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We present a field-calibrated electro-optic sensing system for measurement of the electric field radiating from a high-power vacuum oscillator at ~95 GHz. The intense electric field is measured in absolute scale via two probe-calibration steps, associated with a photonic heterodyne scheme. First, a micro-electro-optic probe, fabricated to less than one-tenth the oscillation wavelength scale to minimize field-perturbation due to the probe, is placed on the aperture of a field-calculable WR-10 waveguide to calibrate the probe in V/m scale. Then, using this arrangement as a calibrated reference probe at the first-tier position, another probe—bulkier, and thus more robust and sensitive but not accessible to the aperture—is calibrated at the second-tier position away from the waveguide aperture. This two-tier calibrated probe was utilized to diagnose the sub-MV/m scale of intense electric fields and emissions from a high-power W-band gyrotron. The experimental results obtained proved consistent with calculated analytical results—verifying the efficacy of the developed system.
© 2016 Optical Society of America
1. Introduction
High-power millimeter-wave sources, especially at W-band (75 GHz–110 GHz), are important microwave radiation systems because they are used extensively in automobile radars (77 GHz) [1], satellite communications (81 GHz–86 GHz) [2], astronomy/security imaging (94 GHz) [3], and active denial systems (95 GHz) [4] for military applications. The most challenging point in evaluating high-power microwave (HPM) systems is accurately measuring their frequencies and output fields in real time [5]. However, measuring electric fields in HPM generation sources is more challenging owing to lack of a proper measurement system as the frequency increases to millimeter-wavelength and higher [6].
We previously developed a fully-dielectric electro-optic (EO) probe with a wide dynamic range over 100 dB for electric field sensing of HPM sources in the relatively low radio frequency (RF) region (up to 3.5 GHz) [7]. The developed probe expresses the measured electric fields on an absolute value after a probe calibration procedure with a field-calculable micro-transverse electromagnetic (μ-TEM) cell. The bandwidth of our EO sensing system is considerably expanded to W-band by enhancing the modulation bandwidth of the probe beam and down-scaling the probe’s volume in accordance with smaller wavelengths [8]. Our miniaturized, micro (μ-) EO probe is capable of minimally invasive field sensing and resolving highly localized electric fields inside a millimeter-scale waveguide because of its small size compared with the desired radio wavelength (~1/10 λ for 100 GHz) [9]. However, despite the advantages of the μ-EO probe, this technique is still usable only in the laboratory because of relatively low sensitivity, mechanical weakness, and probe fabrication difficulties.
Most practical EO probes require sizes of at least a few millimeters for decent sensing capability. However, for millimeter-wave applications, it is difficult to accurately perform field calibration using millimeter-scale (m-) EO probes owing to the invasiveness caused by its size compared with the working radio wavelengths. Consequently, a novel calibration method that integrates the merits of both probes is needed for practical applications beyond each limit.
In this paper, we present a photonic two-tier calibration system for direct electric field measurement of high-power millimeter-wave radiation systems. First, the minimally invasive μ-EO probe is calibrated at the first-tier position where accurate and controllable electric fields can be readily provided. Then, it is relocated to the second-tier position where both μ- and m-EO probes can be positioned in turn; thereby facilitating calibration of the m-probe with respect to the pre-calibrated μ-EO probe. Finally, the real-time field emission performance of a gyrotron oscillator (electron cyclotron maser), which is an effective, extreme high-power millimeter-wave source [5], is experimentally characterized using the proposed system.
2. Two-tier photonic EO probe calibration
Figure 1(a) outlines the two-tier photonic EO probe calibration process for unknown field measurement from millimeter-wave sources. First, the μ-EO probe uses the “reference procedure” to measure the well-known field, as shown in Figs. 1(b) and 1(c). In the procedure, a rectangular waveguide WR-10 (inner dimensions: 1.27 mm × 2.54 mm) for W-band is used as a reference device under test (DUT) as the field strength inside the waveguide can be accurately calculated based on the output power measured by an RF power meter and the physical properties of the waveguide, as previously reported [8]. Moreover, the fairly small size of the μ-EO probe enables us to endoscopically detect the transverse electric (TE) fields (along the y-direction) at the center of the waveguide aperture with minimal invasiveness. The travelling TE fields are terminated and the corresponding net power is read through a commercial waveguide power sensor. Figure 1(c) shows the high spatial accessibility of the μ-EO probe, which is placed precisely at the center of the WR-10 waveguide—perpendicular to the propagation direction of the millimeter wave (configuration A). The μ-EO probe is assembled with a 0.1-mm-thick x-cut LiTaO3 wafer mounted onto an optical bare fiber faucet that is completely embedded along a 0.2 mm groove to one side on a narrow wall. Thus, simply terminating the open-ended waveguide aperture with a power sensor does not disturb the sensing configuration in Fig. 1(c).
Fig. 1 Two-tier photonic system calibration process. (a) Overview of the calibration procedure. (b) Endoscopic calibration procedure for reference μ-EO probe. (c) Cross-sectional sensing geometry of (b). (d) First calibration procedure. (e) Second calibration procedure.
The electric field is maximized at the waveguide center and rapidly weakens closer to the narrow walls. The EO sensing exclusively occurs within 0.1 mm of the wafer tip and the remaining bare fiber support does not disturb the fields because it is fundamentally transparent to microwaves and is also exposed under weaker fields. The probe is sensitive to the electric fields along its optic-axis (c-axis). Hence, even when the probe is rotated from the x- to the z-direction, it still measures the electric fields with equal sensitivity. The μ-EO probe, set along the z-direction, is presented in Fig. 1(d). The μ-EO probe is calibrated to measure the absolute electric fields at the center of the open-ended waveguide aperture (z = 0 mm, the first-tier configuration B). Then, the probe is translated back ~λ (z = 3 mm, the second-tier configuration B’) where the practical m-probe is replaced, as shown in Fig. 1(e). The m-EO probe is also fabricated with a 0.1 mm thick x-cut LiTaO3 crystal mounted onto a pig-tailed glass ferrule. In this case, the probe’s invasiveness, associated with the radiation source, is primarily influenced by the source-to-probe distance [9]. Consequently, the proper offset between the EO probes and WR-10 is required in order to minimize the sensing distortion due to the device invasiveness while maintaining sensitivity. A distance of approximately one wavelength from the radiation device is typically interpreted as the boundary of the near-field region where the fields can still be seminal to evolve as radiating Fraunhofer fields. Thus, the second-tier calibration for the practical probe should begin at least one wavelength away, as shown in Fig. 1(e).
Figure 2 shows the experimental results obtained with the WR-10 at 95.21 GHz (which is the gyrotron frequency explored under our experiment condition) following the two-tier photonic calibration process outlined in Fig. 1. The details of the experimental arrangement used for the probing are given in [8]. For the first-tier calibration in Fig. 1(c), because the electric fields guided inside the WR-10 are simply transverse along the y-direction and also linearly controllable by adjusting the microwave input power, we can produce the calculable, thus well-known field and calibrate the μ-EO probe by using it to measure the “characterized field.” The left axis in Fig. 2(a) shows the μ-EO probe signal versus the WR-10 output power with a dynamic range of approximately 30 dB while maintaining high linearity. In addition, the electric field strength (E) in the center of the rectangular WR-10 with respect to the applied power (P) can be analytically calculated using Eq. (1) [8]:
In Eq. (1), a, Z, and λ are the narrow wall length of 1.27 mm, waveguide impedance of 377 ohms, and the wavelength of the working frequency, respectively. The output power of the WR-10 is accurately measured via the terminated commercial WR-10 power sensor shown in Fig. 1(b). Accordingly, the measured probe signal can be mapped onto the right axis in the absolute electric field (V/m) using Eq. (1). By measuring the sensing signals as a function of the output power of the WR-10 in configurations B, B’, and C’, we obtain field-calibration lines for two-tier photonic calibration of configurations B, B’, and C’, respectively. As shown in Fig. 2(b), it was also confirmed that the μ-EO probe signal in configuration A (Sμ-EO, A) is equivalent to that in configuration B (Sμ-EO, B) through the first calibration procedure. With the open-ended scheme depicted in Fig. 1(d), the non-radiating, evanescent field intensity (I = E2) in the reactive near-field region (z << λ) decays rapidly with distance z [10]. This results in significant erosion of Sμ-EO,B as the calibration point is shifted to B’. By assuming a simple exponential decay function, we can describe the near-field intensity from the aperture aswhere Ii is the intensity at z = 0 and β is the decay length. From the TE10 mode propagation vector kz of the WR-10 waveguide aperture, kz is determined as [11]where λ0 is the free space wavelength of 3.151 mm at 95.21 GHz. Further, assuming, we can estimate the decay length aswhere d is the radiated field diameter of 1.44 mm given by full width at half maximum (FWHM) of the radiated field based on our previous measurement [8]. From Eq. (4), we obtain 0.810 mm for the decay length β, which is consistent with our simulation result of 0.858 mm. By substituting the β calculated using Eq. (4) into Eq. (2), we can analytically estimate the intensity decrease by factors of 40.65 and ∆|Sμ-EO, B − Sμ-EO, B’| of 16.01 dB at z = 3 mm. Figure 2(b) shows the offset measurement results (B → B’) for the μ-EO probe and the measured ∆|Sμ-EO, B − Sμ-EO, B’| of approximately 16.50 dB. The experimental results for the signal difference are reasonably consistent with the analytically estimated results from the simple decay curve. By increasing 16.50 dB to the measured signal in configuration C’, we finally obtain the field-calibrated plot of configuration C for the practical m-EO probe, as shown in Fig. 2(c). This is how the probe would perform in practice if its invasiveness was not significantly degraded in the transition from C’ to C, as is the case with μ-EO. Figures 2(b) and (c) also show that the sensitivity of the μ-EO probe is relatively less than that of the m-EO probe. The noise equivalent signal level is ~−120 dBm in both, which corresponds to sensitivities of ~100 V/m and ~10 V/m for the μ- and m-EO probes, respectively. This is because the geometry and orientation of the EO crystal primarily affect the sensitivity of the EO probe [12]. According to Garzarella and Wu [12], the depolarization effect inside the EO crystals plays a significant role in the sensitivity of the EO probes. The effect makes the thinner and wider EO crystals more advantageous in a transverse scheme of EO sensors. Consequently, the m-EO probe tip is more sensitive than that of the μ-EO probe as a result of the depolarization effect due to the different field effectiveness of each EO crystal. The μ- and m-EO probe have areas of ~0.30.3 mm2 and ~1.51.5 mm2 with the same 0.1 mm thickness of x-cut LiTaO3 crystal, respectively. Accordingly, the m-EO probe will exhibit high sensitivity as a result of the low depolarization factor due to ~25 times larger surface area. Since the probes were all manually assembled, each probe generally shows ~∆10 dB and ~∆5 dB of sensitivity deviation for the μ- and m-EO probes, respectively. Consequently, it is difficult to quantitatively compare the EO sensitivity of the theoretical calculation from the material and size of EO crystals with that of the fabricated EO probes. However, the overall sensitivity difference between the fabricated μ- and m-EO probes is ~∆20 dB, which qualitatively agrees with an order of the internal electric-field difference by theoretically calculated dielectric constant based on the depolarization factors in [12]. The probes also need frequency-dependent calibration factors for the possible frequency drifts in millimeter-wave sources. Figure 2(d) shows each EO probe’s response fluctuating about 1 dB over the narrow bandwidth of 0.3 GHz in 10 MHz steps. Utilizing the field-calibration results in Fig. 2(c), the m-EO probe can also be employed as a field probe for absolute electric field measurements at arbitrary locations from a high-power millimeter waveguide.Fig. 2 (a) Measured μ-EO probe signal strength (left axis) and absolute electric field strength (right axis) versus the output power in the WR-10 at 95.21 GHz. (b) First μ-EO probe calibration process (A → B) and μ-EO probe offset measurement result (B → B’). (c) Second m-EO probe calibration process (C’ → C), achieved by summing ∆|Sμ-EO, B − Sμ-EO, B’|. (d) Frequency response of the EO probes in a narrow 0.3 GHz band. The error bar shows a typical standard deviation of the data points. The standard deviations (σ) of RF power, the μ- and m-EO probe are 0.01 dB, 0.44 dB, and 0.21 dB, respectively.
3. High-power millimeter-wave source measurement and discussion
Figure 3 depicts our photonic-assisted EO system with the high-power millimeter-wave source. We used a distributed feedback (DFB) laser with a wavelength of 1547.3 nm as a probe beam. This laser was modulated through a Mach-Zehnder modulator at precisely 94 GHz, which was realized by frequency-doubling a 47 GHz local oscillator (LO). The optical carrier-suppressed modulation spectrum at 94 GHz is shown in the top-left inset in Fig. 3. The modulation quality was enhanced through a carrier-suppression grating filter and an optical amplifier. This modulated beam was delivered to the calibrated m-EO probe positioned in front of the W-band gyrotron. The gyrotron, depicted in Fig. 3, was oscillated at ~95 GHz and deliver output power at tens of kW with a highly Gaussian beam profile [5]. Further details about the gyrotron are given in [5]. As the m-EO probe is exposed under electric fields of 95.21 GHz, it serves as a frequency mixer for RF and LO, yielding 1.21 GHz intermediate frequency (IF) components. This down-mixed, optically modulated component was demodulated through a photodiode and a spectrum analyzer.
Figure 4(a) shows the signal from the m-EO probe measured using a real-time spectrum analyzer at an axial distance of 1 m from the gyrotron waveguide exit with a pulsed output of 17.1 kW. While the gyrotron was running at repetition rate of 2 Hz with 10 ms pulse length, the EO probe signal was measured in maximum hold mode with frequency span of 160 MHz. A frequency downshift from 95.21 GHz to 95.20 GHz during the 10 ms pulse can be observed. This phenomenon is as a result of the cavity broadening effect due to the heating of the gyrotron cavity [13]. Figure 4(b) shows the measured direct electric field of the high-power W-band gyrotron obtained experimentally. The EO probe signal was converted to the absolute electric field to give the field-calibration plot shown in Fig. 4(b) via the two-tier photonic calibration. According to the field-calibration, we obtain fitting curves of (black dashed-line) and (red dashed-line) for the μ- and m-EO probes, respectively. Under the same condition as the gyrotron in both probes, the measured sensing signal is −75.65 0.34 dBm and −57.030.33 dBm, which corresponds to electric fields of 13.010.49 kV/m and 12.790.48 kV/m for the μ- and m-EO probes, respectively. With only a 1.7% deviation, the signals are virtually equivalent and confirm that the proposed two-tier photonic calibration method is effective.
Fig. 4 (a) m-EO probe signal measured using a real-time spectrum analyzer (in maximum hold mode). (b) Absolute electric field as a function of the measured EO probe signal. (The black and red dashed-lines are the electric field-calibration curves for the μ- and m-EO probes, respectively.) Further, the black square indicates the experimental result for the μ-EO probe while the red circle indicates that for the m-EO probe.
We also measured the spatial field distribution of the gyrotron waveguide using the m-EO probe. Figure 5(a) shows the lateral electric field distributions 1 m away from the gyrotron waveguide, with the probe translated in the x-direction with respect to the center (x = 0 cm). The gyrotron was running at a 2 Hz repetition rate with a pulse length of 10 ms. The total radiation power of the gyrotron in free space can be readily estimated through Gaussian beam approximation of the measured lateral electric field |E(x)| distributions [5]. Consequently, the power density P(x, z) = |E(x)|2/377 of the gyrotron waveguide is given by
where, P0 is the maximum power density at x = 0 cm and ω(z) is the beam radius. The constants P0(z) of 447.87 kW/m2 and ω(z) of 15.99 cm are determined by simply fitting the Gaussian curve of the measured result, as shown in Fig. 5(b). The measured result is consistent with the Gaussian beam profile. In addition, the total power is proportional to the power integrated over the area of the beam passing through the propagation plane, and is given asSubstituting constants P0(z) and ω(z) into Eq. (6), we obtain a total power of 17.97 kW for the gyrotron used in this study. This result verifies that the power measured by the m-EO probe sensing system is close to that obtained 17.10 kW using the calorimetric method.Fig. 5 (a) Lateral electric field |E(x)| distribution and (b) power density P(x) distribution at z = 1 m. (The red-square is the measurement results for the m-EO probe and the black dashed-line represents the Gaussian curve fitting of the experimental data.)
Figure 6 shows the axial electric field distribution from the gyrotron waveguide along the z-axis. The sensing axis of the m-EO probe is set along the z-axis at x = 0 cm. The measured electric field rapidly increases to ~180 kV/m as the axial distance z decreases to 0.5 m, as shown in Fig. 6. We initially expected that the electric field from the gyrotron waveguide would decay as 1/z, but the measured electric field exponentially decayed with the distance z. This discrepancy may be as a result of the unexpectedly higher complex mode of the millimeter wave close to the reactive near-field regions. Further study is necessary to better understand this phenomenon.
Fig. 6 Measured electric field distribution as a function of distance z from the gyrotron waveguide.
The proposed system can also be used to carry out extreme high-power measurements that are far beyond the capability of typical commercial sensors. We sacrificed the m-probe to determine its damage field level. Its operation was adequate up to approximately the 1 MV/m level, which is consistent with the known damage field level of EO crystals [14]. For the higher fields, the sensing signal of the m-EO probe gradually lost linearity, and abruptly disappeared as a result of thermal damage at slightly above ~1.28 MV/m.
4. Conclusion
In this study, we developed a two-tier photonic calibration system using heterogeneous EO probes and experimentally demonstrated its efficacy by conducting electric field measurement of a high-power millimeter-wave source. To the best of our knowledge, this is the first system that utilizes EO probes to accurately measure the absolute electric field in practical applications that are beyond the ability of conventional waveguide-style probes. The m-EO probe enables measurement of electric fields up to ~1 MV/m with a dynamic range of 100 dB (10 V/m to 1 MV/m) by virtue of the electromagnetically robust feature of its all-dielectric embodiment. We also presented the lateral and axial electric field distributions of a W-band gyrotron and showed that the Gaussian beam approximation is consistent with the measured results of the lateral power density distribution. Thus, EO probes field-calibrated using the photonic two-tier method developed in this study can be used for high-power/frequency microwave device characterization where absolute field strength measurement with wide dynamic range is required.
Acknowledgments
This work was supported by National Research Foundation of Korea (NRF) through grant number 2015R1C1A1A02037632 and Agency for Defense Development (ADD) of Korea.
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