1. Introduction

Techniques for visual observations of invisible propagating waves have been scientifically and technologically important. This is because they have helped us much to provide an intuitive grasp of essential characteristics for the invisible wave of interest as implied in examples in the references list [1–6]. Especially, those provided with the visualization functionalities for wave fronts and phase evolutions are fairly effective to interpret wave dynamics.

These visualization techniques have been frequently utilized both experimentally and numerically. Experimental techniques are sometimes more realistic and/or reliable than numerical ones, which could be attributed to the fact that quality of numerical wave simulation results depend critically on availabilities of well-developed and optimized models for wave media and their boundaries. Therefore, simple and easy experimental approaches with high accuracy are attractive and potentially beneficial. Consequently, their real-time properties have been always desired.

In this context, the optical visualization methods are considerably powerful [1–3]. Indeed, invisible propagating waves such as sound and light waves have been visualized in the phase-resolved manners. For example, the shadowgraph method is one of the most well-known and successful wave visualization techniques [1]. The method has been applied to visualization of aerial shock waves in the development of ultrasonic airplanes.

It should be noticed, however, that there have been no report on the phase-resolved visualization of electromagnetic waves propagating in air. Although the single-channel electro-optic (EO) sensing technique can be used for the detection of a radio frequency (RF) electric field [7,8], its spatial scan cannot perform instantaneous two-dimensional imaging and its preservation of phase relationship in an image is not sufficient enough. However, what the live electro-optic imaging (LEI) technique has brought about has been changing the situation [9–14]. One of the most attractive features of the LEI technique for the purpose is its ultra-parallel coherent acquisition of RF field distributions, which has been utilized to provide phase-resolved images and real-time videos of evanescent fields of propagating RF signals within planar circuitry.

Recently, we reported preliminarily on visual observations of propagating W-band (75 - 100 GHz) electromagnetic waves in a slab waveguide mode of a semiconductor plate [15–17]. In this study, we have extended the target to their aerial propagations. It has been brought about by a novel geometrical configuration of an EO sensor plate with an appropriate crystallographic orientation. In addition, a stable generation technique for a 100-GHz optical local oscillator (LO) signal is a key to the experimental demonstration.

2. W-band LEI system for aerially propagating electromagnetic waves

2.1 W-band LEI setup

A schematic of the experimental setup for traveling W-band millimeter-wave visualization is shown in Fig. 1 , which is based on the LEI technique. The optical configuration in the setup can be found in our previous papers [10–12] and, therefore, explanations on their details are omitted here. Instead, an outline of the setup and some specific features for the present paper are described as follows. The optical local oscillator (LO) signal is generated on the basis of a photonic frequency quadrupling method as described later and used to sense two-dimensional distribution of changes in the refractive index of the EO sensor plate ((100) ZnTe). The refractive index changes originate from the EO effect induced by electric fields of aerially traveling W-band millimeter-waves at a frequency of f _W-band. The sensing light reflected from the bottom surface of the EO sensor plate, which is high-reflection (HR) coated, is thus phase-modulated at f _W-band additionally with the original intensity-modulation of optical LO signal at f _LO. Then the optical mixing effect takes place and the resultant frequency-down-converted optical signal is generated at the polarization beam splitter (PBS). Consequently, the light reflected at PBS contains an intermediate frequency (IF) component at f _IF = |f _W-band – f _LO|. The data acquisition rate of the silicon-based complementary metal-oxide-semiconductor (Si-CMOS) image sensor at f _IS is set approximately to a quadruple of f _IF (20 kHz), which leads to sufficiently sensitive image acquisitions of electric fields distribution by means of the π-phase difference subtraction algorithm in the digital signal processor (DSP) [13]. The frequency of phase evolution in an LEI video is given by the slight frequency difference δf = |f _IF – f _IS/4|.

 

Fig. 1 Schematic of experimental setup for visualization of aerially traveling W-band electromagnetic waves. AR: anti-reflection coat, CCD: charge-coupled device, DSP: digital signal processor, EO: electro optic, HR: high reflection, LED: light-emitting diode, PBS: polarization beam splitter, PC: personal computer.

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The bandwidth of the EO effect in the ZnTe plate itself is in the terahertz frequency range and, therefore, the bandwidth of the LEI setup is mainly determined by the round trip time of the sensing light within the EO sensor plate. The thickness of the EO sensor plate is 1 mm, which corresponds to the bandwidth of 190 GHz. The areal size of the EO sensor plate is 25 × 25 mm² and the number of pixels in the present high-speed Si-CMOS image sensor is 100 × 100, which provides the spatial resolution of 0.25 mm / pixels in an image frame.

For the generation of aerially traveling W-band millimeter-waves, an RF signal source consisting of commercially available harmonic mixer and synthesized sweeper is used as shown in the bottom of Fig. 1. The signal is then boosted by a W-band waveguide amplifier and is emitted into air from an opening of a WR-10 waveguide flange. Both the optical LO signal generator and the signal source of W-band millimeter-waves are synchronized with the Si-CMOS image sensor so that the phase relationship of those signals are well preserved and the ultra-parallel coherent acquisition of RF field distributions is possible.

Figures 2(a) and 2(b) show the geometrical configuration of the EO sensor plate and the opening of the WR-10 waveguide flange. In the waveguide, TE-mode waves are excited with its electrical polarization in the z-direction. The crystallographic orientation of the (100) ZnTe crystal plate, which is sensitive to z-components of electrical fields, together with this polarization origin of the emitted W-band electromagnetic waves allows visual observations of two-dimensional behaviors of the waves [18]. In other words, the system is sensitive to the cross-sectional and phase-resolved view of spherically expanding electromagnetic waves in air if the interaction between the aerial waves and the internal wave components within the EO sensor plate is appropriate.

 

Fig. 2 (a) Side and (b) top views for the geometrical configuration of 1-mm-thick (100) ZnTe EO sensor plate with respect to an opening of WR-10 waveguide flange are schematically drawn. The latter acts as a point source of spherically traveling W-band electromagnetic waves. The broken line in (b) indicates the metal film at the surface of an electromagnetic-wave reflector, which is also shown in a CCD image in Fig. 4(a).

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The EO sensor plate is shifted vertically by approximately 4 mm with respect to the opening of the flange. Note that this vertical offset allows the visual acquisition of the result of aerial electromagnetic wave propagations and related phenomena beneath the EO sensor plate.

2.2 100-GHz optical LO signal generator

Another important issue of the present paper is the generation of optical LO signals at a frequency of 100 GHz. This is because an optical modulator with a high enough bandwidth for the W-band operation is not available at 780 nm, which is within the wavelength range suitable for the Si-CMOS image sensor. Here, we propose a method where high bandwidth optical components in the 1550-nm waveband for high speed optical telecommunication systems are used together with the optical frequency conversion technique [19,20]; the optical second harmonic generation provides the conversion of the optical wavelength from 1550-nm to 775-nm.

Figure 3(a) shows a schematic diagram of the experimental setup of the 100-GHz optical LO signal generation. The optical band elimination filter (BEF) and the periodically polled lithium niobate (PPLN) waveguide module are key components for an appropriate wavelength conversion as described below. 1550-nm light emitted from a laser diode is modulated by a Mach-Zehnder-interferometer type optical modulator driven at a frequency of 25 GHz [Fig. 3(b)]. There exist harmonic sidebands up to 5th order in the optical spectrum. Its central part is then suppressed by BEF as shown in Fig. 3(c) and, simultaneously, the chirp characteristics of the originally modulated signal are modified. The resultant optical signal is injected into the PPLN waveguide of a bandwidth of 100 GHz and the optical spectrum at 775 nm is generated as shown in Fig. 3(d). Note that the harmonic components of the second order are enhanced selectively, which results from appropriate adjustments of spectral intensity profile and chirp characteristics of the injected light. The frequency interval between these two components is 100 GHz, and their side-mode suppression ratios are as high as 8 dB. Detailed theoretical explanations supporting these results are in preparation and will be reported elsewhere [21].

 

Fig. 3 (a) Schematic diagram of 100-GHz optical LO generator. Spectra of the modulated optical signal in the 1550-nm band are shown for (b) before and (c) after the optical band elimination filter (BEF). Optical power spectrum after the second harmonic generation is shown in (d). BEF: band elimination filter, EDFA: erbium-doped fiber amplifier, PPLN: periodically-poled lithium niobate.

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3. Results of W-band millimeter-waves Visualization

W-band millimeter waves traveling in air were successfully visualized as shown in Fig. 4 . Figure 4(a) show a photograph taken by the charge-coupled device (CCD) camera with an illumination of the 640-nm light-emitting diode (LED) (Fig. 1). The top view of the geometrical configuration, which is schematically indicated in Fig. 2(b), was thus monitored visually during the experiment. The output power and the frequency of the W-band waves were 10 dBm and 100 GHz, respectively. The IF and phase evolution frequencies were 5 kHz and 2 Hz, respectively.

 

Fig. 4 Experimental results of visual observations of W-band electromagnetic waves traveling in air. (a) Top-view photograph of the geometrical configuration. Acquired images of phasor, magnitude and phase for an electromagnetic-wave reflector at (b) 45° and (c) at an obtuse angle. The phasor images are extracted from the corresponding real-time videos (Media 1 and Media 2 for (b) and (c), respectively). The solid lines in those images indicate the surface of the reflector as a guide for eyes.

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Here, we focus on a simple but essential phenomenon of propagating electromagnetic waves: a mirror reflection at a surface of metal film. For this purpose, a hand-made metal film reflector was prepared, which consists of an adhesive copper foil and a styroform block, and was set beneath the ZnTe EO sensor plate. The reflector appears in the upper right region of Fig. 4(a) through the EO sensor plate that is transparent at the wavelength of the LED illumination. The electromagnetic-wave emitter, the opening of flange, is also shown in the left-hand side of the same photograph.

The observed phasor, magnitude and phase images are shown in Fig. 4(b). Here, the pixel signal of the phasor image S(i, j) is derived as a function of time t as follows;

Those images imply that phase-resolved visualization of W-band electromagnetic waves propagating in air is fairly successful and suggests intuitively how the electromagnetic waves behave. Indeed, what is visualized in Fig. 4(b) is an electromagnetic wave propagating from the flange opening toward the reflector, being reflected at the surface of the reflector, and propagating in the direction of reflection. In addition, the interference between the incident and reflected waves is clearly indicated at the central region of the images.

More quantitatively, the peak-to-peak distance of waves is measured on the phasor and phase images to be 3.05 mm. This value is in good agreement with the aerial wavelength of the W-band millimeter-wave signal (3 mm). This agreement implies that the W-band waves are visualized without missing their properties of aerial wave propagations. Furthermore it is suggested that the interactions between the aerial and the EO sensor plate wave are sufficiently appropriate for visualization of wave events outside the EO sensor plate, although further discussions are necessary for its details.

In addition, the propagating W-band waves are also visualized for the case of a reflector positioned at an obtuse angle, as shown in Fig. 4(c). Again, the mirror reflection and interference of incident and reflected waves are well visualized. It should be noted in both image sets that there exist some waves propagating beyond the reflector film, i.e., in the upper-right regions of images. Their wave fronts are in a reflection-symmetry with those of the reflected waves, indicating that their phases are spatially continuous with those of reflected waves. These wave images could correspond to the wave components traveling over the top of the reflector film as well as the EO sensor plate. The preservation of phase relationship between two electromagnetic waves having the same origin is thus clearly displayed.

The corresponding videos to these phasor images in Fig. 4(b) and 4(c) are available as Media 1 and Media 2. Their frame rate is 10 frames per second. These videos were acquired in real time, which implies that the present technique is potentially useful for in situ visual analyses of more sophisticated wave structures such as two-dimensionally periodic metamaterial structures [5,6].

4. Conclusion

The real-time visualization of 100-GHz electromagnetic waves propagating in air has been successfully demonstrated for the first time. The geometrical and crystallographic configurations of an EO sensor plate are keys for the demonstration together with the W-band LEI system equipped with a 100-GHz optical LO signal generator. The acquired images and videos of aerially propagating electromagnetic waves clearly show some of the most typical characteristic features of wave dynamics: propagation, reflection, and interference. The present results imply promisingly that the technique used here could be useful for revealing novel electromagnetic phenomena in novel wave media.