Mid-infrared frequency comb generation using a continuous-wave pumped optical parametric oscillator a,b
a
c
a
Markku Vainio* , Ville Ulvila , C.R. Phillips , Lauri Halonen a Laboratory of Physical Chemistry, Dept. of Chemistry, University of Helsinki, P.O. Box 55 (A.I. b Virtasen aukio 1), FI-00014 University of Helsinki, Finland; Centre for Metrology and c Accreditation (MIKES), P.O. Box 9, FI-02151 Espoo, Finland; ETH Zürich, Ultrafast Laser Physics, Wolfgang-Pauli-Strasse 16, 8093 Zürich, Switzerland ABSTRACT We report a mid-infrared frequency comb generator, which produces up to 3 W of output power. The comb mode spacing is 208 MHz, the spectral bandwidth is ~300 GHz, and the center wavelength is tunable between 3 and 3.4 µm. The comb generation is based on intracavity difference frequency mixing between near-infrared pump and signal beams of a continuous-wave-pumped optical parametric oscillator. The signal beam, which is resonant in the cavity, acquires a comb structure through cascading quadratic nonlinearities in a periodically poled lithium niobate crystal. This comb structure is transferred to the spectrum of the mid-infrared idler beam via the difference frequency mixing process. Keywords: Frequency comb, mid-infrared, optical parametric oscillator, cascading quadratic nonlinearities
1. INTRODUCTION Optical frequency combs (OFCs) are important tools in several fields of scientific research, including frequency metrology, calibration of astronomical spectra, and molecular spectroscopy. The spectrum of an optical frequency comb consists of a large number of discrete and equidistant lines. Multiple molecular absorption lines and species can hence be simultaneously measured using a frequency comb as a light source in spectroscopy. Both the detection sensitivity and speed can be significantly improved compared to conventional multispecies detection methods, such as Fourier transform infrared (FTIR) spectroscopy that uses incandescent lamp as a light source [1]. Wide-spread use of the frequency comb technology in applied spectroscopy, such as in environmental monitoring or medical diagnostics, has been precluded mainly for two reasons: (1) OFC sources based on mode-locked lasers are rather expensive and bulky instruments; (2) Mid-infrared region ( > 2.5 µm), which is the spectral region where most molecules have strong absorption bands, cannot be readily covered with mode-locked lasers [2]. Direct frequency comb generation in the mid-infrared has proven difficult, but several methods based on nonlinear frequency conversion have been developed [2]. One possibility is to transfer a visible/near-infrared OFC to the midinfrared region by difference frequency generation (DFG). The infrared combs generated by difference frequency mixing often suffer from low output power, although intracavity DFG has recently been used to produce a relatively high-power comb in the mid-infrared [3]. Another solution is to use a near-infrared OFC laser to synchronously pump an optical parametric oscillator, which produces an output beam at a longer wavelength [4-6]. A special case of this is degenerate OPO, which has the advantage of producing extremely stable and broad infrared spectrum – instantaneous spectral coverage of more than an octave has been reported [6]. Molecular spectroscopy with mid-infrared combs based on both DFG and synchronously pumped OPOs has been demonstrated [1, 7-9]. The search for a simple and inexpensive OFC generator has triggered research of continuous-wave pumped mid-infrared OFCs. Comb generators based on quantum cascade lasers have been reported [10], but mostly the research has focused on so-called Kerr combs based on optical microresonators. So far, it has proven difficult to produce Kerr combs at wavelengths longer than 2.5 m [11]. In this contribution, we present a new method for mid-infrared comb generation by a continuous-wave pumped parametric source: The source is based on a singly-resonant OPO, which is pumped by a commercially available cw Yb-fiber laser at 1064 nm. The resonant beam of the OPO, also typically in the near infrared, is spectrally broadened owing to cascading quadratic nonlinearities in a nonlinear crystal. These cascading quadratic nonlinearities mimic the third order optical nonlinearity, i.e., the method has some similarities to Kerr comb generation. *
[email protected];
However, the effective third order nonlinearity arising from the cascading quadratic effect can be extremely high, which makes comb generation possible in bulk systems, not just in microresonators. The generated near-infrared comb is transferred to the mid-infrared region by an intracavity DFG process, which is inherently phase-matched in the OPO. The advantages of this new method are high infrared output power, stable “lock-free” operation, and simple realization without the need for mode-locked lasers. In the following, we describe the new method, present the characterization of the generated mid-infrared OFC, and discuss the limitations and potential of the method.
2. EXPERIMENT 2.1 Method Our method for mid-infrared OFC generation is illustrated in Fig. 1. It can be divided in three parts: (1) A single-frequency cw laser at p near-infrared frequency is used to pump a singly-resonant OPO, which comprises a nonlinear crystal (PPLN 1) placed in an optical cavity. The cavity is formed by mirrors that are highly reflective for the resonant signal beam ( s) of the OPO. In addition to the near-infrared signal beam, the OPO produces a mid-infrared idler beam at frequency i = p – s. (2) The spectrum of the signal beam that resonates in the cavity is broadened by self-phase modulation (SPM), which is due to cascading quadratic nonlinearities provided by a second nonlinear crystal (PPLN 2) placed in the OPO cavity [12]. The broadened spectrum is a comb, i.e., it consists of equidistant modes. The mode separation is determined by the free spectral range of the cavity. (3) The generated frequency comb at the signal wavelength is transferred to the mid-infrared idler wavelength by difference frequency generation (DFG), where the signal comb modes mix with the pump laser beam. This mixing takes place in the OPO crystal (PPLN 1), and it obeys the same phase matching condition as the OPO process.
Figure 1. Principle of mid-infrared comb generation in the cw-pumped OPO. See text for details.
Cascading quadratic nonlinearity is provided by a nonlinear crystal, which is designed for phase-mismatched second harmonic generation of the signal beam that resonates in the OPO cavity. The effective third order nonlinearity, or casc nonlinear refractive index n 2 , arising from the cascading effect depends on the phase mismatch as [13]
n
casc 2
2 eff
4 d 1 2 k n n2 s
0
c
.
(1)
In this equation, k = ks – kshg – is the wave-vector mismatch, with ks and kshg being the wave vectors of the signal and its second harmonic wave, respectively. The poling period of the crystal is denoted by , deff is the second order nonlinear coefficient of the crystal, and n s and n shg are refractive indexes of the signal and its second harmonic wave. The
signal wavelength is denoted by respectively.
s,
and
0
and c are the vacuum permittivity and the speed of light in vacuum,
As can be seen from Eq. (1), both the sign and magnitude of the effective nonlinear refractive index, which leads to selfphase modulation of the signal wave at s, can be varied by varying the phase mismatch k. In practice, the magnitude casc of n2 can be several orders of magnitude larger than the natural third order nonlinearity of typical crystalline materials [13, 14]. For this reason, the cascading quadratic nonlinearity can lead to significant spectral broadening and comb generation even with bulk OPO cavities [12, 15], while the use of material’s inherent third order nonlinearity for (Kerr) comb generation requires the use of microresonators to reach high enough field intensity for spectral broadening to take place. 2.2 Experimental Setup The experimental setup used to realize the method described in paragraph 2.1 is outlined in Fig. 2. The singly-resonant OPO is pumped at 1064 nm by a cw Yb-fiber laser, which consists of a 21 W Yb-fiber amplifier (IPG Photonics YAR20K-1064-LP-SF) seeded by an Yb-fiber laser (NKT Photonics Koheras BasiK). The pump beam is focused into a 50mm long MgO-doped, periodically poled lithium niobate crystal (PPLN 1). The signal beam resonates in the OPO cavity, while the mid-infrared idler beam is coupled out after PPLN 1. The idler wavelength can be tuned between 3 and 3.4 µm by changing the poling period and/or temperature of PPLN 1. The corresponding signal wavelength range is approximately 1550 to 1650 nm. The tuning range is limited by the cavity mirrors and the poling periods ( = 31.0 µm and 31.5 µm) of the crystal. Another 50-mm long MgO-doped periodically poled lithium niobate crystal (PPLN 2) is placed in the other focus of the 2 symmetric OPO cavity. The 1/e -radius of the signal beam in the crystal is 50 m, corresponding to confocal focusing. Crystal PPLN 2 is designed for phase-mismatched intracavity second harmonic generation of the OPO signal beam. The o phase mismatch k can be adjusted by changing the crystal poling period (19.5-21.3 µm) and temperature (20-200 C). As indicated by Eq. (1), the effective nonlinear refractive index arising from the cascading quadratic nonlinearity casc -13 2 -1 changes accordingly. The calculated value of n2 is of the order of –2.1 × 10 cm W for the typical operating parameters that lead to efficient comb generation [12].
Figure 2. Schematic picture of the experimental setup for mid-infrared frequency comb generation.
3. RESULTS 3.1 Optical spectrum and tuning Figure 3a shows an example of a measured signal spectrum of the OPO under spectral broadening due to the cascading quadratic nonlinearities. This spectrum was measured with the following operating parameters: Pump power at 1064 nm: 21 W (~ 2 × OPO threshold); temperatures of PPLN 1 and PPLN 2: T1 = 75.0°C and T 2 = 120.4°C, respectively; poling periods of PPLN 1 and PPLN 2: 1 = 30.5 µm and 2 = 19.7 µm, respectively. These are the optimum conditions in terms of maximal spectral broadening of the signal beam in our current experimental system. However, we note that no 3 2 dispersion compensation has been applied. The dispersion due to the two crystals alone is approximately 11 × 10 fs , which is likely to limit spectral broadening. Introduction of dispersion compensating elements, other than dispersion compensating cavity mirrors is difficult due to the singly-resonant OPO structure. Operation closer to the zero-dispersion wavelength (~1920 nm) of bulk PPLN may provide a path to a wider spectrum. The optical spectrum around the OPO signal wavelength can be significantly varied by adjusting the phase mismatch k of second harmonic generation in PPLN 2, either by changing the crystal temperature or poling period. The spectrum also depends on the alignment of the OPO cavity. As an example, one can observe a spectrum that consists of several narrow combs, as indicated by Fig. 3b. In general, the observed spectra bear resemblance to those previously reported for microresonator Kerr combs [16-18]. We note that the observed spectra, as well as the average output power, are stable without any active stabilization of the OPO cavity length, pump power, etc.
Figure 3. Optical spectrum of the signal comb measured with two different sets of operating parameters: (a) T1 = 75.0°C, T 2 = 120.4°C, 1 = 30.5 µm 2 = 19.7 µm, pump power 21 W (pump depletion 50%), and (b) T 1 = 60°C, T2 = 60°C, 1 = 30.5 µm, 2 = 20.3 µm, pump power 12 W (pump depletion 90%).
An example of the mid-infrared spectrum of the OPO under the influence of cascading quadratic effect is shown in Fig. 4 for the same operating parameters as in the case of the signal spectrum of Fig. 3a. As expected, the mid-infrared 2 spectrum typically has a sinc shape. The width of the spectrum is limited by the phase matching bandwidth of DFG, and hence depends on the wavelength, as well as on the crystal length. At the short-wavelength end (3 m) of the idler tuning range the 3-dB width of the spectrum is ~ 500 GHz. Tuning of the mid-infrared center wavelength between 3 and 3.4 m is presented in Fig. 5. Tuning was done by changing the poling period and temperature of PPLN 1, and by subsequently optimizing the respective parameters of PPLN 2 for the broadest mid-infrared spectrum. In practice, the temperature of PPLN 2 can typically be varied by several degrees without significantly affecting the width of the comb spectrum.
2
Figure 4. Optical spectrum of the mid-infrared idler comb centered at 3051 nm. The red curve shows a sinc -fit to the measured data (black curve).
Figure 5. Tuning of the mid-infrared comb between 3 and 3.4 m. Tuning was done by changing the temperatures and poling periods of PPLN 1 and PPLN 2.
3.2 Radio-frequency spectrum The optical spectrum analyzers used to measure the optical spectra presented in Figs. 3-5 have insufficient resolution to resolve the underlying comb structure. The existence of the comb structure was therefore confirmed by measuring the radio frequency (RF) spectra. Fast enough mid-infrared photodetectors for such measurements are not readily available, so the idler beam was first frequency doubled in a 20-mm long MgO:PPLN crystal. The RF spectrum of the frequencydoubled mid-infrared idler beam was then measured with a fast InGaAs-photodiode connected to a 500-MHz bandwidth RF spectrum analyzer. The RF spectrum (Fig. 6 a) consists of beat notes at the mode spacing of the comb (207.5 MHz) and its multiples. This mode spacing corresponds to the free spectral range of the OPO cavity, as expected. Note that, owing to energy conservation in the DFG process, the mode spacing of the mid-infrared idler comb is the same that of the signal comb. As the idler beam is upconverted, second harmonic generation produces a peak separation twice the original mode spacing. However, in addition to second harmonic generation, the mid-infrared comb peaks mix with each other by sum frequency generation, hence filling the gaps and producing an upconverted comb with the original peak spacing. The -3 dB width of the RF beat notes of the upconverted comb is ~ 1 MHz, while mode-locked laser combs typically have intermode beat notes orders of magnitude narrower. The origin of the relatively broad beat note is unclear, but it is obvious that our cw-pumped OPO comb operates in a state which is not mode locked. In fact, the pulse envelope of the signal comb (Fig. 6 b), which was recorded with a fast photodiode and displayed on an oscilloscope, reveals a small modulation on top of a large cw background. This resembles the output of combs based on quantum cascade lasers [10]. Many microresonator-based comb generators also produce OFCs without generating short pulses [17-19]. Another phenomenon analogous to our observation is partial mode-locking of a solid state laser due to intracavity cascading quadratic effect [20]. The possibility of obtaining true mode-locked operation in our OPO – similar to what has been reported for microresonator Kerr combs [21] – is under investigation.
0.5
Photodiode signal (a.u.)
(b) 0.4
0.3
50 ns 0.2
0.1
0.0 0.0
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Figure 6. (a) The first RF beat note of the frequency-doubled idler comb. The -3 dB width of the beat note is 1.2 MHz. (b) Pulse envelope of the signal comb recorded with a fast (1 GHz bandwidth) photodiode. The inset shows a close-up of the signal.
3.3 Mid-infrared output power One of the advantages of the mid-infrared OFC generator reported here is the high output power. The OPO threshold is reached at 8 to 10 W of pump power at 1064 nm, and with the maximum available pump power of 21 W, we obtain an average mid-infrared power of up to 3.1 W. This corresponds to an average power of ~ 3 mW per mode of the comb. Both the total output power and the power per mode are the highest reported for a mid-infrared frequency comb [2-6, 10].
4. CONCLUSIONS In conclusion, we have reported a high-power mid-infrared optical frequency comb generator. The comb generator is based on cascading quadratic nonlinearities inside a cw-pumped OPO. Stable operation without any active locking or synchronization of the OPO cavity length, pump power, etc. is obtained. The cascading nonlinear effect generates a comb around the near-infrared signal beam, which resonates in the OPO. The generated comb is transferred to the midinfrared by DFG which is inherently phase-matched in the OPO. We have demonstrated tuning of the comb center wavelength between 3 and 3.4 m, with a maximum average output power of 3.1 W. Our future research will focus on improvement of the comb’s phase coherence and spectral coverage.
ACKNOWLEDGEMENTS We thank IPG Photonics for a generous loan of the fiber amplifier which made these experiments possible. We are grateful to the University of Helsinki and the Academy of Finland for funding the research reported here.
REFERENCES [1] Keilmann, F., Gohle, C. and Holzwarth, R., "Time-domain mid-infrared frequency-comb spectrometer," Optics Letters 29(13), 1542-1544 (2004). [2] Schliesser, A., Picqué N. and Hänsch, T.W., "Mid-infrared frequency combs," Nature Photonics 6, 440–449 (2012). [3] Galli, I., Cappelli, F., Cancio, P., Giusfredi, G., Mazzotti, D., Bartalini, S and De Natale, P., "High-coherence midinfrared frequency comb," Optics Express 21(23), 28877-28885 (2013). [4] Adler, F., Cossel, K. C., Thorpe, M. J., Hartl, I., Fermann, M. E. and Ye, J., "Phase-stabilized, 1.5 W frequency comb at 2.8–4.8 m," Optics Letters 34(9), 1330-1332 (2009). [5] Leindecker, N., Marandi, A., Byer, R. L. and Vodopyanov, K. L. "Broadband degenerate OPO for mid-infrared frequency comb generation," Opt. Express 19(7), 6296–6302 (2011). [6] Leindecker, N., Marandi, A., Byer, R. L., Vodopyanov, K. L., Jiang, J., Hartl, I., Fermann, M. and Schunemann, P. G., "Octave-spanning ultrafast OPO with 2.6-6.1µm instantaneous bandwidth pumped by femtosecond Tm-fiber laser," Optics Express 20(7), 7046-7053 (2012). [7] Baumann, E., Giorgetta, F. R., Swann, W. C., Zolot, A. M., Coddington, I. and Newbury, N. R., "Spectroscopy of the methane 3 band with an accurate midinfrared coherent dual-comb spectrometer," Phys. Rev. A 84(6), 062513 (2011). [8] Adler, F., Mas owski, P., Foltynowicz, A., Cossel, K. C., Briles, T. C., Hartl, I. and Ye, J., "Mid-infrared Fourier transform spectroscopy with a broadband frequency comb," Opt. Express 18(21), 21861–21872 (2010). [9] Haakestad, M. W., Lamour, T. P., Leindecker, N., Marandi, A. and Vodopyanov, K. L., "Intracavity trace molecular detection with a broadband mid-IR frequency comb source," JOSA B 30(3), 631-640 (2013). [10] Hugi, A., Villares, G., Blaser, S., Liu, H. C. and Faist, J., "Mid-infrared frequency comb based on a quantum cascade laser," Nature 492, 229–233 (2012). [11] Wang, C. Y., Herr, T., Del’Haye, P., Schliesser, A., Hofer, J., Holzwarth, R., Hänsch, T. W., Picqué, N. and Kippenberg, T. J., "Mid-infrared optical frequency combs at 2.5 m based on crystalline microresonators," Nat. Commun. 4, 1345–1348 (2013). [12] Ulvila, V., Phillips, C. R., Halonen, L. and Vainio, M., "Frequency comb generation by a continuous-wave-pumped optical parametric oscillator based on cascading quadratic nonlinearities," Optics Letters 38(21), 4281-4284 (2013). [13] Desalvo, R., Hagan, D. J., Sheikbahae, M., Stegeman, G., Vanstryland, E. W. and Vanherzeele, H., "Self-focusing and self-defocusing by cascaded second-order effects in KTP," Optics Letters 17(1), 28-30 (1992). [14] Ashihara, S., Shimura, T., Kuroda, K., Yu, N. E., Kurimura, S., Kitamura, K., Ro, J. H. and Cha, M., "Groupvelocity-matched cascaded quadratic nonlinearities of femtosecond pulses in periodically poled MgO:LiNbO 3" Optics Letters 28(16), 1442-1444 (2003). [15] Phillips, C. R., Langrock, C., Pelc, J. S., Fejer, M. M., Hartl, I. and Fermann, M. E., "Supercontinuum generation in quasi-phasematched waveguides," Optics Express 19(20), 18754-18773 (2011). [16] Grudinin, I. S., Yu, N. and Maleki, L., "Generation of optical frequency combs with a CaF2 resonator," Optics Letters 34(7), 878-880 (2009).
[17] Herr, T., Hartinger, K.., Riemensberger, J., Wang, C. Y., Gavartin, E., Holzwarth, R., Gorodetsky, M. L. and Kippenberg, T. J., "Universal formation dynamics and noise of Kerr-frequency combs in microresonators," Nature Photonics 6, 480–487 (2012). [18] Ferdous, F., Miao, H., Leaird, D. E., Srinivasan, K., Wang, J., Chen, L., Varghese, L. T. and Weiner, A. M., "Spectral line-by-line pulse shaping of on-chip microresonator frequency combs, "Nature Photonics 5(12), 770–776 (2011). [19] Papp, S. B., Del’Haye, P. and Diddams, S. A., "Self-injection locking and phase-locked states in microresonatorbased optical frequency combs," arXiv:1307.4091 (2013). [20] Zondy, J. J., Camargo, F. A., Zanon, T., Petrov, V. and Wetter, N. U., "Observation of strong cascaded Kerr-lens dynamics in an optimally-coupled cw intracavity frequency-doubled Nd:YLF ring laser," Optics Express 18, 47964815 (2010). [21] Herr, T., Brasch, V., Jost, J. D., Wang, C. Y., Kondratiev, N. M., Gorodetsky, M. L. and Kippenberg, T. J., "Modelocking in an optical microresonator via soliton formation," arXiv:1211.0733v2 (2013).
