Abstract

When a laser pump beam of sufficient intensity is incident on a Raman-active medium such as hydrogen gas, a strong Stokes signal, redshifted by the Raman transition frequency ΩR, is generated. This is accompanied by the creation of a “coherence wave” of synchronized molecular oscillations with wave vector Δβ determined by the optical dispersion. Within its lifetime, this coherence wave can be used to shift by ΩR the frequency of a third “mixing” signal, provided phase matching is satisfied, i.e., Δβ is matched. Conventionally, this can be arranged using noncollinear beams or higher-order waveguide modes. Here we report the collinear phase-matched frequency shifting of an arbitrary mixing signal using only the fundamental LP01 modes of a hydrogen-filled hollow-core photonic crystal fiber. This is made possible by the S-shaped dispersion curve that occurs around the pressure-tunable zero dispersion point. Phase-matched frequency shifting by 125 THz is possible from the UV to the near IR. Long interaction lengths and tight modal confinement reduce the peak intensities required, allowing conversion efficiencies in excess of 70%. The system is of great interest in coherent anti-Stokes Raman spectroscopy and for wavelength conversion of broadband laser sources.

© 2015 Optical Society of America

Coherence waves (Cws) of collective molecular oscillation, created by stimulated Raman scattering (SRS) [15], are useful in the synthesis of ultrashort pulses [6] and for efficient frequency conversion [35]. They arise through the beating between two intense quasi-monochromatic laser beams whose frequencies differ by the Raman transition frequency ΩR. The resulting Cw takes the form of a traveling refractive index grating. Under phase-matched conditions, an arbitrarily weak mixing signal at a different wavelength can be scattered off this Cw, which is coherently amplified when the mixing signal is downshifted by ΩR and absorbed when the mixing signal is upshifted by ΩR [25].

Phase matching can be achieved using noncollinear beams in bulk materials [7,8] or higher-order guided modes in optical fibers [5,9]. Broadband-guiding kagomé-style hollow-core photonic crystal fiber (kagomé-PCF) is particularly attractive since the dispersion can be precisely controlled by varying the gas pressure [10]. In addition, tight modal confinement and long light–gas interaction lengths dramatically reduce the peak laser intensities required for the efficient excitation of Cws.

In this Letter, we report how a Cw, excited by an LP01 pump pulse in a hydrogen-filled kagomé-PCF, can be used, within its coherence lifetime, for the efficient phase-matched frequency-shifting of an LP01 mixing pulse at an entirely different wavelength. The process is made possible by the unique S-shaped dispersion curve that forms around the pressure-tunable zero dispersion point (ZDP) in a kagomé-PCF [10].

To illustrate the concept, the dispersion curve in the vicinity of a ZDP at wave vector β0 and frequency ω0 is drawn schematically in Fig. 1, assuming no dispersion terms higher than third order. A Cw is first “written” by pump and Stokes waves, labeled by W0 and W1, respectively, on the diagram. The ωβ “four vector” of the resulting Cw is marked by the blue dashed line. Once created, this Cw can be used for fully phase-matched frequency upconversion to point M1 of an optical mixing signal at point M0 on the opposite side of the ZDP. It may also be used to seed frequency downconversion to M0 of a signal at M1, during which process it will be amplified. This procedure will of course also work the other way around, i.e., with writing signals on the low-frequency side of the ZDP and mixing signals on the high-frequency side.

 figure: Fig. 1.

Fig. 1. (a) Sketch of the dispersion of a gas-filled kagomé-PCF in the vicinity of the ZDP (the gray dot at ω=ω0 and β=β0), assuming no dispersion terms higher than third order. The blue dashed lines indicate the coherence wave Cw excited by the writing signals W0 and W1. Cw is a four vector with frequency ΩR and wave vector Δβ given by the difference between the wave vectors of the writing signals. It can be used either to upshift the frequency of a mixing signal M0 placed at the position symmetric to W0 on the opposite side of the ZDP or to seed the downconversion of a signal placed at M1.

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In general, higher-order dispersion will increasingly distort the perfect S-shape as one moves further away from the ZDP. Nevertheless, as we shall see, it is always possible to find two distinct pairs of points, albeit asymmetrically placed about the ZDP, that are connected by the identical Cw. If the frequency of the mixing beam is not precisely correct, however, the upconversion process will be dephased at a rate given by

ϑ=Δβ(βM1βM0),
where the full dispersion relation of the LP01 mode must be taken into account. Its propagation constant β01 can be approximated to good accuracy by
β01=k02ngas2(p,λ)u2/a2(λ),
where k0=2π/λ is the vacuum wave vector, ngas is the refractive index of the filling gas, p is the gas pressure, u=2.405 for the fundamental core mode, and a(λ)=aAP/(1+sλ2/(aAPd)), where aAP is the area-preserving core radius, s=0.08 is an empirical dimensionless parameter, and d is the core wall thickness [11]. This dispersion relation is plotted in Fig. 2(a) at three different pressures for the fiber used in the experiments (aAP=23.4μm and d=97nm). In order to magnify the very flat S-shape, we have subtracted off the linear dispersion by plotting frequency versus (βrefβ), where βref is a pressure-dependent linear function of frequency chosen such that (βrefβ) is 0 at 800 THz.

 figure: Fig. 2.

Fig. 2. (a) Dispersion curves of the LP01 mode for pressures of 3, 12, and 30 bar (see text). The notation is the same as in Fig. 1, and for clarity, only the 30 bar case is fully labeled. (b) Phase-matched frequency pairs (solid lines) and ZDPs (dotted line) as a function of pressure for a pump frequency (W0) of 563 THz (532 nm). The ZDPs for the three pressures in (a) are marked with gray dots.

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The wavelength of the ZDP shifts from 400nm to 1.1μm as the pressure increases from 1 to 100 bar [Fig. 2(b)].

The mixing frequencies of perfectly phase-matched pairs can be accurately calculated by solving Eqs. (1) and (2). Figure 2(a) shows the Cws created at three different pressures by beating a pump signal W0 at 532 nm (563 THz) with a Stokes signal W1 at 685 nm (438 THz). The presence of higher-order dispersion shifts the positions of the two perfectly phase-matched pairs asymmetrically about the ZDP. At 30 bar, both the pump (W0) and Stokes (W1) signals lie in the normal dispersion region (ω>ω0), and the phase-matched mixing pair (M1, M0) is at (322, 197) THz in the anomalous dispersion region. At 3 bar, on the other hand, the Cw is excited in the anomalous dispersion region and the mixing pair is phase matched at (749, 624) THz in the normal dispersion region.

A special situation occurs at 12 bar, when the lower frequency of the upper pair and the upper frequency of the lower pair coincide; this causes a strong second Stokes (W2) signal to appear when pumping with W0 (see below). Overall, Fig. 2 shows that for a fixed W0 frequency of 563 THz, the frequency of M1 for perfect phase matching can be tuned from the UV to the near IR simply by changing the pressure.

To confirm these predictions experimentally, we developed a setup for exciting and probing Cws under different conditions (see Fig. 3). The output of a linearly polarized 1064 nm laser, delivering nanosecond pulses, was split into two parts. The first part was used to generate the W0 signal by frequency-doubling to 532 nm in a KTP crystal. The second was spectrally broadened to 350nm in a 4 m long solid-core PCF and used as the M0 mixing signal. The pulse durations were 3.2 ns for W0 and 2.0 ns for M0. Both pulses were then recombined and launched into the LP01 mode of a 1 m long gas-filled kagomé-PCF. The signals exiting the fiber endface were monitored using an optical spectrum analyzer and imaged using a CCD camera. The intensity of the mixing beam was kept low so as to avoid the onset of SRS, which would influence the Cw. The interaction was found to be strongest when the mixing pulse was delayed by 1ns from the pump pulse.

 figure: Fig. 3.

Fig. 3. Schematic of the experimental setup. BS, beam splitter; DBS, dichroic BS; OAP, off-axis parabolic mirror; SC-PCF, solid-core photonic crystal fiber; DL, delay line; OSA, optical spectrum analyzer.

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The vibrational Raman gain of hydrogen saturates for pressures above 10bar [12]. In this regime, the behavior of the system is dominated by changes in the phase-matching conditions. Below 10 bar, both the phase-matching conditions and the Raman gain are pressure-dependent and play a role.

We recorded the spectra generated when scanning the pressure from 5 to 40 bar, for two pulse energies, EP=20 and 30 μJ (Fig. 4). The photon rates in the W0, W1, and W2 bands are plotted in Figs. 4(a) and 4(c) and those in the mixing signals are in Figs. 4(b) and 4(d). Note that, for clarity, the sum of the rates in the two upshifted sidebands M1 at 730 nm (411 THz) and M2 at 560 nm (535 THz) is plotted, along with the signal M0 at 1048 nm (286 THz); the full experimental data are available in Fig. S2 of Supplement 1.

 figure: Fig. 4.

Fig. 4. Experimental and theoretical normalized photon rates of the various signals, plotted against increasing pressure. (a) Pump (W0), first (W1), and second (W2) Stokes waves for EP=20μJ. (b) Mixing (M0) and upshifted anti-Stokes (M1+M2) signals, coupled by the Cws created in (a). (c) Pump (W0), first (W1), and second (W2) Stokes waves for EP=30μJ. (d) Mixing (M0) and upshifted anti-Stokes (M1+M2) signals, coupled by the Cws created in (c). The green solid lines show the pressure dependence of the phase-match parameter ϑ. Note that the Cw generated by the W1W2 conversion creates a second phase-matching pressure at point B. Upshifting to M1 is most efficient at the phase-matching pressures (points A and B).

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In Fig. 4(a), the pump pulse energy was EP=20μJ (injected into the kagomé-PCF with 40% coupling efficiency). As the pressure increases, W0 converts to W1 via SRS, giving rise to a Cw and becoming significantly depleted. At 12 bar, W1 is itself depleted and light appears at the W2 frequency (i.e., the second Stokes). This is because at this pressure both the W0W1 and W1W2 processes are phase-matched to the same Cw. At higher pressures, the W1W2 phase mismatch increases and the W2 signal drops again.

At 14.2 bar, the Cw created in the W0W1 process is able to phase-match the M0M1 conversion from 1048 to 730 nm, with photon number conversion efficiencies (based on the depletion of the M0 signal) well above 50% at the peak [Fig. 4(b)].

At 30 μJ pump pulse energy, a strong W2 signal appears for pressures above 15 bar [Fig. 4(c)]. This is because the W1 signal is strong enough to reach the threshold for SRS, generating a strong W2 signal and an independent Cw. This new Cw causes a new phase-matching point to appear at a pressure of 27bar, resulting in a second peak of M0M1 conversion [Fig. 4(d)]. At the same time, the first conversion peak reaches conversion efficiency above 70%.

As shown in the right-hand column of Fig. 4, these measurements are in good overall agreement with numerical solutions of a set of coupled spatiotemporal Maxwell–Bloch equations [13]. Note that the model is only valid for pressures above 10 bar, i.e., outside the shaded region in Fig. 4, when the Raman gain is independent of pressure (see Supplement 1 for details).

The simulations also allow us to study the behavior of the Cw amplitude |Q|, a quantity that is not accessible in the experiment. Figure 5 plots the evolution of both |Q| and the (M1+M2) photon rate along the fiber at gas pressures of 12 and 27 bar for EP=30μJ. At 12 bar, |Q| grows through a SRS-related exponential gain in the W1 signal (upper left-hand panel in Fig. 5). It peaks at 40cm, decreasing thereafter because by that point the majority of pump photons have been converted to the W1 band. Note that the temporal peak of |Q| is delayed by 1ns relative to the center of the pump pulse, as expected in transient Raman scattering. For this special pressure (as explained above in Fig. 2), the same Cw is simultaneously able to seed the downconversion from the W1 to the W2 band (and thus be amplified), giving rise to the strong W2 signals observed in Figs. 4(a) and 4(c). As expected, upconversion from the M0 to the M1 band is highest when |Q| is strongest (upper right-hand panel in Fig. 5).

 figure: Fig. 5.

Fig. 5. Simulated spatiotemporal evolution of the normalized Cw amplitude |Q| and the normalized (M1+M2) photon rate for EP=30μJ at pressures of 12 bar (upper) and 27 bar (lower). The Cws created in the W0W1 process are marked with (I) and those created by the W1W2 process with (II). The inset in the upper right panel shows the normalized temporal profiles of the W0 and M0 pulses at the entrance to the fiber. Time is relative to a frame traveling at the group velocity of the W0 pulse. The origin of the periodic oscillations in the lower left panel is discussed in Supplement 1.

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This special dual phase-matching condition is no longer valid at 27 bar, because the W0W1 and W1W2 conversion processes produce different Cws. As a result, the first peak in |Q| at 25cm originates from W0W1, whereas the second peak at 60cm is created by the W1W2 conversion and appears at a later time (lower left-hand panel in Fig. 5). For the mixing beams, although the M0M1 conversion is very weak at the 25 cm point due to strong dephasing (ϑ=1.6cm1), it is strong at 60 cm because of phase matching with the second Cw (lower right-hand panel in Fig. 5). This illustrates the supreme importance of phase matching for efficient frequency conversion.

From coupled mode theory, the bandwidth Δν of the upconversion process covers the range π<ϑLc<π, where Lc is the length over which the Cw amplitude is significant (10cm in the experiments). Δν depends on the curvature of the dispersion curve for the M0M1 process and ranges from 250THz for M0 at 800 THz, to 20THz for M0 at 300 THz. These large bandwidths make it possible to frequency-shift and replicate broadband signals, as shown in Fig. 6 where the full recorded spectrum at 14.5 and 27.6 bar is plotted for EP=30μJ. Cascaded upshifting to the M2 band is possible in the case of 14.5 bar (upper panel in Fig. 6) because of the relatively flat dispersion curve from 300 to 600THz [see for instance the 12 bar curve in Fig. 2(a)]. In contrast, at 27.6 bar, efficient conversion is only possible to the first (M1) sideband (lower panel in Fig. 6), owing to the strong curvature of the dispersion over the whole frequency range [see for instance the 30 bar curve in Fig. 2(a)].

 figure: Fig. 6.

Fig. 6. Demonstration of broadband frequency shifting for 14.5 bar (upper panel) and 27.6 bar (lower panel). The broadband mixing signal M0 is frequency-upshifted to the first (M1) and second (M2) anti-Stokes bands. The original spectrum M00 (pump switched off) is depleted accordingly. The photon rates are normalized to the peak of the broadband mixing M00 signal at 1064 nm.

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Since ϑ is also a function of pressure, it determines the width of the conversion peaks as shown in Fig. 4(d), where ϑ is plotted for the two Cws excited in that case. It is clear that a weaker pressure dependence of ϑ translates into broader conversion peaks.

In this Letter, we have concentrated on frequency upshifting. As mentioned in the introduction, it is also possible to use a Cw to frequency downshift a mixing signal. In this case, the Cw acts as a (potentially very strong) seed, being amplified in the conversion process. In Fig. 7, we show the result of an experiment with the same setup where a broadband signal at 325THz (920 nm) is downshifted. The maximum conversion efficiency achieved is 25%. Note also that since the phase-matching frequency shifts with pressure, so does the peak of the downshifted frequency band. The experimental trace nicely follows the analytical curve for perfect phase matching (the dashed curve in Fig. 7). Taken together with all-LP01 operation, this further demonstrates the wide usable frequency range and versatility of this unique wavelength convertor.

 figure: Fig. 7.

Fig. 7. Frequency-downshifted signal versus pressure. The dashed line represents the theoretical perfectly phase-matched frequencies.

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In conclusion, the S-shaped dispersion curve in the vicinity of the ZDP makes the hydrogen-filled kagomé-PCF an ideal vehicle for highly efficient wavelength conversion of broadband optical signals. A Cw (which behaves like a traveling refractive index grating) is first excited by SRS on one side of the ZDP. It is then used for the phase-matched conversion of a signal on the opposite side of the ZDP. The system is widely pressure-tunable, permitting highly efficient up- and downconversion, by 125 THz, of LP01 signals from the UV to the near IR. The system offers a new route for the frequency conversion of ultrashort laser pulses from mode-locked lasers. Further flexibility is possible by changing the fiber design, working with different Raman active gases, adding buffer gases, or working with a different pump wavelength. This uniquely flexible system has many potential applications in ultrasensitive Raman spectroscopy and laser science.

 

See Supplement 1 for supporting content.

REFERENCES

1. S. E. Harris and A. V. Sokolov, Phys. Rev. Lett. 81, 2894 (1998). [CrossRef]  

2. A. Nazarkin, G. Korn, M. Wittmann, and T. Elsaesser, Phys. Rev. Lett. 83, 2560 (1999). [CrossRef]  

3. J. Q. Liang, M. Katsuragawa, F. L. Kien, and K. Hakuta, Phys. Rev. Lett. 85, 2474 (2000). [CrossRef]  

4. J. J. Weber, J. T. Green, and D. D. Yavuz, Phys. Rev. A 85, 013805 (2012). [CrossRef]  

5. S. T. Bauerschmidt, D. Novoa, B. M. Trabold, A. Abdolvand, and P. St.J. Russell, Opt. Express 22, 20566 (2014). [CrossRef]  

6. S. Baker, I. A. Walmsley, J. W. G. Tisch, and J. P. Marangos, Nat. Photonics 5, 664 (2011). [CrossRef]  

7. A. C. Eckbreth, Appl. Phys. Lett. 32, 421 (1978). [CrossRef]  

8. T. Wilhelm, J. Piel, and E. Riedle, Opt. Lett. 22, 1494 (1997). [CrossRef]  

9. J. Demas, P. Steinvurzel, B. Tai, L. Rishøj, Y. Chen, and S. Ramachandran, Optica 2, 14 (2015). [CrossRef]  

10. P. St.J. Russell, P. Holzer, W. Chang, A. Abdolvand, and J. C. Travers, Nat. Photonics 8, 278 (2014). [CrossRef]  

11. M. Finger, N. Y. Joly, T. Weiss, and P. St.J. Russell, Opt. Lett. 39, 821 (2014). [CrossRef]  

12. W. K. Bischel and M. J. Dyer, J. Opt. Soc. Am. B 3, 677 (1986). [CrossRef]  

13. M. G. Raymer and I. A. Walmsley, Progress in Optics, E. Wolf, ed. (Elsevier, 1990), p. 181.

References

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  1. S. E. Harris, A. V. Sokolov, Phys. Rev. Lett. 81, 2894 (1998).
    [Crossref]
  2. A. Nazarkin, G. Korn, M. Wittmann, T. Elsaesser, Phys. Rev. Lett. 83, 2560 (1999).
    [Crossref]
  3. J. Q. Liang, M. Katsuragawa, F. L. Kien, K. Hakuta, Phys. Rev. Lett. 85, 2474 (2000).
    [Crossref]
  4. J. J. Weber, J. T. Green, D. D. Yavuz, Phys. Rev. A 85, 013805 (2012).
    [Crossref]
  5. S. T. Bauerschmidt, D. Novoa, B. M. Trabold, A. Abdolvand, P. St.J. Russell, Opt. Express 22, 20566 (2014).
    [Crossref]
  6. S. Baker, I. A. Walmsley, J. W. G. Tisch, J. P. Marangos, Nat. Photonics 5, 664 (2011).
    [Crossref]
  7. A. C. Eckbreth, Appl. Phys. Lett. 32, 421 (1978).
    [Crossref]
  8. T. Wilhelm, J. Piel, E. Riedle, Opt. Lett. 22, 1494 (1997).
    [Crossref]
  9. J. Demas, P. Steinvurzel, B. Tai, L. Rishøj, Y. Chen, S. Ramachandran, Optica 2, 14 (2015).
    [Crossref]
  10. P. St.J. Russell, P. Holzer, W. Chang, A. Abdolvand, J. C. Travers, Nat. Photonics 8, 278 (2014).
    [Crossref]
  11. M. Finger, N. Y. Joly, T. Weiss, P. St.J. Russell, Opt. Lett. 39, 821 (2014).
    [Crossref]
  12. W. K. Bischel, M. J. Dyer, J. Opt. Soc. Am. B 3, 677 (1986).
    [Crossref]
  13. M. G. Raymer, I. A. Walmsley, Progress in Optics, E. Wolf, ed. (Elsevier, 1990), p. 181.

2015 (1)

2014 (3)

2012 (1)

J. J. Weber, J. T. Green, D. D. Yavuz, Phys. Rev. A 85, 013805 (2012).
[Crossref]

2011 (1)

S. Baker, I. A. Walmsley, J. W. G. Tisch, J. P. Marangos, Nat. Photonics 5, 664 (2011).
[Crossref]

2000 (1)

J. Q. Liang, M. Katsuragawa, F. L. Kien, K. Hakuta, Phys. Rev. Lett. 85, 2474 (2000).
[Crossref]

1999 (1)

A. Nazarkin, G. Korn, M. Wittmann, T. Elsaesser, Phys. Rev. Lett. 83, 2560 (1999).
[Crossref]

1998 (1)

S. E. Harris, A. V. Sokolov, Phys. Rev. Lett. 81, 2894 (1998).
[Crossref]

1997 (1)

1986 (1)

1978 (1)

A. C. Eckbreth, Appl. Phys. Lett. 32, 421 (1978).
[Crossref]

Abdolvand, A.

S. T. Bauerschmidt, D. Novoa, B. M. Trabold, A. Abdolvand, P. St.J. Russell, Opt. Express 22, 20566 (2014).
[Crossref]

P. St.J. Russell, P. Holzer, W. Chang, A. Abdolvand, J. C. Travers, Nat. Photonics 8, 278 (2014).
[Crossref]

Baker, S.

S. Baker, I. A. Walmsley, J. W. G. Tisch, J. P. Marangos, Nat. Photonics 5, 664 (2011).
[Crossref]

Bauerschmidt, S. T.

Bischel, W. K.

Chang, W.

P. St.J. Russell, P. Holzer, W. Chang, A. Abdolvand, J. C. Travers, Nat. Photonics 8, 278 (2014).
[Crossref]

Chen, Y.

Demas, J.

Dyer, M. J.

Eckbreth, A. C.

A. C. Eckbreth, Appl. Phys. Lett. 32, 421 (1978).
[Crossref]

Elsaesser, T.

A. Nazarkin, G. Korn, M. Wittmann, T. Elsaesser, Phys. Rev. Lett. 83, 2560 (1999).
[Crossref]

Finger, M.

Green, J. T.

J. J. Weber, J. T. Green, D. D. Yavuz, Phys. Rev. A 85, 013805 (2012).
[Crossref]

Hakuta, K.

J. Q. Liang, M. Katsuragawa, F. L. Kien, K. Hakuta, Phys. Rev. Lett. 85, 2474 (2000).
[Crossref]

Harris, S. E.

S. E. Harris, A. V. Sokolov, Phys. Rev. Lett. 81, 2894 (1998).
[Crossref]

Holzer, P.

P. St.J. Russell, P. Holzer, W. Chang, A. Abdolvand, J. C. Travers, Nat. Photonics 8, 278 (2014).
[Crossref]

Joly, N. Y.

Katsuragawa, M.

J. Q. Liang, M. Katsuragawa, F. L. Kien, K. Hakuta, Phys. Rev. Lett. 85, 2474 (2000).
[Crossref]

Kien, F. L.

J. Q. Liang, M. Katsuragawa, F. L. Kien, K. Hakuta, Phys. Rev. Lett. 85, 2474 (2000).
[Crossref]

Korn, G.

A. Nazarkin, G. Korn, M. Wittmann, T. Elsaesser, Phys. Rev. Lett. 83, 2560 (1999).
[Crossref]

Liang, J. Q.

J. Q. Liang, M. Katsuragawa, F. L. Kien, K. Hakuta, Phys. Rev. Lett. 85, 2474 (2000).
[Crossref]

Marangos, J. P.

S. Baker, I. A. Walmsley, J. W. G. Tisch, J. P. Marangos, Nat. Photonics 5, 664 (2011).
[Crossref]

Nazarkin, A.

A. Nazarkin, G. Korn, M. Wittmann, T. Elsaesser, Phys. Rev. Lett. 83, 2560 (1999).
[Crossref]

Novoa, D.

Piel, J.

Ramachandran, S.

Raymer, M. G.

M. G. Raymer, I. A. Walmsley, Progress in Optics, E. Wolf, ed. (Elsevier, 1990), p. 181.

Riedle, E.

Rishøj, L.

Russell, P. St.J.

Sokolov, A. V.

S. E. Harris, A. V. Sokolov, Phys. Rev. Lett. 81, 2894 (1998).
[Crossref]

Steinvurzel, P.

Tai, B.

Tisch, J. W. G.

S. Baker, I. A. Walmsley, J. W. G. Tisch, J. P. Marangos, Nat. Photonics 5, 664 (2011).
[Crossref]

Trabold, B. M.

Travers, J. C.

P. St.J. Russell, P. Holzer, W. Chang, A. Abdolvand, J. C. Travers, Nat. Photonics 8, 278 (2014).
[Crossref]

Walmsley, I. A.

S. Baker, I. A. Walmsley, J. W. G. Tisch, J. P. Marangos, Nat. Photonics 5, 664 (2011).
[Crossref]

M. G. Raymer, I. A. Walmsley, Progress in Optics, E. Wolf, ed. (Elsevier, 1990), p. 181.

Weber, J. J.

J. J. Weber, J. T. Green, D. D. Yavuz, Phys. Rev. A 85, 013805 (2012).
[Crossref]

Weiss, T.

Wilhelm, T.

Wittmann, M.

A. Nazarkin, G. Korn, M. Wittmann, T. Elsaesser, Phys. Rev. Lett. 83, 2560 (1999).
[Crossref]

Yavuz, D. D.

J. J. Weber, J. T. Green, D. D. Yavuz, Phys. Rev. A 85, 013805 (2012).
[Crossref]

Appl. Phys. Lett. (1)

A. C. Eckbreth, Appl. Phys. Lett. 32, 421 (1978).
[Crossref]

J. Opt. Soc. Am. B (1)

Nat. Photonics (2)

S. Baker, I. A. Walmsley, J. W. G. Tisch, J. P. Marangos, Nat. Photonics 5, 664 (2011).
[Crossref]

P. St.J. Russell, P. Holzer, W. Chang, A. Abdolvand, J. C. Travers, Nat. Photonics 8, 278 (2014).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Optica (1)

Phys. Rev. A (1)

J. J. Weber, J. T. Green, D. D. Yavuz, Phys. Rev. A 85, 013805 (2012).
[Crossref]

Phys. Rev. Lett. (3)

S. E. Harris, A. V. Sokolov, Phys. Rev. Lett. 81, 2894 (1998).
[Crossref]

A. Nazarkin, G. Korn, M. Wittmann, T. Elsaesser, Phys. Rev. Lett. 83, 2560 (1999).
[Crossref]

J. Q. Liang, M. Katsuragawa, F. L. Kien, K. Hakuta, Phys. Rev. Lett. 85, 2474 (2000).
[Crossref]

Other (1)

M. G. Raymer, I. A. Walmsley, Progress in Optics, E. Wolf, ed. (Elsevier, 1990), p. 181.

Supplementary Material (1)

» Supplement 1: PDF (879 KB)     

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Figures (7)

Fig. 1.
Fig. 1. (a) Sketch of the dispersion of a gas-filled kagomé-PCF in the vicinity of the ZDP (the gray dot at ω=ω0 and β=β0), assuming no dispersion terms higher than third order. The blue dashed lines indicate the coherence wave Cw excited by the writing signals W0 and W1. Cw is a four vector with frequency ΩR and wave vector Δβ given by the difference between the wave vectors of the writing signals. It can be used either to upshift the frequency of a mixing signal M0 placed at the position symmetric to W0 on the opposite side of the ZDP or to seed the downconversion of a signal placed at M1.
Fig. 2.
Fig. 2. (a) Dispersion curves of the LP01 mode for pressures of 3, 12, and 30 bar (see text). The notation is the same as in Fig. 1, and for clarity, only the 30 bar case is fully labeled. (b) Phase-matched frequency pairs (solid lines) and ZDPs (dotted line) as a function of pressure for a pump frequency (W0) of 563 THz (532 nm). The ZDPs for the three pressures in (a) are marked with gray dots.
Fig. 3.
Fig. 3. Schematic of the experimental setup. BS, beam splitter; DBS, dichroic BS; OAP, off-axis parabolic mirror; SC-PCF, solid-core photonic crystal fiber; DL, delay line; OSA, optical spectrum analyzer.
Fig. 4.
Fig. 4. Experimental and theoretical normalized photon rates of the various signals, plotted against increasing pressure. (a) Pump (W0), first (W1), and second (W2) Stokes waves for EP=20μJ. (b) Mixing (M0) and upshifted anti-Stokes (M1+M2) signals, coupled by the Cws created in (a). (c) Pump (W0), first (W1), and second (W2) Stokes waves for EP=30μJ. (d) Mixing (M0) and upshifted anti-Stokes (M1+M2) signals, coupled by the Cws created in (c). The green solid lines show the pressure dependence of the phase-match parameter ϑ. Note that the Cw generated by the W1W2 conversion creates a second phase-matching pressure at point B. Upshifting to M1 is most efficient at the phase-matching pressures (points A and B).
Fig. 5.
Fig. 5. Simulated spatiotemporal evolution of the normalized Cw amplitude |Q| and the normalized (M1+M2) photon rate for EP=30μJ at pressures of 12 bar (upper) and 27 bar (lower). The Cws created in the W0W1 process are marked with (I) and those created by the W1W2 process with (II). The inset in the upper right panel shows the normalized temporal profiles of the W0 and M0 pulses at the entrance to the fiber. Time is relative to a frame traveling at the group velocity of the W0 pulse. The origin of the periodic oscillations in the lower left panel is discussed in Supplement 1.
Fig. 6.
Fig. 6. Demonstration of broadband frequency shifting for 14.5 bar (upper panel) and 27.6 bar (lower panel). The broadband mixing signal M0 is frequency-upshifted to the first (M1) and second (M2) anti-Stokes bands. The original spectrum M00 (pump switched off) is depleted accordingly. The photon rates are normalized to the peak of the broadband mixing M00 signal at 1064 nm.
Fig. 7.
Fig. 7. Frequency-downshifted signal versus pressure. The dashed line represents the theoretical perfectly phase-matched frequencies.

Equations (2)

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ϑ=Δβ(βM1βM0),
β01=k02ngas2(p,λ)u2/a2(λ),

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