November 1, 2013 / Vol. 38, No. 21 / OPTICS LETTERS
4281
Frequency comb generation by a continuous-wavepumped optical parametric oscillator based on cascading quadratic nonlinearities Ville Ulvila,1 C. R. Phillips,2 Lauri Halonen,1 and Markku Vainio1,3,* 1
Laboratory of Physical Chemistry, Department of Chemistry, P.O. Box 55 (A.I. Virtasen aukio 1), FI-00014 University of Helsinki, Finland 2 ETH Zürich, Ultrafast Laser Physics, Wolfgang-Pauli-Strasse 16, 8093 Zürich, Switzerland 3
Centre for Metrology and Accreditation, P.O. Box 9, FIN-02151 Espoo, Finland *Corresponding author: [email protected]
Received August 16, 2013; revised September 19, 2013; accepted September 20, 2013; posted September 20, 2013 (Doc. ID 195935); published October 17, 2013 We report optical frequency comb generation by a continuous-wave pumped optical parametric oscillator (OPO) without any active modulation. The OPO is configured as singly resonant with an additional nonlinear crystal (periodically poled MgO:LiNbO3 ) placed inside the OPO for phase mismatched second harmonic generation (SHG) of the resonating signal beam. The phase mismatched SHG causes cascading χ 2 nonlinearities, which can substantially increase the effective χ 3 nonlinearity in MgO:LiNbO3 , leading to spectral broadening of the OPO signal beam via self-phase modulation. The OPO generates a stable 4 THz wide (−30 dB) frequency comb centered at 1.56 μm. © 2013 Optical Society of America OCIS codes: (190.4970) Parametric oscillators and amplifiers; (190.5940) Self-action effects; (190.4360) Nonlinear optics, devices; (190.4223) Nonlinear wave mixing. http://dx.doi.org/10.1364/OL.38.004281
An optical frequency comb (OFC), that is, coherent broadband light that has a spectrum consisting of many equidistant discrete lines, has become a valuable tool in many research areas, such as time and frequency metrology and molecular spectroscopy. Mode-locking of lasers is the most common method used to generate OFC [1]. Other methods include phase-modulated Fabry–Perot cavities [2], and optical microresonators [3]. Octave spanning frequency comb generation [4] and mode-locking [5,6] have recently been demonstrated with such microresonators. Optical parametric oscillators (OPOs) offer an attractive solution for OFC generation due to their easy tunability, large tuning range, power scalability, and access to the mid-infrared region while using near-infrared pump lasers that are readily available. Intracavity modulated OPOs and synchronously pumped OPOs have previously been used to generate OFCs [7,8] and to convert output of the mode-locked lasers to different wavelength regions [9], respectively. While these existing approaches require active modulation, synchronous pumping, or control of the OPO cavity, a passive solution would be simpler and thus preferable—in the same manner as passively mode-locked lasers are in many cases preferred to actively mode-locked lasers. Frequency comb generation in the optical microresonators is usually explained by the Kerr effect [3], which originates from the third-order nonlinearity χ 3 and the related nonlinear refractive index n2 . This χ 3 is the lowest-order nonlinearity in materials that possess inversion symmetry, i.e., materials from which optical microresonators are usually constructed. Typical values of n2 for materials used in microresonators are in the order of 10−15 –10−16 cm2 W−1 [10]. OFC generation by continuous-wave-pumped (CW-pumped) OPOs (without active modulation) has remained challenging until now due to the low n2 values associated with typical OPO crystals 0146-9592/13/214281-04$15.00/0
(e.g., LiNbO3 ), combined with the use of bulk resonators instead of microresonators. Also, traditional modelocking with saturable absorbers used in passively mode-locked lasers is difficult to implement with CWpumped OPOs [11] since there is no pump energy storage in the OPO cavity. Here we show that OFC generation is possible in bulk OPO cavities and can be explained via the extremely large nonlinear refractive index, which can be obtained from a cascading χ 2 effect. Reviews of the cascading effect can be found in [12,13]. The key to this cascading χ 2 effect is to have phase mismatched second harmonic generation (SHG) of the fundamental wave. A simplified explanation to this effect is as follows: part of the fundamental wave is converted to the second harmonic wave, but because the process is phase mismatched, the second harmonic wave is soon converted back to the fundamental wave. In this process, the back-converted fundamental wave acquires a phase difference to the original, unconverted fundamental wave, owing to the different phase velocity of the second harmonic wave. The nonlinear refractive index ncasc originating from 2 the cascading χ 2 effect can be approximated by [14]: − ncasc 2
1 4πd2eff ; Δk n2ω n2ω λε0 c
(1)
where deff is the effective second-order nonlinear coefficient, Δk k2ω − 2kω − 2πΛ−1 is the wave-vector mismatch, nω and λ are the refractive index and wavelength at the fundamental frequency, respectively, and n2ω is the refractive index at the second harmonic frequency. The quantity Λ is the poling period of a quasi-phase matched nonlinear crystal, ε0 and c are the vacuum permittivity and the speed of light in vacuum, respectively. From Eq. (1), it can be seen that the magnitude and sign of ncasc can be varied by varying the magnitude and sign 2 © 2013 Optical Society of America
4282
OPTICS LETTERS / Vol. 38, No. 21 / November 1, 2013
of Δk. It is worth noting that Eq. (1) is valid only until the second harmonic conversion efficiency becomes significant or, in the case of a frequency comb, components of the comb spectrum approach phase-matching due to the frequency-dependence of the phase mismatch [14,15]. The wave-vector mismatch Δk can be varied by changing, e.g., the temperature or poling period of the nonlinear crystals. Including contributions from the cascading and the normal nonlinear refractive index, effective nonlinear refractive index of −2.9 × 10−14 to 3.3 × 10−14 cm2 W−1 have been reported by tuning the phase-mismatch in periodically poled MgO:LiNbO3 (PPLN) [15]. If available, such highly nonlinear response enables substantial selfphase modulation during a single round-trip in the OPO cavity, potentially leading to OFC generation. The cascaded quadratic nonlinearities have been utilized in supercontinuum generation in PPLN waveguides [16] and theoretically investigated in the context of OFC generation in microresonators [17]. In the following, we describe the first experimental demonstration of OFC generation based on this approach. In our experimental setup, two 50 mm long periodically poled MgO:LiNbO3 nonlinear crystals (PPLN1 and PPLN2, HC Photonics) are placed inside an optical bow-tie ring cavity (Fig. 1). The PPLN1 crystal is pumped at λp 1.064 μm with a narrow-linewidth high-power laser (IPG Photonics Yb-fiber amplifier YAR-15K-1064LP-SF or YAR-20K-1064-LP-SF seeded with a distributed feedback diode laser) and it produces two singlefrequency beams, the signal and the idler (1∕λp 1∕λs 1∕λi , where λp , λs , and λi are the wavelengths of the pump, signal, and idler, respectively). In the experiments reported here, the PPLN1 poling period and temperature were Λ1 30.5 μm and 60°C, respectively. This gives signal wavelength λs ∼ 1.56 μm and idler wavelength λi ∼ 3.35 μm. The cavity mirrors are highly reflective only for the signal wavelength, so without PPLN2, the OPO would be a normal continuous-wave singly resonant OPO, similar to that described for example in [18]. The 1∕e2 waist sizes of the resonating signal beam in the crystals were designed to be 55 μm. We made no attempt to compensate the dispersion of the mirrors or the crystals. The dispersion accumulated by the signal beam in a single round trip due to the crystals alone is ∼11 × 103 fs2 . Frequency comb generation is enabled via the cascading χ 2 effect, which occurs in PPLN2. The poling period of PPLN2 is Λ2 19.7 μm and the temperature (T 2 ) of
the crystal can be tuned from room temperature to 200°C. This period provides phase mismatched SHG for the resonating signal beam, while perfect phase matching is achieved with Λ2 19.5 μm and T 2 ∼ 65–70°C. The generated second harmonic power and a small fraction (
4281
Frequency comb generation by a continuous-wavepumped optical parametric oscillator based on cascading quadratic nonlinearities Ville Ulvila,1 C. R. Phillips,2 Lauri Halonen,1 and Markku Vainio1,3,* 1
Laboratory of Physical Chemistry, Department of Chemistry, P.O. Box 55 (A.I. Virtasen aukio 1), FI-00014 University of Helsinki, Finland 2 ETH Zürich, Ultrafast Laser Physics, Wolfgang-Pauli-Strasse 16, 8093 Zürich, Switzerland 3
Centre for Metrology and Accreditation, P.O. Box 9, FIN-02151 Espoo, Finland *Corresponding author: [email protected]
Received August 16, 2013; revised September 19, 2013; accepted September 20, 2013; posted September 20, 2013 (Doc. ID 195935); published October 17, 2013 We report optical frequency comb generation by a continuous-wave pumped optical parametric oscillator (OPO) without any active modulation. The OPO is configured as singly resonant with an additional nonlinear crystal (periodically poled MgO:LiNbO3 ) placed inside the OPO for phase mismatched second harmonic generation (SHG) of the resonating signal beam. The phase mismatched SHG causes cascading χ 2 nonlinearities, which can substantially increase the effective χ 3 nonlinearity in MgO:LiNbO3 , leading to spectral broadening of the OPO signal beam via self-phase modulation. The OPO generates a stable 4 THz wide (−30 dB) frequency comb centered at 1.56 μm. © 2013 Optical Society of America OCIS codes: (190.4970) Parametric oscillators and amplifiers; (190.5940) Self-action effects; (190.4360) Nonlinear optics, devices; (190.4223) Nonlinear wave mixing. http://dx.doi.org/10.1364/OL.38.004281
An optical frequency comb (OFC), that is, coherent broadband light that has a spectrum consisting of many equidistant discrete lines, has become a valuable tool in many research areas, such as time and frequency metrology and molecular spectroscopy. Mode-locking of lasers is the most common method used to generate OFC [1]. Other methods include phase-modulated Fabry–Perot cavities [2], and optical microresonators [3]. Octave spanning frequency comb generation [4] and mode-locking [5,6] have recently been demonstrated with such microresonators. Optical parametric oscillators (OPOs) offer an attractive solution for OFC generation due to their easy tunability, large tuning range, power scalability, and access to the mid-infrared region while using near-infrared pump lasers that are readily available. Intracavity modulated OPOs and synchronously pumped OPOs have previously been used to generate OFCs [7,8] and to convert output of the mode-locked lasers to different wavelength regions [9], respectively. While these existing approaches require active modulation, synchronous pumping, or control of the OPO cavity, a passive solution would be simpler and thus preferable—in the same manner as passively mode-locked lasers are in many cases preferred to actively mode-locked lasers. Frequency comb generation in the optical microresonators is usually explained by the Kerr effect [3], which originates from the third-order nonlinearity χ 3 and the related nonlinear refractive index n2 . This χ 3 is the lowest-order nonlinearity in materials that possess inversion symmetry, i.e., materials from which optical microresonators are usually constructed. Typical values of n2 for materials used in microresonators are in the order of 10−15 –10−16 cm2 W−1 [10]. OFC generation by continuous-wave-pumped (CW-pumped) OPOs (without active modulation) has remained challenging until now due to the low n2 values associated with typical OPO crystals 0146-9592/13/214281-04$15.00/0
(e.g., LiNbO3 ), combined with the use of bulk resonators instead of microresonators. Also, traditional modelocking with saturable absorbers used in passively mode-locked lasers is difficult to implement with CWpumped OPOs [11] since there is no pump energy storage in the OPO cavity. Here we show that OFC generation is possible in bulk OPO cavities and can be explained via the extremely large nonlinear refractive index, which can be obtained from a cascading χ 2 effect. Reviews of the cascading effect can be found in [12,13]. The key to this cascading χ 2 effect is to have phase mismatched second harmonic generation (SHG) of the fundamental wave. A simplified explanation to this effect is as follows: part of the fundamental wave is converted to the second harmonic wave, but because the process is phase mismatched, the second harmonic wave is soon converted back to the fundamental wave. In this process, the back-converted fundamental wave acquires a phase difference to the original, unconverted fundamental wave, owing to the different phase velocity of the second harmonic wave. The nonlinear refractive index ncasc originating from 2 the cascading χ 2 effect can be approximated by [14]: − ncasc 2
1 4πd2eff ; Δk n2ω n2ω λε0 c
(1)
where deff is the effective second-order nonlinear coefficient, Δk k2ω − 2kω − 2πΛ−1 is the wave-vector mismatch, nω and λ are the refractive index and wavelength at the fundamental frequency, respectively, and n2ω is the refractive index at the second harmonic frequency. The quantity Λ is the poling period of a quasi-phase matched nonlinear crystal, ε0 and c are the vacuum permittivity and the speed of light in vacuum, respectively. From Eq. (1), it can be seen that the magnitude and sign of ncasc can be varied by varying the magnitude and sign 2 © 2013 Optical Society of America
4282
OPTICS LETTERS / Vol. 38, No. 21 / November 1, 2013
of Δk. It is worth noting that Eq. (1) is valid only until the second harmonic conversion efficiency becomes significant or, in the case of a frequency comb, components of the comb spectrum approach phase-matching due to the frequency-dependence of the phase mismatch [14,15]. The wave-vector mismatch Δk can be varied by changing, e.g., the temperature or poling period of the nonlinear crystals. Including contributions from the cascading and the normal nonlinear refractive index, effective nonlinear refractive index of −2.9 × 10−14 to 3.3 × 10−14 cm2 W−1 have been reported by tuning the phase-mismatch in periodically poled MgO:LiNbO3 (PPLN) [15]. If available, such highly nonlinear response enables substantial selfphase modulation during a single round-trip in the OPO cavity, potentially leading to OFC generation. The cascaded quadratic nonlinearities have been utilized in supercontinuum generation in PPLN waveguides [16] and theoretically investigated in the context of OFC generation in microresonators [17]. In the following, we describe the first experimental demonstration of OFC generation based on this approach. In our experimental setup, two 50 mm long periodically poled MgO:LiNbO3 nonlinear crystals (PPLN1 and PPLN2, HC Photonics) are placed inside an optical bow-tie ring cavity (Fig. 1). The PPLN1 crystal is pumped at λp 1.064 μm with a narrow-linewidth high-power laser (IPG Photonics Yb-fiber amplifier YAR-15K-1064LP-SF or YAR-20K-1064-LP-SF seeded with a distributed feedback diode laser) and it produces two singlefrequency beams, the signal and the idler (1∕λp 1∕λs 1∕λi , where λp , λs , and λi are the wavelengths of the pump, signal, and idler, respectively). In the experiments reported here, the PPLN1 poling period and temperature were Λ1 30.5 μm and 60°C, respectively. This gives signal wavelength λs ∼ 1.56 μm and idler wavelength λi ∼ 3.35 μm. The cavity mirrors are highly reflective only for the signal wavelength, so without PPLN2, the OPO would be a normal continuous-wave singly resonant OPO, similar to that described for example in [18]. The 1∕e2 waist sizes of the resonating signal beam in the crystals were designed to be 55 μm. We made no attempt to compensate the dispersion of the mirrors or the crystals. The dispersion accumulated by the signal beam in a single round trip due to the crystals alone is ∼11 × 103 fs2 . Frequency comb generation is enabled via the cascading χ 2 effect, which occurs in PPLN2. The poling period of PPLN2 is Λ2 19.7 μm and the temperature (T 2 ) of
the crystal can be tuned from room temperature to 200°C. This period provides phase mismatched SHG for the resonating signal beam, while perfect phase matching is achieved with Λ2 19.5 μm and T 2 ∼ 65–70°C. The generated second harmonic power and a small fraction (
