Brillouin filtering of optical combs for narrow linewidth frequency synthesis
Juan Galindo-Santos1,*, Aitor V. Velasco1, Ana Carrasco-Sanz2 and Pedro Corredera1
1Institute of Optics, Spanish National Research Council (IO-CSIC), Serrano 121, 28006 Madrid, Spain.
2Department of Optics, Faculty of Science, University of Granada, Campus Fuentenueva, 18071, Granada Spain
*Corresponding author: , Phone:+34 91 561 88 06 E230, Fax:+34 91 411 76 51
We report a tunable monochromatic source generation scheme, based on Brillouin filtering of a self-referenced optical frequency comb. The system benefits from the high stability and mode linewidth of the frequency comb, significantly improving the performance of the original laser source used as Brillouin pump. A synthesized frequency with stability under 4×10-10 and a linewidth under 75 kHz was experimentally demonstrated for two separate pump lasers in the C-band. The proposed monochromatic source can be tuned with high precision in a very broad band by combining a coarse control with the pumping source and a fine control with the optical frequency comb references. In our experimental setup, coarse and fine tuning resolutions were 4 MHz and 20 Hz, respectively. Influence of Brillouin pump fluctuations in the synthesized signal stability were also analyzed for observation times up to 104 s.
Keywords: Stimulated Scattering Brillouin, Self-referenced Optical Frequency Combs, Lasers
1. Introduction
Optical frequency references play a fundamental role in equipment calibration for diverse fields such as metrology, atomic and molecular spectroscopy and optical communications. For the past 60 years, the caesium ground-state hyperfine transition at 9.2 GHz has provided our main standard for measuring time and frequency [1, 2]. In order to translate this reference into the terahertz ranges, traditional schemes relied on intricate and delicate harmonic frequency chains to generate successive harmonics from the Cs radio reference [3, 4]. The development of optical frequency combs (OFC) revolutionized optical frequency metrology by providing equally-spaced spectral lines over broad wavelength ranges [5, 6]. These spectral structures enabled to measure trapped ion optical frequencies with accuracies close to the Cs fountain clock used as reference [7, 8] and develop new optical frequency standards such as acetylene transitions in the 1.5-μm band [9] or Hg+ and Al+ ions in the petahertz range [10], to name a few.
However, when an arbitrary comb line outside these standards needs to be extracted, optical filtering of the OFC becomes necessary. Array-waveguide gratings, fiber Bragg gratings, and optical injection locking have been proposed for this task [11, 12], albeit showing limitations in terms of response speed, tunability and output power. In 2009, Subías et al. demonstrated selective stimulated Brillouin amplification of an OFC for metrological purposes [13]. Single comb lines in the C-band were selected, preserving a relative frequency accuracy in the order of Hz. Nevertheless, OFC generated by Cross Phase Modulation (XPM) fail to provide absolute frequency references. Furthermore, only instantaneous measurements were provided, whereas typical calibration techniques require a sustained stability characterization of the involved signals.
In this paper, we present an absolute single-frequency synthesis scheme based on Stimulated Brillouin Scattering (SBS) filtering of a self-referenced OFC spectrum, building upon the preliminary results presented in [14] . Long-term relations between the stabilities of the input and output signals are also analyzed. The proposed system benefits both from the stability and narrow linewidth of the frequency comb, and from the tunability of the reference laser source used as Brillouin pump. Absolute frequencies are hence synthesized at an arbitrary wavelength within the OFC supercontinuum range with a tuning resolution down to the OFC precision.
2. Operation principles
Optical frequency combs are generated from a train of periodic femtosecond pulses emitted by a tightly mode-locked laser. In the spectral domain, this structure results in a large number of equally-spaced frequency lines (teeth) spanning across the spectrum [5-8]. The frequency accuracy of each line equals that of the reference clock, typically reaching 10-15 or 1 Hz in the infrared range [15]. A remarkably precise tool for optical frequency metrology is hence provided, since the frequency of the N-th OFC line, fN, can be readily determined as:
(1)
where frep is the repetition frequency, set by the separation between two comb lines; and fCEO, is the offset frequency, set by the distance to zero frequency of the first tooth of the comb. frep and fCEO are locked by controlling the resonating cavity and the pump conditions of the source oscillator with frequency-difference-based feedback loops operating in the MHz range. frep is set by direct comparison with a frequency synthesiser, whereas fCEO is controlled in a f-2f interferometer stabilization unit after spectral broadening and frequency doubling of the oscillator output.
In order to access the formidable accuracy and resolution of OFCs in the synthesis of a monochromatic signal with an arbitrary absolute wavelength, we selectively filtered a tooth of a self-referenced OFC through stimulated Brillouin scattering (SBS). SBS is a nonlinear effect in which an acoustic wave scatters photons from a pump wave into a counter propagating Stokes wave [16, 17]. The separation between pump and Stokes waves, known as Brillouin shift, νB, is typically in the range of gigahertz and responds to the following equation:
(2)
where n is the refractive index of the optical fibre, va is the acoustic velocity along the optical medium and λp is the pump wavelength.
This interaction exhibits a particularly high efficiency in optical fibres, therefore providing narrowband amplification and filtering with relatively low pumping power [18, 19]. The bandwidth of the SBS gain spectrum, which is intrinsically determined by the fibre material, presents a Lorentzian shape with a bandwidth related to the phonon lifetime of the acoustic wave, TB [16]:
(3)
ΔνB is typically in the range of several tens of megahertz and is inversely proportional to λp2 [20]. This narrow bandwidth originally limited the applications of SBS, although this disadvantage can be readily overcome through gain-broadening schemes relying on direct frequency modulation of the pump laser [21]. Alternatively, the bandwidth of the SBS spectrum can also be further restricted by superposition of multiple losses from the same source [22]. Furthermore, a more complex tailoring can achieved yielding a rectangular filter showing a passband ripple about 1 dB and a bandwidth about 493 MHz [23]. Nevertheless, given the narrow linewidth of the OFC teeth and their relatively broad separation, the natural bandwidth of the SBS gain spectrum is perfectly suited for our current purposes. Other recent applications for filters are based on dynamic Brillouin gratings [24] in polarization-maintaining fibres and on SBS in nanophotonic wavegides [25]
3. Experimental setup
To experimentally prove this scheme, we filtered a single line of the OFC spectrum using stimulated Brillouin scattering in the C-band. For exemplary purposes, two distinct lasers, centred at 1541 nm and 1532 nm respectively, were used as Brillouin pump. To enable the characterization of the synthesized signals, the filtered comb line was modulated to induce a frequency shift that enabled its analysis with the OFC in an all-fibre beat unit. The main elements of the experimental setup are shown in Fig. 1.
Fig. 1: Experimental setup
The OFC is based upon a commercial mode-locked laser centred at 1560 nm comprising an Er-doped fibre ring oscillator [26]. The oscillator output is split into three signals, namely a first output for the all-fibre beat unit, a second output for a free space beat-unit (not applied to the present work), and a third output for offset frequency locking. All the system is referenced to a Rb clock (RefGen 10491 from TimeTech), linked by GPS to the international reference.
Repetition frequency is stabilized by comparing the outputs of a frequency generator (DDS120 from Menlo Systems) and the OFC oscillator within a phase detector (PHD110 from Toptica). Oscillator cavity length is modified accordingly through a piezoelectric actuator controlled by a PID feedback loop (PID110 from Toptica). Tunability between 98 MHz and 102 MHz with a 10 mHz resolution is provided. In order to lock the offset frequency at the f-2f interferometer stabilization unit [27], the third oscillator output is amplified at an Er-doped-fibre and fed into a Highly Non-Linear Fibre (HNLF) for supercontinuum generation. Variable dispersion control (VDC) of the amplified signal is implemented through prism compressors to compensate pulse broadening. Frequency doubling at the 2-2f stabilization unit is performed through a non-linear crystal in order to beat the spectral regions around 1050 nm and 2100 nm in an InGaAs detector (FPD510-F from Menlo System). After filtering and amplification, the resulting beat signal is compared to a 20 MHz reference signal in a digital phase detector (DXD200 from Menlo Systems). The 20 MHz reference signal is generated at a reference distributor module (RFD10 from Menlo Systems). Offset frequency deviations from the target 20 MHz reference are controlled by modulating the output power of the oscillator pumping laser through a PI feedback loop (PIC201 from Menlo Systems).
The first output of the OFC oscillator was injected through an isolator into a 1-km-long single mode fibre (Pirelli SMF28) for SBS filtering. Two lasers diodes (EP1550-DM-VAD-001 and EP1550-NLW-BBI-001 from Eblana) were tested for the generation the counter-propagating Brillouin pump wave. Each source was stabilized on the slope of the P11 (1531.5879 nm) and P25 (1540.82744 nm) absorption lines of acetylene 12C2H2, respectively. The output of the pump laser was amplified using an EDFA (EDFA-TV-24-FC/APC-B-11 from Accelink) working on saturated conditions, generating a fixed output power of 23 dBm. Polarization and power of the pump wave were tuned before injection in the opposite end of the SMF to adjust the SBS process. A SBS gain in the order of 6 dB was selected.
In order to characterize the filtered mode, the synthesized frequency was down-converted with the comb itself in the all-fibre beat unit. The OFC output was filtered with a tunable optical fibre filter (FOTF-025121333 from Agiltron, ranging from 1510 nm to 1580 nm) before beating. Since the SBS filtering process preserves the original OFC frequency, a frequency shift needs to be induced in the isolated mode for heterodyne characterization. A single-sideband Mach-Zehnder (MZ) optical modulator operating in the Vπ-bias point for carrier suppression was selected for this purpose. Polarization control (PC) was included in both ends of the MZ to optimize modulation and signal beat, respectively. The beat frequency between the filtered mode, after modulation, and the OFC was measured by a high-sensitivity PIN photodetector (FPD510 from Menlo Systems). A 430 MHz modulation frequency was chosen in the MZ to match the central frequency of the beat frequency detection electronics after down-conversion. The frequency and linewidth of the beat signal were characterized using a 1-mHz-resolution frequency counter (FXM50 from Menlo Systems), and an Electric Spectrum Analyser (ESA, HM5014-2 from HAMEG) with a 9 kHz resolution.
4. Results
4.1. Linewidth and stability
For each of the selected laser sources, frequency stability of the Brillouin pump, the original OFC tooth and the SBS-filtered signal were characterized during 8-hour spans of sustained operation. Their respective Modified Allan Deviation curves are presented in Fig. 2.
Fig. 2: Modified Allan Deviation of Brillouin pump laser (dashed blue), OFC tooth (solid green) filtered OFC tooth (dotted red), for Brillouin pumps centred at 1542 nm (a) and 1532 nm (b).
For short observation times (τ), the filtered signal inherits the OFC stability. In particular, for τ = 1 s, a stability of 4×10-10 in the filtered tooth is observed in both cases, regardless of the original pump stability. This implies up to a 70-fold improvement between the original pump source and the synthesized frequency. Since the improvement is limited by the OFC stability, larger increments could potentially be achieved for less stable pump signals.
As observation times increase, the stability of the filtered signal follows the same trends affecting the pump laser. In particular, the synthesized frequency is affected by both the periodic artifacts around τ ≈ 100 s of the first laser and the long-term frequency drifts of the second laser. These instabilities are transmitted to the filtered signal through the phase noise of the Brillouin amplification process. Regardless of these trends, the stability increment is mostly maintained through the analyzed time range.
Linewidth of the involved signals was also characterized, as shown in Fig. 3. For a pump laser linewidth of 440 kHz and a comb tooth well below the measurement resolution of 9 kHz, the synthesized signal linewidth is shown to be below 75 kHz. Measured linewidth and stability hence provide significant improvement in the performance as optical frequency reference compared to the original pump source.
Fig. 3: Normalized spectra of pump laser (dashed blue), original OFC tooth (solid green) and filtered OFC tooth (dotted red), for a Brillouin pump centred at 1542 nm.
4.2. Tunability and filtering
Given the flexibility provided by SBS filtering, the proposed scheme can be used for the synthesis of any arbitrary frequency within the emission range of the OFC (Fig. 4a). The synthesized frequency is selected in a two-step tuning process: first a coarse amplification band is selected by adjusting the SBS process, and then the OFC tooth is finely tuned within said band. As an example, Brillouin shift dependence on the wavelength of the pump laser was characterized in the C-band for the fibre used in the experiment (Fig. 4b). A 11 GHz shift is measured for a pump source centred at 1530 nm, with a decreasing trend of 7 MHz/nm. An amplification of 46 dB for the SBS process was measured with an Optical Spectrum Analyzer (OSA, Q8384 from ADVANTEST).
Fig. 4: (a) Optical frequency comb spectrum. (b) Wavelength dependence of Brillouin shift in the C-band for the selected optical fibre (linear fit in grey)
In order to characterize the SBS filtering process in our setup, we also measured the Brillouin gain spectra with two separate techniques for the pump laser centred at 1541 nm. In the first method, heterodyne detection was used to directly measure the anti-Stokes band in the ESA. In the second method, the power of the filtered mode was measured while scanning the pump laser frequency. Results are shown in Fig. 5.