Open Access
Add to BibSonomyAbstract
Highly stable electro-optic field probe with wide dynamic range is presented. The highly efficient electro-optic modulation mechanism – based on interference and field-induced phase retardations using a new embodiment with a relatively thick sensor crystal mounted on a fiber – is explained. The probe is calibrated up to 3.5 GHz through the use of a micro-TEM cell and a standard gain horn antenna, both devices in which the electric field may be calculated at the specific sensing location of an electro-optic probe. The field-calibrated sensor shows over 100 dB (≤ 1 V/m to > 100 kV/m) of linear dynamic range. Also, an issue with the instability of the sensors that often occurs in intense electric-field measurements associated with electro-optic crystals is overcome by a real-time, bias-control loop. The stabilized sensor performance and its potential use for (pulsed) high-power-microwave applications are discussed.
©2011 Optical Society of America
1. Introduction
For characterizing the amplitude and phase of the components of traveling or localized electromagnetic waves, electric-field probes have commonly been employed. Most field probes consist of electrical components such as miniaturized receiver antennas and their associated circuitry [1]. The signals that are coupled through a receiving antenna, which then contains valuable field information, are generally delivered to receiver instrumentation via two schemes. One involves the transfer of the electric-field information onto an optical beam using a signal-modulation device, and then the propagation of the signal over an optical link to a remote test area for demodulation and read-out. The other scheme uses signal conversion onto a DC voltage through a rectification circuitry, before transmission over electrical cables that are generally lossy. The use of either the optical fiber or the lossy cables is intended to suppress undesired noise coupling to the final detection termination. Both types of field probes enable good sensitivity and stability through the use of mature microwave-electronics technologies [1].
Although these probes are suitable for sensing weak fields when reasonable noise prevention is practiced, their use has been challenging for detection of intense fields such as those generated from high power microwave (HPM) sources or created by intentional electromagnetic interference (IMEI). This is not only because the health of microwave receiver components may be vulnerable to intense fields, but also because many parts of the system are susceptible to EMI noise. To address these obstacles, fully-dielectric, electro-optic (EO) field sensors have been proposed and viably developed [2–5]. The electrically insulating and electromagnetically transparent sensor material and supporting media are extraordinary solutions for characterizing intense electric-field distributions with little or no risk of breakdown.
This EO-sensing technology has served as a practical and unique method for characterizing electric fields in a minimally invasive way. Fiber-coupled EO probes have been introduced as a preferable solution for relieving the cumbersome optical alignment of free-space optics and to increase probe mobility while maintaining excellent spatial resolution (on the order of the mode-field diameter of a light beam within a single-mode optical fiber). Such a probing scheme is particularly suitable for investigating the relative, detailed field distributions of sophisticated radiation devices, often within the reactive near-field region of a microwave device – e.g., typically within one wavelength of an antenna, where valuable field information and most microwave energy may exist within the evanescent fields [6].
In contrast, non-evanescent fields evolve to the radiating near-field region and then propagate into the far-field region. The field strength diminishes linearly in the far-field region and quadratically in the radiating near-field region, as waves in these regimes propagate significant distances away from the source compared to the situation in the reactive region [6]. However, field distortion and noise-coupling interactions between the source and probe become less of a concern in these regions. Having high sensitivity, conventional electric-field probes are suitable for the far- and, arguably, a limited distance into the radiating near-field regions. To expand the sensing region closer to the radiation source, photonic-assisted (i.e., EO) electric-field probes – where dipole antennas serve as electrodes to modulate the beam in EO medium – have been developed [7,8]. This scheme significantly reduces the invasiveness of the probe while maintaining moderate sensitivity.
In pursuit of non-intrusive sensing in regions closer to the radiation source, it becomes highly recommended to reduce or eliminate all metallic components in the probe. This is due to the fact that the degree of field perturbation and the risk of probe breakdown, due to high radio frequency (RF) power, increase according to the relative scale of a probe’s metallic antenna structure compared with both the size of the source and the distance between source and probe.
In this paper, we present a highly efficient, all-dielectric EO field probe that utilizes interferometric modulation in a relatively thick EO crystal. Its sensitivity has been enhanced enough over previous non-invasive EO field probes that it may more readily cover the radiating-near-field and far-field regions of RF emitters, including those employed for wireless communications and the typical HPM bands. The measured field signals were calibrated to the absolute electric-field strength in units of V/m. Moreover, the calibration techniques, stabilization of the sensor for long-term HPM use, and its pulse-measurement capability are all discussed.
2. Interferometric Probe Using a Thick EO Crystal
Unlike conventional reflective probes that use a double-pass EO-modulation scheme, a novel and simple interferometric EO probe has been recently proposed [9,10]. These interference-type probes utilize the slope of a fringe of the interferometric reflectance response to modulate the light beam as the EO crystal is exposed to microwave or other low-frequency electric fields. The degree of EO amplitude modulation is linearly proportional to the gradient of the fringe slope and the amount of optical phase modulation. Hence, it is highly desirable to enhance these properties to achieve an improvement in sensitivity.
Previously, we demonstrated an interferometric electric-field probe with a thin (0.1 mm), uncoated LiTaO3 wafer tip, and minimally invasive, reactive-near-field, calibrated imaging was successfully realized [9]. The basic principle of an interference-type EO probe is illustrated in Fig. 1(a) . There, a reasonably thin (~0.1-mm-thick), x-cut LiTaO3 crystal was mounted directly on the fiber facet (with n ~1.5). The incident optical-beam component from the fiber core was reflected at the first interface (fiber-LiTaO3) with the Fresnel coefficient r1 (≡ R1). The transmitted field component (t1) is then reflected at the second interface (LiTaO3-air) with another Fresnel coefficient r2. Since the EO wafer is fairly thin, the majority of this component is coupled back onto the original beam path in the fiber. The amount of this coupled component is Ct12r2 (≡ R2), where C is a coupling factor strongly associated with the numerical aperture of the fiber and the optical path length of the crystal. The optical path difference between the components reflected from R1 and R2 primarily controls the phase retardation – given by δ(E,λ) = 4πno,e(E,λ)h/λ – which governs the overall interferometric reflection, including the EO modulation by the RF E fields intercepted by the probe.
Fig. 1 Fiber-coupled EO field probe: (a) structure of an interferometric probe; (b) structure of a thick, balanced-interferometric probe; (c) detailed interference components within the fiber core of a thick, balanced-interferometric probe.
The EO crystal LiTaO3 is positive uniaxial (i.e., ne > no), and thus it has two birefringence terms; (ne-no) and (ne3r33-no3r13)E/2 [11]. The former and latter terms are the natural and electrically-induced birefringences, respectively. As the light is linearly polarized along the e-axis (or o-axis), the phase retardation by the crystal is δe(E,λ) = 4πneh/λ + 2πne3r33hE/λ (or δo(E,λ) = 4πnoh/λ −2πno3r13hE/λ), since the light experiences only one refractive index throughout the crystal. The r1 component serves as the fixed reference path in the interferometer whereas the Ct12r2.exp(δ(E,λ)) component is a controllable path with polarization, wavelength and applied low-frequency electric fields.
Because one wishes to use such an interferometric fiber sensor as a practical field probe for both the radiating near-field and the far-field regions, it would be best if the sensitivity was enhanced significantly. Simply employing a thicker EO wafer would be a straightforward solution because the EO phase retardation and the fringe sharpness become enhanced altogether. In actuality, however, it is crucial to balance the amplitude of the two interference components in order to maximize the fringe contrast. In the case of interference with a thin crystal wafer, the amplitudes of the two beam paths (r1 . and Ct12r2) were made comparable in a relatively straightforward fashion, because r2 (at the crystal-air interface) is always a bit larger than r1 (at the fiber-crystal boundary), and their scale difference can be compensated by Ct12, which is accordingly smaller than unity if a crystal that is appropriately thin is used.
The coupling factor degrades rapidly due to the beam divergence for thicker wafers, so that the crystal/air interference term – which contains the valuable EO-phase-modulation information – becomes less associated with the fiber/crystal interference term. The reduced coupling efficiency can be compensated by increasing the reflection at the crystal-air interface (r2) through application of a high-reflection (HR) coating on that crystal surface. Figure 1(b) shows such a balanced-interferometric probe with an EO crystal that is thick and terminated with a mirror. Detail of the reflected field components that generate the balanced-interferometric EO modulation is illustrated in Fig. 1(c).
3. Evaluation of a Thick Interferometric Probe
It was determined that the first round-trip EO modulation component (R2 in Fig. 1(c)) became well-balanced when a ≥0.5-mm-thick LiTaO3 crystal with a ≥99% reflectance dielectric coating was used. The EO probe is mated to a fiber-optic link that starts with a 1550-nm-wavelength distributed feedback (DFB) laser diode that provides 13.7 mW of power at room temperature. Most commercial telecommunication-grade DFB laser diodes are wavelength-tunable by several nanometers through use of a thermo-electric control (TEC) circuit. Such wavelength tunability is important to create and control the interference fringes of a probe.
The known birefringence terms of LiTaO3 at 1558 nm are ne = 2.1224 and no = 2.1186 [12]. This magnitude of refractive index (n ~2.12 at 1550 nm) yields a spacing for each interference fringe of ~1.06 nm for a 0.5-mm-thick LiTaO3 wafer. To utilize the interference-based modulation, the laser ought to have enough tuning range that it covers at least one fringe. Our DFB laser (JDSU: model CQF915) exhibits 0.09836 nm/°C of tunability, allowing a range of > 4.9 nm with our ΔT = 50 deg. TEC controller.
For clear fringes with high extinction, the interference component (R2 in Fig. 1(c)) for LiTaO3 must experience a single refractive index (i.e., without birefringence). An in-line polarization controller can readily adjust the beam’s polarization so that it is linear and align it along either the ne or no axis. Both of the comparable but still distinct refractive indices yield similar fringes with a small spectral offset. Figure 2 shows such a situation for the measured fringes that arise from a 0.5-mm-thick LiTaO3 etalon possessing a refractive index of ne (for the solid line) or no (for the dashed line). The reflectance of the probe is normalized for laser power and system losses. The reflectance fringes could be suppressed to as low a level as ~1%, which indicates that the difference of the two interference field components is ~10%. As the two components build up constructively, the reflectance reaches ~31%, which means that the two actual field components coupled into the core have R1 ~0.23 and R2 ~0.33. In practice, the Fresnel-reflection field coefficient, r1 = R1, arising from the fiber-LiTaO3 interface, is found to be larger than expected for its refractive index mismatch. This is because the mismatch has been increased by the use of optical adhesive to mount the crystal.
Fig. 2 Experimental interference fringes for a thick, balanced-interferometric probe. (Each fringe spectra arises from a 0.5-mm-thick LiTaO3 etalon with refractive index ne (solid line) or no (dashed line)). (Points a - d are efficient biases for EO amplitude modulation).
The reflected beam at the probe tip is electro-optically amplitude modulated as the tip is exposed to, for instance, fringing or radiated RF electric fields. As mentioned, besides its natural birefringence (ne vs. no), LiTaO3 also possesses the electrically-induced birefringence terms, ne3r33E/2 or no3r13E/2, where r33 = 27.4 (pm/V), and r13 = 6.92 (pm/V) at 1558 nm [12]. Hence, the field-induced dynamic birefringence is approximately four times larger when the light polarization in the LiTaO3 is set linearly along the ne axis rather than along no.
Using the interference fringes associated with ne, the maximized EO amplitude modulation can be achieved at the point where the slopes of the fringes are steepest. Although the steepest slope exists over a wide range, thus creating highly modulation-efficient fringe bands, it is advantageous to use the lower part of the fringe band for reasons dictated by noise suppression [13]. The four gray points (a - d) on the 10% reflectance line in Fig. 2 are these modulation bias points that will yield good signal-to-noise ratio. One may readily tune to each spectral bias point by appropriate control of the temperature.
Employing a thick crystal, the EO modulation slopes at the bias points could be quite steep. We have compared the balanced-interference fringes for transmissive [14] and reflective [10] cases, respectively. Both cases explored the period and contrast of the fringes for LiTaO3 wafers that were ~five times thicker that those explored previously. Verified from their accordingly steepened slopes, the thicker EO wafers exhibited 4-5 times stronger signals. This is a benefit for sensitivity enhancement, but one drawback lies in the possible drift of the bias point, especially for long-term or high-power-sensing applications.
Such instability problems can be overcome by using a TEC control loop that will lock the wavelength (and, hence, temperature) bias at a particular point on the interference fringe. A probe-evaluation system with a TEC loop, i.e., upgraded compared to our previous one [9,10], is presented in Fig. 3 . To test the EO probe over a wider dynamic range, an RF power amplifier (Amplifier Research: 50W 1000) was used to provide up to 50 W of continuous wave (cw) input power to a device under test, and the bandwidth of the optical receiver element was extended to 3.5 GHz with a photodetector (Newfocus: 1952NF) and spectrum analyzer (Agilent Technologies: E4448A) that have a faster response time.
Fig. 3 Experimental schematic of the all-fiber-based EO-probe calibration system. (The gray and black lines are optical fibers and electrical connections, respectively).
It has been reported that an electronics system such as one within an automobile that is unprotected from HPM can be vulnerable to electric fields of relatively low magnitude. Specifically, a field level of 500 V/m or even less has the capability to stop a vehicle (including the engine) due to the failure of electronic systems. Permanent damage of systems, including engine control units, relays, speedometer, tachometer, security alarm, and video camera, have been shown to occur for 15 kV/m at 1.3 GHz and 24 kV/m at 2.86 GHz [15].
To characterize such different levels of damages, it is necessary for the EO field probes to resolve the absolute strength of electric fields. The calibration of an EO probe may be performed by exposing it to a known electric field that is generated with a standard micro transverse electromagnetic (μ-TEM) cell. In Fig. 3, the electromagnetic waves travel in the y-direction, and its electric field is linearly polarized along the x-axis. The strength of this field can be accurately calculated based on the net power read by an RF power meter and the physical parameters of the cell, and a detailed explanation of such field calculations in the cell may be found in previous publications [9,16].
Since the strength of the TEM-cell internal fields is linearly controllable through adjustment of the RF input power to the cell, we can generate calculable fields with known strength and calibrate the EO probe by letting it sense the “known fields.” In our case, the probe head was placed in the center of the cell and the c-axis of the LiTaO3 was aligned along the x-direction so as to sense the electric fields travelling in the same direction. The measured signal trace versus the net power in the cell is presented in Fig. 4 . As the absolute fields that modulated the light beam within the probe are characterized versus the power in the cell, the measured field signals (Fig. 4. left axis) can be re-expressed in the units of V/m (Fig. 4. right axis). The noise-equivalent field strength was found to be ~0.6 V/m, and thus the sensitivity of this probe is arguably comparable to that of typical dipole-based EO sensors.
Fig. 4 Measured EO-signal strength (left axis) and actual electric-field strength (right axis) versus the net power in the μ-TEM cell at 1 GHz. (This calibrates the measured signals into field with units of V/m).
It has also been reported that when fields that are relatively weak for EM threats – as low as 30 V/m – reach the inside of a personal computer, its operation could be disrupted [17]. This field level is considered to be mid-scale for typical field probes. Here, we chose such a 30-V/m-magnitude electric field as a standard reference strength. Mapping the two vertical axes in Fig. 4, the 30 V/m line corresponds to −89.56 dBm of EO-modulated light power at 1 GHz. Knowing these two values should be identical, the scale factor that relates the two different units is determined to be 20log(30/(scale factor)) = −89.56 dBm. Here, the scale factor is 902,000 at 1 GHz, and it is effective for different signal strengths as long as the signal maintains its linearity. This factor serves as a probe calibration factor and needs to be determined separately at each frequency of interest.
The reliable bandwidth of the micro-TEM cell is 0.1 MHz - 1.5 GHz. For calibration beyond this band, a standard gain horn antenna in an anechoic chamber (as in Fig. 5 ) can be employed to generate a test electric field as follows:
where Pmain is the output power of the directional coupler “through” port that would be delivered to a matched load at the end of the cable to the antenna, R is the separation distance between the antenna and the probe, Go(R) is the gain of the antenna at a distance R (here, 1.5 m), and ΓANT is the reflection coefficient of the antenna. The Pmain is given by the expressionwhere Pside is the output power of the “coupled” port of the coupler, R21 is the insertion loss, which includes the coupler and the RF cable between the coupler and the antenna, and R31 is the coupling factor of the coupler.Fig. 5 Experimental block diagram of EO-probe calibration system with a standard-gain horn antenna. (The E-field line in the chamber is vertically and linearly polarized).
By propagating the 30-V/m field to the probe position, the calibration of the EO probe can be extended up to the full bandwidth of the photodetector. The overall calibration factors for the bandwidth of the detector are shown in Fig. 6 . The first 16, and then the next 17, calibration values are determined by the μ-TEM cell and the standard gain horn antenna, respectively. The first point is 1 MHz and, from the second point (100 MHz) to the last (3.5 GHz) point, calibration is performed every 100 MHz.
The calibration factors in Fig. 6 are effective as long as the probe signals maintain their linearity. This all-dielectric probe enables evaluation of intense electric fields with magnitudes as high as on the order of 100 kV/m. This feature is particularly useful where intense-field characterization, typically close to a radiation source, is desired. For instance, Fig. 7 is the amplitude and phase distribution of the electric field over a 20-mm-wide coplanar waveguide (CPW) transmission line. The CPW line was fed with 50 W ( + 47 dBm) of power at 1 MHz. The end port of the line was open-terminated to create even stronger fields due to the presence of a standing wave. The probe is scanned at a height of ~0.2 mm from the plane of the CPW line. The strongest signals observed were a pair of global maxima at the gaps between the center CPW electrode and the side ground lines. In addition, another minor pair of signal maxima was observed at the edges of both the ground lines. We used a lock-in amplifier to resolve valuable phase information as well. For each of the signal pairs, the polarities of the two signals are opposite to each other, and thus the field over the CPW line does not evolve by combining constructively and radiating to the far-field.
Fig. 7 Vector-field distributions over a coplanar waveguide transmission line at 1 MHz (solid lines: amplitude, dotted lines: phase).
The most intense signal levels are found apparently at the two gaps between the central and ground lines. This level is maximized as the probe is gently positioned to touch the plane of the CPW within each of the two gaps. At these points the highly localized electric fields were being transversely applied to the crystal. In this case, the central and ground lines behave as metallic electrodes similar to the case of a Mach-Zehnder interferometric modulator, where the electrodes are situated between the EO medium to yield efficient phase modulation.
The phase-modulated beam becomes intensity modulated by the slope of the probe interferometric fringes. The intensity-modulated EO signal – modulated by the electric fringe fields within the gap – versus power to the CPW line is shown in Fig. 8 . The driving RF power was increased up to + 47 dBm at 1 GHz. Using the probe’s calibration factor as in Fig. 4, the measured and calibrated absolute fields show over 100 dB (from at least 1 V/m to 100 kV/m) of dynamic range with excellent linearity. The maximum demodulated EO signal power is −17.24 dBm (corresponding to 124 kV/m) at + 47 dBm input power. The rough field level for damage of EO probes is known to be on the order of 1 MV/m [18]. In the near future, we should be able to report more specific damage or saturation (i.e., 1-dB suppression point) values for this type of probe when higher fields may be supplied without air break down.
Fig. 8 Measured EO-signal strength (left axis) and actual electric-field strength (right axis) over the gap of a coplanar waveguide line at 1 GHz.
4. Strong-Field Stabilization of the EO Probe Signal
In addition to an absolute field-measurement capability with wide dynamic range, stability is another important concern for probes used to sense high-amplitude electric fields. Electro-optic devices for light modulation, which may utilize LiTaO3 or LiNbO3, often suffer from instability due to the nature of the crystals. Typically, an externally applied DC voltage sets a specific bias point on the interferometric-modulation fringes. In the case of interferometric probes, the main reason for possible signal instability is bias fluctuation due to wavelength drift of the laser, as the bias point on a fringe is set by controlling the wavelength (or temperature). Such a voltage bias could drift frequently over periods of long-term use. However, the drift can be monitored and compensated by virtue of a bias-voltage-feedback loop control [19]. Similarly, these potential wavelength-drifts can be managed using a TEC loop control, but this is generally less effective.
Figure 9 shows stabilized, calibrated electric-field measurements extracted over a one-hour time period while a probe was situated within 30 V/m and 1 V/m magnitude signals at a frequency of 1 GHz. With the TEC loop control, the signals have been found to fluctuate mainly within ± 1% and ± 20% of the mean values for the 30 V/m and 1 V/m fields, respectively, over the course of an hour. The degree of stabilization basically follows that of the reflectance from the probe. The reflected power was set at 1 mW and locked by the TEC bias control. The black level in Fig. 10 is the 1 mW-locked power under 30 V/m exposure for an hour. When this power is demodulated through a photodiode, the stabilized signal shown in Fig. 9 was obtained.
Fig. 10 Comparison of stabilized probe reflectance at 1 mW optical power when using TEC loop with DFB laser (black: sensing 30 V/m electric field ; gray: sensing 124 kV/m).
The bias instability increases when sensing stronger fields, and thus the bias control used to compensate the bias-drift becomes accordingly more active. For instance, the gray level in Fig. 10 is the 1 mW-locked power under 124 kV/m exposure for an hour. The deviation from its 1-mW average level became more significant for stronger fields such as these.
The bias transitions employed to lock the power at 1 mW for both normal (30 V/m) and hyper-intense (124 kV/m) fields are shown in Fig. 11 . The bias b (i.e., the room temperature bias in Fig. 2) was chosen and the colors of the biases are accordingly matched with those of the plots in Fig. 10. The bias for 30 V/m (black trace) did not have to shift significantly over an hour, while the other (gray trace) varied over a much greater range. In most practical EO sensing applications, EO probes are subjected to fields that are typically below the kV/m range. For such field levels, just a simple TEC-controlled laser without the TEC feedback loop was sufficient to characterize relative field distributions over radiation devices under test [13]. However, the TEC loop control must be used for long-term and/or high-power applications.
Fig. 11 Comparison of temperature (and wavelength) bias drifts at the 1 mW “locked” probe reflectance shown in Fig. 10 (black: sensing 30 V/m electric field ; gray: sensing 124 kV/m).
5. Application to High-Field Pulsed Signals
Intentional EMI, which one may consider to be a form of EM Terrorism, is categorized into two basic types of IEMI waveforms: Narrowband and Wideband [20]. The former category describes a nearly single frequency and virtually cw type of threat. It is often referred to as HPM and is used for attacks in relatively narrow ranges around 0.2-5 GHz [19].
In pursuing wideband threats, the IEMI waveform needs to be employed in a pulse mode. To investigate the effectiveness of EO probes for IEMI pulse threats, we changed the previous maximum cw-feeding condition ( + 47 dBm at 1 GHz) into a square-pulse mode (repetition rate, 1 ms; duty cycle, 10%). The measured spectrum of the pulse train using the EO probe is shown in Fig. 12 . The sinc-squared envelope corresponds to square pulses in the time domain. Additionally, the number of sinc nulls (i.e., 10) and the fine combs (100) under the envelope in the 100 kHz span are related to the pulse width (0.1 ms) and the repetition rate ( = 1 ms), respectively.
Fig. 12 Spectrum of EO signal for square-pulses with 10% duty cycle at 1 GHz (average RF power of + 37 dBm).
For a reduced duty cycle, down to 1%, the spacing between sinc-nulls has been expanded 10 times, while the repetition rate remained same. This can be seen in Fig. 13 with a 1-MHz span. Also, the distorted and thus asymmetric sinc-squared envelope indicates that the pulses evolve to a non-ideal square shape as they become narrower. The reduced duty cycle with the same repetition rate is advantageous for spreading its spectra. However, as observed in Figs. 12 and 13, the drawback is signal reduction: as the ~20 dB peak signal was diminished for every 10´ reduction in duty cycle.
Fig. 13 Spectrum of EO signal for square-pulses with 1% duty cycle at 1 GHz (average RF power of + 27 dBm).
6. Conclusions
We have demonstrated an efficient electro-optic field probe that is suitable for high power microwave (HPM) applications where absolute-field characterization is needed. The all-dielectric embodiment of the probe enables the measurement of electric fields that exceed 100 kV/m amplitude, and an efficient sensing mechanism utilizing the balanced interference of modulated beams reduces the minimum detectable field to a level below 1 V/m. Thus, 100 dB of dynamic range was demonstrated for the EO probe. Also, field-calibration and stabilization techniques for HPM signals are presented. The probe’s reliable and calibrated field-measurement capability, combined with its wide linear dynamic range, could lead to a promising diagnostic solution for EM threats in electronic warfare.
Acknowledgments
This material is based upon work supported by the Korea Research Institute of Standards and Science (KRISS) and Agency for Defense Development (ADD).
References and links
1. H. I. Bassen and G. S. Smith, “Electric field probes,” IEEE Trans. Antenn. Propag. 31(5), 710–718 (1983). [CrossRef]
2. K. Yang, L. P. B. Katehi, and J. F. Whitaker, “Electro-optic field mapping system utilizing external gallium arsenide probes,” Appl. Phys. Lett. 77(4), 486–488 (2000). [CrossRef]
3. S. Wakana, T. Ohara, M. Abe, E. Yamazaki, M. Kishi, and M. Tsuchiya, “Fiber-edge electrooptic/magnetooptic probe for spectral-domain analysis of electromagnetic field,” IEEE Trans. Microw. Theory Tech. 48(12), 2611–2616 (2000). [CrossRef]
4. K. Yang, L. P. B. Katehi, and J. F. Whitaker, “Electric-field mapping system using an optical-fiber-based electro-optic probe,” IEEE Microwave Wireless Comp. Lett. 11(4), 164–166 (2001). [CrossRef]
5. H. Togo, N. Shimizu, and T. Nagatsuma, “Near-field mapping system using fiber-based electro-optic probe for specific absorption rate measurement,” IEICE Trans. Electron E90-C, 436–442 (2007). [CrossRef]
6. A. G. Yaghjian, “An overview of near-field antenna measurements,” IEEE Trans. Antenn. Propag. 34(1), 30–45 (1986). [CrossRef]
7. M. Hirose, T. Ishizone, and K. Komiyama, “Antenna pattern measurements using photonic sensor for planar near-field measurement at X band,” IEICE Trans. Comm, E87-B, 727–734 (2004).
8. E. Suzuki, S. Arakawa, M. Takahashi, H. Ota, K. I. Arai, and R. Sato, “Visualization of Poynting vectors by using electro-optic probes for electromagnetic fields,” IEEE Trans. Instrum. Meas. 57(5), 1014–1022 (2008). [CrossRef]
9. D. J. Lee, N. W. Kang, J. Y. Kwon, and T. W. Kang, “Field-calibrated electro-optic probe using interferometric modulations,” J. Opt. Soc. Am. B 27(2), 318–322 (2010). [CrossRef]
10. D. J. Lee, N. W. Kang, J. H. Choi, J. Y. Kim, and J. F. Whitaker, “Recent advances in the design of electro-optic sensors for minimally destructive microwave field probing,” Sensors (Basel Switzerland) 11(1), 806–824 (2011). [CrossRef]
11. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley Interscience, 2003), Ch. 8.
12. J. L. Casson, K. T. Gahagan, D. A. Scrymgeour, R. K. Jain, J. M. Robinson, V. Gopalan, and R. K. Sander, “Electro-optic coefficients of lithium tantalite at near-infrared wavelengths,” J. Opt. Soc. Am. B 21(11), 1948–1952 (2004). [CrossRef]
13. D. J. Lee and J. F. Whitaker, “Optimization of sideband modulation in optical-heterodyne-downmixed electro-optic sensing,” Appl. Opt. 48(8), 1583–1590 (2009). [CrossRef] [PubMed]
14. D. J. Lee and J. F. Whitaker, “A simplified fabry–pérot electrooptic-modulation sensor,” IEEE Photon. Technol. Lett. 20(10), 866–868 (2008). [CrossRef]
15. M. Bäckström, “HPM testing of a car: a representative example of the susceptibility of civil systems,” W4, In Proceedings of 13th International Zurich Symposium and Technical Exhibition on EMC, (Zurich, Switzerland, 1999), pp. 189–190.
16. N. W. Kang, J. S. Kang, D. C. Kim, J. H. Kim, and J. G. Lee, “Characterization method of electric field probe by using transfer standard in GTEM cell,” IEEE Trans. Instrum. Meas. 58(4), 1109–1113 (2009). [CrossRef]
17. J. LoVetri, A. Wilbers, and A. Zwamborn, “Microwave interaction with a personal computer: experiment and modeling,” In Proceedings of 13th International Zurich Symposium and Technical Exhibition on EMC, (Zurich, Switzerland, 1999), pp. 203–206.
18. A. Garzarella, S. B. Qadri, and D. H. Wu, “Optimal electro-optic sensor configuration for phase noise limited, remote field sensing applications,” Appl. Phys. Lett. 94(221113), 1–3 (2009). [CrossRef]
19. A. Dandridge and A. B. Tveten, “Phase compensation in interferometric fiber-optic sensors,” Opt. Lett. 7(6), 279–281 (1982). [CrossRef] [PubMed]
20. M. W. Wik and W. A. Radasky, “Intentional electromagnetic interference (IEMI)—Background and status of the standardization work in the International Electrotechnical Commission,” In Proceedings of URSI General Assembly, (Maastricht, The Netherlands, 2002).
