1. Introduction

Photonic down-mixing of signals in the microwave and millimeter-wave regimes to the ultrasonic range of the radio-frequency (RF) spectrum has emerged as an important process in electro-optic (EO) nondestructive probing of, for example, phased-array radar panels and RF communication circuits [1–6]. This extraction of amplitude and phase information from radiated and fringing microwave fields begins with the generation of local-oscillator (LO) sidebands on an optical-carrier, either inherently through the evenly spaced harmonics of the repetition frequency of a short-duration-pulse laser [1–3], or with a continuous-wave (cw) laser diode and an external device such as a commercial electro-optic modulator (EOM) [4–6]. The RF electric field at the signal frequency (f_RF), which modifies the polarization of the optical beam via the Pockels effect in the EO-probe medium, also mixes with the optical carrier and its LO sidebands within the nonlinear-response crystal to yield additional sidebands. Upon photodetection of the optical beam with a low-bandwidth photodiode, the down-converted intermediate frequency (f_IF), stripped of the optical carrier so that f_IF=|f_RF - f_LO|, is isolated via filtering, and its amplitude and phase displayed. These amplitude and phase values of the demodulated IF are proportional to those of the RF signal, and when a scanning, fiber-coupled EO probe is used, they can be employed to reconstruct an RF spatial field distribution.

With the use of high-order harmonics of the repetition rate of an ultrafast-pulsed laser for creating an LO signal, it is found that the measurement bandwidth of EO probing can in principal be extended to the terahertz range, although literally a price is paid for this capability through the greater expense of the laser source compared to a cw laser diode. In previous work using the pulsed-laser-harmonic LO generation, the 1,250^th harmonic of an 80-MHz-repetition-rate pulsed laser was mixed with the 100.003-GHz output of a millimeter-wave frequency multiplier [7], yielding an IF signal with f_IF = 3 MHz at the output of the probe-beam photodetector. The resulting electrical amplitude and phase of the IF were measured using the narrow-band input of a lock-in amplifier.

While having a large number of uniform spectral harmonics from the ultrafast laser allows access to LO-sideband frequencies with millimeter-wave separation from the carrier wavelength, when employing a cw laser diode it is more difficult to achieve a reasonably high-power LO-sideband at such high frequencies. This is due to the limitations and costs of millimeter-wave, commercial-grade EOMs and the high-frequency signal sources necessary to drive them. In this paper, we present an alternative to the creation of optical sidebands at the fundamental driving frequency of an EOM for use as the local oscillator in EO photonic-down-mixing test-and-measurement applications. Either by driving an EOM at a frequency of f_LO/2 and operating the device at a DC-bias point where it efficiently produces a second-order harmonic intensity modulation, or by utilizing an input signal of frequency f_LO/3 and overdriving the EOM to produce a third-order harmonic intensity modulation, LO signals can be generated at up to three times the rated fundamental frequency of the EOM. The effectiveness of utilizing these harmonic sidebands as LO frequencies to photonically down-mix microwave signals is evaluated through comparisons of EO experimental measurements on X and K-band patch antennas.

2. Bandwidth of modulator sideband generation with fundamental-drive frequency

The double sidebands (DSB) imparted onto the output of a cw, telecommunications-qualified, distributed-feedback laser using a conventional Mach-Zehnder type EOM can be used as the LO for mixing down, within an EO probe, a signal at f_RF to one at f_IF [4–6]. The frequency components generated by the ac driving signal and the DC bias point on the modulator transmission function determine the bandwidth. That is, the modulated light output is predominantly determined by the frequency and amplitude of the ac-driver swings along the modulation function around a given DC bias point. Typically, to avoid the creation of RF-harmonic information on a cw optical beam, the DC bias is set at the symmetric point a on the sine-squared intensity-modulation function shown in Fig. 1(a).

To enhance the EO sensing component, which is the signal at f_IF, for a given RF condition, it is important to maximize the LO sideband component per unit light power. For an intensity modulator driven about point a with +14 dBm of RF power, the amplitude-modulated light has DSB around the carrier (Fig. 1(b)), and the modulation depth can be specified by the ratio of the carrier and sideband. The average power of the modulated beam at the EOM output, which is dominated by the carrier component, is ~10 mW for all the driving frequencies. Measured with 0.01-nm resolution on an optical spectrum analyzer at the output of a 1% tap from the EOM, the carrier power level is maintained, while the low-level sideband power decreases rapidly for higher frequencies: from 25% to 18.6%, 13.1%, and 7.6% for modulation frequencies of 5.241, 10.482, 15, and 25 GHz, respectively. Overall, the sideband degradation follows a slope of -0.41 dB/GHz over the C to K-band microwave regions. Thus, when an optical sideband is conventionally generated using a fundamental-driving frequency harmonic in an EOM, a relatively large amount of the carrier wavelength remains in the beam, the modulation depth is relatively small, and the intensity of the sidebands decreases rapidly with increasing frequency.

 

Fig. 1. (a) Amplitude modulations at three symmetric DC-bias points of a sine-squared modulation function. The input sinusoids are drawn with vertical time axes and the modulation outputs with horizontal time axes. (b) Modulated spectra and evolution of modulation depth at operating point a for several fundamental driving frequencies (Black, red, green and blue: f_LO = 5.241, 10.482, 15, 25 GHz, respectively; input LO-drive power is +14 dBm).

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3. Second-order-harmonic intensity modulation for local-oscillator bandwidth enhancement

The useful bandwidth of the optical LO sidebands generated by the EOM can be increased significantly by modifying the DC bias and operating point of the device. Specifically, instead of biasing the EOM for 50% intensity transmission at point a (Fig. 1(a)), operating the device at its minimum transmission-intensity point at b also balances the LO output intensity oscillations induced by the driving signal. However, as the input oscillates to its maximum and minimum values, the output is rectified compared to operation at point a. That is, the periodic output cycles are still balanced and identical, but the original LO driving period gets ‘folded in half,’ resulting in efficient generation of sidebands at the second-order harmonic of the EOM driving frequency. Although both bias points b and b′ in Fig. 1(a) are seen to fold the original LO period in half, operation at point b minimizes the carrier intensity, while operating at point b′ maximizes the carrier intensity and minimizes the modulation efficiency (or sideband-to-carrier ratio). Illustrating the suppression of the optical carrier intensity when biasing the EOM at point b, the black curve in Fig. 2(a) shows the LO sidebands achieved when the driving frequency is at f_LO/₂. The suppressed carrier in the second-order harmonic case transforms the DSB modulation (black plot in Fig. 1(b)) to single-sideband (SSB) modulation with equal sideband amplitudes. This indicates that a nearly full modulation depth is achieved at 2fLO/2, or twice the driving frequency. As the carrier is suppressed enough to be essentially negligible, each sideband becomes effectively an adjacent band to the other, yielding a second-order harmonic with greatly improved modulation depth.

 

Fig. 2. (a) Modulated spectra and evolution of modulation depth for several driving frequencies (Black, red, green and blue: f_LO/₂ = 5.241, 10.482, 15, and 25 GHz, respectively; +14 dBm LO drive power) at the second-order harmonic operating points (bias b in Fig. 1(a)). (b) Modulated spectra and change in modulation depth for various driving power levels (Red, black and green: +11, +14, and +17 dBm, respectively, at 25 GHz. Blue: optically amplified black spectrum).

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As the sidebands decrease in intensity in Fig. 1(b), the modulation efficiency, already poor due to the strong carrier intensity, decreases further, and the sidebands cannot function as the LO past about 15 GHz for our Ku-band EOM. However, in the SSB case, the carrier is suppressed, and the matched sets of sidebands, now essentially without a carrier, have equal intensity. Consequently, even though the modulation slope still degrades by -0.41 dB/GHz (Fig. 2(a)), the intensities of the optical sidebands at the second-order harmonic are sufficient to serve as the LO out to much greater frequencies than the 15 GHz of the DSB case, operating at point b. The light intensity due to the carrier does not noticeably change for higher driving frequencies (Fig. 2(a)) or larger drive-signal amplitudes (Fig. 2(b)). In the latter, the RF drive power has been increased in 3 dB increments from +11 to +17 dBm, to the maximum available power at 25 GHz available in our facility. While the sideband intensity increases much more than that of the carrier with increasing RF-driving power, it was necessary to utilize optical amplification of the EOM output with an Er-doped fiber amplifier to create an SSB sideband strong enough to use as an LO signal. The second-order-harmonic LO intensity was thus boosted by 15.5 dB, effectively extending the photonic heterodyne capability of the system completely through the microwave Q-band.

Although an increasingly large EOM-drive input power would result in diminishing benefits for operation at point a, overdriving is actually beneficial in the second-order-harmonic generation case, with higher input-oscillation amplitudes nonlinearly increasing the output-modulation amplitude and yielding the higher optical-sideband intensity. The relative optical-sideband intensity ratios for operation at b compared to conventional operation at a (input signal at 5.241 GHz), with EOM-drive power as a variable for the former and +14 dBm for the latter, are shown in Fig. 3(a). The second-order-harmonic optical-sideband power when using the maximum safe EOM-drive input of +26-dBm becomes comparable to the optical power level in the conventional EOM operation at point b. The corresponding spectra of the fundamental- and second-order-harmonic modulations with comparable modulated output power are presented in Fig. 3(b). The red and black plots both yield a 10.482-GHz LO for optical down-mixing, the former via DSB operation at point a and the latter via SSB operation at point b.

 

Fig. 3. (a) Ratio of second-order-harmonic optical-sideband power (driven at 5.241 GHz, operating point b) to fundamental optical-sideband power (driven at 10.482 GHz and +14 dBm, operating point a) vs. EOM-drive power for the former. (b) Comparison of DSB (red: driven by +14 dBm at 10.482 GHz; green: drive power off) and SSB (Black: driven by +26 dBm at 5.241 GHz; blue: drive power off) modulated spectra for comparable optical power.

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4. Third-order-harmonic intensity modulation for local-oscillator bandwidth enhancement

Without switching to an EOM of higher bandwidth or increasing the EOM drive frequency, the bandwidth of the optical LO sidebands can also be increased even further through the nonlinear dynamic behavior of the EOM. Specifically, overdriving the EOM while it is biased at the 50% transmission position a of Fig. 1(a) produces the next higher odd-order harmonic [8]. This can be interpreted as nonlinear generation in a perfect centro-symmetric optical media (i.e., χ ⁽²⁾ = 0 as in optical fibers), so that the next nonlinearity is given by the third-order harmonic. Figure 4(a) illustrates this harmonic generation for large-amplitude, EOM-input signals. Biasing at the exactly symmetric point a, the two second-order harmonics at operating points b and b′ cancel each other out, as they are out of phase with equal amplitude. While this is true in a precisely symmetric condition, for high frequency bands it is not technically trivial to fully suppress the second-order-harmonic sideband generation.

Figure 4(b) shows the combinations of the fundamental, second- and third-order-harmonic spectra when the EOM is driven by a signal at f_LO/₃. Each of the spectra has essentially the same average output power, while the carrier depletes rapidly for higher EOM-drive power to yield a larger nonlinearity and sideband for the same output power. The black plot (driven with +26 dBm at f_LO/₃) contains multiple major third-order harmonic components as indicated by the vertical dashed lines in Fig. 4(b). The energy at this frequency can then be used to extend the bandwidth of an EOM to three times its rated maximum frequency for generating LO sidebands.

 

Fig. 4. a) Overdriven amplitude modulations using the symmetric bias point, a. (b) Modulated spectra and evolution of modulation depth for several EOM-input-drive power levels (Green, red and black: +18, +22 and +26 dBm, respectively, at f_LO/₃. Blue: +14 dBm at f_LO for comparison).

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5. Photonic down-conversion EO sensing with higher-order harmonics

Compared with using an ultrafast pulsed laser, an EOM has a limited modulation bandwidth, and its use becomes the greatest factor increasing the cost for high frequency measurement applications extending up into the millimeter-wave regime. Conventionally, in EOM applications such as Radio over Fiber (ROF) systems, a high degree of system linearity is preferred to reduce the impact of nonlinear distortion (i.e., harmonic or intermodulation distortion) and to deliver modulated RF information via an optical carrier using fiber. Thus, mitigating signal distortion induced by the nonlinear response of the EOM is one of the main concerns in ROF systems [9]. However, for EO probing, the RF signal is the radiation field from the DUT. Because the LO is used only as a beating source for the IF-down-mixing, where the IF contains the signal information, a strong and precise LO component is more important than its harmonic-order origin. Thus, the nonlinearity in the EOM operation is not detrimental, but beneficial for enhancing the bandwidth of the EO measurement without RF-signal distortion.

To demonstrate the utilization of second- and third-order-harmonics of the EOM-drive frequency in EO sensing, we adopted a photonic-down-mixing platform used previously for vector-RF-electric-field sensing with a fiber-mounted, microcavity-EO sensor [6,10–12]. The experiment was arranged so that the entire laser-beam path was enclosed within optical fiber, and the probe light beam with the LO modulation was passed down the fiber to a LiTaO₃ EO probe tip. The probe was raster-scanned over an X-band-patch-antenna device-under-test (DUT) (resonance frequency of 10.485 GHz) using a computer-controlled translation stage, and the probe light, now with the optically-mixed sidebands, was reflected back up the fiber and directed by an optical circulator to a photodetector for demodulation.

The evolution of the peak EO signal levels for three cases – mixed down using each of the first three harmonics of the EOM-drive signal – versus LO drive power are presented in Fig. 5(a). The signal builds up at 0.96 dB per 1 dB at the fundamental LO drive frequency, and this slope becomes steeper for the two higher-order harmonics, 1.76 dB per 1 dB and 2.60 dB per 1 dB of EOM-drive power for the second- and third-order harmonics of LO/2 and LO/3, respectively. The higher-order harmonics have the higher thresholds to emerge, but they then grow faster according to these slopes. Although the intercept points for the second- and third-order are expected to be +31.7 dBm and +29.06 dBm of the respective LO power, both cases pass their 1-dB suppression points before they reach the EOM maximum safe input power.

 

Fig. 5. (a) Down-mixed EO-signal strengths using the first three modulation harmonics as the LO, versus modulator driving power (Black, red and blue: fundamental-, second- and third-order, respectively). (b) EO field maps of the transverse near-field distribution (horizontal polarization) from an X-band patch antenna for different modulator-drive powers, (as indicated, +18 to +26 dBm). The top (bottom) scans use the second (third)-order harmonic LO sideband to mix down the signal frequency to f_IF. As amplitude and phase are measured simultaneously in this EO measurement technique, the two terms may be combined together to illustrate the temporal nature of the sinusoidal microwave electric field around the patch antenna (Media 1) for the 26-dBm case with the second-order harmonic LO sideband).

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The horizontal transverse electric-field distributions 200 µm above the DUT antenna are shown in Fig. 5(b) versus EOM-drive power for both the second- and third-order harmonic LO cases. The field distributions are virtually the same as those found using the fundamental LO previously [6]. Furthermore, the field distribution for the entire driving power range – even beyond the 1 dB suppression power level – is uniform when mixing with either of the higher-order-harmonic LO frequencies, demonstrating that noninvasive near-field EO measurements can be extended to frequencies up to two and three times that of the EOM-drive frequency without loss of fidelity.

In Fig. 5(b), the utility of the field-mapping technique becomes apparent, as one is able to isolate highly detailed field information on the microwave DUT. In this case, since the length of the antenna is designed to be a half-wavelength at the resonance frequency, the potential reaches its maximum value at the edges of the patch, close to the recessed feed line and at the farthest extent from the feed. The transverse field of Fig. 5(b), in a pattern expected from the potential distribution, has its peak amplitude outside the antenna conductor near the corners of the patch and within the gaps between the patch and the feed line. Here the probe captures the electric field component that is parallel to the plane of the patch.

6. Harmonic-photonic heterodyne EO probing applied to a K-band antenna array

As the response of the EOM is consistently rolling off as the driving frequency increases past the X-band maximum at 12.5 GHz, use of a fundamental LO sideband at driving frequencies up into the K-band (18–26.5 GHz) limits the sensitivity of the EO measurements. Thus, the second-order harmonic LO sideband has been utilized in the characterization of two orthogonal transverse electric fields of a 2 × 2 array of patch antennas having a resonant frequency of 18.535 GHz. As with the horizontal field component in the single, X-band patch antenna, each of the array patches (positioned in the four corners of the viewing window) has fields at their corners that are out of phase with their neighboring fields (Fig. 6(b) (Media 2) However, each of the patches cycles through its field maxima in phase with the other three, indicating that the interconnects and reactive parasitic circuit effects were chosen so as to maintain a constant phase between each radiating element. One can also notice the feed microstrip, entering the window from the left-center and supporting the field of the incident signal, as well as the nodes in the center of the window where the input is divided into individual incident signals for the four antennas.

 

Fig. 6. (a) 2 × 2 array of K-band patch antennas. (b) Horizontal (x-component) EO field amplitude maps of (a) using 2^nd harmonic LO (Media 2) for amplitude-phase animation. (c) Vertical (y-component) EO field amplitude maps of (a) using 2^nd harmonic LO (Media 3) for amplitude-phase animation). (EOM-LO: +26 dBm at 9.266 GHz, DUT-RF: +10 dBm at 18.535 GHz). (Fig.6 (a) is one half of a 4 × 2 array of the patch antennas. (Media 4), and (Media 5), are expanded versions of Media 2 and 3, respectively, for the entire symmetric 4 × 2 array, including the feed line).

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The phase effects for the entire array are seen even more easily in field animations for the vertical transverse component (Fig. 6(c) (Media 3)) Now, the field is strongest at the top and bottom edges of each patch, and while all of the four patches are still in phase with each other, the strong fields within each individual patch are also in phase. This confirms that the vertical direction will correspond to the polarization of the antenna in the far field, as these field components will add together coherently as they propagate.

7. Conclusions

Utilizing higher-order harmonics during the operation of an EOM to generate a photonic LO, we have demonstrated that the finite bandwidth of a typical low-cost amplitude modulator can be expanded by two to three times, into the millimeter-wave regime. Both second- and third-order-harmonic regimes of the modulator can be used to extend operating bandwidths to millimeter-wave bands. The application to the near-field analysis of microwave patch antennas and arrays was demonstrated.