, f2 = 15 cm and the focus length of the third lens is 15 cm. The left bottom inset shows schematic illustration of THz generation in LN crystal. Yellow lines represent THz waves generated when the pump is focused into the sample by a 20 cm focal length cylindrical lens. Yellow arrows show the propagation directions of THz waves, which are along the LN plane. Blue probe beam covers the whole sample.
The 400 nm probe beam (frequency-doubled, 120 fs duration, 1 μJ/pulse) was spatially filtered and expanded to obtain a large spot with minimal spatial variation before passing through the crystal. For optimum signal, the polarizations of the pump, probe, and THz field were all parallel to the LN extraordinary axis. The sample was imaged onto a CCD camera using three lenses, and a phase plate was placed in the Fourier plane of the first lens. The phase plate was fabricated using double sided optical flat made of fused silica with a surface area of 25×25 mm and a thickness of 1 mm. A 222±5 nm layer of (n ∼ 1.45 at 400 nm) silicon dioxide was coated onto the substrate and a 35×35 μm area in the center of the plate was developed using electron beam lithography and removed. This led to phase plate with an extremely flat surface that was transparent in the visible with a central square recessed by 222±5 nm, ∼ λ/4 for the 400 nm probe wavelength. At the center of the sample surface, bar arrays metamaterials structure was deposited as shown in Fig. 3(a). The structure consisted of 30×40 (x direction 30) unit cells.
Fig. 3 ( Media 1) (a) Schematic illustration of pump geometry and LN sample with surfaced metamaterials structure. The 800 nm pump beam (red) propagates through the crystal, while the THz wave (yellow) is guided in the slab. Metamaterials structure is composed of gold bar arrays, which are deposited on the front surface of the sample. The width of bar is w = 5 μm, the length L= 50 μm, and the gaps between bars at x and z directions are both equal to 50 μm. Figures (b)–(d) show the images of the THz electric field distribution taken at different time delays, the region within the red dotted lines is filmed with metamaterials structure. Pictures were captured (b) 20 ps, (c) 40 ps, and (d) 54 ps after THz wave was generated respectively.
The unit cell contained one 50 μm long 5 μm wide gold bar and had the dimensions 55 μm (x direction) × 100 μm (y direction). Each bar was composed of about 10 nm adhesion layer of titanium followed by a 150 nm layer of gold. Polarized probe beam passes through the sample, where it accumulates a spatially varying phase shift due to the THz-induced change in index. Subsequently, the phase plate brings about phase to amplitude conversion and the signals can be recorded by the CCD camera. The relationship between the induced THz field and phase shift is
where L is the slab thickness, λ is the probe wavelength, neo is the extraordinary index of refraction of LN for the probe, and r 33 is the electro-optic coefficient. ETHz is the average THz field experienced by the probe pulse as it propagates through the crystal in the y direction. In our experiment, the index change depends only on the z (vertical) component of the THz E-field. By this way, it is possible to quantitatively measure the THz fields in the images. By changing the delay between the pump and probe pulses, a series of images can be obtained. The image sequence can be compiled to form a movie ( Media 1) showing THz wave propagation.3. Results and discussion
The central wavelength of THz pulse is about 120 micrometers in the sample, while the thickness of LN waveguide is 53 micrometers. So the sample acts as a sub-wavelength waveguide, and the THz wave is broken up into discrete waveguide modes, the first three of which are visible as shown in Fig. 3(b). Electromagnetic waves of different frequencies have different phase velocities and group velocities in the medium waveguide, hence the energy of the THz pulse is allocated to different modes and the energy of each mode that propagates in the waveguide is not stable. In our experiment, the electric field amplitude is almost exclusively concentrated in the zeroth- and first-order waveguide modes. Owing to the dispersion of the slab structure, degradation of energy of all the three modes occurs as they propagate.
In Figs. 3(b)–3(d), the yellow arrows show the propagation directions of different modes of THz waves. The metamaterials structure is deposited in the region within the red dotted lines. For comparison, there are no patterns deposited on the upper part of the LN crystal. Figure 3(c) shows an image captured 40 ps after the THz wave generation. Most of the higher order modes are blocked back by the metamaterials structure and propagate oppositely. As a comparison, they still propagate forward with the zeroth-order mode in the upper part of the sample. After 54 ps, only the zeroth-order mode passes through the whole metamaterials structure, as shown in Fig. 3(d). The alternating arranged electric resonant gold bars change the effective ’through plane’ refractive index, which causes the lag in the THz wave propagation in Figs. 3(c) and 3(d). The transition process is a through plane process, and the periodic electric resonant gold bars along the propagation direction make a periodic boundary condition for THz wave. That leads to a band gap in a range of 0.6–1.0 THz as shown in Figs. 4(b) and 5(d). The active area includes a 2D array of 30×40 periodical gold bars, and the length of area is about 1.7 mm, which is relatively long to change the propagation properties of a THz pulse. Secondly, the central wavelength of the THz pulse is about 120 μm in the sample, while the thickness of LN waveguide is 53 μm. The sample acts as a sub-wavelength waveguide and the evanescent wave of different order modes in the air is strong enough to be affected by the metamaterial region. It can be seen in Fig. 3(d) that after transmitting through the metamaterials region, the 0th order mode has a little delay than the reference in the upper part without metamaterials. It means that the group velocity is slowed down when the 0th order mode transmits the metamaterials region.
Fig. 4 (a) Space-time plot of the propagating THz waves. Specific THz frequency band is blocked from the edge of metamaterials structure region (Meta region), and specific frequency band of the zeroth-order mode passes through the Meta region (within the dashed lines). The horizontal axis is the x-axis of the coordinate system in Fig. 3 and vertical axis is the delay time between the probe and pump pulses. The white lines are three selected positons for further analysis, x = 2.75 mm in reflection region, x = 1.75 mm in Meta region, and x = 0.5 mm in transmitted region, respectively. The lengths of these white lines are equal to 30 ps. Figures (b) and (c) are the THz field traces (measured at x = 2.75 mm and x = 1.75 mm, respectively) and their normalized Fourier spectrums. These two positions are equidistant to the incident boundary of Meta structure (at x = 2.25 mm). Figure (d) shows comparison of the Fourier spectrum in transmitted region (red, at x = 0.50 mm) with that in reflected region (blue, at x = 2.75 mm).
Fig. 5 Dispersion curves of the THz waves in the LN slab waveguide computed by taking 2D Fourier transformation of different regions of Fig. 4(a) and corresponding simulation results: (a) the initial incident wave (Inci. Region, 10–30 ps); (b) the Meta Region, 25–60 ps; (c) the transmitted wave (Tran. Region, 40–70 ps), which passes through the whole metamaterials structure; (d) the reflected wave (Relf. Region, 35–50 ps); (e) the transmitted dispersion curves from simulation; (f) the reflected dispersion curves from simulation. The horizontal axis of the figure is the wave vector, and the vertical axis is the frequency of THz wave in the sample. Overlaid on the experimental data (red curves) are the theoretical dispersion curves in air (white line), bulk LN (blue line), and the first three waveguide modes for a 53 μm slab waveguide (green curves).
Because the pump beam, which is line focused by a cylindrical lens, launches plane-wave THz transients that propagate laterally away from the focal region, in each image recorded at a different probe time delay the signal is uniform along the direction of the line focus (z direction). Therefore at each propagation distance from the origin, we can average the signal over vertical dimension, collapsing each 2D matrix of values and the corresponding image to 1D. In this way, the full temporal and spatial evolution of propagating THz waves can be displayed in a single graphic, as shown in Fig. 4(a). At x = 2.75, 1.75 mm positions, we measured the THz E-field and its Fourier spectrum, shown in Figs. 4(b) and 4(c). Furthermore, comparison of Fourier spectrums of transmission (red, at x = 0.50 mm) and reflection (blue, at x = 2.75 mm) is shown in Fig. 4(d). It is obvious that the first two order modes separate before they propagate into the metamaterials region (Meta region). In addition, most of the first-order mode is blocked back by the Meta region and reverses its propagation direction, while the zeroth-order mode out of band-stop range transmits through the whole Meta region. By this way, we select the fundamental mode using the metamaterials, which achieves as a THz filter for sub-wavelength waveguide. Since the energy of the second-order mode is much lower than that of the first two, considering the structure dispersion and material damping, we cannot detect its behavior in our experimental setup. It is interesting that the metamaterials can operate as a frequency filter to realize transparent transmission for the fundamental mode of the slab over a special range.
To compare the transmitted wave with the reflected wave, we select the signals in different regions of Fig. 4(a), and obtain the dispersion curves by taking two-dimensional Fourier transform of these regions, as shown in Fig. 5. In Fig. 5(a), the three bright dispersion curves (red) reveal three TE modes existing in the waveguide generated in the incident region. The dispersion curves of the zeroth- and first-order modes are much brighter than that of the second-order mode, that is to say, more energy concentrates in the zeroth- and first-order modes. Although in the Meta region we can see very weak signal of the first-order mode in Fig. 5(b), it is blocked by the Meta region gradually because of the through plane process. After the THz wave transmits through the metamaterials structure region, the first- and second- order modes are not exist, as shown in Fig. 5(c). Closer inspection of Fig. 5(c) shows that the signal appears weakly at around 0.75–0.85 THz, and this band can be also found in simulated results as shown in Fig. 5(e). Figure 5(d) shows the experimental dispersion curves of the reflected THz waves, which conclude most of the first-order mode and part of the zeroth-order mode over the range of 0.6–1.0 THz. The reflected zeroth-order mode concludes a strong signal part at 0.6–0.75 THz and a relative weak part in a range of 0.85–1.0 THz. Simulation results show that the metamaterials we designed can act as a band-stop filter in a range of 0.58–0.75 THz. However the experimental band-stop frequency range is a little broader than the simulated one. The experimental admissible error may be caused by the fabrication parameters accuracy of metamaterials structures. Figures 5(e)–5(f) show the dispersion curves of the transmitted and the reflected THz waves from FDTD simulation results, respectively. Comparing to figures 5(c)–5(d), they match the experimental results very well. Overlaid on top of the experimental dispersion curves in green curves are the theoretical dispersion curves for a 53 μm LN slab, where we use the frequency dependent index of refraction from [3]. The calculated dispersion curves in air and bulk LN are shown as white and blue lines respectively for a reference. The experimental data fit the theoretical results quite well.
4. Conclusion
In conclusion, we have designed and fabricated a THz metamaterials structure surfaced on a LiNbO3 crystal slab. By using phase contrast imaging method, the spatial electric field profiles of the THz waves are time-resolved recorded and analyzed. We coherently measure the reflected and transmitted components of a single-cycle THz pulse propagating through the metamaterials structure. We show the separation process of different modes with different frequencies in a movie. Furthermore, we calculate the dispersion curves that show wavevector-frequency distributions and guided wave modes. It is interesting that the metamaterials structure we designed can operate as a band-stop filter, which can block back THz waves generated in LN slab in a band range of 0.6–1.0 THz, while realize low loss, less crosstalk transparent transmission for the fundamental mode of the slab in a range of 0.3–0.6 THz. The alternating arranged electric resonant gold bars make a periodic boundary condition and significantly affect the through plane propagation of THz wave. In this way, the metamaterials structure can be served as a THz Spoof plasmonic crystal, which exhibits a band gap. The results presented in this paper will facilitate the design of functional devices with new capabilities for the LN sub-wavelength slab, which can serve as an integrated platform for THz processing because generation, propagation, detection, and control can be fully integrated in one sample.
Acknowledgments
This work was supported by the National Basic Research Program of China ( 2013CB328702), the National Natural Science Foundation of China ( 61378018), the 111 Project ( B07013) and the Program for Changjiang Scholars and Innovative Research Team in University ( IRT0149).
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