Suitable use of stimulated Brillouin amplification (SBA) effect for selective single peak amplification in an optical frequency comb is demonstrated to provide high accuracy in optical frequency metrology. A pump wave generated by a tunable laser source (TLS) is used to stimulate SBA of such optical comb along an optical fiber and selectively amplify only one single peak of the comb. Nature of SBA preserves both linewidth and absolute wavelength position of the selected comb peak. All of these features result in a simple, robust and compact all in fiber system. Relative optical frequency accuracy in the order of Hz is confirmed.
© 2009 Optical Society of America
Optical frequency combs (OFC) are attractive optical reference sources providing a precise ruler in the frequency space, which are of interest for various applications such as optical frequency metrology, optical clocks or high-resolution spectroscopy. In most cases, optical combs coming from pulsed lasers are composed of thousands of lines with very narrow spacing that extend its spectrum over several tens of nanometers, providing accordingly optical powers per peak which could be limited to some hundreds of nanowatts.
In reference , a 0.08 pm wavelength accuracy optical spectrometric technique using an OFC as a ruler in a high resolution optical spectrum analyzer was presented. So far, higher wavelength accuracies are not accomplishable by direct optical filtering, but in the rf spectrum, although techniques for selectively amplifying each of the OFC peaks are then required. In references [2–6], methods to obtain individual comb lines by phase locking and injection locking techniques in laser diodes of different types are presented. Phase locking techniques [2–4] allow the integration of a phase-locked optical comb in a system for the generation of tunable absolute optical frequencies by synchronizing a particular comb line with a tunable diode laser. Injection locking methods [5–6] can be applied to obtain an absolute frequency referenced laser source selecting only one desired line of the OFC and amplifying the power of the selected peak several thousand times, in the overall tunable range given by the gain curve of the laser diode lasing medium, typically 5 to 10 THz about a certain center frequency. It generally requires a previous optical filtering process before introducing the signal in the resonant cavity of a feedback laser. Reference  provides a counterpoint to these methods, using Stimulated Brillouin Amplification (SBA) effect in a single mode fiber as a narrow optical selective amplifier to generate millimeter waves by amplification of desired waves from a comb.
In this letter, suitable use of SBA effect for single line amplification in an OFC is demonstrated to make compatible the wide spectral operation range offered by optical spectrometric instrumentation, with the very high frequency accuracy suitable by conventional electrical spectrometry. The use of SBA occurring along a fiber between the desired comb peak and a pump wave generated from a TLS provides up to several tens of dB amplification of desired comb peak with a narrow full width at half maximum (FWHM) Lorenzian function gain profile around 10 MHz [8,9], without degradation of neither its linewidth nor its absolute frequency position. In contrast with previous techniques, selective line amplification through stimulated Brillouin does not require the introduction of any active optical element nor filtering process, along the signal path, resulting in a fully all in fiber system. SBS provides as well, in an intrinsic way, the phase-matching between output and original comb line. The use of the TLS as pump wave allows moving the comb peak selection zone over its entire tunable range, C-band in our experiment, in a very simply way.
2. Principles of selective single peak amplification and experimental lay-out
The general setup for SBA of a single peak in an optical frequency comb is depicted in squared part of Fig. 1. The OFC signal is injected in a 4 km dispersion shifted fiber through an optical isolator that prevents any perturbation on the pulsed source due to the pump beam optical power. Pump wave for SBA generation is obtained from the TLS2, which is intensity modulated by a Mach-Zehnder (MZ) optical modulator operating in the Vπ-bias point for carrier suppression. One of the modulated sidebands is used as the pump wave, which provides a precise wavelength tuning by simply controlling the modulation frequency. This is required for fine positioning of the pump wavelength a Brillouin Doppler shift (≈ 10 GHz) far from the desired comb peak with precision compatible with the Brillouin gain curve width. Pump wave is intensity amplified by an EDFA and injected in the fiber in a counter propagating scheme through the 50:50 optical coupler. The polarization controller (PC) allows proper alignment between polarization states of both interacting beams in order to get the highest efficiency in the generation of the SBA effect.
In order to confirm the validity of using SBA, an OFC generated by Cross Phase Modulation (XPM) effect from a gain switched pulsed laser diode generating 12 picoseconds pulses at Ω=100 MHz pulse repetition frequency described in , centered at TLS1 wavelength, is used. Its optical spectrum measured at point A is shown in Fig. 2. Zooms of this OFC are superimposed on the same figure to better distinguish the equal spaced peaks of the comb. The use of this OFC allows confirming the good performance of the method without the need of calibrated wavelength sources since TLS1 carrier wave works as a reference signal in the measured rf spectra as it is described below. Obviously, this method can be implemented on any OFC generated by different kinds of optical pulsed sources such as mode-locked solid state or fiber ring lasers.
The optical signal exiting from the fiber output is measured in both electrical spectrum analyzer (ESA from Agilent E4407B) and high resolution optical spectrum analyzer (HR-OSA from Aragon Photonics Labs BOSA-C). The 50:50 coupler is used to allow measuring both electrical and optical spectra at the same time.
The optical fiber simply provides the medium for the nonlinear interaction between pump and the optical comb signal giving rise to the Brillouin scattered signal. The power of this scattered signal is governed by the product :
where λp is the pump wavelength, Pp(z,λp) is the pump beam intensity in a point of the fiber and Pc (z,λp + λB) is the intensity of the amplified measured optical comb signal, in the same point, at the wavelength λp +λB determined by the pump beam and the slight Doppler shift λB associated with the Brillouin effect, which is around 10 GHz in single mode fibers.
Brillouin gain profile gB has a FWHM bandwith ΔλB that is around 10 MHz in single mode fibers. Therefore, according with (1), amplification of a given comb peak with wavelength λC requires interaction with a pump beam whose wavelength must be fine tuned to λC-λB with MHz precision. This precision is easily achieved by intensity modulation of the TLS2 as described before. On the other hand, stability of the amplification level of the selected comb peak will be given by the wavelength stability of the pump wave with respect to the optical comb signal, which can be better than ΔλB in commercial TLS equipment, assuring a 3 dB stability of the SBA process. For long term stability, a simple feedback method controlling the modulation frequency Ω in function of the measured power of the amplified comb peak is implemented.
In Fig. 3 the optical spectrum of the comb measured at point B is shown for comparison, in a condition of phase matching (a) and no phase matching (b) between pump and desirable comb peak. We select the 5th peak upper wavelength from TLS 1. In this case, pump optical power entering into the fiber is around 10 mW, whereas comb peak optical power is around 10 nW. In the high resolution optical spectrum, it is clearly seen the 20 dB amplification of the comb peak when it achieves the phase matching requirement for SBA generation. In the case of no phase matching condition, spontaneous Brillouin scattering is generated by the backscattered pump signal, which is around 10 dB less effective than SBA. Difference between SBA peak and spontaneous Brillouin peak is used as visual reference for fine wavelength tuning of the pump.
Corresponding measured rf spectra along a pump tuning process around the 5th and 6th peaks of the comb are shown in Fig. 4. For their correct understanding it is necessary to point out that in our experiment we use an OFC generated by XPM on the TLS1 signal, which imply the following two aspects: first, the OFC is a phase signal, which contributes in the optical spectrum but not in the rf one. Second, the TLS1 carrier wave contributes in the rf spectrum, so that curves measured in the rf spectra corresponds to the beat signals generated between the amplified comb peaks and the TLS1 carrier.
Figure 4(a)–(f) show ESA measurements with a span of 200 MHz and resolution bandwidth of 3 kHz. In these rf spectra, the approximately 10 MHz linewidth low amplitude peak corresponds to the beat signal generated between the TLS1 carrier and the spontaneous Brillouin signal. It indicates frequency location of the Brillouin process with respect to the TLS1 carrier and hence with respect to the comb modes. It differentiates clearly from peaks generated by the beating between TLS1 carrier and comb peaks amplified by SBA. Amplification of a selected comb peak by the SBA process occurs within the 10 MHz FWHM real part of the complex gain profile of the Brillouin effect, with a maximum in the center of the Brillouin gain wavelength range. In Fig. 4(c) and Fig. 4(f) can be clearly seen the rf peak corresponding to the beat signal between the TLS1 carrier and respectively the 5th and the 6th amplified comb modes. However, the imaginary part of this gain profile  extends over adjacent peaks of the comb giving rise to a small contribution in the measured rf spectrum (Fig. 4(a) and Fig. 4(e)). Potential contribution of the other TLS2 modulation sideband is avoidable in the practice because the two parameters involve in the comb peak selection, TLS2 wavelength and modulation frequency Ω, allow to select a situation in which the phase-matching condition is achieved only for one of the two modulation sidebands.
The fundamental validity criteria for the use of SBA in optical comb applications is that both linewidth and frequency position, and hence the wavelength position, of the amplified comb peak remains unalterable, as can be seen in Fig. 4. On one hand, Figs. 4(a)–(f) show that wavelength of the amplified comb peak remains constant in spite of its concrete wavelength position inside the Brillouin gain wavelength range. To confirm this point, Fig. 4(g) shows the measured rf spectra for condition of the 5th comb mode selection, with an ESA resolution bandwidth of 1 Hz. The corresponding measured peak frequency, f 5th=500.001698MHz ±1Hz, agree with the pulse repetition rate (PRR) of the OFC, PRR=100.000340 MHz ±0.5 Hz.
On the other hand, rf peaks associated with the amplified comb modes do not present any type of jitter apart from the intrinsic one present in the comb, since SBA effect does not modify neither spectral width nor phase condition of the selected peak . It can be seen in Fig. 4(g) where the measured spectral width is compatible with the measuring ESA resolution bandwidth of 1Hz, whereas any change in the spectral width or phase condition of the selected peak due to Brillouin effect would become noticeable as a broadening in the rf spectrum. Notice that peaks of the OFC obtained through XPM effect inherit the natural TLS1 linewidth and are phase correlated.
3. Application of single peak selection in optical frequency metrology
To demonstrate the suitability of this line selection method for optical frequency metrology purposes, relative frequency position of a signal under test (SUT) is measured with respect to the center of the comb. To generate a SUT located at a readily controlled position determined with high relative frequency accuracy, TLS1 is intensity modulated by a MZ so that the OFC is preserved whereas well controlled modulation sidebands appears in the optical spectrum as it is shown in Fig. 3(c). In the rf spectrum, the three beating peaks generated between the SUT, the amplified comb mode and the TLS1 carrier wave can be clearly seen as shows Fig. 5. Thanks to the nature of the used OFC, TLS1 carrier works as a reference signal avoiding necessity of calibrated and very stable wavelength sources. By implementing the frequency count option of the ESA, frequency of the signals can be measured with 1 Hz precision.
In these figures, SUT was generated at Θ =560.000300 MHz apart from the TLS1 optical carrier. For metrology purposes, only frequency measurement of the beat signal between SUT and the 5th amplified comb peak is needed. In the experiment, it reports a frequency of f SUT-5th = 59.998602 MHz ±1 Hz. Considering the PRR of the comb, the measured SUT relative frequency, f SUT-5th + 5PRR, reports the real one Θ within the accuracy of 3 Hz.
Suitable use of SBA effect for single peak selection in an OFC is demonstrated to provide high accuracy in optical frequency metrology. The use of a TLS as pump wave provides suitable wavelength tunability for the peak selection along the entire C-band. Nature of SBA preserves both linewidth and absolute wavelength position of the original comb peak, so that it is suitable for metrology purposes. Measurements are carried out, obtaining relative optical frequency accuracy in the order of Hz, confirming the good performance of the method, whereas the absolute optical frequency would be given by the used OFC. All of these features result in a simple, robust and compact all in fiber system, which offers a considerable improvement in complexity with respect to previous techniques.
This work was supported by the Spanish “Secretaría de Estado de Universidades e Investigación (MEC)” under Project FIS2007-64443.
References and links
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