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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 24 — Nov. 21, 2011
  • pp: 24298–24307
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Control of quantum pathways for the generation of continuous-wave Raman sidebands

Shin-ichi Zaitsu and Totaro Imasaka  »View Author Affiliations


Optics Express, Vol. 19, Issue 24, pp. 24298-24307 (2011)
http://dx.doi.org/10.1364/OE.19.024298


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Abstract

The generation of a multifrequency continuous-wave laser through stimulated Raman scattering and phase-matched four-wave mixing in a medium-filled optical cavity is demonstrated. Three different quantum pathways for the four-wave mixing, two of them degenerate and one of them nondegenerate, can be excited independently by tuning the intracavity dispersion. The results suggest that phase-matched Raman sidebands were generated on the longer wavelength side as well as on the shorter wavelength side, which can be used for the Fourier synthesis of a train of ultrashort optical pulses.

© 2011 OSA

1. Introduction

Nonlinear optical interactions rely on the phase-relationship between multiple laser fields coupled to each other through the strongly-driven nonlinear polarization of optical materials. A constant relationship between the phases of the nonlinear polarization and those of the laser fields substantially enhances the energy transfer from one beam to the others in the frequency conversion process; this is known as “phase-matching”. The phase-mismatch, Δk, is defined as the difference between wavevectors of the interacting laser fields, and the efficiency of the nonlinear optical interaction is maximized for Δk = 0. Unfortunately, perfect phase-matching is generally prevented by the chromatic dispersion of nonlinear optical materials that disturbs the phase-relationship during the propagation of the laser fields. To solve this problem, sophisticated techniques based on the use of birefringent crystalline materials [1

1. P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21–22 (1962). [CrossRef]

] and periodically-poled structures [2

2. N. Bloembergen and A. J. Sievers, “Nonlinear optical properties of periodic laminar structures,” Appl. Phys. Lett. 17, 483–486 (1970). [CrossRef]

] are widely used for efficient frequency conversions.

Meanwhile, for the use of isotropic nonlinear optical materials, such as gases, the anomalous dispersion of optical waveguides [3

3. C. G. Durfee III, St. Backus, M. M. Murnane, and H. C. Kapteyn, “Ultrabroadband phase-matched optical parametric generation in the ultraviolet by use of guided waves,” Opt. Lett. 22, 1565–1567 (1997). [CrossRef]

, 4

4. C. G. Durfee III, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high-order harmonics in hollow waveguides,” Phys. Rev. Lett. 83, 2187–2190 (1999). [CrossRef]

] and negative-dispersive optical cavities [5

5. S. Zaitsu, H. Izaki, and T. Imasaka, “Phase-matched Raman-resonant four-wave mixing in a dispersion-compensated high-finesse optical cavity,” Phys. Rev. Lett. 100, 073901 (2008). [CrossRef] [PubMed]

] can be utilized to improve the efficiency of the frequency conversion. In these methods, the phase-slip caused by the positive dispersion of nonlinear optical materials can be compensated for by the negative dispersion of an optical waveguide or an optical cavity, leading to the extension of the effective coherent length of the nonlinear optical interaction. The generation of deep-ultraviolet ultrashort pulses [3

3. C. G. Durfee III, St. Backus, M. M. Murnane, and H. C. Kapteyn, “Ultrabroadband phase-matched optical parametric generation in the ultraviolet by use of guided waves,” Opt. Lett. 22, 1565–1567 (1997). [CrossRef]

] and high-order harmonics [4

4. C. G. Durfee III, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high-order harmonics in hollow waveguides,” Phys. Rev. Lett. 83, 2187–2190 (1999). [CrossRef]

] was successfully demonstrated in filled hollow optical waveguides, and a phase-matched nonlinear optical interaction pumped by a low-power continuous wave (cw) was demonstrated in a dispersion-compensated high-finesse optical cavity [5

5. S. Zaitsu, H. Izaki, and T. Imasaka, “Phase-matched Raman-resonant four-wave mixing in a dispersion-compensated high-finesse optical cavity,” Phys. Rev. Lett. 100, 073901 (2008). [CrossRef] [PubMed]

].

To generate broadband radiation through these frequency conversion processes, a large-bandwidth dispersion-compensated region for the phase-matched interactions is required. In the case of frequency conversion using solid materials, noncollinear beam geometries allow us to increase the bandwidth for the phase-matching [6

6. A. Shirakawa and T. Kobayashi, “Noncollinearly phase-matched femtosecond optical parametric amplification with a 2000 cm−1 bandwidth,” Appl. Phys. Lett. 72, 147–149 (1998). [CrossRef]

9

9. J. L. Silva, R. Weigand, and H. M. Crespo, “Octave-spanning spectra and pulse synthesis by nondegenerate cascaded four-wave mixing,” Opt. Lett. 34, 2489–2492 (2009). [CrossRef] [PubMed]

]. For the use of isotropic gases as nonlinear optical materials, photonic bandgap crystal fibers are a promising tool for broadband frequency conversion [10

10. F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002). [CrossRef] [PubMed]

]. The control of the dispersive properties of hollow-core waveguides by altering the photonic bandgap structure [11

11. M. G. Welch, K. Cook, R. A. Correa, F. Gérôme, W. J. Wadsworth, A. V. Gorbach, D. V. Skryabin, and J. C. Knight, “Solitons in hollow core photonic crystal fiber: engineering nonlinearity and compressing pulse,” J. Lightwave Technol.27, 1644–1652 (2009). [CrossRef]

,12

12. T. Le, J. Bethge, J. Skibina, and G. Steinmeyer, “Hollow fiber for flexible sub-20-fs pulse deliver,” Opt. Lett. 36, 442–444 (2011). [CrossRef] [PubMed]

] has the potential to achieve broadband frequency conversion, but the bandwidth is still limited at this time. However, the progress in design schemes for negative dispersive mirrors associated with ultrafast laser technology pushes the limit of the tunability of the intracavity dispersion, leading to the generation of mode-locked ultrashort pulses with a bandwidth of greater than one octave [13

13. R. Ell, U. Morgner, F. X. Kärtner, J. G. Fujimoto, E. P. Ippen, V. Scheuer, G. Angelow, T. Tschudi, M. J. Lederer, A. Boiko, and B. Luther-Davies, “Generation of 5-fs pulses and octave-spanning spectra directly from a Ti:sapphire laser,” Opt. Lett. 26, 373–375 (2001). [CrossRef]

15

15. T. M. Fortier, D. J. Jones, and S. T. Cundiff, “Phase stabilization of an octave-spanning Ti:sapphire laser,” Opt. Lett. 28, 2198–2200 (2003). [CrossRef] [PubMed]

]. Therefore, the dispersion-compensated optical cavity is a promising candidate for the realization of the broadband frequency conversion through the phase-matched processes even when pumped by low-power cw lasers. Such frequency conversions will allow for molecular optical modulators [16

16. K. Ihara, C. Eshima, S. Zaitsu, S. Kamitomo, K. Shinzen, Y. Hirakawa, and T. Imasaka, “Molecular-optic modulator,” Appl. Phys. Lett. 88, 074101 (2006). [CrossRef]

, 17

17. J. T. Green, J. J. Weber, and D. D. Yavuz, “Continuous-wave light modulation at molecular frequencies,” Phys. Rev. A 82, 011805(R) (2010). [CrossRef]

] or molecular mode-locked lasers [18

18. K. Shinzen, Y. Hirakawa, and T. Imasaka, “Generation of highly repetitive optical pulses based on intracavity four-wave Raman mixing,” Phys. Rev. Lett. 87, 223901 (2001). [CrossRef] [PubMed]

] that operate at frequencies of more than 10 THz through the generation of a cw multifrequency laser.

In this paper, the frequency conversion from a single frequency laser into a broadband (∼52.8 THz) multifrequency laser in a high-finesse optical cavity is demonstrated. Broadband compensation of the dispersion of an optical cavity enables us to drive two types of cw-based four-wave mixing, coherent anti-Stokes Raman scattering and nondegenerate four-wave mixing, which involve four single-frequency emission lines. We found that the control of total intracavity dispersion allows us to differentiate the phase-matching conditions for three different pathways in the intracavity four-wave mixing processes. The results suggest that there is phase-matched generation of Raman sidebands on both the shorter and longer wavelength sides, which allows for the Fourier synthesis of a cw-based optical pulse train with an arbitrary waveform [19

19. H. Chan, Z. Hsieh, W. Liang, A. Kung, C. Lee, C. Lai, R. Pan, and L. Peng, “Synthesis and measurement of ultrafast waveforms from five discrete optical harmonics,” Science 331, 1165–1168 (2011). [CrossRef] [PubMed]

].

2. Theoretical background

Nonlinear optical interactions in gas-phase media are mainly based on the third-order susceptibility (χ(3)) because of its isotropic nature [20

20. Y. R. Shen, The Principle of Nonlinear Optics (Wiley-Interscience, 2003).

]. Herein, we focus on coherent anti-Stokes Raman scattering (CARS), which is a χ(3) effect, in a Raman-active gas-phase medium that has a Raman shift frequency of ΩR between three singe-frequency emissions at a pump emission, ω0, a Stokes emission, ω1, and an anti-Stokes emission, ω−1 (see Fig. 1(a)). The phase-mismatch, Δk of CARS is defined by the difference between the wavevectors, i.e. Δk = 2k0k1k−1, as shown in Fig. 1(b). The efficiency of the process is maximized for phase-matched conditions, i.e. Δk = 0. This Δk can be expressed using ΩR = ω0ω1 = ω−1ω0 and even-order dispersion coefficients, β2n [21

21. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001).

]:
Δk=m=2n2m!βmΩR.
(1)
Equation (1) indicates that the compensation of all the even-order dispersion of the medium satisfies the phase-matching condition for the CARS process. When the CARS process is driven in an optical cavity, three longitudinal modes spaced at the frequency of ΩR interact with each other through the χ(3)-response of the intracavity medium (see Fig. 1(c)). In this intracavity CARS, the phase-matching condition is satisfied when the separation frequencies between these three longitudinal modes are equal, i.e. Ω1 = Ω−1 in Fig. 1(c). Unfortunately, the frequency intervals between adjacent longitudinal modes, i.e. the free spectral range (FSR), of a medium-filled optical cavity are not constant as a function of the pump frequency because of the dispersion of the intracavity medium [22

22. P. A. Siegman, Lasers (University Science Books, 1986).

]. The frequency dependence of FSR, δΩ(ω), is calculated by the sum of the contributions of the dispersion given by the intracavity medium and the cavity mirrors:
δΩ(ω)=c2(Lng(ω)+cβmirror(ω)),
(2)
where c is the speed of light; ng is the group refractive index of the intracavity medium; L is the length of the optical cavity; and βmirror(ω) is the group delay given by one bounce of light on the surface of the cavity mirror. Using this δΩ(ω), the frequency intervals between longitudinal modes responsible for the CARS (Ωj, j = −1, 1) can be calculated by the following equation:
Ωj=N=N0NjδΩ(ωN),
(3)
where ωN is the frequency of the Nth longitudinal mode and Nj is the number of the longitudinal mode responsible for ωj, j = −1,0,1. The solid circles in Fig. 2(a) show the wavelength dependence of Ωj for an 8-cm-long Fabry-Perot-type optical cavity filled with hydrogen gas at a pressure of 750 kPa, calculated using Eq. (2) and (3) for βmirror(ω) = 0. These plots show that the large wavelength dependence of Ωj prevents the phase-matching in the CARS process. However, the use of cavity mirrors with negative dispersive properties enables us to compensate for the dependence of Ωj to satisfy the phase-matching condition of CARS in an optical cavity [5

5. S. Zaitsu, H. Izaki, and T. Imasaka, “Phase-matched Raman-resonant four-wave mixing in a dispersion-compensated high-finesse optical cavity,” Phys. Rev. Lett. 100, 073901 (2008). [CrossRef] [PubMed]

]. Figure 2(b) shows the wavelength dependence of group delay dispersion (GDD) for a mirror with a negative value of GDD from 740 nm to 950 nm, which was used in the following experiment.

Fig. 1 (a) Energy diagram for coherent anti-Stokes Raman scattering (CARS). ω0, ω1, and ω−1 are the pump emission, Stokes emission, and anti-Stokes emission, respectively. (b) Phase-mismatch, Δk, for CARS shown in (a). k0, k1, and k−1 are wavevectors for ω0, ω1, and ω−1, respectively. (c) Longitudinal modes responsible for the intracavity CARS.
Fig. 2 Dependence of the frequency intervals between the longitudinal modes for ω0 and ω1. The solid circles and the solid squares are calculated for an 8-cm-long optical cavity consisting of non-dispersive mirrors and negative dispersive mirrors (NDMs) having a property shown in (b), respectively. Both cavities are filled with hydrogen gas at 750 kPa. ΩR is the Raman shift frequency of hydrogen, which is assumed to be 17594.79 GHz in this calculation. (b) Wavelength dependence of the group delay dispersion of the NDM used in this experiment. (c) The pressures for the phase-matching condition, Ω−1 = Ω1, as a function of a wavelength of the pump emission.

The solid squares in Fig. 2(a) represent the dependence of Ωj on the pump wavelength for the use of a pair of these negative dispersive mirrors (NDMs) as cavity components under the same conditions as for the solid circles in Fig. 2(a). These plots indicate that the compensation of the positive dispersion of the hydrogen gas by the negative dispersion of the cavity mirrors reduces the dependence of Ωj. Figure 2(c) shows the pressures that satisfy Ω1 = Ω−1, i.e. the phase-matching condition, as a function of wavelength when the negative dispersive cavity mentioned above is used. This indicates that the phase-matching condition for CARS in the dispersion-compensated optical cavity can be found from 700 kPa to 900 kPa in the wavelength range from 785 nm to 800 nm.

Fig. 3 (a) Longitudinal modes responsible for the intracavity four-wave mixing (FWM) including four emission lines. (b–d) Relationship between longitudinal modes and energy diagrams for FWM processes: (b) the pump frequency of ω1 is degenerate, (c) ω0 is degenerate, and (d) nondegenerate FWM including all four emission lines. (e) Dependence of the frequency intervals, Ωj (j = −1,1,2) shown in (a) calculated for an 8-cm-long optical cavity, consisting of the NDMs used in this experiment, filled with hydrogen gas at a pressure of 750 kPa.

3. Experimental setup

Fig. 4 Schematics of the experimental setup. The high-finesse optical cavity is installed in a stainless-steel chamber equipped with silica windows on both input and output side. The mode-matching lenses (ML) consist of a beam expander (×2.5) and a lens with f = 800 mm. The measuring system includes a beam profiler, a power meter, a spectrometer, and a photo detector. Operating parameters of the cw Ti:sapphire laser and properties of the negative dispersive mirrors are described in text.

4. Results and discussions

Figures 5(a) and (b) show the spectra measured for the two different situations that allowed us to generate four emission lines at the maximum output power (∼50 mW): the first anti-Stokes emission (ω−1), the fundamental emission (ω0), the first Stokes emission (ω1), and the second Stokes emission (ω2). The frequency of ω0 and the hydrogen pressures in the cavity for obtaining these spectra are shown in the inset of the figures. Figures 5(c) and (d) show the dependence of the intensities of ω−1, ω1, and ω2 as a function of the total output power measured for Figs. 5(a) and (b), respectively. Note that there is a difference between the thresholds for the generation of the emission lines. In Fig. 5(c), the threshold for the generation of ω−1 coincides with that of ω1 at 15 mW. The threshold for the generation of ω2 (30 mW) is larger than this value. However, in Fig. 5(d), the threshold for the generation of ω−1 corresponds to that of ω2 at 20 mW. The threshold for the generation of ω1 (8 mW) is substantially lower than this value. From Figs. 3(b–d), it can be seen that FWM is a process that generates two photons at the frequencies of the sidebands at the expense of two photons at the fundamental frequency (or frequencies). This leads to the identical thresholds for the generation of the sidebands through the FWM process. Therefore, the coincidence of the thresholds of ω−1 and ω1 in Fig. 5(c) suggests that ω−1 was generated through a CARS process that satisfies the phase-matching condition, Δk0 = 2k0k1k−1 = 0 (Fig. 2(c)). In this case, ω2 was generated thorough cascaded SRS using ω1 as a pump frequency. On the other hand, in the case of the FWM shown in Figs. 5(b) and (d), ω1 was first generated through SRS from ω0 at 8 mW. Then, the photons of ω−1 and ω2 were generated at 20 mW at the expense of the photons of ω0 and ω1 because the phase-matching condition of NDFWM, Δk0 = k0 + k1k−1k2 = 0, was satisfied at this fundamental wavelength (800.380 nm) and intracavity pressure (819 kPa). This is the first demonstration of phase-matched NDFWM in an optical cavity driven by a cw laser. In addition, we showed that the dispersion in the optical cavity determined the pathway for the frequency conversion based on χ(3) nonlinearity.

Fig. 5 (a) and (b) Spectra measured at a pump wavelength of 802.337 nm and an intracavity hydrogen pressure of 805 kPa, and at a pump wavelength of 800.380 nm and an intracavity hydrogen pressure of 819 kPa, respectively. (c) and (d) Evolution of intensities of ω−1, ω1, and ω2 as a function of the total output power measured under the conditions for (a) and (b), respectively.

It was also found that the phase-matching for FWM affected the cascaded SRS for the generation of the high-order Stokes emission in the longer wavelength side. When the pump wavelength was set at 800.355 nm, different behaviors for the generation of ω2 were observed at different intracavity pressures. Figures 6(a) and (b) show the spectra of the cavity output beam measured at intracavity pressures of 787 kPa and 800 kPa, respectively. Although these two spectra are similar, the thresholds for the generation of ω2 shown in Figs. 6(c) and (d) are different. Fig. 6(c) shows the typical situation for cw-based cascade SRS in an optical cavity [24

24. S. Zaitsu and T. Imasaka, “Continuous-wave multifrequency laser emission generated through stimulated Raman scattering and four-wave Raman mixing in an optical cavity,” IEEE J. Quantum Electron. 47, 1129–1135 (2011). [CrossRef]

], in which the threshold for the generation of ω2 (20 mW) is larger than that of ω1 (10 mW). On the other hand, Fig. 6(d) shows that ω2 was first generated at 10 mW, which exactly coincides with the generation threshold of ω1. Because SRS does not need to satisfy the phase-matching conditions, the threshold power for the Stokes emission through intracavity SRS is determined by the ratio between the Raman gain and the cavity loss, which are independent of the material dispersion [25

25. K. S. Repasky, J. K. Brasseur, L. Meng, and J. L. Carlsten, “Performance and design of an off-resonant continuous-wave Raman Laser,” J. Opt. Soc. Am. B 15, 1667–1673 (1998). [CrossRef]

]. However, FWM affects SRS through Stoke-anti-Stokes coupling for these phase-matching conditions [26

26. R. W. Boyd, Nonlinear Optics (Academic Press, 2003).

]. The coincidence between the thresholds for ω1 and ω2 suggests that the phase-matching condition of FWM, Δk = 2k1k2k0 (Fig. 3(b)) was satisfied at a pressure of 800 kPa, and hence ω2 was generated through both the cascade SRS and the phase-matched FWM. With regard to the synthesis of optical pulses, constant frequency intervals are essential for forming a periodical optical pulse train. Raman sidebands generated by SRS in the longer wavelength side can not contribute to the formation of an optical pulse train because of the wavelength variation in the bandwidth of SRS gain [23

23. S. Zaitsu, C. Eshima, K. Ihara, and T. Imasaka, “Generation of a continuous-wave pulse train at a repetition rate of 17.6 THz,” J. Opt. Soc. Am. B 24, 1037–1041 (2007). [CrossRef]

]. On the other hand, the sidebands generated through parametric FWM process, as shown in Fig. 6(b), can be equally spaced because of the conservation of energy in the frequency conversion process, i.e., ω0ω1 = ω1ω2 [27

27. T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011). [CrossRef] [PubMed]

]. This implies that the Raman sidebands measured in Fig. 6(b) are allowed to contribute to the formation of a periodical optical pulse, which should be experimentally demonstrated in the future work by measuring the stability of the waveform synthesized by such phase-locked Raman sidebands.

Fig. 6 (a) and (b) Spectra measured at a pump wavelength of 800.355 nm at an intracavity hydrogen pressure of 787 kPa and 800 kPa, respectively. (c) and (d) Evolution of intensities of ω1 and ω2 as a function of the total output power measured for the conditions for (a) and (b), respectively.

5. Conclusion

In this paper, we demonstrated the generation of four lines of a single transverse/longitudinal emission via intracavity SRS and phase-matched FWM based on a cw laser. These emission lines arose from two types of pathways: (1) CARS and subsequent SRS, and (2) SRS and subsequent NDFWM. The specific pathway of the intracavity SRS/FWM that occurred depended on the intracavity dispersion to satisfy the phase-matching conditions for each pathway. We also found that the second-order Stokes emission in the SRS process had the same threshold as that of the first-order Stokes emission when the intracavity dispersion was adjusted to a value that satisfies the phase-matching condition of FWM. This suggests that the phase-matched FWM contributed to the generation of the Raman sidebands on both the longer wavelength side and the shorter wavelength side. By synthesizing multiple single-frequency emission lines, these results may lead to the generation of a phase-locked multifrequency cw laser. Subsequently, this system may be used to create a train of optical pulses with a repetition rate of more than 10 THz or an arbitrary waveform.

Acknowledgments

This research was supported by the PRESTO program from the Japan Science and Technology Agency (JST), Grants-in-Aid for Scientific Research, and the Global COE Program, ”Science for Future Molecular Systems,” of the Ministry of Education, Culture, Sports, Science and Technology of Japan.

References and links

1.

P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21–22 (1962). [CrossRef]

2.

N. Bloembergen and A. J. Sievers, “Nonlinear optical properties of periodic laminar structures,” Appl. Phys. Lett. 17, 483–486 (1970). [CrossRef]

3.

C. G. Durfee III, St. Backus, M. M. Murnane, and H. C. Kapteyn, “Ultrabroadband phase-matched optical parametric generation in the ultraviolet by use of guided waves,” Opt. Lett. 22, 1565–1567 (1997). [CrossRef]

4.

C. G. Durfee III, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high-order harmonics in hollow waveguides,” Phys. Rev. Lett. 83, 2187–2190 (1999). [CrossRef]

5.

S. Zaitsu, H. Izaki, and T. Imasaka, “Phase-matched Raman-resonant four-wave mixing in a dispersion-compensated high-finesse optical cavity,” Phys. Rev. Lett. 100, 073901 (2008). [CrossRef] [PubMed]

6.

A. Shirakawa and T. Kobayashi, “Noncollinearly phase-matched femtosecond optical parametric amplification with a 2000 cm−1 bandwidth,” Appl. Phys. Lett. 72, 147–149 (1998). [CrossRef]

7.

M. Zhi and A. V. Sokolov, “Broadband coherent light generation in a Raman active crystal driven by two-color femtosecond laser pulses,” Opt. Lett. 32, 2251–2253 (2007). [CrossRef] [PubMed]

8.

J. Liu and T Kobayashi, “Cascaded four-wave mixing and multicolored arrays generation in a sapphire plate by using two crossing beams of femtosecond laser,” Opt. Express 16, 22119–22125 (2008). [CrossRef] [PubMed]

9.

J. L. Silva, R. Weigand, and H. M. Crespo, “Octave-spanning spectra and pulse synthesis by nondegenerate cascaded four-wave mixing,” Opt. Lett. 34, 2489–2492 (2009). [CrossRef] [PubMed]

10.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002). [CrossRef] [PubMed]

11.

M. G. Welch, K. Cook, R. A. Correa, F. Gérôme, W. J. Wadsworth, A. V. Gorbach, D. V. Skryabin, and J. C. Knight, “Solitons in hollow core photonic crystal fiber: engineering nonlinearity and compressing pulse,” J. Lightwave Technol.27, 1644–1652 (2009). [CrossRef]

12.

T. Le, J. Bethge, J. Skibina, and G. Steinmeyer, “Hollow fiber for flexible sub-20-fs pulse deliver,” Opt. Lett. 36, 442–444 (2011). [CrossRef] [PubMed]

13.

R. Ell, U. Morgner, F. X. Kärtner, J. G. Fujimoto, E. P. Ippen, V. Scheuer, G. Angelow, T. Tschudi, M. J. Lederer, A. Boiko, and B. Luther-Davies, “Generation of 5-fs pulses and octave-spanning spectra directly from a Ti:sapphire laser,” Opt. Lett. 26, 373–375 (2001). [CrossRef]

14.

A. Bartels and H. Kurz, “Generation of a broadband continuum by a Ti:sapphire femtosecond oscillator with a 1-GHz repetition rate,” Opt. Lett. 27, 1839–1841 (2002). [CrossRef]

15.

T. M. Fortier, D. J. Jones, and S. T. Cundiff, “Phase stabilization of an octave-spanning Ti:sapphire laser,” Opt. Lett. 28, 2198–2200 (2003). [CrossRef] [PubMed]

16.

K. Ihara, C. Eshima, S. Zaitsu, S. Kamitomo, K. Shinzen, Y. Hirakawa, and T. Imasaka, “Molecular-optic modulator,” Appl. Phys. Lett. 88, 074101 (2006). [CrossRef]

17.

J. T. Green, J. J. Weber, and D. D. Yavuz, “Continuous-wave light modulation at molecular frequencies,” Phys. Rev. A 82, 011805(R) (2010). [CrossRef]

18.

K. Shinzen, Y. Hirakawa, and T. Imasaka, “Generation of highly repetitive optical pulses based on intracavity four-wave Raman mixing,” Phys. Rev. Lett. 87, 223901 (2001). [CrossRef] [PubMed]

19.

H. Chan, Z. Hsieh, W. Liang, A. Kung, C. Lee, C. Lai, R. Pan, and L. Peng, “Synthesis and measurement of ultrafast waveforms from five discrete optical harmonics,” Science 331, 1165–1168 (2011). [CrossRef] [PubMed]

20.

Y. R. Shen, The Principle of Nonlinear Optics (Wiley-Interscience, 2003).

21.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001).

22.

P. A. Siegman, Lasers (University Science Books, 1986).

23.

S. Zaitsu, C. Eshima, K. Ihara, and T. Imasaka, “Generation of a continuous-wave pulse train at a repetition rate of 17.6 THz,” J. Opt. Soc. Am. B 24, 1037–1041 (2007). [CrossRef]

24.

S. Zaitsu and T. Imasaka, “Continuous-wave multifrequency laser emission generated through stimulated Raman scattering and four-wave Raman mixing in an optical cavity,” IEEE J. Quantum Electron. 47, 1129–1135 (2011). [CrossRef]

25.

K. S. Repasky, J. K. Brasseur, L. Meng, and J. L. Carlsten, “Performance and design of an off-resonant continuous-wave Raman Laser,” J. Opt. Soc. Am. B 15, 1667–1673 (1998). [CrossRef]

26.

R. W. Boyd, Nonlinear Optics (Academic Press, 2003).

27.

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011). [CrossRef] [PubMed]

OCIS Codes
(140.3550) Lasers and laser optics : Lasers, Raman
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(230.5750) Optical devices : Resonators
(290.5910) Scattering : Scattering, stimulated Raman

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: June 21, 2011
Revised Manuscript: October 12, 2011
Manuscript Accepted: October 13, 2011
Published: November 14, 2011

Citation
Shin-ichi Zaitsu and Totaro Imasaka, "Control of quantum pathways for the generation of continuous-wave Raman sidebands," Opt. Express 19, 24298-24307 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-24-24298


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References

  1. P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett.8, 21–22 (1962). [CrossRef]
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