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We demonstrate the generation of microwave and millimeter-wave frequencies from 26 to 100 GHz by heterodyning the output modes of a dual-wavelength fiber laser based on stimulated Brillouin scattering. The output frequency is tunable in steps of 10.3 MHz, equal to the free spectral range of the resonator. The noise properties of the beat frequency indicate a microwave linewidth of < 2 Hz. We discuss potential for operation into the terahertz regime.
©2010 Optical Society of America
1. Introduction
Fiber-coupled sources of microwave frequency signals are valuable in many applications, such as fiber remoting of antennas for fiber radio [1,2], phased-array radars [3], and long-baseline radio astronomy [4]. For many applications, it is desirable that the RF signal be tunable, potentially over a broad frequency range, that it have low phase noise, or be capable of extending into the millimeter-wave regime. A number of tunable, high-frequency sources have been demonstrated based on the heterodyning of two laser frequencies, either between independent lasers [5–7] or between two laser modes sharing a common cavity and common gain [8–13]. However, in the first approach, all phase noise and drift from each laser is directly transferred onto the RF signal, so that exceptionally stable lasers are required to obtain a narrow linewidth and low phase noise in the RF domain. The second approach eliminates this problem in that the dominant laser noise processes originate with the laser cavity, and so affect each mode equally: the noise is cancelled out when the two frequencies are differenced. However, most laser gain media are homogeneously broadened. For dual-wavelength operation, this can cause strong competition between the two operating wavelengths, which can severely degrade the phase noise of the RF beat frequency.
The dual-wavelength operation of a fiber laser based on stimulated Brillouin scattering (SBS) gain [14] avoids gain competition between wavelengths and has been employed to generate discretely tunable beat frequencies [15–17]. We have previously reported beat frequencies up to 40 GHz [18] and linewidths < 1 Hz [19]. We have used this source for wireless data transmission at rates > 1 Gb/s [19]. In this article, we demonstrate operation of the SBS fiber laser at frequencies up to 100 GHz, and discuss what factors limit operation at even higher frequencies (principally the photodetector and components downstream thereof) and how this technique could be extended into the terahertz regime. Additionally, we characterize the linewidth of the RF output at millimeter-wave frequencies and describe the operation of the source in detail.
2. Setup and operation
2.1 Experimental setup
Figure 1 illustrates the system setup. The CW laser produces a single line with wavelength λ = 1550.1 nm (optical frequency ν = 193.4 THz) and linewidth of < 10 kHz. The amplitude modulator (EOSPACE AZ-series, 3-dB bandwidth of 25 GHz) is biased at a null using a commercial bias controller (YY Labs Mini MBC1). The modulator is driven by the RF oscillator (Agilent E8752D) at frequency f0 (equal to half of the desired output frequency), generating sidebands at ν ± f0, which dominate over the original optical carrier tone, as illustrated in the left half of Fig. 2 . The phase modulator (EOSPACE PM-series) provides a small dither signal at ~100 kHz to key the inner servo loop. The erbium-doped fiber amplifier (EDFA) compensates for losses in the modulators.
Fig. 1 Experimental setup. CW: continuous-wave. Amp mod: amplitude modulator. EDFA: erbium-doped fiber amplifier. φ-mod: phase modulator. SBS: stimulated Brillouin scattering. OSA: optical spectrum analyzer. HV: high-voltage amplifier. PID: proportional-integral-differential amplifier. (Not all parameters are used.) RFSA: radio-frequency spectrum analyzer.
Fig. 2 Diagram of cavity resonances, pump lines, gain bands, lasing lines, and beatnote. ΔνFSR: free spectral range. ΔνFSR: cavity-resonance full width at half maximum. ν1-pump and ν2-pump: lower and higher pump frequencies. f 0: drive frequency. V bias: bias voltage. N: an integer. νpump: center pump frequency. νB: Brillouin shift. Δνgain: gain-band full width at half maximum. ν1-out and ν2-out: lower and higher lasing frequencies. f out: beatnote frequency.
The SBS cavity consists of an 80/20 coupler, a piezoelectric fiber stretcher (General Photonics FPS-series, maximum recommended frequency of 20 kHz), and a coil of fiber; all intracavity components are polarization-maintaining, as are all components in the pump path. The total length of the cavity is ~20 m, yielding a free spectral range (FSR) of ~10 MHz and a resonance width of 527 kHz, as shown in Fig. 3 . The two pump lines are introduced into the cavity via a circulator and the coupler, and they propagate clockwise around the cavity. By aligning the frequencies of the two pump tones with the resonances of the cavity, as illustrated in Fig. 2, pump power builds up in the cavity. Each line produces an SBS gain band downshifted in frequency by the Brillouin shift, which corresponds to the energy of an acoustic phonon in the fiber [20]. For the fiber used in these experiments (Fujikura PANDA 1550 SM.15-P-8/125-UV-UV-400), we measured [21] the peak shift and FWHM to be 10.868 GHz and 14.6 MHz, as shown in Fig. 3. Note that the SBS is a back-scattering phenomenon: The gain is unidirectional and counterpropagating with respect to the pump [22], or counterclockwise in Fig. 1.
Fig. 3 The Brillouin gain spectrum, measured at ~20 °C for the Fujikura PANDA used in the system of Fig. 1 (light red crosses), a Lorentzian fit of the gain (dark red curve), and the transmission spectrum of the resonator (green curve). The fit is centered at 10.868 GHz and has full width at half maximum (FWHM) of 14.6 MHz. The cavity resonances were also fit, on average, to a Lorentzian with a FWHM of 527 kHz.
As shown schematically in Fig. 2, when the cavity FSR is arranged to be on the order of or less than the Brillouin gain bandwidth, at least one cavity resonance will overlap the SBS gain band. Figure 3 illustrates an exemplary case of the relative position of the measured cavity resonance profile with respect to the SBS gain spectrum measured at room temperature (~20 °C). In operation, the cavity is maintained at an elevated temperature (36 °C) so that the intracavity SBS gain spectrum is expected to be shifted to higher frequency by approximately 20 MHz [23]; nonetheless, it is clear from Fig. 3 that at least one resonance would see appreciable gain for each pump wavelength. If sufficient pump power is provided, lasing obtains within each SBS gain band on the resonance of highest net gain, with the exact lasing frequency determined by the cavity. Note that, because the two lasing lines share the same cavity, any technical noise due to vibration or thermal drift of the cavity length will be canceled to first order [16], so that the beat-frequency noise will be markedly reduced compared to the cavity noise. Drift and acoustic noise are minimized by enclosing the entire cavity within three layers of thermal control and vibration isolation (illustrated in Fig. 1 by the gray hatched box).
A key advantage of the dual-wavelength SBS laser, as compared to alternative dual-wavelength laser techniques for generating high-frequency RF signals, is that the gain for the two modes is independent: Each mode obtains gain exclusively from its respective SBS gain band. With respect to gain competition, this is equivalent to ideal inhomogeneous broadening: There is no gain competition between the two lasing modes, and thus no competition-induced phase or amplitude noise. Note, however, that the SBS gain itself is homogeneously broadened. This fact helps to ensure that only a single lasing mode operates on each gain band, minimizing mode-hopping and amplitude noise on each mode.
The SBS lasing lines are coupled out of the cavity and separated from the pumps by the circulator. The two lasing modes mix on a photodiode (Picometrix P-50A/Z50, 3-dB bandwidth > 50 GHz with measureable response to 100 GHz), producing a beatnote with frequency fout equal to the difference between the two lasing optical frequencies, or approximately 2f 0. Because the optical mode frequencies are determined by the cavity resonances, the beatnote resists drift in f 0; therefore fout will remain nearly constant even with variation in the RF input frequency [19]. The RF properties are characterized using a Rhode & Schwarz FSEK microwave spectrum analyzer with external mixer sets for operation in the millimeter-wave regime. (Setup and operation of this instrument are described in detail later.)
The laser is stabilized using two servo loops: The inner, Pound-Drever-Hall loop [24] uses a dither tone of ~100 kHz with a lock-in amplifier (Stanford Research 830) to detect the positions of the pump lines with respect to the cavity resonances; this instrument feeds a proportional-integral-differential (PID) amplifier (Stanford Research SR900) that in turn drives the intracavity phase shifter through a high-voltage amplifier (New Focus 3211, 600-kHz maximum bandwidth) to keep the resonances locked to the pump tones. This loop operates on a fast time scale, with a bandwidth of ~2 kHz, and its purpose is to compensate for short-term, small-amplitude fluctuations of the cavity length and pump-laser wavelength. The outer loop integrates the correction signal from the inner loop in a second PID amplifier (also an SR900) to drive the fine-tuning port of the master pump laser. This loop is much slower (< 100-Hz bandwidth), and its purpose is to compensate for long-term drift of the cavity or pump laser. Locking of the pump and cavity can be maintained over periods of hours.
2.2 Operation
The laser is operated using the following procedure: The pump laser is turned on and the RF synthesizer is set to a frequency, f 0, equal to one half of the desired f out. To set f 0 precisely, the inner servo loop output is disconnected and a triangle-wave function is applied to the high-voltage amplifier while the inner servo loop’s error signal (the output from the lock-in) is monitored on an oscilloscope. As the cavity length is ramped, each time a pump line passes through resonance with the cavity, the error signal traces out a typical bipolar error function. Thus, the oscilloscope shows three of these functions—a strong one for each sideband, and a weak one for the residual central pump tone. The driving frequency is then tuned to bring the two sideband error functions together, ensuring that both pump tones are simultaneously resonant for a given cavity length. The inner servo loop is then reconnected and engaged to lock the pump tones to the cavity, and the outer loop is engaged. It should be noted that both sets of PID parameters require careful optimization for best performance.
One noteworthy detail of the RF tuning procedure is the parity of 2f 0/ΔνFSR (rounded to the nearest integer), representing the number of cavity free spectral ranges between the pump tones. If the parity is even, then the center tone will also be simultaneously resonant, and a third, central SBS line may result if the center tone power exceeds the Brillouin threshold. This additional line will yield an undesired beatnote at f 0. It is thus important, in the even-parity case, to keep the central pump tone below threshold by maintaining the bias at a null. If the parity is odd, the center tone will be antiresonant and no spurious signal at f 0 will result.
3. Performance
3.1 Single-frequency operation up to 100 GHz
Figure 4(a) illustrates an exemplary microwave spectrum for operation at 33.989 GHz. The RF spectrum is a composite assembled from four spectra (0–26, 26–40, 40–60, and 60–90 GHz) recorded using the appropriate downconversion mixers. The varying noise floors reflect the differing downconversion losses and input-amplifier noise floors for each each segment; however, the power levels are scaled to reflect the true relative powers of the RF features. The RF output is nearly spectrally pure, dominated by the target frequency at 34 GHz, with no spurious tones greater than−40 dBc over the entire 0–90 GHz span. The origin of the weak spurious tones in Fig. 4(a) are identified in Fig. 4(b), which shows the corresponding output optical spectrum; a copy of the input pump spectrum is also included, offset vertically, to approximately indicate the Rayleigh scattering contribution to the output spectrum. Tone A is of course the desired beatnote between the SBS lasing lines. Tone B at ~11 GHz is due to beating between each SBS lasing line and its respective Rayleigh-scattered pump; the 40-dB suppression of B relative to A corresponds to the ratio of the SBS lasing tones to the Rayleigh scattered lines. The even weaker tones at ~23 and ~45 GHz (C- and C + , respectively) are due to beating between each SBS lasing line and the other line’s Rayleigh-scattered pump, and thus are at frequencies fout ± νB. Tones D, E, and F represent mixing of the SBS modes with even weaker optical components (tone D may also include some RF second harmonic generated at the photodiode), as illustrated in Fig. 4(b). Note that the expected E + tone at ~79 GHz is obscured by the instrument noise floor.
Fig. 4 (a) Composite microwave spectrum showing the beatnote at 33.989 GHz and mixing products. Resolution bandwidth (RBW): 1.0 MHz; video bandwidth: 10 kHz. (b) Optical spectrum corresponding to the conditions of (a). RBW: 2.0 GHz. The RF tone labels A–F in (a) correspond to the indicated optical tone separations in (b).
This technique for generating micro- and mm-waves is readily extended to higher frequencies, and we have operated this system at up to 0.1 THz. Specifically, this configuration of our system has been used to generate beatnotes of 26.00405, 33.99974, 42.99588, 50.00142, 58.31609, 65.99242, 73.99846, 80.00897, 88.01391, and 99.97136 GHz, all without any component changes. Figures 5 and 6 illustrate the microwave spectra of beatnotes at four selected frequencies ranging from the microwave Ka-band into the W-band.
Fig. 5 RF spectra of beatnotes at exemplary frequencies of (a) 26.004 05 GHz, (b) 50.001 42 GHz, (c) 73.998 46 GHz, and (d) 99.971 36 GHz. Traces (a-c) use the vertical axis on the left; the resolution and video bandwidths (RBW and VBW) for these traces are 200 kHz and 10 kHz, respectively. The right-hand vertical axis corresponds to trace (d) only; the RBW and VBW for trace (d) are 200 Hz and 20 Hz.
Fig. 6 RF spectra of beatnotes at exemplary frequencies of (a) 26.004 05 GHz, (b) 50.001 42 GHz, (c) 73.998 46 GHz, and (d) 99.971 36 GHz. For clarity, each trace is offset by ~20 dB from the next, and each is plotted against the frequency offset from its peak frequency. Resolution bandwidth: 50 Hz. Video bandwidth: 50 Hz.
In its standard configuration, the RFSA can measure signals up to 40 GHz, and this configuration was used to directly measure the 26 GHz signals in Figs. 5(a) and 6(a). Beyond this limit, one of two external harmonic mixer sets was employed. For the 50-GHz measurements of Figs. 5(b) and 6(b), we used a model FS-Z40 mixer (calibrated for 40–60 GHz operation), which mixes the test signal with the fourth harmonic of the RFSA local oscillator (LO, tunable sweep over 7.5–15.2 GHz). For the 74-GHz measurements of Figs. 5(c) and 6(c), the signal was mixed with the sixth harmonic of the LO using an FS-Z60 mixer set (calibrated for 60–90 GHz operation). Each mixer set has a table of conversion losses that the RFSA loads when the corresponding frequency band is selected, enabling the instrument to accurately back-calculate the original power in the RF tone from the measured power in the downconverted mixing product. To measure beyond 90 GHz [Figs. 5(d), 6(d)], the FS-Z60 mixer was used but was configured to mix the test signal with the eighth harmonic of the LO. No conversion-loss table is defined for this configuration, so the RFSA uses an estimated conversion loss to calculate the approximate power in the RF tone. The power measurement is thus uncalibrated, but the signal power relative to noise floor is accurately scaled.
In comparing the illustrated spectra, we note that the measurements at > 40 GHz are complicated by ripple due to impedance mismatches and waveguide cutoff frequencies between the coaxial-connectorized photodiode and the waveguide-based mixers, as well as limitations of the photodiode (3-dB bandwidth nominally > 50 GHz, not specified more precisely). This ripple is the primary reason for the ~5 dB lower power at 74 GHz compared to lower frequencies. We observe significant beatnote-generated power over the entire calibrated frequency range; −17 and −21 dBm are obtained at 80 and 88.0 GHz, respectively. High conversion loss at the eighth harmonic for measurements at > 90 GHz results in only a weak detected signal at 100 GHz, estimated at −68 dBm for Fig. 5(d). The resolution bandwidth of 200 Hz is used to obtain good contrast to the noise floor due to this low power.
3.2 Linewidth characterization
Figure 6 illustrates high-resolution (50-Hz RBW) spectra for each of the frequencies plotted in Fig. 5. For clarity, the traces are offset vertically by 20 dB and are plotted against the offset from carrier center frequency. The resolution is limited by the capability of the RFSA and by drift of the RF frequency over the course of the sweep: 6 s for trace (a), 12 s for traces (b-d). The RF tone is not resolved; the profile of the central component (within ± 100 Hz) reflects the instrument response of the RFSA, rather than the RF signal. However, the power spectral density (PSD) of the wings (beyond ± 100 Hz) does reflect the true spectral content of the RF lines; the measured power was confirmed to be > 20 dB above the instrument noise. The PSD in this region is observed to roll off as f − 2, where f represents the magnitude of the frequency offset from the carrier. Despite the widely different carrier frequencies, the PSD relative to carrier and the rolloff with frequency are very similar for all of the illustrated traces. Other spectra, recorded at spans intermediate between those of Figs. 5 and 6 but not included here, are also very similar for all measured frequencies and do not show any additional, unwanted structure. These lineshapes result from both amplitude and phase noise, so they represent an upper bound on the phase noise of this micro- and mm-wave source at each frequency.
The similarity between the spectra recorded for different beatnotes is to be expected for any optical-beat-frequency RF source, as the optical mixing downconverts the phase noise on each optical wavelength onto the RF beat note. If the beatnote were generated by two independent lasers, the production of a low-noise, narrow-linewidth RF signal would require both signal lasers to have an optical linewidth and noise spectrum comparable to that desired for the RF signal. High-performance, very-narrow-linewidth (sub-Hz) lasers would thus be required to obtain RF performance competitive with that of RF frequency synthesizers. In the case of a dual-wavelength SBS laser, however, technical noise sources (cavity drift, vibration, amplitude-to-phase noise conversion), which are the dominant contributions to the linewidth and phase noise for most lasers, will be common to both modes and thus cancel in the optical mixing process. The noise of the resulting RF signal will reflect only the uncorrelated noise on each optical tone, e.g., that due to the underlying instantaneous Lorentzian linewidth. Fitting the wings of each of the traces in Fig. 6 to a Lorentzian function yields an equivalent FWHM < 2 Hz for each RF signal, implying that the Lorentzian component of the optical linewidths are on the order of 1 Hz. We emphasize that this level of performance is obtained directly from the laser output; to attain comparable RF performance by beating two separate lasers together, a complicated optical phase-locked loop must be implemented [7].
3.3 Fine frequency tuning and stepsize
As mentioned, the beatnote can be tuned in steps equal to the FSR; this is demonstrated in the composite spectrum of Fig. 7 . The laser was operated to generate every available beat frequency over a range of > 100 MHz, beginning at 58.26468 GHz. Earlier, we discussed the significance of the parity of the rounded ratio 2f 0/ΔνFSR. As the laser is tuned in steps equal to the FSR, this parity alternates between even and odd; in Fig. 7, the first, third, etc., traces through the last (shown in blue) have even parity, while the second, fourth, etc., traces (red) have odd parity. Despite the potential for compromised operation with even parity, we are able to avoid this problem by holding the residual center pump tone below the SBS threshold. As the figure indicates, the beatnotes are essentially identical from one step to the next.
Fig. 7 Composite spectrum showing stepwise tunability of the laser. The steps are equal to the FSR of the cavity (10,290,487 ± 80 Hz). Alternating traces have even parity (first trace, third, etc., shown in blue) or odd parity (second, fourth, etc., shown in red).
By combining the beatnote frequencies for the traces in Fig. 7 with the range of frequencies given in section 3.1, we can determine the FSR to parts-per-million precision. The spacing between the first and eleventh tones shown in the figure is used to compute an estimated FSR, accurate to within ± 400 Hz. This estimate is used to compute the harmonic number (i.e., multiple of the FSR) for each measured operating frequency. Averaging eleven frequency measurements over 26–100 GHz yields a value for the FSR of 10,290,487 ± 80 Hz.
The beatnote is also tunable over a limited range around the values of this 10-MHz grid. The intracavity phase shifter (~2 waves of range) gives a tuning range of the FSR of approximately ± 1 Hz, corresponding to a beatnote tunability of ± 5 kHz at 50 GHz. As currently implemented, cavity temperature regulation limits the thermal drift rate of the FSR to < 1 mHz/s; the temperature can be varied to enable somewhat larger (but not dynamic) frequency tuning. As discussed earlier, the lasing frequencies are determined primarily by the cavity resonances; however, when the drive frequency is tuned and the SBS gain bands are shifted, some gain-pulling does occur. We have been able to tune the output over a range of ~7.5 kHz around each grid point using this mechanism, albeit with a reduction in the beatnote power of 3 dB at the edges of the range [19].
4. Discussion
In this paper, we have described an SBS-based photonic source of microwaves and mm-waves. This source is able to produce frequencies up to 100 GHz, tunable in 10-MHz steps. We believe our approach could potentially be extended to operation at frequencies up to multiple hundreds of GHz.
In our current setup, the beatnote frequency is limited by the bandwidths of the RF oscillator, the amplitude modulator, and the photodetector. We can obviate the oscillator and the modulator by using two separate lasers to provide the two pump tones [17]. One of these must be tunable in order to tune the beatnote. These lasers can be arbitrarily far apart in frequency, enabling arbitrarily high beatnotes. Compared with heterodyning the two pump lasers directly, the beat frequency from the SBS modes would be expected to have superior noise and stability properties. With dual-laser pumping, only the photodetector prevents production of higher frequencies. Detector technology is advancing steadily, with 100-GHz photodiodes now commercially available [25], and > 300 GHz demonstrated [26]. Potential applications for a dual-wavelength SBS laser operating at these frequencies include distribution of the master oscillator in millimeter-wave radio astronomy arrays [4], transport of very-high-speed fiber-wireless data signals [1,2], and precision terahertz spectroscopy [27].
Acknowledgments
This material is based upon work supported by the National Science Foundation under Grant No. IIP-0924028 and by the Internal Research and Development program of the Johns Hopkins University Applied Physics Laboratory’s Air and Missile Defense Department.
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