Experimental Results

Ⅴ. Electrically Tunable Beam Manipulation from Intersubband Polaritonic Metasurfaces

5.5 Experimental Results

Figure 5.5.1 shows the results of the intersubband absorption measurement and its optical configuration. The intersubband absorption was measured by using FTIR (Vertex70, Bruker), liquid nitrogen cooled HgCdTe detector (MCT, InfraRed Associates, Inc.) with 400 Hz of chopper frequency.

For the intersubband absorption measurement for no bias, MQWs piece sample was finely polished on both edges with a slope of 45 degrees for minimizing scattering and deposited with 150 nm-thick Au films on both sides for total internal reflection. From absorbance spectrum for no bias at room temperature, the intersubband absorption peak and half width half maximum (HWHM) were observed at 6.75 μm and 14.23 meV, respectively, and the transition linewidth was obtained as 2ℏγ12 ≈ 28.46 meV.

The measured absorption peak was revealed at about 0.5 μm higher than that of the designed MQWs.

From measured absorbance as shown in Figure 5.9 (b), the absorption coefficient αIST was extracted by the following equation.¹¹⁰

𝛼_𝐼𝑆𝑇 = 1

𝐿_𝑚𝑝𝑙𝑙𝑛(10) 𝑙𝑜𝑔₁₀(𝐼_𝑇𝐸 𝐼_𝑇𝑀)

(5.4) Where Lmpl = 0.6 μm is the effective multipath length of passing through MQW piece sample. The ITE

and ITM are the transmitted intensities for TE and TM linearly polarized lights, respectively. Assuming that the undoped narrow well width is 1.9 nm in the MQW design and the doping level in the wide well is 4.3, the extracted absorption coefficients are in good agreement with the absorption coefficients of the designed MQWs and absorption peaks. From the measured absorbance spectrum, the real and imaginary parts of the calculated dielectric function of MQWs are similar to that of the modified MQWs in a design under the above conditions. Therefore, we use the optical properties of MQWs that have been modified in a design from the results of the intersubband absorption measurement and apply them to FDTD simulations (in 5.3 session for Simulation and Calculation of Optical Responses).

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Figure 5.5.1. (a) Optical configuration for the intersubband absorption measurement. The TM linearly polarized (signal) and TE linearly polarized (background) infrared light incident from the FTIR broadband source was measured by the MCT detector by passing through a piece of MQW finely polished on both sides with a slope of 45 degrees. The transmitted light was collected by the pair of ZnSe lenses and MCT detector. (b) Absorbance (black) spectrum with zero bias for intersubband absorption was measured by normalizing the TM signal to TE background signal. Absorption coefficient (red) spectrum was calculated considering the effective multipaths in MQWs from measured absorbance. (c) The real (black) and imaginary (red) parts of the z-component of dielectric constant for measured MQWs.

Figure 5.5.2 shows the experimentally measured results and physical analysis of the fabricated one- dimensional phase grating metasurface. Figure 5.2.2 (a) shows an SEM image for the fabricated metasurface with a size of 200 μm × 200 μm to measure the polaritonic reflection responses and dynamic beam diffraction through the quantum-confined Stark shifts. The phase grating metasurface from Figure 5.2.2 (b) was determined with geometrical parameters of the period (P = 1.28 μm), line width (W = 0.92 μm) to achieve strong coupling at V2a = V2b = 0 V. Figure 5.5.2 (c) shows the current- voltage characteristics from -3 V to +6 V. Both sides of the semiconductor heterostructure of the fabricated sample showed a Schottky-like curve in contact with the Cr metal as an adhesive layer. Figure 5.2.2 (d) shows that the polaritonic reflection spectra of the phase grating metasurface were measured with change of external DC voltage (V2a = V2b) from -3 V to +6 V with +1 V step for negative bias, and +2 V step for positive bias, respectively under the TM-polarized incident light by using FTIR spectrometer equipped with an optical microscope. It leads to achieve the effectively spectral shifts from the negative to positive voltages in the vicinity of the anti-crossing region at 6.90 μm for the condition of V2a = V2b = 0 V as shown in green semitransparent windows. The measured polaritonic absorption peaks show blue-shifts entirely by the QCSE from negative to positive voltages, and these are well agreement with the trend of FDTD simulation results. As the external voltage continues to be increased from negative to positive values, we confirmed that coupling mode was converted through shifting major polaritonic reflection peak gradually from the right to left. The left and right reflection peaks of the polaritonic response show the spectral tuning from 6.25 μm to 6.6 μm, and from 7.3 μm to

(a) (c)

5 6 7 8 9

0 2 4 6 8 10 12

Wavelength (μm) Absorption Coefficient (cm-1)

240 220 200 180 160 140 IST Energy (meV)

(b)

4 5 6 7 8 9 10

6 7 8 9 10 11 12 13

Real Imag

Wavelength (μm)

Real ()

0 1 2 3 4 5 6 7 8 9

Imag ()

73

7.75 μm, respectively, with change of the negative to positive voltages. Their main peak shifts the anti- crossing region, resulting in a polaritonic phase difference. The measured polaritonic shifts were slightly observed less pronounced than the simulation results. In the simulation results, only the QCSE caused by the electric field induced from the external bias voltage was considered, but in the actual sample, it is expected that a higher electric field from the capacitance is not formed due to the current injection by the external voltage.

Figure 5.5.2. Experimental results and physical analysis of the phase grating metasurface. (a) SEM image of the fabricated one-dimensional grating metasurface for electrical beam diffraction. Inset: zoom-in view of the top edge of one superlattice (Γs = 15.36 μm), where the background metal-isolated 6 gratings (orange shadow) are connected to left contact pad, and the background metal-connected 6 gratings (green shadow) are contacted to right pad. (b) Zoom-in view of SEM images for grating superlattice. (c) The current-voltage characteristics. (d) The measured polaritonic reflection spectra added vertically by +0.25 value each to better display visually. The red dash lines represent the position of the polaritonic reflection peaks under linearly TM-polarized light with change of DC voltages from -3 V to +6 V (V2a = V2b). (e) The solid black and red dash lines indicate reflection spectra, and TCMT fitting curves for phase grating metasurfaces for 3 conditions of (V2a = V2b = -3 V, 0 V and +6 V), respectively. (f) Extracted phase responses of the reflected waves from the metasurface by TCMT analysis.

V2a

V2b

(a)

-3 -2 -1 0 1 2 3 4 5 6 -150

-100 -50 0 50 100 150

Current (mA)

Voltage (V)

4 5 6 7 8 9 10

0.0 0.5 1.0 1.5 2.0 2.5

Reflection

Wavelength (μm)

-3 V -2 V -1 V 0 V +2 V +4 V +6 V

(d) (e)

(b) (c)

(f)

4 5 6 7 8 9 10

-1.50 -1.25 -1.00 -0.75 -0.50

Phase (p)

Wavelength (μm)

V_2a = V_2b = -3 V V_2a = V_2b = 0 V V_2a = V_2b =+6 V V2a V2b

5 μm 200 μm

4 5 6 7 8 9 10

0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0

Wavelength (μm)

Mesurement (V2a = V2b = -3 V) TMCT Fitting

Reflection Mesurement (V_2a = V_2b = 0 V)

TCMT Fitting

Mesurement (V2a = V2b = +6 V) TCMT Fitting

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We employ the framework of temporal coupled mode theory (TCMT) for tracking intersubband polaritonic phase responses of fabricated metasurfaces and theoretical analysis of physical parameters.

In here, metamaterial absorber structure can be considered as single port optical system of the MIM nanocavity, and their interaction can be modeled by the following the coupled mode equation.¹¹¹

𝑑𝐶

𝑑𝑡 = 𝑗𝜔_𝑐𝐶 − (𝛾_𝑐𝑎+ 𝛾_𝑐𝑟)𝐶 + 𝑗𝛺𝑄 + 𝑆⁺√2𝛾𝑐𝑟

(5.5) 𝑑𝑄

𝑑𝑡 = 𝑗𝜔_𝑄𝑄 − 𝛾_𝑄𝑄 + 𝑗𝛺𝐶

(5.6)

|𝑆⁻〉= − |𝑆⁺〉+ 𝐶√2𝛾_𝑐𝑟

(5.7)

𝜃 = tan⁻¹ (−1 + 2𝛾𝑐𝑟

𝑖(𝜔 − 𝜔_𝑐− 𝜔_𝜇) + (𝛾_𝑐𝑎+ 𝛾_𝑐𝑟+ 𝛾_𝜇))

(5.8)

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Figure 5.5.3. The schematic of the coupled oscillator model between the plasmonic nanocavity and the intersubband transition.

Figure 5.5.3 shows the coupled oscillator model between the nanocavity and the intersubband transition for the condition of ωc = ωQ. The |S⁺⟩ and |S^-⟩ is amplitudes of the incoming and outgoing electromagnetic waves in single port system. The C and Q are mode amplitudes of nanocavity and intersubband polariton, respectively. The ωc and ωQ are resonance frequencies for the nanocavity and the intersubband energies, respectively. The total loss rate of a nanocavity can be considered as the sum of the absorption loss rate (γca) and radiation loss rate (γcr). The Ω is the coupling rate from vacuum- Rabi splitting (ΩR = 2Ω) known as an anti-crossing in energies with a separation. The higher value of Ω, the more pronounced the peak splitting, allowing for broad spectral tuning and phase shifting, which depends on the capabilities of the volume integral of the Ez nearfields confined to the plasmonic nanocavity. The value of γQ for intersubband absorption loss rate (HWHM) is used from intersubband

|S ⁺ ⟩

|S ^- ⟩

γ _cr

E

₁₂

ω _c = ω _Q

Ω

γ _ca

76

absorption measurement. The ωμ and γμ are an effective frequency shift and an effective loss rate from the coupling phenomenon.

Table 5.5.1. Extracted TCMT fitting parameters of intersubband polaritonic metasurfaces with change of an external bias voltage.

Figure 5.5.2 (e) shows TCMT fitting curves of the measured spectra in Figure 5.5.2 (d) at condition of V2a = V2a = -3 V, 0 V, and +6 V, respectively. From the TCMT fitting curves, we extracted TCMT physical parameters as shown in Table 5.5.1. In this coupling system, the resonance frequency of the nanocavity almost does not change because the coupling is changed by the input of an external voltage bias rather than by the geometric change of it. The resonance frequencies of IST show the values that increase as the voltage rises in the positive direction, which is well matched to the QCSE and has been properly fitted. The coupling rate of Ω shows the greatest value at 0 V as the energies of the two systems are best matched, and the lower value as it deviates from anti-crossing by an external voltage bias. Figure 5.5.2 (f) shows the polaritonic phase responses of a fabricated phase grating metasurface in condition at -3 V (bottom), 0 V (middle), and +6 V (top) through the TCMT analysis. The polaritonic phase profiles of the total reflected waves are extracted from the equation (5.8). The estimated polaritonic phase response shows a phase difference of about 45 degrees at 6.8 μm for the condition of -3 V and +6 V. It can be seen that the main resonance peak induced from the coupling phenomenon between IST energy tuning by the QCSE and plasmonic resonance of the grating cavity is converted to a short wavelength or a long wavelength with respect to the anti-crossing region at 0 V, which can cause a phase change.

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Figure 5.5.4. Experimental results of tunable beam diffraction measurement for an external DC voltage bias at V2a < 0 V and V2b > 0 V from 6.15 μm to 6.90 μm with 0.5 μm step. The signals are normalized to each zeroth peak value.

-40 -30 -20 -10 0 10 20 30 40 0.0

0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Normalized Intensity

Polar Angle (degree) V2a = 0 V V2b = 0 V

Normalized Intensity

V2a = -3 V V_2b = 6 V

-40 -30 -20 -10 0 10 20 30 40 0.0

0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Normalized Intensity

Polar Angle (degree) V2a = 0 V V2b = 0 V

Normalized Intensity

V2a = -3 V V_2b = 6 V

-40 -30 -20 -10 0 10 20 30 40 0.0

0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Normalized Intensity

Polar Angle (degree) V2a = 0 V V2b = 0 V

Normalized Intensity

V2a = -3 V V_2b = 6 V

-40 -30 -20 -10 0 10 20 30 40 0.0

0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Normalized Intensity

Polar Angle (degree) V2a = 0 V V2b = 0 V

Normalized Intensity

V2a = -3 V V_2b = 6 V

-40 -30 -20 -10 0 10 20 30 40 0.0

0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Normalized Intensity

Polar Angle (degree) V_2a = 0 V V2b = 0 V

Normalized Intensity

V2a = -3 V V2b = 6 V

-40 -30 -20 -10 0 10 20 30 40 0.0

0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Normalized Intensity

Polar Angle (degree) V_2a = 0 V V2b = 0 V

Normalized Intensity

V2a = -3 V V2b = 6 V

-40 -30 -20 -10 0 10 20 30 40 0.0

0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Normalized Intensity

Polar Angle (degree) V_2a = 0 V V2b = 0 V

Normalized Intensity

V2a = -3 V V2b = 6 V

-40 -30 -20 -10 0 10 20 30 40 0.0

0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Normalized Intensity

Polar Angle (degree) V_2a = 0 V V2b = 0 V

Normalized Intensity

V2a = -3 V V2b = 6 V

-40 -30 -20 -10 0 10 20 30 40 0.0

0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Normalized Intensity

Polar Angle (degree) V2a = 0 V V_2b = 0 V

Normalized Intensity

V2a = -3 V V2b = 6 V

-40 -30 -20 -10 0 10 20 30 40 0.0

0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Normalized Intensity

Polar Angle (degree) V2a = 0 V V_2b = 0 V

Normalized Intensity

V2a = -3 V V2b = 6 V

-40 -30 -20 -10 0 10 20 30 40 0.0

0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Normalized Intensity

Polar Angle (degree) V2a = 0 V V_2b = 0 V

Normalized Intensity

V2a = -3 V V2b = 6 V

-40 -30 -20 -10 0 10 20 30 40 0.0

0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Normalized Intensity

Polar Angle (degree) V2a = 0 V V_2b = 0 V

Normalized Intensity

V2a = -3 V V2b = 6 V

-40 -30 -20 -10 0 10 20 30 40 0.0

0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Normalized Intensity

Polar Angle (degree) V2a = 0 V V2b = 0 V

Normalized Intensity

V2a = -3 V V2b = 6 V

-40 -30 -20 -10 0 10 20 30 40 0.0

0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Normalized Intensity

Polar Angle (degree) V2a = 0 V V2b = 0 V

Normalized Intensity

V2a = -3 V V2b = 6 V

-40 -30 -20 -10 0 10 20 30 40 0.0

0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Normalized Intensity

Polar Angle (degree) V2a = 0 V V2b = 0 V

Normalized Intensity

V2a = -3 V V2b = 6 V

-40 -30 -20 -10 0 10 20 30 40 0.0

0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Normalized Intensity

Polar Angle (degree) V2a = 0 V V2b = 0 V

Normalized Intensity

V2a = -3 V V2b = 6 V

6.15 μm

6.35 μm

6.55 μm

6.75 μm

6.20 μm

6.40 μm

6.60 μm

6.80 μm

6.25 μm

6.45 μm

6.65 μm

6.85 μm

6.30 μm

6.50 μm

6.70 μm

6.90 μm

78

We experimentally demonstrate electrically tunable beam manipulation for diffraction (both sides) and steering (selective one side). The dimensions of the superlattice and line width of the grating unit structure for the phase grating and phase gradient metasurfaces were fabricated slightly different due to manufacturing errors. Both active metasurfaces were fabricated with a size of 200 μm × 200 μm, and the superlattice was repeated 13 times. As shown in Figure 5.5.2 (a), to build electrical phase sequence as ‘…101010…’ of grating phase elements, the phase grating metasurface is composed of the arrays of the grating nanocavity grouped alternately into 6 lines which control ±1^st order diffraction beam intensities through polaritonic phase change electrically. Figure 5.5.2 (b) shows the SEM image of superlattice for the phase grating metasurface, where the 6 gratings are controlled by V2a, and the other 6 gratings are working by V2b of bias voltage, respectively, so they are electrically separated. Figure 5.5.4 shows the experimental results of electrically tunable beam diffraction profiles as a function of the polar angle from -40 to 40 degrees with operating wavelengths from 6.15 μm to 6.90 μm with 0.5 μm step. Under the electrical bias condition for V2a = V2b = 0 V (bottom panel), the ±1^st order diffraction beam intensities are almost suppressed, and the zeroth order beam was observed only due to the subwavelength scale of the grating unit structure compared to the operating wavelengths. For beam diffraction measurement, the metasurface is applied with an electrical bias condition for V2a = -3 V and V2b = +6 V. This condition shows maximum polaritonic phase shifts at operating wavelength, efficiently supporting beam diffraction response. The maximum efficiency of beam diffraction is achieved around 6.55 μm, and it gradually decreases as the distance from the that wavelength. This means that the largest phase difference occurs at 6.55 μm in the actually fabricated sample, and the phase change becomes smaller around it. Although the extracted phase responses from the TMCT deviated slightly with respect to wavelength, the phase change expected from the measured beam diffraction tendency with wavelength is very similar. For an operating wavelength of 6.55 μm, the top panel indicates the observed the maximum value of ±1^st order diffraction beam intensities with the similar values of about 15 %, and the beam diffraction signals is normalized to each zeroth peak signal value. The first diffraction angle of about ±25 degrees in the ±1^st order beam is calculated from the equation 5.2, but it was experimentally observed at +23 degrees slightly deviated for the +1^st order diffraction. We attribute the optical path to slight misalignment between the metasurface, optics, and detector scanner. In the case of the 1-bit phase grating, the zeroth order diffraction is totally suppressed at 180 degrees of phase difference, as maximum efficiency of beam diffraction. However, our phase grating metasurface shows experimental results considering a phase difference of 45 degrees at an operating wavelength of 6.55 μm.

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Figure 5.5.5. Experimental results of selective beam steering by the electrical bias voltages. (a) SEM image of the tunable phase gradient metasurface with two metal contact pads for applying difference electrical bias. Inset: zoom-in view of the bottom edge of one superlattice (Γg), where no voltage is applied to the left background metal-isolated 4 gratings (orange shadow), and 4 grating elements (blue and green shadows) are contacted to left (V3a) and right (V3b) contact pads, respectively.

(b) Experimental beam steering measurement of the diffraction beam profiles normalized to each zeroth peak signal. The dimensions of the fabricated phase gradient metasurfaces from the SEM images is Γg = 15.12 μm, P (period) = 1.26 μm, W (line width) = 0.86 μm, respectively. (c) The current-voltage characteristics of the phase gradient metasurface. (d) The applied square voltage pulse of V3b at 10 kHz in range from -1.5 V to +6 V (top panel). The MCT photodetector signal difference at DC bias voltage of V3a = -3 V position of +1^st order diffraction intensity from the phase gradient metasurface (bottom panel).

GND V_3a V_3b

-40 -20 0 20 40

0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0

Polar Angle (degree)

V_3a = 0V V_3b = 0V

Normalized Intensity (a.u.)

V_3a = -3V V_3b = 6V V_3a = 6V V_3b = -3V

V_3a

V_3b

(a) (b)

(c)

0 100 200 300 400 500 0

1 2 -2 0 2 4 6 8

Time (μsec)

 MCT Photodetector Signal

Voltag e (V)

Modulation Signal

(d)

-3 -2 -1 0 1 2 3 4 5 6 -300

-200 -100 0 100 200 300

Current (mA)

Voltage (V)

200 μm

80

To build phase sequences as ‘…210210…’ or ‘…012012…’ of electrical gradient phase elements, the phase gradient metasurface is composed of the arrays of the grating meta-atoms grouped alternately into 4 lines which selectively control +1^st or -1^st order diffracted beam intensities. The inset of Figure 5.5.5 (a) shows the SEM image of electrically tunable phase gradient metasurface, where the 4 grating are controlled by V3a (blue shadow), other 4 grating are working by V3b (green shadow), and no bias voltage (orange shadow) is applied to the other 4 gratings, respectively. Therefore, they should be also electrically separated for forming an electrical gradient phase sequence. Figure 5.5.5 (b) shows the experimental results in selective beam steering measurement for two different DC bias voltages at normal incidence with 6.45 μm of an operating wavelength. The beam steering signals are normalized to each zeroth peak signal value. For selective beam steering measurement, under the electrical bias condition for V3a = +6 V and V3b = -3 V as phase sequence of ‘…210210…’, the -1^st order diffracted beam intensity was characterized only. The top panel of Figure 5.5.5 (b) shows beam steering signal of 11 % for -1^st order intensity at -27 degrees, and opposite side intensity rarely appears. In contrast with this case, when V3a = -3 V and V3b = +6 V as phase sequence of ‘…012012…’, the +1^st order beam intensity was observed only shown in middle panel. The middle panel indicates 11 % of +1^st order beam steering signal at +25 degrees. The electrically tunable phase gradient metasurfaces experimentally achieved demonstration on the generalized Snell’s law.³³ Figure 5.5.5 (c) shows the current-voltage characteristics of the fabricated phase gradient metasurface. To verify electrically dynamic modulation of intersubband polaritonic response via the Stark shift, we measured modulation signal at position of +1^st order diffraction from the phase gradient metasurface. Figure 5.5.4 (d) shows the square voltage pulse signal of V3b at 10 kHz in range from -1.5 V to +6 V, and MCT photodetector signal difference at fixed bias condition for the DC bias voltage of V3a = -3 V. The MCT photodetector signal is well followed to the applied modulation pulse train signal.

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Figure 5.5.6. Optical system configuration for the electrically tunable beam diffraction and steering measurement. (a) Overall optical system configuration. (b) Pinhole on the MCT detector window for high spatial resolution of beam profiles. (c) Optical path of beam diffraction, and vertical scanning of the MCT detector. (d) The posterior portion of the motorized controller for vertical scanning of the MCT detector.

Figure 5.5.6 shows an optical configuration for electrically dynamic beam diffraction and selective beam steering measurement. First, the irradiated IR wave propagates from the tunable quantum cascade laser (QCL) with a tuning range from 6.15 μm to 6.90 μm, and then is focused at the fabricated metasurface by passing through a ZnSe objective lens at an effective focal length of about 10 mm. Then, the beam diffraction or selective beam steering, generated from the metasurface, is collimated by backwards passing through the ZnSe objective lens, and then it is reflected by the beam splitter and detected by the motorized MCT scanner. The MCT detector with pinhole diameter of 0.2 mm scanned a total range of 16 mm (±40 degrees of polar angle) with an interval of 0.2 mm along the vertical direction. The pinhole with 0.2 mm of diameter is used for high spatial resolution of vertical beam profiles.

(a)

CCD Motorized MCT Detector

Tunable QCL

Metasurface

illuminator

(d)

Motorized MCT scanning Probe 1

Probe 2

ZnSe B/S

(c)

MCT Scanning

(b)

Scanner controller

Pinhole

82