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An optical two-tone (OTT) signal is generated with a wide frequency separation, based on the suppression of ± 1st-order optical sidebands without using optical band-rejection filtering. By combining two orthogonally polarized lightwaves modulated with different modulation indices, each optical sideband constituting the combined lightwave has a different polarization. Some of these optical sidebands can be suppressed using a polarizer. By using a single Mach-Zehnder optical modulator to achieve two optical modulations, an OTT signal with a 60-GHz frequency-separation was successfully generated with 32-dB suppression of undesired ± 1st-order optical sidebands. An rf signal was also obtained from the OTT signal.
© 2015 Optical Society of America
1. Introduction
The use of a pair of coherent monochromatic lightwaves is becoming increasingly popular for distributing radio-frequency (RF) signals over optical single-mode fibers [1,2], and also for generating terahertz waves [3]. This is due to their extremely low attenuation within single-mode optical fibers, compared to millimeter-long waves in the atmosphere. Such a pair of coherent lightwaves is called as an optical two-tone (OTT) signal [4]. By adequately preparing an optical-frequency interval between two carriers, the two constitutive signals of an OTT signal are converted into an RF carrier with a predefined frequency. For this application, a sufficient degree of phase synchronization is required within the OTT signal, so that travelling-wave type external electro-optical (EO) modulator [5] is suitable for generating the OTT signal. Until now, several high-precision optical modulations have been demonstrated, such as single-side-band modulation [6], optical minimum-shift keying [7], high-precision 16-level optical quadrature-amplitude modulation close to the Shannon limit [8, 9], and extremely flat frequency combs [10]. Frequency doubling, in which a spurious residual carrier disappears with an extremely high suppression ratio [11, 12], has already been achieved using EO modulation. By using further frequency upconversion of RF carriers, it is believed that both the energy consumption and complexity of RF electronics can be reduced by decreasing the driving frequency [13].
To generate an OTT signal with a wide frequency separation by EO modulation, higher-order optical sidebands must be extracted. One conventional approach is to eliminate the undesired optical carrier and harmonics with an optical band-rejection filter [13–15], which involves fixing the absolute wavelength of the OTT lightwave. Other approaches, such as degenerate four-wave mixing of two coherent lightwaves in highly nonlinear fiber [16] and semiconductor optical amplifier [17], and utilizing dispersion of an optical fiber [18] also requires the optical filter. Such a constraint on the wavelength can be relaxed by exploiting destructive interference in a Mach-Zehnder optical modulator (MZM). Cascade configurations of single MZMs [17, 19] and nested MZMs [20, 21] have thus been investigated. However, in general, for 2m-order frequency upconversion, m-MZMs must be driven by phase-synchronized RF signals. Although the integration of several MZMs became possible [22–24] thanks to sophisticated techniques, wavelength-independent OTT lightwave generation based on a single MZM would be useful. RF frequency sextupling using one dual-parallel MZM has been already investigated theoretically [25]. In this scheme amplitude of two electric signals driving the dual-parallel MZM should be adjusted to the zero of 1st-order Bessel function, which is not so small. Precise adjustment of these amplitudes is also required to avoid spurious RF signals.
Recently, it has been shown that only ± 2nd-order optical sidebands can be obtained from one MZM nested within an arm of a polarization-maintaining Sagnac interferometer [26, 27]. In this configuration, the polarization of the residual optical carrier is oriented so as to allow suppression by a conventional polarizer, serving in effect as an alternative optical band-rejection filter. By exploiting the polarization as a degree of freedom of the lightwave, quadruple RF signals have been achieved successfully. Here, we demonstrate that a sophisticated configuration can be applied to RF-signal sextupling, utilizing a single MZM in which RF signals are oppositely propagated. By reflecting the RF signal at the RF port, two lightwaves can be modulated simultaneously with different modulation indices in the single MZM, thanks to the exceptional features of a travelling-wave-type single MZM. By superposing the modulated lightwaves with orthogonal polarizations, the polarizations of the undesired ± 1st-order optical sidebands are selectively rotated. Using a polarizer, the ± 3rd-order optical sidebands are selectively extracted to produce a 60-GHz RF signal by converting the lightwave into an RF signal. This scheme does not need large-amplitude RF signals, and uses only one RF signal terminated by one load, so that decrease of electric power consumption would be promised. Effect of RF signal amplitude deviation would be also moderated.
2. Basic principle and its implementation
The basic principle of our proposed method is illustrated in Fig. 1. When a lightwave E0, linearly polarized at an angle α relative to the P polarization, enters a polarizing beam splitter(PBS), it divides into orthogonal components. These can then be used to perform carrier-suppressed optical modulation using two MZMs, as shown in Fig. 1(a). The modulation indices of each lightwave are adjusted so that one has the desired sidebands while the other has only undesired sidebands to be suppressed. It is assumed that the two RF signals are in phase, so that no additional phase shift is acquired during the modulation, depending on the order of the sidebands. Upon recombination of the two lightwaves by a second PBS, the polarizations of the undesired sidebands are rotated while the desired sidebands, originating from the large modulation index, retain its polarization as described in Fig. 1(b). Ideally, the extinction ratio of the MZMs is infinite, so that the electric field Eout of the lightwave upon traversing the second PBS is described as
where the first and second rows represent the P and S polarizations, respectively. Δθ is the induced optical phase of the optical modulation, η (< 1) expresses the ratio between the induced optical phases, Jm(x) are the mth-order Bessel functions of the first kind, f0 is the frequency of the RF signals driving the MZMs, c0 is the speed of light in vacuum and υ0 is the frequency of the carrier lightwave. Optical-path length of P(S)-polarization lightwave between the PBSs are denoted as np(s)lp(s). By projecting the polarization of Eout onto the polarizer axis, the electric field at the polarizer Apol, normalized by E0, is given bywhere ϕ is the angle of the polarizer relative to the P polarization. Equation (2) implies that, by a suitable adjustment of η and ϕ, the first-order sidebands can be made to disappear while other sidebands are partially transmitted through the polarizer, as expected from Fig. 1(b). The condition where the first-order sidebands disappear entirely can be expressed aswhen nplp equals to nsls. The suffix ±1 denotes the values of ϕ and α that satisfy Eq. (3). It should be noted that the polarization of the ± 1st-order sidebands are oriented at an angle of π/2–ϕ±1 relative to the P polarization. The normalized amplitudes of the nth-order components Apol(n) (n = 3, 5, 7, …) are given byFor n = 3, the second term in the brackets in the numerator of Eq. (4) is less than 0.05, so that the S-polarized lightwave is almost entirely composed of first-order sidebands when η < 0.23 (−13 dB in power). Figure 2 shows the polarization orientation and the intensity of the undesired first-order sideband relative to those of the third-order sideband Apol(n = 3), derived analytically assuming α = π/4. The horizontal and vertical axes express η2 (in units of dB) and Δθ, respectively.To calculate the intensity ratio, the suppression ratio of the undesired first-order sidebands was assumed to be 35 dB, a typical value in commercially available polarizers. As the induced optical phase increases, the polarization is rotated much more so that the undesired sidebands also decrease. It also becomes apparent that, with decreasing intensity ratio of undesired sidebands, minimum of Δθ is increased and η corresponding to the Δθ decreases (i.e. increase in RF attenuation). The configuration shown in Fig. 1(a) involves two MZMs, which are nested in arms of the interferometer composed of two PBSs. However stabilization of this setup would be so complicated. We therefore adopted an alternative configuration, shown in Fig. 3, which is based on a sophisticated combination of a single MZM and the polarization-maintaining (PM) Sagnac interferometer. The polarization-rotating element inserted here is coupled with the MZM [26]. In this configuration each polarization is oppositely propagated on the same ONE mode of the Sagnac interferometer so that optical-path lengths of them, nplp and nsls, are also the same [27], while two polarization modes are supported in the Sagnac interferometer. PM fiber connecting the interferometer and the polarizer is not so long, so that its retardation is sufficiently small. Since it can be compensated using conventional waveplates before polarization projection, nplp and nsls in Eqs. (1) and (2) can be neglected when these eqs. are applied to the configuration shown in Fig. 3(a). We used a travelling-wave-type single MZM, equipped with RF ports at both edges of its travelling-wave electrodes. The RF signal introduced at one RF port is reflected at the other port of the same electrode when it is opened. To modulate the lightwave using the travelling-wave MZM, the lightwave should propagate in the same direction as the RF signal applied to the electrode, in order to satisfy the velocity-matching condition [5]: i.e. when two lightwaves enter an MZM in opposite directions, where the RF port(s) of this single MZM for the external load is connected with opened attenuators, two sinusoidal optical modulations areproduced with different modulation depths. The power ratio between these two opposing lightwaves is adjusted by the polarization of the lightwave entering the PBS.
Fig. 1 (a) OTT signal generation. The solid and dashed arrows denote P- and S-polarized lightwaves, respectively. PBS1, PBS2: polarizing beam splitters; IM1, IM2: optical-intensity modulators; M1, M2: mirrors. (b) Optical spectrum of the output light wave. Because of the different modulation indices of the sidebands at each polarization, low-order sidebands in the gray region are tilted, as shown by solid arrows. Thick dotted lines indicate the carrier of the incident lightwave.
Fig. 2 Intensity of the first–order optical sidebands (thin solid lines) and their polarization tilt in degrees (colored). Both are shown in relation to those of the third–order sidebands. The vertical axis gives the induced optical phase Δθ due to the strong RF signal applied to one of the MZMs. The horizontal axis is η2 in units of dB, the power ratio of the RF signals applied to each MZM. A diamond indicates the conditions where optical spectra shown in Fig. 4 were acquired.
Fig. 3 (a) Setup utilizing a MZM with ports for external RF termination, equivalent to that shown in Fig. 1(a). OC: optical circulator; 1-3: port of optical circulator; PBS: polarizing-beam splitter; In1, In2: RF input ports; Out1, Out2: RF ports for external termination; PRE: polarization-rotation elements; POL: polarizer. Double lines and single lines indicate optical paths and RF lines, respectively. (b) Configuration for RF signals driving the MZM. P1, P2, P3: ports of the RF circulator; HC: 3-dB RF hybrid coupler; E1, E2: modulation electrodes; G1, G2: ground electrodes; C1, C2: DC blocks; PS1, PS2: RF phase shifters; Att1, Att2: RF power attenuators; T1, T2: RF terminators. Thick lines and thin lines indicate RF signal lines and ground, respectively.
3. Experiment
The MZM used in this study was integrated on Z-cut lithium niobate and comprises two traveling-wave electrodes on each of its arms. The optical extinction ratio, insertion loss, and (being a phase modulator) half-wave voltage for each arm were evaluated as 38.5 dB, 5.7 dB and 2.4V, respectively. The evaluated optical return losses were less than 47 dB, thereby preventing the appearance of undesired residual carriers in the setup. Because the phases of RF signals applied to the same electrode on the MZM should be in phase, we adjusted the phase of the RF signal propagating from the one electrode to the another (using PS2 in Fig. 3(b)). In the two-electrode optical-intensity modulator, two modulation indices are also achieved in the single MZM by connecting the two electrodes, via RF attenuators and an RF phase shifter together with capacitors as shown in Fig. 3(b), instead of opening their RF ports as described above. To drive the MZM, an RF signal generated by a 10-GHz RF signal source was amplified using an RF -clock amplifier (Ciao Wireless, CA910-4042). After passing through an RF circulator, the RF signal was attenuated to produce the desired modulation indices. The attenuated RF signal was introduced into a 3-dB hybrid RF coupler (Krytar, model 1830), one output of which was fed into an RF phase shifter to generate a pair of out-of-phase RF signals. Using this pair of RF signals, a precise optical-intensity modulation was achieved. Bias tees were inserted in front of the MZM RF ports to adjust its optical-path length difference.
An incident linearly polarized lightwave with an output power of 6.3 dBm was generated using an external-cavity diode laser (Agilent, 81689A). After adjusting its polarization angle, the lightwave entered port 1 of an optical circulator (Haphit; insertion loss < 1.0 dB; isolation between each port > 45 dB), while the output from port 2 was introduced into a PBS (OZ optics; polarization extinction ratio > 24 dB; insertion loss < 1.0 dB). The polarization-rotation element shown in Fig. 3 was realized using the configuration where the propagation modes of the polarization-maintaining optical fiber coupled with each port of the PBS were orthogonalized. After passing through a quarter-wavelength plate (Optoquest, PCC-5Q) and a polarizer (Optoquest, PCC15-P, extinction ratio > 35dB), the lightwave was amplified (Optohub, OA-1305-A; saturation output 18 dBm; small-signal gain 28 dB) and divided usinga 3-dB optical coupler. One of the coupler outputs was connected to an optical spectrum analyzer (Ando, AQ6317) and the other to an RF harmonic mixer (HP, 11970U) connected with an RF spectrum analyzer (HP, 8563E), via a photodiode (PD) with a 3-dB bandwidth of 70 GHz (Finisar, XPDV3120R).
Figure 4 shows optical spectra obtained from experimental setup. Some parameters in the setup were adjusted to the condition shown by a diamond in Fig. 2. The horizontal axis in Fig. 4 is normalized by the frequency of the RF signal driving the MZM, and its zero corresponds to the optical frequency of the incident carrier. Note that it corresponds to harmonics order of the signal when value of the horizontal axis is in integer. The vertical axis gives the lightwave power, normalized by that of the third-order optical sideband. The powers of the ± 1st-order optical sidebands are clearly suppressed by more than 32dB. The suppression ratio is comparable to that achieved using destructive interference in a conventional MZM. It should be noted that power loss of the ± 3rd -order sidebands implicitly occurs due to the passage through the polarizer in the above setup. However, the insertion loss was moderated using an erbium-doped fiber amplifier, so that the absolute optical power in the ± 3rd-order optical sidebands was increased from −17.2 dBm to −7.8 dBm. The insertion loss is sufficiently low to generate a sextupling RF signal.
Fig. 4 Optical spectra measured at the optical output of the setup shown in Fig. 3 (solid line) and at the position of the PRE in order to evaluate the lightwave propagating from the MZM to the PRE (dashed line). The zero of horizontal axis corresponds to the carrier frequency. The horizontal and vertical axes are normalized by the modulation frequency and the power of third-order optical sidebands, respectively. The driving conditions of the MZM are indicated by the white diamond in Fig. 2.
Although some residual optical sidebands (such as the fifth-order optical sidebands) are still apparent in Fig. 4, the main contribution of the sidebands is at 20 GHz in the optical/electrical (O/E)-converted RF signal. To evaluate the effect of such undesired optical sidebands and carriers on spurious RF signals converted from the OTT signal, we evaluated the RF power from the photodiode. Figure 5 shows the RF signal power at 60 GHz plotted versus induced optical phase Δθ. A 60-GHz RF signal was successfully generated using the PD. The RF power obtained from the PD reached −43 dBm when Δθ was adjusted to 2.68. Signal-noise ratio of the 60-GHz RF signal reaches into 33 dB against background noise. With decreasing Δθ, the RF signal power decreased gradually. Since these RF powers per power of the optical two-tone signal were the same, this effect is a consequence of the characteristics of the ± 3rd-order Bessel functions of the first kind. Figure 5 also compares the RF power at other, undesired frequencies against the desired 60-GHz RF power. The odd-order RF harmonics are expected to be weak, due to the fact that these originate from beating between the odd-order and even-order optical sidebands, and the even-order optical sidebands are suppressed at the Y junction of the MZM. The RF power was evaluated at driving frequencies 10GHz, 20 GHz and 40 GHz. The power ratio for the spurious 20-GHz RF signal was approximately −10 dB for Δθ in the range 2.3-2.6. This is mainly due to beating between the ± 5th- and ± 3rd-order optical sidebands. This result is also confirmed from the above model assuming that η = 0.1995 (14dB attenuation), which is drown using red solid line in Fig. 5. For comparison, 20-GHz RF power are also calculated when η is 0.316 (10 dB attenuation) and 0.501 (6 dB attenuation). Degree of η less affects power of the 2nd-order spurious power: 8-dB difference of η would bring 1.6-dB increase of the power. The 1st-order spurious signal power is also evaluated to be around −21 dB from the calculation, and also shows few dependence on η. Both the spurious 20-GHz and 10-GHz RF signals would be easily suppressed using a conventional RF filter because their frequency is sufficiently lower than the desired RF frequency, 60 GHz. The power of the 40-GHz RF signal shows almost the same strength as that at 10 GHz. From the model analysis, the 40-GHz spurious signal power gradually decreases with increase of Δθ. And it is also confirmed that extinction ratio of the polarizer directly affects the 4-th order spurious RF signal level. This fact implies that the spurious RF signal is mainly originates from beating between ± 3rd- and ± 1st-order optical sidebands. The 40-GHz RF signal would be suppressed further by decreasing the optical power of ± 1st-order optical sidebands due to Δθ.
Fig. 5 Sextupling RF -signal power (filled circles) and power ratio of spurious RF signals plotted versus the induced optical phase Δθ. Origin of the right vertical axis corresponds to 60-GHz RF power. Triangles, squares, and open circles denote the 10-GHz (1st-order), 20-GHz (2nd-order) and 40-GHz (4th-order) RF signal powers, respectively. Thin lines, red lines and thick lines are obtained from the model analysis, each of which indicates 10-GHz, 20-GHz and 40-GHz RF signal powers, respectively. Solid lines, dashed lines and dotted lines are the cases when η is set at 0.1995 (14 dB), 0.316 (10dB) and 0.501 (6dB), respectively. For the analysis, extinction ratios of both the intensity modulator and the polarizer are assumed to be 32 dB.
4. Conclusion
In conclusion, we demonstrated RF-frequency sextupling via an OTT signal with a wide frequency separation, generated by an experimental setup that does not employ an optical band-rejection filter. By rotating the polarization of the ± 1st-order optical sidebands, the optical sidebands can be suppressed by 32 dB using a conventional polarizer to obtain the ± 3rd-order optical sidebands selectively. This result can be achieved using our sophisticated setup, composed of a polarization-maintaining Sagnac interferometer coupled to a single MZM with RF ports for external loads. Using the OTT signal thus generated, we successfully achieved RF-frequency upconversion from 10 GHz to 60 GHz with sufficiently-low spurious RF signals. By avoiding the use of an optical band-rejection filter in the proposed setup, frequency upconversion would be made possible via an OTT signal of arbitrary wavelength. This would be useful for increasing the rate of data transfer via a “radio-over-fiber” signal and clock synchronization.
Acknowledgment
The authors are grateful to Mr. K. Higuma of Sumitomo Osaka Cement Co., Ltd., for supplying a high-quality MZM, and to Prof. K. Motojima and Prof. N. Haga for supporting the S-parameter evaluation of the MZM. This work was supported in part by the Ministry of Internal Affairs and Communications, Japan (SCOPE, 142103013) and JSPS (15K06050).
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