Visualization of the spatial&#x2013;temporal evolution of continuous electromagnetic waves in the terahertz range based on photonics technology

Shintaro Hisatake; Hai Huy Nguyen Pham; Tadao Nagatsuma

doi:10.1364/OPTICA.1.000365

1. INTRODUCTION

Regardless of the spectral range, there has been a strong demand for the visualization of not only propagating electromagnetic (EM) waves, but also local fields. As proven in the microwave range, near-field measurements are useful for diagnosing devices such as antennas and integrated circuits, because far-field measurements never show what happens inside or in the close vicinity of the devices [1]. Particularly, techniques for the visualization of the spatial and temporal evolution of the fields have attracted a great deal of interest because they can reveal the device dynamics.

In the terahertz (THz, 0.1–10 THz) region, the need for ultrafast wireless communication [2] has been the driving force behind a lot of research about metallic or plasmonic devices [3]. Up to now, most of the visualizations of the THz field have been based on an electro-optic (EO) sampling technique using a pulsed THz wave and femtosecond lasers. Recently, several THz devices based on plasmonics [4], metamaterials [5], and photonic crystals [6] have been investigated using pulsed near-field measurements in order to understand the physical properties of the devices. Based on the EO sampling technique, it has been proven that the field visualization of the THz beam is useful for understanding the dynamics of optically unique beams such as vortex beams [7]. For the frequency characteristic measurements, however, a continuous wave (CW) technique is indispensable because it offers precise frequency tunability and a higher frequency resolution. The CW technique also offers a higher signal-to-noise ratio (SNR), and a higher linearity of the measurements compared with the pulsed technique. In spite of their many benefits, however, so far only very limited CW-based techniques have demonstrated the visualization of the continuous THz wave.

Using a frequency multiplier for generation and an optical frequency comb for detection, a THz wave (100 GHz) has been visualized [8,9]. Thanks to the electric phase locking between the generation and the detection, this optoelectronic technique precisely measures the phases of the THz waves. However, it sacrifices the frequency tunability, which is important for the device characterization. To realize precise phase measurement at THz range with wide frequency tunability, we have recently proposed a self-heterodyne technique in which two frequency-detuned free-running lasers are used both for the generation (photomixing) and detection of the THz waves [10]. In this system, the frequency fluctuation and the phase noise of the THz wave originated from the lasers can be canceled out in the detection process without sacrificing the tunability [11]. We demonstrated the visualization of the freely propagating continuous wave (125 GHz) with the self-heterodyne system based on the conventional polarimetric EO detection technique, in which a small EO crystal mounted on an optical fiber was used as an EO sensor [12]. Although the amplitude and the phase distributions were visualized, we found that the stability and the repeatability of the measurements were too low for practical applications due to the sensitivity fluctuation problem of the conventional polarimetric EO detection. The fiber-mounted EO sensor enables us to measure the field with minimal invasiveness [13]. However, the sensitivity of the measurement can fluctuate drastically due to the fluctuation of the polarization state of the probe beam in the fiber [14]. As a result, we could not visualize the field distribution unless the device under test with the THz source, instead of the EO sensor, was scanned three-dimensionally, a procedure which significantly limits the flexibility of the system [15]. Moreover, this problem has prevented the visualization of the spatial–temporal evolution of a three-dimensionally propagating continuous THz wave because it requires repeated measurements of field distribution without sensitivity fluctuation and additive noise.

In this work, we demonstrate a new system in which a nonpolarimetric EO detection technique [16] is adapted to the self-heterodyne system to solve the intrinsic problem of the conventional polarimetric EO detection technique. We show here that the nonpolarimetric self-heterodyne technique enables us to measure the amplitude and phase distribution of the THz wave (electric field, E-field) repeatedly with significantly lower invasiveness and without degrading the sensitivity or imposing excess noise when moving the fiber-mounted EO sensor. Simultaneous achieving of minimal invasiveness and stable measurement enables us to visualize the spatial–temporal evolution of freely propagating continuous THz waves.

2. SYSTEM CONFIGURATION

Figure 1 shows the experimental setup. Two free-running 1.55 μm laser diodes (LDs, KOSHIN 601A), whose linewidth is less than 100 kHz, are used as optical sources. The frequencies of the LDs were set to be $f_{1}$ and $f_{2}$ ( $f_{2} > f_{1}$ ), and combined using polarization-maintaining fiber (PMF) couplers to produce a beat note at a frequency of $f_{THz} = f_{2} - f_{1} - f_{s}$ for THz wave generation (RF). Here, an EO frequency shifter was used to shift the frequency of the LD1 ( $f_{1}$ ) by $f_{s} = 500 kHz$ for self-heterodyne detection. A unitravelling-carrier photodiode was used as an optical-to-electrical (O/E) converter. We used an F-band horn antenna whose radius was about 13 mm.

Fig. 1. Experimental setup. LD, laser diode; FS, electrooptic frequency shifter; EDFA, erbium-doped fiber amplifier; FBG, fiber Bragg grating; PD, photodiode; PMF, polarization-maintaining fiber.

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The frequency of the radiated THz field was $f_{THz} = 125.66 GHz$ , calculated from the laser frequencies measured with the optical wave meter. The radiated power was 650 μW. The optical delay line was used to set the initial phase offset between the optical local oscillator (LO) signal and the radiated THz field. For detection, a ZnTe EO crystal ( $1 mm \times 1 mm \times 1 mm$ ) was mounted on a PMF. The 1.55 μm probe beam (LO signal) emitted from the PMF was collimated by a gradient index (GRIN) lens. The propagation direction of the probe beam was parallel to the $〈 110 〉$ direction of the ZnTe EO crystal. The relative angle between the polarization direction of the probe beam (slow-axis of the PMF) and the $〈 001 〉$ direction was 45°. The diameter of the collimated probe beam in the EO crystal was 0.2 mm, which limits the ultimate spatial resolution. The THz field (RF signal) emitted from the antenna interacted with the optical LO (probe beam) in the EO crystal. The probe beam was reflected by the high-reflective-coated surface of the EO crystal and focused onto the PMF by the GRIN lens. The reflected probe beam that passed through the optical filter (fiber Bragg grating) was detected with the photodiode (PD). The amplitude and phase of the intermediate frequency (IF) signal were measured with a lock-in amplifier.

In Fig. 2, we show the frequency spectra to illustrate the principle of the nonpolarimetric self-heterodyne EO detection technique. The EM field to be detected is up-converted to the optical frequency region through the phase modulation of the probe beam. Then, the generated sideband is down-converted to the IF frequency band by the optical coherent detection. In the EO crystal the optical LO, which consists of two frequency components $f_{1}$ and $f_{2}$ , interacts with the EM field (RF signal), and sidebands are generated. The upper sideband of $f_{1}$ and the lower sideband of $f_{2}$ are shown here. Because the frequency of the RF signal is $f_{THz} = f_{2} - f_{1} - f_{s}$ , the frequency of the upper sideband for $f_{1}$ is $f_{2} - f_{s}$ , whereas the frequency of the lower sideband for $f_{2}$ is $f_{1} + f_{s}$ . Therefore, there are two carrier and sideband pairs to be considered as heterodyne candidates: the pair made up of the $f_{1} + f_{s}$ component (sideband) and the $f_{1}$ component (carrier), and the pair consisting of the $f_{2} - f_{s}$ component (sideband) and the $f_{2}$ component (carrier). A single pair is extracted by the optical filter, and then detected with the O/E converter (PD). The coherent detection of the weak sideband, which reflects the amplitude and the phase information of the EM wave to be detected, is achieved with a strong LO signal. The amplitude and the phase of the IF signal are simultaneously measured using a lock-in amplifier.

Fig. 2. Principle of the nonpolarimetric self-heterodyne EO detection technique.

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3. EVALUATION OF THE SYSTEM

The noise of the IF signal comes from that of the LO signal ( $f_{2}$ ) and sideband component ( $f_{2} - f_{s}$ ). In our technique, the sideband component propagates through the fiber and the optical filter, along with the LO carrier component. As a result, the relative polarization state of the sideband and carrier is maintained. Moreover, the optical phase fluctuations imposed on the propagating sideband and the carrier are in the common mode. Therefore, they will be canceled out as a result of the heterodyne detection process. These effects enable us to achieve stable measurements when we move the fiber-mounted EO sensor.

The excess phase noise of the IF signal comes from the phase noise imposed independently on the LO carrier and the sideband components. Referring to Fig. 1, the phase noise of the RF signal, $θ_{RF}$ , at the EO sensor can be written as

θ_{RF} = (ϕ_{LD 2} - ϕ_{LD 1}) + (ϕ_{32} - ϕ_{12}) + (ϕ_{2 g 2} - ϕ_{2 g 1}) + φ_{RF},

where

ϕ_{LD 1}

and

ϕ_{LD 2}

are the laser phase noises including phase noises added by the EDFAs,

ϕ_{i j}

is the optical phase noise added in the fiber between node

i

and

j

,

ϕ_{2 g 2}

and

ϕ_{2 g 1}

are the optical phase noises added in the fiber between node 2 and the RF generator (O/E converter) to the

f_{2}

and

f_{1}

carrier components, respectively, and

φ_{RF}

is the phase noise added to the RF signal. On the LO side, the optical phase noise of the

f_{2}

carrier component can be written as

θ_{LO c} = ϕ_{LD 2} + ϕ_{34} + ϕ_{4 s 2},

where

ϕ_{4 s 2}

is the optical phase noise added to the

f_{2}

component in the fiber between node 4 and the sensor. The optical phase noise of the

f_{2} - f_{s}

component is a mixture of the phase noise of the

f_{1}

component and the phase noise of the RF signal,

θ_{LO s} = ϕ_{LD 1} + ϕ_{14} + ϕ_{4 s 1} + θ_{RF},

where

ϕ_{4 s 1}

is the optical phase noise added to the

f_{1}

component in the fiber between node 4 and the sensor. As a result, the phase noise in the IF signal can be written as

θ_{IF} = θ_{LO s} - θ_{LO c} = (ϕ_{32} - ϕ_{34}) + (ϕ_{14} - ϕ_{12}) + (ϕ_{4 s 1} - ϕ_{4 s 2}) + (ϕ_{2 g 2} - ϕ_{2 g 1}) + φ_{RF} .

The components

(ϕ_{4 s 1} - ϕ_{4 s 2})

and

(ϕ_{2 g 2} - ϕ_{2 g 1})

are the phase noises added to the optical beat signal, whereas the components

(ϕ_{32} - ϕ_{34})

and

(ϕ_{14} - ϕ_{12})

are the phase noises added to the optical signal. In this experiment, the wavelength of the RF beat signal is 2.4 mm (125 GHz), whereas that of the optical signal is 1.55 μm in vacuum. Therefore, the influence of the ambient thermal and vibrational noise on the phase of the optical signal is

2400 / 1.5 = 1600

times greater than that on the beat signal. These optical phase noises can be reduced drastically by temperature control and/or integration of the fiber components in the dashed box in Fig. 1.

Figures 3(a) and 3(b) show the normalized amplitude and the phase of the detected THz wave signal, respectively. The EO sensor is placed at the center of the antenna aperture. The lock-in time constant is 30 ms. The optical delay line was set so that the initial phase offset was zero. The SNR is $SNR = 20 \log_{10} (S_{m} / S_{d}) = 31 dB$ , where $S_{m}$ and $S_{d}$ are the mean value and the standard deviation of the detected amplitude for 60-s measurement, respectively. The slight drift in the amplitude data is likely due to the RF power drift. There is no phase drift during 10-min measurement. The standard deviation of the 10-min phase measurement is 81 mrad.

Fig. 3. Measured THz E-field. (a) Normalized amplitude and (b) phase. The EO sensor was placed at the center of the antenna surface. The lock-in time constant was 30 ms.

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For comparison, we measured the THz wave phase using a photoconductive antenna (PCA) as a THz wave detector in the self-heterodyne system. Note that the PCA was placed at the far-field region so as not to disturb the field to be measured through the coupling between the horn antenna and antenna fabricated on the photoconductive material. The standard deviation of the phase measurement was 80 mrad for a SNR of 29 dB. On the other hand, the standard deviation of the phase measurement theoretically limited by the SNR can be calculated by $S_{ϕ} = 10^{- SNR / 20}$ , which leads the theoretically limited standard deviation of 35 mrad for the SNR of 29 dB. From these comparisons, we conclude that the stability of the phase measurement is currently limited not by the nonpolarimetric EO detection but by the excess phase noise in the self-heterodyne module, i.e., $(ϕ_{32} - ϕ_{34}) + (ϕ_{14} - ϕ_{12})$ in Eq. (4).

In the last part of this section, we will evaluate the repeatability of the measurements when moving the fiber-mounted EO sensor to visualize the field distribution. In this evaluation, we measure the THz field distribution repeatedly in both the E-plane and the H-plane at $Z_{8}$ , where the distance from the antenna aperture is 8 mm. Note that the origin of the coordinate was set at the center of the antenna aperture. The lock-in time constant was 100 ms and the maximum SNR obtained at the position of $(x, y, z) = (0, 0, Z_{8})$ was 36 dB. In this situation, the standard deviation of the amplitude measurement was $S_{d 0} = 40 mv$ .

Figure 4 is a typical correlation map between two independently measured amplitude distributions, $A_{1} (x, 0, Z_{8})$ and $A_{2} (x, 0, Z_{8})$ , with $- 50 mm < x < 50 mm$ . The data were acquired by moving the fiber-mounted EO sensor in the $x$ direction. The slope of the solid red line is 1. Mapped data almost fit to the solid red line, which indicates a good correlation between the two distinct measurements. The standard deviation of the error between the two distinct measurements ( $A_{m} (x, 0, Z_{8}) - A_{n} (x, 0, Z_{8})$ ) was $S_{d c} = 43 \pm 8 mv$ . The standard deviation of the phase error between the two distinct measurements was $S_{ϕ_{d c}} = 80 \pm 5 mrad$ . The standard uncertainties of the standard deviations were evaluated based on twelve sets of two distinct field-distribution measurements (six sets for the E-plane and six for the H-plane). The standard deviations of the error between the repeated measurements coincide with the standard deviations of the measurement without moving the EO sensor. This guarantees that there are no sensitivity fluctuations and additive noises in the repeated visualizations.

Fig. 4. Typical correlation map between two independently measured amplitude distributions, $A_{1} (X, 0, Z_{8})$ and $A_{2} (X, 0, Z_{8})$ .

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4. FIELD VISUALIZATION

Figure 5 shows the amplitude and the phase distributions in the near-field region of the horn antenna. The distance from the antenna aperture was $Z = 1.0 mm = 0.4 λ$ . The open circles are measured data, and the red curves are calculated distributions. The finite integration technique (FIT) was used for the calculations. The lock-in time constant was 30 ms, and the maximum SNR of the amplitude measurements obtained at the center of the antenna aperture was 31 dB. The moving speed of the EO sensor was about $6.7 mm / s$ , and the sampling interval was 0.2 mm. The measured data coincide with the calculations within the hatched area ( $- 8 mm < x, y < 8 mm$ ), where the SNR was sufficient for the phase measurement. Enhancement of the SNR will result in the enlargement of the measurable area of the THz beam. The minimum error in the amplitude measurement should be about 3%, for a SNR of 31 dB. Compared with the simulated results, the maximum error in the amplitude measurements was 14% at $x = - 5.2 mm$ and 4% at $y = - 1.0 mm$ in Figs. 5(a) and 5(c), respectively. This error seems to be due to the rounding of the steep change of the field distribution. The rounding is attributed in part to the field invasiveness of the EO probe, because larger dimensions of the EO probe tend to degrade the spatial resolution [13]. Although this effect can be minimized by reducing the probe size, current fidelity of measurement seems to be sufficient for some applications such as antenna characterization [17] and electromagnetic compatibilities inspection [18].

Fig. 5. Measured and simulated near-field (E-field) distributions of the horn antenna. (a) and (b) distributions in the E-plane. (c) and (d) distributions in the H-plane.

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Figure 6 shows the three-dimensional distributions of the freely propagating THz wave. The measured data [Figs. 6(a) and 6(b)] were acquired with the time constant of 30 ms. The amplitude data were normalized to their maximum values in each plane. Although the scan area ( $20 λ = 50 mm$ ) has been limited by the mechanical stage, it can be further improved. Figures 6(c) and 6(d) are the calculated field distributions. The measured spatial evolutions of the THz field emitted from the horn antenna agree well with the FIT calculations.

Fig. 6. Measured (a) amplitude and (b) phase of the THz E-field. Calculated (c) amplitude and (d) phase.

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Figure 7 shows the measured spatial–temporal phase evolution of the freely propagating CW-THz field. The horn antenna in this figure is the polygon data used in the simulation, i.e., the 3D simulation model and the 3D experimental results are put together to show the field evolution. The animation consists of five distinct field distributions. Therefore, the phase steps of the evolution are $2 π / 5 rad$ , which corresponds to the optical delay changes of 0.5 mm. The time constant of the lock-in detection was 3 ms. The maximum SNR obtained at the center of the antenna aperture was 27 dB. It took about 15 min ( $5 \min \times 3 planes$ ) to acquire a single snapshot. Therefore, it took about $15 \min \times 5 steps = 75 \min$ to acquire all the animation data. Currently, the measuring time is limited by the moving speed of the stage ( $67 mm / s$ ). Thanks to the good stability and the repeatability of our measurements, the propagation of the phase front can be clearly and smoothly observed.

Fig. 7. Measured spatial–temporal phase evolution of the freely propagating CW-THz field (Media 1). The horn antenna is the polygon data used in the simulation.

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5. CONCLUSION

We demonstrated a new field visualization system revealing the spatial–temporal evolution of not only the near-field but also the freely propagating continuous EM wave in the THz range for the first time to our knowledge. Adaptation of the nonpolarimetric EO detection technique to the self-heterodyne system was the key to significantly improving the stability and repeatability of the measurements. As a result, there is no sensitivity fluctuation, no additive amplitude noise, and no additive phase noise in the repeated measurements using a fiber-mounted EO crystal for minimal field invasiveness. Therefore, the evolution of the THz field (125 GHz) was visualized with a maximum SNR of 27 dB and a phase resolution of $2 π / 78 rad$ (80 mrad). Visualization of the field evolution of the continuous THz waves with high phase and spatial resolution can be a new approach to the study of the physical dynamics of unique beams. Our system is also applicable to near-field diagnostics of THz devices.

FUNDING INFORMATION

Adaptable and Seamless Technology Transfer Program Through Target-driven R&D, JST (AS242Z03673H); MEXT KAKENHI (25709028, 23656049).

REFERENCES

1. J. J. Lee, E. M. Ferren, D. P. Woolen, and K. M. Lee, “Near-field probe used as a diagnostic tool to locate defective elements in an array antenna,” IEEE Trans. Antennas Propag. 36, 884–889 (1988). [CrossRef]

2. T. Nagatsuma, S. Horiguchi, Y. Minamikata, Y. Yoshimizu, S. Hisatake, S. Kuwano, N. Yoshimoto, J. Terada, and H. Takahashi, “Terahertz wireless communications based on photonics technologies,” Opt. Express 21, 23736–23747 (2013). [CrossRef]

3. D. Kim, J. Hirokawa, M. Ando, J. Takeuchi, and A. Hirata, “4 × 4-element corporate-feed waveguide slot array antenna with cavities for the 120 GHz-band,” IEEE Trans. Antennas Propag. 61, 5968–5975 (2013). [CrossRef]

4. J. R. Knab, A. J. L. Adam, M. Nagel, E. Shaner, M. A. Seo, D. S. Kim, and P. C. M. Planken, “Terahertz near-field vectorial imaging of subwavelength apertures and aperture arrays,” Opt. Express 17, 15072–15086 (2009). [CrossRef]

5. A. Bitzer, A. Ortner, H. Merbold, T. Feurer, and M. Walther, “Terahertz near-field microscopy of complementary planar metamaterials: Babinet’s principle,” Opt. Express 19, 2537–2545 (2011). [CrossRef]

6. K. Nielsen, H. K. Rasmussen, A. J. Adam, P. C. Planken, O. Bang, and P. U. Jepsen, “Bendable, low-loss Topas fibers for the terahertz frequency range,” Opt. Express 17, 8592–8601 (2009). [CrossRef]

7. J. He, X. Wang, D. Hu, J. Ye, S. Feng, Q. Kan, and Y. Zhang, “Generation and evolution of the terahertz vortex beam,” Opt. Express 21, 20230–20239 (2013). [CrossRef]

8. M. Tsuchiya, A. Kanno, K. Sasagawa, and T. Shiozawa, “Image and/or movie analyses of 100-GHz traveling waves on the basis of real-time observation with a live electrooptic imaging camera,” IEEE Trans. Microwave Theor. Tech. 57, 3373–3379 (2009).

9. M. Tsuchiya and T. Shiozawa, “Phase-space analyses of electrooptically visualized 100 GHz waves employing complex phasor images,” Appl. Phys. Express 7, 032401 (2014). [CrossRef]

10. S. Hisatake, G. Kitahara, K. Ajito, Y. Fukada, N. Yoshimoto, and T. Nagatsuma, “Phase-sensitive terahertz self-heterodyne system based on photodiode and low-temperature-grown GaAs photoconductor at 1.55 μm,” IEEE Sens. J. 13, 31–36 (2013). [CrossRef]

11. S. Hisatake, J.-Y. Kim, K. Ajito, and T. Nagatsuma, “Self-heterodyne spectrometer using uni-traveling-carrier photodiodes for terahertz-wave generators and optoelectronic mixers,” J. Lightwave Technol. 32, 3683–3689 (2014). [CrossRef]

12. S. Hisatake and T. Nagatsuma, “Continuous-wave terahertz field imaging based on photonics-based self-heterodyne electro-optic detection,” Opt. Lett. 38, 2307–2310 (2013). [CrossRef]

13. D.-J. Lee and J. F. Whitaker, “An optical-fiber-scale electro-optic probe for minimally invasive high-frequency field sensing,” Opt. Express 16, 21587–21597 (2008). [CrossRef]

14. A. Garzarella, S. B. Qadri, D. H. Wu, and R. J. Hinton, “Responsivity optimization and stabilization in electro-optic field sensors,” Appl. Opt. 46, 6636–6640 (2007). [CrossRef]

15. K. Yang, L. P. B. Katehi, and J. F. Whitaker, “Electric field mapping system using an optical-fiber-based electrooptic probe,” IEEE Microw. Wirel. Compon. Lett. 11, 164–166 (2001). [CrossRef]

16. S. Hisatake and T. Nagatsuma, “Nonpolarimetric technique for homodyne-type electrooptic field detection,” Appl. Phys. Express 5, 012701 (2012). [CrossRef]

17. H. Togo, A. Sasaki, A. Hirata, and T. Nagatsuma, “Characterization of millimeter-wave antenna using photonic measurement techniques,” Int. J. RF Microwave Comput. Aided Eng. 14, 290–297 (2004).

18. C. T. Rodenbeck, K. A. Peterson, C. E. Sandoval, K. Brakora, J. Thiesen, E. M. Russick, and R. A. Ortiz, “Electrooptic inspection of vector leakage in radiofrequency multichip modules,” IEEE Trans. Electromagn. Compat. 55, 1093–1099 (2013). [CrossRef]

Visualization of the spatial–temporal evolution of continuous electromagnetic waves in the terahertz range based on photonics technology

Abstract

1. INTRODUCTION

2. SYSTEM CONFIGURATION

3. EVALUATION OF THE SYSTEM

4. FIELD VISUALIZATION

5. CONCLUSION

FUNDING INFORMATION

REFERENCES

Supplementary Material (2)

Cited By

Figures (7)

Equations (4)

Optica