We numerically and experimentally investigate the field invasiveness of microwave signals using an electro-optic technique. The distortion of the standing wave voltage and pulse waveform probed by the electro-optic technique is explored through both minimally invasive external and non-invasive internal sensing configurations. First, we analyzed the continuous wave microwave field imaging on a millimeter- scale coaxial transmission line using a highly accurate and stable electro- optic scanning system. The electric field images from the microwave device are attained virtually non-invasively using a miniaturized fiber-coupled electro-optic probe. The accuracy of the field imaging associated with various probe styles is investigated by numerical analysis and experiment. Then, we analyzed the waveform of the coaxial transmission line up to 50 GHz using a pulsed electro-optic system with an external probe set. Finally, the invasive analysis was extended to the sub-millimeter-scale on-wafer coplanar waveguides, where the voltage waveforms are measured using a minimally invasive external probe as well as an internal wafer probe for non-invasive sampling.
© 2014 Optical Society of America
The minimally invasive or non-invasive nature of electro-optic (EO) sensing/sampling is one of its most unique and distinguishing features. Inherently minimally invasive EO techniques have become established solutions for the accurate field characterization of high-speed electronic devices where conventional electrical methods become challenging . The EO effect is capable of detecting both continuous (CW) and pulsed electrical signals. For (quasi) CW sensing, as the laser beam passes through the EO media under electric (E-) field exposure, the field-exposed media modulates the light that is to be demodulated through the readout instrument [2–9]. In the case of pulsed field sampling, a synchronized laser and E-field can be spatially and temporally overlapped to cause “CW-like” EO effects through interferometric configurations. Thus, the reconstruction of the pulsed signal can be achieved by an appropriate delay control of an interference path [10–15].
Both CW and pulsed electro-optic sensing/sampling (EOS) techniques are characterized using external [3–11] and internal schemes [11–15]. The external scheme is more widely employed over the internal scheme because of its numerous practical advantages . In particular, the external scheme (i) can be applied to electronic devices that typically do not show EO effects, (ii) has greater accessibility as the probe can be placed in arbitrary locations over the device under testing, and (iii) generally shows higher efficiency as the unnecessary volume of the EO media can be minimized. Despite the practical advantages of the external schemes, the distinguished advantage of the internal scheme is its non-invasiveness; the sensing configuration of the internal scheme becomes inherently non-invasive when the EO material is used as a substrate of the device under test.
In this paper, we fabricated a miniaturized – and thus minimally invasive – external micro-probe, and then we numerically and experimentally compared its invasiveness with a conventional probe over a coplanar waveguide (CPW) transmission line. The experimental comparison of the external probes was presented with both CW and pulsed EOS configurations. Finally, we experimentally justified that our external micro-probe is virtually non-invasive by comparing it with internal sampling over a sub-millimeter-scale on-wafer CPW line.
2. Invasiveness analysis of external EO probes: CW sensing
The external EO probes have evolved in various schemes since the EO sensing technique became an established tool for diagnosing microwave devices. Today, fiber-coupled probes are generally preferred because they are easily aligned and compact [3–6]. Because probes often require bulky EO materials to compensate for the relatively low EO effects of the material, most fiber-coupled probes are at least on the millimeter-scale when the support optics for the sensor are included [4–6]. To reduce the thickness of an EO medium while maintaining the sensitivity, a resonance-based enhancement technique is developed for the longer interaction length of the sensor. The reduced probe embodiment could become small enough to directly mount the probe onto a bare fiber faucet, and such an optical-fiber-scale probe is considered to be the most minimally invasive of its kind .
We quantitatively analyze the field invasiveness of such a minimally invasive probe with respect to a conventional probe. We fabricated another set of bulky, thick-interference probes (defined as type III in ) and resonance-based micro probes (in ). The bulky and micro probes are made of 2 mm × 2 mm × 0.5 mm and ~0.2 mm × ~0.2 mm × 0.1 mm LiTaO3 wafer crystals, and they are defined as Probes A and B, respectively. The assembled probes are placed vertically (z direction) over the CPW lines as shown in Fig. 1. The microwave signals propagate along the y direction, yielding their transverse E-field along the x direction. Because the optic axis of a LiTaO3 wafer specifies the direction of the E-field to be measured, it must be aligned in the x direction. We will adhere to this sensing geometry and the direction of each path (x: E-field, y: microwave, z: light) throughout this paper for clarity. All the probes detect the E-fields across the gap over the CPW lines. The probe’s field sensitivity is maximized when the laser beam is linearly polarized along the optic axis of the EO wafer by a polarization controller. The detailed probe structures and their sensing principles, which are not the theme of this paper, are discussed in [3,4].
For the numerical analysis of the field invasiveness of each probe, we set the probes over the line gap as illustrated in Fig. 1(b). The E-field distribution is computed with the finite-element-method-based High Frequency Structural Simulator (HFSSTM) field analysis tool. Probe A is placed in the transverse field (±x direction) at 0.1 mm above the transmission line. Because the wafer of Probe A is 0.5 mm thick, the E-field inside the large LiTaO3 volume is not uniform. In fact, the probe measures the overall field along the interaction path and the average field distribution inside the EO wafer (h = 0.1 mm–0.6 mm) at approximately h = 0.25 mm, which is where we placed Probe B to provide a fair comparison of the fields being measured.
The horizontal (xy-plane) and vertical (xz-plane) field distribution over the gap in the transmission line is computed in Fig. 2. Both Probes A and B were simulated with LiTaO3 and GaAs in the configuration shown in Fig. 1(b) because the field distortion heavily depends on the physical parameters of an EO wafer. For instance, the lower volume and dielectric constant of the wafer reduce the field invasiveness of the probes.
The field invasiveness along the line where the xy- and xz-planes intersect is presented in Fig. 3. The field penetration into the wafer is primarily dependent on the dielectric constant of the wafer. The relatively lower dielectric constant of GaAs enables ambient fields to penetrate deeper into the wafer than those of LiTaO3. The unpenetrated fields reside at the rim of the wafer, which is typically quite intense because significant portion of fields are rejected at the interfaces. Because of the opaque nature of the EO material, Probe A pushes the ambient field significantly out of the wafer, thus considerably distorting the original field distribution. Probe B not only pushes the measurement field away but its minute structure causes greater field scattering around the rim than Probe A does, causing the actual field penetration into the Probe B to be lower than that of Probe A. Despite the negative effects of Probe B, the field distortion observed is lower due to the slender profile of Probe B. Both the LiTaO3 Probe B and GaAs Probe B show comparable field strengths at the rim because the scattering is a dominant factor for such a minute structure. However, the fields inside the crystals show a clear dependence of the dielectric constant. The typical dielectric constants of GaAs (εr = 12.9) and LiTaO3 (εr = 43) allow a field penetration of only 28.9% and 11.1% with respect to the field at the peak of transmission line. Although the LiTaO3 probe shows less field penetration, it would be much more efficient (≥10) than the GaAs probe because the EO coefficient of LiTaO3 is about 30 times higher than that of GaAs . Furthermore, the two EO media show comparable scattering, which is a primary cause of the field-distortion for a miniaturized structure like Probe B. Therefore, we choose LiTaO3 for the actual probe fabrication and experimentally quantify its invasiveness for Probes A and B.
The electric field distribution over the CPW line is evaluated with both measurement and simulation as shown in Fig. 4. We have built a highly stabilized phase-locked EO imaging system for accurate measurement of near-field scanning . The field distribution measured using Probes A and B are shown in Figs. 4(b) and 4(c), where a +20 dBm of power at 10-GHz is fed to the 100-mm CPW line that is terminated by a short calibration kit. The effective measurement plane (xy-plane) is ~0.25 mm above the line as shown in Fig. 1(b). At this plane, we present the HFSSTM simulated field in Fig. 4(d). Figures 4(e)–4(g) show normalized log scale versions of Figs. 4(b)–4(d). Probe A shows a greater signal-to-noise ratio than probe B because it has a longer interaction length.
Two clear 10 GHz standing waves are formed in the scan area. The probes do not excite undesirable slotline modes, which are often excited when asymmetric discontinuities are added over symmetric CPW lines . The probes indeed cause some discontinuities as they become capacitively loaded to the CPW while accessing it. However, these discontinuities are evenly distributed overall throughout the raster scanning; thus, fairly symmetric field distributions are obtained regardless of the probe size.
The Probe A results show that the measured field pattern is significantly distorted where Probe A pushed the field out of its body, while Probe B does not. The degree of field invasiveness measured with Probe B is compared to the simulation field distribution in Figs. 4(c) and 4(d). Probe B realizes virtually non-invasive field imaging due to its infinitesimal volume at 10 GHz. This non-intrusive feature is maintained for fields up to 50 GHz, and we verify this in the next section using broadband pulsed EO sampling of the probe.
3. Invasiveness analysis of external EO probes: pulsed sampling
Both EO sampling and photoconductive (PC) sampling are established techniques for detecting extremely fast and transient electromagnetic signals. The PC technique is generally preferred when relatively high efficiency signal generation and detection is desired. However, because the PC scheme is inherently associated with the conductive metallic components in the detection scheme, it is quite challenging to avoid distortion of the waveform. In case of metrology or instrumentation, minimally invasive and precise sampling is more important than efficiency, thus the internal EO technique is widely used because of its absolute non- invasiveness [11–15]. The internal scheme utilizes EO materials as the dielectric substrate of the transmission lines. The guided fields within the substrate can be detected by illuminating the guided spot with pulsed light, which is demodulated to an electrical signal.
We use a conventional pump-probe-style EO sampling technique with a femto-second pulsed laser. The detailed experimental configuration is discussed in . We upgraded the excitation path with a 67-GHz photodiode and replaced the free space section with fiber optics to match the fiber-coupled probes. The Probes A and B were designed for a CW laser source as their sensing performances were enhanced by interferometric resonance of the laser within the wafer. For pulsed sampling, a conventional double-pass style probe with a thin wafer is preferred because of its excellent temporal resolution. We used a 0.1-mm thick LiTaO3 wafer with a high reflection coating on the bottom surface to assemble another bulky double-pass probe, which was introduced as Type I in . We made another minute version of it with the same dimensions as Probe B. We define these bulky and minute probes for pulsed sampling as Probes C and D, respectively. The 0.1-mm-thick double-pass geometry of both LiTaO3 probes produces an optical sampling time of ~1.4 ps, which is short enough to resolve the fast electrical pulses that are measured throughout the experiment.
The pump side beam excites the photodiode to generate 67-GHz broad-pulsed signals while the other probe side beam serves as an optical sampling beam. By placing the probe with a programmable delay line, the two excited EM and fiber-coupled sampling pulses meet temporally and spatially, and then the EM pulse waveform can be reconstructed through EO sampling.
The measured pulse train over the 100-mm long CPW line is shown in Fig. 5. Both Probes C and D measure pulses at the gap close to the signal line where the signal is strongest in the measurement plane. Each probe gently imprints the gap, maximizing both the signal strength and the invasiveness. Then, Probes C and D were lifted by ~0.09 mm and ~0.04 mm where the peaks were diminished by half, respectively, to investigate position-dependent invasiveness of the two probes. The translation and location of the probes were controlled and monitored with a tool used in sub-millimeter wave on-wafer probing.
Each four pulse train in Fig. 5 consists of five distinct signal sessions. The first session is the normalized incident pulse. The second and third sessions, shown in Fig. 6(b), are the primary and secondary echo pulses reflected by the co-axial connector mismatch and the short termination load, which reflects the majority of incoming signals with the opposite phase. The secondary echo pulse is reflected at the other connector mismatch, resulting in the tertiary echo (or fourth pulse). Finally, the fifth pulse is echo of the fourth pulse with the opposing phase produced by reflection with the short termination load. We did not include the higher- order echoes beyond 2 ns because of their weakness and ambiguity.
We find the fast Fourier transform of the incident and echo pulse train spectral response (Fig. 5) as shown in Fig. 7. The overall spectra are complicated because it is heavily related to the waveform, transition time, relative amplitude, phase, position and number of the pulses, and so on. Because the incident and secondary echo pulses are two dominant pulses with comparable amplitudes and a separation of ~630 ps, we see the apparent spectral fringes with a ~1.6 GHz beating period.
To investigate the invasiveness of EO probes, we must eliminate the effect of mismatched echo pulses because only the pure incident pulses can be considered for the analysis. Simply employing a longer CPW line temporally isolates the incident pulse against the echoes. Thus, we repeated the experiment with an identical CPW line that is twice as long as the original line. As we see in Fig. 8, the entire incident pulse is detected without disturbance. Therefore, the far tail of the incident pulse, where the echoes are found, can simply be padded with zeros for spectral analysis.
The spectra of the incident pulses are transformed as shown in Fig. 9. As expected in the previous simulation and CW experiment, the bulky size of Probe C causes a significantly different spectral response when compared to Probe D. Probe D shows the typical spectral response of a broadband CPW line with an almost identical spectral shape, even at different heights, while Probe C does not. This is possible because Probe D is virtually non-invasive.
The difference of each spectrum indicates the degree of invasiveness because non- invasive probing would not cause position dependence of the waveform. The spectral difference of Probe D at 50% signal attenuation (blue line in Fig. 10) shows a relatively flat 6- dB line up to the 50 GHz band, whereas the position dependent invasiveness occurs after 10 GHz for Probe C (green line in Fig. 10). The deviations of the relative invasiveness of the probes also indicate that Probe C is relatively non-invasive up to 10 GHz (black and red lines Fig. 10).
4. Invasiveness analysis of EO probes: internal vs. external pulsed sampling
To corroborate the virtually non-invasive nature of Probe D, we have modified our EO sampling system from an external scheme to an internal scheme as shown in Fig. 11. The excitation path up to the photodiode is identical, and the signal leaving the photodiode is launched on an 80-mm long CPW line through a 0.25-mm pitch on-wafer probe tip. A 4-inch x-cut LiTaO3 wafer with 0.5 mm thickness is used as the line substrate. The signal line and gap width, shown in the inset of Fig. 11, are 0.05 mm and 0.2 mm, respectively. Such a CPW line on a high-dielectric substrate confines the E-fields at its upper surface. Thus, the interaction path, where the optical and electrical pulses meet, is actually shorter than that of external Probes C and D.
Because the LiTaO3 is utilized as an EO sensor wafer, Probe D has been replaced with a fiber-coupled GRIN lens to focus the probe beam onto the measurement spot. The probe beam travels in the –z-direction, and the ~0.03 mm beam waist is placed at one edge of the CPW line as shown in Fig. 11. The EO-modulated transmissive beam through the wafer under the exposure of travelling EM pulses is demodulated by the polarization optics and read-out instrument. This sensing configuration inherently becomes non-invasive as the substrate itself serves as a probe.
We measured pulses at different locations from the launching probe (L). The first five pulse sets were measured at every 10 mm, and its corresponding spectra are shown in Fig. 12. The on-wafer CPW line is highly dispersive and attenuative as the pulses broaden and their high frequency portions are eroded. The pulse travels with 21.8% of the speed of light, resulting in an effective dielectric constant of the CPW of 21.1.
Finding non-invasive pulse waveforms using internal sampling, we can quantify the invasiveness of the external probes. We used Probe D at L = 20 mm to measure the various height pulses. The maximum value of Probe D occurs when it imprints on the CPW line edge, shown in the inset of Fig. 11. We normalized this value and lifted the probe to reduce the signal to 25% × n (n =1, 2, 3) of its peak value. These four pulses, as well as the internal pulse, are normalized and shown in Fig. 13(a). Two of the normalized internal and external pulses (magenta and blue lines) are almost indistinguishable, which provides good insight into the virtual non-invasiveness of the external probe.
The relative spectra of the four external pulses with respect to that of internal pulse are provided in Fig. 13(b) to quantitatively compare the invasiveness. The external sampling shows fairly low deviation compared to internal sampling up to ~30 GHz. In fact, the primary cause of the deviation seems to be due to the significant signal erosion over 30 GHz rather than invasiveness of the probe. If Probe D had invasiveness, it would have caused a different field perturbation depending on probe height because the capacitive loading effect of the CPW line associated with the probe volume is highly position dependent. However, the four deviation plots in Fig. 13(b) are simply attenuated in log-scale while they maintain the same shape. This means that Probe D would be virtually non-invasive up to 50 GHz or even higher.
We will experimentally justify this assumption with faster photodiodes, associated with CPW lines up to 100 GHz in the near future.
We numerically and experimentally analyzed the invasiveness of electro-optic probes for high-speed microwave sensing/sampling. The quantitative perturbation of continuous and pulsed electric fields due to different probe volumes is also discussed. The minute, optical- fiber-scale probe is the least invasive fiber-coupled probe for microwave diagnosis. The probe shows virtual non-invasiveness up to 50 GHz for the typical electrical transmission line and up to 30 GHz (or arguably 50 GHz) for the on-wafer configuration. The non-invasive feature of the external probe is verified through the internal method, which realizes genuinely non- invasive probing. This invasive analysis of the electro-optic probe can be a good guideline where non-invasive or minimally invasive field characterization is required for accurate and high-frequency applications.
This work was supported by the Korea Research Institute of Standards and Science under the “Development of Technologies for Next-Generation Electromagnetic Wave Measurement Standards” project, grant 13011011.
References and links
1. K. Yang, G. David, S. Robertson, J. F. Whitaker, and L. P. B. Katehi, “Electro-optic mapping of near-field distributions in integrated microwave circuits,” IEEE Trans. Microw. Theory Tech. 46(12), 2338–2343 (1998). [CrossRef]
2. A. Yariv and P. Yeh, Optical waves in crystals (Wiley, 1984) Chap. 8.
4. 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) 11(12), 806–824 (2011). [CrossRef] [PubMed]
5. P. Jarrige, N. Ticaud, S. Kohler, R. P. O’Connor, L. Duvillaret, G. Gaborit, D. A. Cormos, and P. Leveque, “Electrooptic probe adapted for bioelectromagnetic experimental investigations,” IEEE Trans. Instrum. Meas. 61(7), 2051–2058 (2012). [CrossRef]
6. 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(2), 436–442 (2007). [CrossRef]
7. 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(22), 221113 (2009). [CrossRef]
8. H. Jamshidifar, G. Spickermann, H. Schafer, and P. H. Bolivar, “200-GHz bandwidth on wafer characterization of CMOS nonlinear transmission line using electro-optic sampling,” Microw. Opt. Technol. Lett. 54(8), 1858–1862 (2012). [CrossRef]
9. D. J. Lee, J. Y. Kwon, N. W. Kang, J. G. Lee, and J. F. Whitaker, “Vector-stabilized reactive near-field imaging system,” IEEE Trans. Instrum. Meas. 60(7), 2702–2708 (2011). [CrossRef]
10. D. J. Lee, J. Y. Kwon, and J. G. Lee, “Spectro-temporal mismatch analysis of a transmission line based on on-wafer optical sampling,” Prog. Electromagn. Res. Lett. 30, 153–162 (2012). [CrossRef]
11. S. Seitz, M. Bieler, G. Hein, K. Pierz, U. Siegner, F. J. Schmückle, and W. Heinrich, “Characterization of an external electro-optic sampling probe: Influence of probe height on distortion of measured voltage pulses,” J. Appl. Phys. 100(11), 113124 (2006). [CrossRef]
12. H. Fuser, S. Eichstadt, K. Baaske, C. Elster, K. Kuhlmann, R. Judaschke, K. Pierz, and M. Bieler, “Optoelectronic time-domain characterization of a 100 GHz sampling oscilloscope,” Meas. Sci. Technol. 23(2), 025201 (2012). [CrossRef]
13. D. F. Williams, P. D. Hale, T. S. Clement, and J. M. Morgan, “Calibrated 200-GHz waveform measurement,” IEEE Trans. Microw. Theory Tech. 53(4), 1384–1389 (2005). [CrossRef]
14. M. Bieler and H. Fuser, “Realization of an ultra-broadband voltage pulse standard utilizing time-domain optoelectronic techniques,” Proc. SPIE 8624, 862417 (2013). [CrossRef]
15. M. Bieler, K. Pierz, and U. Siegner, “Simultaneous generation and detection of ultrashort voltage pulses in low-temperature grown GaAs with below-bandgap laser pulses,” Appl. Phys. Lett. 94(5), 051108 (2009). [CrossRef]
16. N. I. Dib, M. G. Gupta, G. E. Ponchak, and L. P. B. Katehi, “Characterization of asymmetric coplanar waveguide discontinuities,” IEEE Trans. Microw. Theory Tech. 41(9), 1549–1558 (1993). [CrossRef]