Tài liệu Abdolvand2012

4362 OPTICS LETTERS / Vol. 37, No. 21 / November 1, 2012 Generation of a phase-locked Raman frequency comb in gas-filled hollow-core photonic crystal fiber A. Abdolvand,* A. M. Walser, M. Ziemienczuk, T. Nguyen, and P. St. J. Russell Max Planck Institute for the Science of Light, Günther-Scharowsky-Strasse 1, Erlangen 91058, Germany *Corresponding author: [email protected] Received July 19, 2012; revised September 17, 2012; accepted September 17, 2012; posted September 17, 2012 (Doc. ID 172878); published October 16, 2012 In a relatively simple setup consisting of a microchip laser as pump source and two hydrogen-filled hollow-core photonic crystal fibers, a broad, phase-locked, purely rotational frequency comb is generated. This is achieved by producing a clean first Stokes seed pulse in a narrowband guiding photonic bandgap fiber via stimulated Raman scattering and then driving the same Raman transition resonantly with a pump and Stokes fields in a second broadband guiding kagomé-style fiber. Using a spectral interferometric technique based on sum frequency generation, we show that the comb components are phase locked. © 2012 Optical Society of America OCIS codes: 060.5295, 190.4370, 290.5910. The development of hollow-core photonic crystal fibers (HC-PCFs) [1] has led to the observation of many interesting phenomena in the field of gas-based nonlinear optics [2]. In particular, studies of gas-based stimulated Raman scattering (SRS) have benefited greatly from the unprecedentedly low Raman threshold offered by low loss HC-PCF [3–5]. This uniquely makes HC-PCF an excellent candidate for the generation of SRS-based optical frequency combs [6,7]. Indeed, recent reports on multioctave Raman frequency comb generation in HC-PCF have attracted a lot of attention [8,9], partly due to the potential of these fibers as new vehicles for ultra lowthreshold molecular modulation of optical pulses. Such frequency combs may find a wide spectrum of applications, ranging from sub-fs pulse synthesis to optical atomic clocks and carrier-envelope control [10]. Essential in these applications is the coherence of the comb, i.e., stable phase locking between individual comb lines. Up to now, the main scheme used for frequency comb generation in gas-filled HC-PCF is based on SRS initiated from quantum noise. In this scheme, an energetic pump pulse is coupled into a HC-PCF filled with a Raman active medium (e.g., hydrogen gas), the buildup of the stimulated Raman signal starting from spontaneous Stokes photons. This can result in generation of an octavespanning frequency comb consisting of rovibrational Raman lines [6]. Although a recent study confirmed the presence of self and mutual coherence between comb lines, the relative phases of these components displayed large pulse-to-pulse fluctuations [7]. In the Letter presented here, we generate a pure rotational frequency comb by colaunching the pump pulse with a weak seed pulse at the first Stokes frequency. This reduces the threshold for rotational SRS, effectively suppressing the vibrational lines. It also imposes coherence on the comb [11]. By passing the comb through a frequencydoubling crystal, stable phase locking between comb lines is demonstrated. A schematic of the experimental setup is shown in Fig. 1(a). It has two stages: (1) preparation of the seed pulse in a narrowband guiding photonic bandgap fiber (PBG-PCF) and (2) comb generation in a broadband guiding hollow-core kagomé-PCF. The output of a 1064 nm microchip pump laser, delivering pulses of 100 μJ energy 0146-9592/12/214362-03$15.00/0 and 2 ns duration at a repetition rate of 1 kHz, was split into two parts. The first part (∼10 μJ) was coupled into a 2 m length of PBG-PCF [loss of 0.13 dB=m at 1100 nm Fig. 1. (Color online) (a) Schematic of the two-color pumping of a hydrogen-filled kagomé-PCF for generating a pure rotational frequency comb. The rotational Raman transition of hydrogen is resonantly driven by pump and first rotational Stokes seed (M, mirror; BS, beam splitter; DM, dichroic mirror). (b) A comparison between loss and transmission windows of a kagomé- and PBG-PCF. Although the transmission window of the PBG-PCF (grey shaded region) is narrower, it offers a much lower propagation loss. (c) A typical purely rotational frequency comb produced using this technique (solid purple line). The solid green line indicates the total (waveguide
gas) wavevector mismatch Δβ across the frequency comb. © 2012 Optical Society of America November 1, 2012 / Vol. 37, No. 21 / OPTICS LETTERS with a 150 nm wide transmission band—see Fig. 1(b)]. The PBG-PCF [3] was filled with hydrogen to a pressure of 6 bars. For our experimental configuration, this pressure provides a good balance between collisional dephasing time and molecular density. The limited transmission bandwidth (∼30 THz) accommodated only the pump and the first rotational Stokes lines (frequency shift 18 THz), resulting in efficient generation of the first rotational Stokes component of ortho-H2 , centered at 1135 nm. After filtering out the residual pump from the output of the PBG-PCF, the generated Stokes signal was used as a seed in the second stage of the setup, which consisted of a 60 cm long kagomé-PCF (300 nm strut thickness and pitch of 13 μm) with a transmission window (loss ∼2 dB=m) extending from ∼800 to 1750 nm [Fig. 1(b)]. This wide transmission band permitted the generation of multiple rotational Raman bands. The kagomé-PCF was filled to exactly the same pressure as the PBG-PCF, the two gas-filling systems being physically connected, and the experiments were carried out at room temperature. This distinguishes the setup from two-color excitation schemes in which the Raman coherence is prepared adiabatically in a cryogenic environment [10]. In the second stage, the seed Stokes pulse generated in the PBG-PCF was timed to coincide with the arrival of the second part of the pump pulse (energies in the range 50–90 μJ) at the kagomé-PCF. The beat note between the pump and Stokes pulses then resonantly drives the rotational Raman transition of the hydrogen molecules, leading to the generation of a comb of frequencies spaced by 18 THz, as shown in the experimental spectrum in Fig. 1(c). The comb extends from ∼850 nm to ∼1600 nm, its overall width being mainly limited by the transmission window of the kagomé-PCF. As expected, no vibrational lines could be detected, irrespective of the polarization state of the input pump pulse. The first hint that the comb has high coherence was obtained by frequency doubling [Fig. 2(a)]. The output of the kagomé-PCF was collimated using an achromatic infrared lens and then focused into a 5 mm thick beta barium borate (BBO) crystal. Figure 2(b) shows a typical frequency-doubled spectrum after the nonlinear crystal, recorded with a spectrometer, while Fig. 2(c) shows photographs of the doubled signal (cast on a screen) for three different angles of the BBO crystal. Close inspection of the spectrum reveals that the generated visible comb contains both second harmonic (SH) and the sum-frequency (SF) components. Any uncorrelated temporal phase variations in the comb lines would result in heavily decreased levels of SF signal. The efficient generation of these components indicates that the individual components of the frequency comb are mutually coherent. Defining the frequency of the nth comb line as ωn  ωp
nΩ, where ωp is the pump frequency and Ω the Raman frequency shift, the mth frequency in the doubled ~ m  ωn
ωm−n  2ωp
mΩ. The spectrum is given by ω ~ m will be the result of the sum over signal amplitude at ω all possible SH and SF signals at this frequency, i.e., Sm ∝ X An Am−n eiϕn
ϕm−n  ; n (1) 4363 Fig. 2. (Color online) (a) Schematic of the frequency doubling arrangement using a 5 mm thick BBO crystal. (b) Typical spectrum recorded by the spectrometer at a fixed tilt angle. (c) Photographs of the frequency-doubled signal for three different tilt angles of the BBO crystal. Apart from SH components, stable sum frequencies of different comb lines are generated as well. where An expiϕn  is the complex amplitude of the nth comb line. It is clear that any uncorrelated shot-to-shot fluctuations in the values of ϕn will result in heavily decreased signal strength S m when averaged over many shots. The temporally steady and efficient generation of these components, seen in the experiments, is an indication that the comb lines are mutually coherent. Frequency doubling not only extends the comb into the visible spectral region, but also provides us with an opportunity to measure the relative phase difference between the comb components [11]. This was done by splitting the frequency comb into two equal parts at a nonpolarizing beam splitter. One part was delayed and filtered so that only pump and first Stokes remained. It was then mixed with the unfiltered comb in the BBO crystal [Fig. 3(a)]. The resulting frequency-doubled spectrum was then dispersed at a grating and the intensity of the individual lines recorded as a function of time delay τ. The resulting signal at frequency ω~ m is then 2 iΩτ
Δϕm 
A A hI m −1 m
1 j i SF τi ∝ hjA0 Am e  hA20 A2m
A2−1 A2m
1
2A0 Am A−1 Am
1 cosΩτ
Δϕm i; (2) where Δϕm  ϕ0 − ϕ−1
ϕm − ϕm
1 and the triangular brackets indicate time and ensemble averaging over many laser shots. The expression in Eq. (2) contains information about the relative phases of the comb lines, encoded in the beat signals generated by the sum frequencies “pump
comb” and “Stokes
comb”. If the comb is phase locked, the intensity of the mth frequency will display a clean sinusoidal variation with delay τ. If, on the other hand, there are large fluctuations in Δϕm 4364 OPTICS LETTERS / Vol. 37, No. 21 / November 1, 2012 modulator would result in the generation of a train of ultrashort pulses at a repetition rate of 18 THz. The purity of the phase locking will be affected by fiber dispersion because it relies on the same coherence wave being able to couple efficiently between all the comb lines. If this is not the case, for example, for Stokes and antiStokes bands far away from the pump and first Stokes frequencies, uncorrelated coherence waves will grow from noise and disturb the overall coherence of the system. The rate of linear dephasing for the mth coherence wave (relative to the 0th wave) is described by the quantity Δβm  βm−1 − βm  − β−1 − β0   coh βcoh m−1;m − β −1;0 and is plotted in Fig. 1(c). We note, however, that nonlinear phase locking can play an important role in maintaining coherence; for example, it can cause efficient anti-Stokes generation in gas-filled HC-PCF even in the presence of large linear phase mismatch [12]. In summary, making use of the unique features of HC-PCF allows generation of a broad, purely rotational Raman frequency comb in hydrogen. Spectral interferometry shows that the comb lines are robustly phase locked. From a practical point of view, this makes the frequency comb attractive for Fourier synthesis of ultrashort pulses [8]. The main advantage of the experimental scheme is its simplicity, i.e., elimination of the need for two synchronized high-energy laser sources or a cryogenic environment. References Fig. 3. (Color online) (a) Schematic of the setup used for extracting phase information using spectral interferometry. (b) Sinusoidal modulation of the SF signal as a function of the delay τ measured for m  0 (beating of 2ω0 with ω−1
ω
1 ), m  −1 (beating of ω0
ω−1 with itself), m  −2 (beating of 2ω−1 with ω0
ω−2 ), and m  −3 (beating of ω0
ω−3 with ω−1
ω−2 ). over time or from shot-to-shot, the modulation term in Eq. (2) will average away to zero. Figure 3(b) shows the experimentally measured (black dots) of the SF intensity as a function of delay. These traces show a stable sinusoidal variation (solid red line) at 18 THz, in good agreement with Eq. (2), indicating that stable phase locking exists among the comb lines. The traces show a robust and reproducible sinusoidal modulation of the SF signal, even though no active stabilization was used in the setup. The temporal shift in the relative position of the peaks in Fig. 3(b) is a direct measure of phase difference between the comb lines. Bringing all the spectral components into phase, for example using a liquid crystal 1. P. St. J. Russell, J. Lightwave Technol. 24, 4729 (2006). 2. J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St. J. Russell, J. Opt. Soc. Am. B 28, A11 (2011). 3. A. Abdolvand, A. Nazarkin, A. V. Chugreev, C. F. Kaminski, and P. St. J. Russell, Phys. Rev. Lett. 103, 183902 (2009). 4. A. Nazarkin, A. Abdolvand, A. V. Chugreev, and P. St. J. Russell, Phys. Rev. Lett. 105, 173902 (2010). 5. F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. J. Russell, Science 298, 399 (2002). 6. F. Couny, F. Benabid, P. J. Roberts, P. S. Light, and M. G. Raymer, Science 318, 1118 (2007). 7. Y. Y. Wang, C. Wu, F. Couny, M. G. Raymer, and F. Benabid, Phys. Rev. Lett. 105, 123603 (2010). 8. H. S. Chan, Z. M. Hsieh, W. H. Liang, A. H. Kung, C. K. Lee, C. J. Lai, R. P. Pan, and L. H. Peng, Science 331, 1165 (2011). 9. S. Baker, I. A. Walmsley, J. W. G. Tisch, and J. P. Marangos, Nat. Photonics 5, 664 (2011). 10. A. V. Sokolov and S. E. Harris, J. Opt. B 5, R1 (2003). 11. T. Suzuki, N. Sawayama, and M. Katsuragawa, Opt. Lett. 33, 2809 (2008). 12. A. Nazarkin, A. Abdolvand, and P. St. J. Russell, Phys. Rev. A 79, 031805(R) (2009).