OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 7 — Mar. 31, 2008
  • pp: 5035–5047
« Show journal navigation

Nonlinear optics in hollow-core photonic bandgap fibers

Amar R. Bhagwat and Alexander L. Gaeta  »View Author Affiliations


Optics Express, Vol. 16, Issue 7, pp. 5035-5047 (2008)
http://dx.doi.org/10.1364/OE.16.005035


View Full Text Article

Acrobat PDF (989 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Hollow-core photonic-bandgap fibers provide a new geometry for the realization and enhancement of many nonlinear optical effects. Such fibers offer novel guidance and dispersion properties that provide an advantage over conventional fibers for various applications. In this review we summarize the nonlinear optics experiments that have been performed using these hollow-core fibers.

© 2008 Optical Society of America

1. Introduction

Hollow-core photonic bandgap fibers (HC-PBGFs) [1

1. P. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003). [CrossRef] [PubMed]

, 2

2. P. St. J. Russell, “Photonic-crystal fibers,” J. Lightw. Technol. 24, 4729–4749 (2006). [CrossRef]

] are a recent addition to the optical fibers which were developed to exhibit unique waveguiding and nonlinear properties. These fibers display great versatility in terms of hosting nonlinear materials and have been instrumental in pushing the boundaries of nonlinear optical applications. As will be discussed here, such fibers provide the potential for applications that require either ultrahigh or ultralow nonlinear response.

Standard single-mode step-index optical fibers, which form the backbone of telecommunications today, work on the principle of total internal reflection [3

3. G. P. Agrawal, Fiber-Optic Communication Systems (Wiley, New York, 1992).

]. The core, which is a higher refractive index glass rod surrounded by a lower index glass cladding, can support light guidance in a single mode with losses as low as 0.15 dB/km [4

4. K. Nagayama, T. Saitoh, M. Kakui, K. Kawasaki, M. Matsui, H. Takamizawa, H. Miyaki, Y. Ooga, I. Tsuchiya, and Y. Chigusa, “Ultra low loss (0.151 dB/km) fiber and its impact on submarine transmission systems,” OFC2002, Paper FA10-1.

]. Nevetheless, solid-core fibers have certain shortcomings. Despite the relatively low losses, the signal sent into the fibers eventually attenuates and needs amplification at regular intervals. The guided light mode is confined within the glass with an effective mode area of the order of 80 µm2, and as the intensity of light is increased, the fiber exhibits nonlinear effects such as stimulated Raman scattering (SRS), stimulated Brillouin scattering (SBS), and self phase modulation (SPM) [5

5. G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 2001).

]. These nonlinearities along with dispersion can lead to distortions in communication signals that result in increased bit-error rates and also effectively put an upper limit on the power of the input signal launched into the fiber, which is relevant for other fiber-based applications such as pulse delivery.

Alternatively, the nonlinearity and scattering losses in air are roughly 1000 times lower than in glass, which has led to efforts to confine light to a low-index air region. This requires a radical shift in the approach towards waveguide structure design, which would be beneficial in a number of ways. The scattering losses due to Rayleigh scattering and due to material defects could be significantly decreased. The threshold powers for unwanted SRS and SBS could be greatly increased, which could not only benefit telecommunications, but also aid in fiber delivery of intense ultrashort pulses over long distances. Also, if the air core is evacuated and then deliberately filled with appropriate gases or liquids, such a fiber represents a novel geometry for achieving very strong nonlinear interactions between light and matter due to the strong confinement of light in a small mode area and to the extremely long interaction lengths. Last, but not the least, if the dispersion of these waveguides can be suitably tailored, nonlinear processes such as four-wave mixing and soliton generation can be greatly enhanced.

It should be noted that glass capillaries have been used succesfully for various nonlinear optical applications. However, such gas-filled capillaries can only be used for high-power pulses since the loss of the fundamental leaky mode increases rapidly as the diameter is decreased, which limits the core diameter to sizes ≥100 µm [6

6. T. Abel, J. Hirsch, and J. A. Harrington, “Hollow glass waveguides for broadband infrared transmission,” Opt. Lett. 19, 1034–1036 (1994). [CrossRef] [PubMed]

]. In addition, glass capillaries offer minimal dispersion control in contrast to HC-PBGFs that allow for significant tuning of the dispersive properties.

2. Photonic bandgap fibers : A brief introduction

Historically, the concept of a photonic bandgap gained significant interest due to it’s potential to curtail spontaneous emission in optical devices [7

7. E. Yablonovitch, “Photonic band-gap structures,” J. Opt. Soc. Am. B 10, 283–295 (1993). [CrossRef]

, 8

8. P. Lodahl, A. Floris van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelberg, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature (London) 430, 654–657 (2004). [CrossRef] [PubMed]

]. The seminal work of Anderson [9

9. P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109, 1492–1505 (1958). [CrossRef]

] and Mott [10

10. N. F. Mott, “Electrons in disordered structures,” Adv. Phys. 16, 49–144 (1967). [CrossRef]

] on localisation of electrons at defect sites in regular solids suggested that the same could be observed for electromagnetic waves in strongly scattering dielectric structures. The first suggestion for guiding light in a low index waveguide by surrounding it with Bragg structures was made by Yeh and Yariv [11

11. P. Yeh and A. Yariv, “Bragg reflection waveguides,” Opt. Commun. 19, 427–430 (1976). [CrossRef]

]. Yablonovitch [12

12. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987). [CrossRef] [PubMed]

] and John [13

13. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987). [CrossRef] [PubMed]

] showed similar and complimentary theoretical results describing prohibited photonic transmission at certain wavelengths and corresponding guidance due to localization at the defect. Various two-dimensional photonic bandgap structures were studied and proposed as possible long distance light guidance structures [14

14. P. R. Villeneuve and M. Piché, “Photonic band gaps in two-dimensional square and hexagonal lattices,” Phys. Rev. B 46, 4969–4972 (1992). [CrossRef]

, 15

15. A. A. Maradudin and A. R. McGurn, “Out of plane propagation of electromagnetic waves in a two-dimensional periodic dielectric medium,” J. Mod. Opt. 41, 275–284 (1994). [CrossRef]

]. Four years after the first calculation of 2-D photonic bandgaps in air-silica structures [16

16. T. A. Birks, P. J. Roberts, P. St. J. Russell, D. M. Atkin, and T. J. Shepherd, “Full 2-D photonic bandgaps in silica/air structures,” Electron. Lett. 31, 1941–1943 (1995). [CrossRef]

], the first critical demonstration of single-mode photonic bandgap guidance in air was made possible using a very similar structure [17

17. R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999). [CrossRef] [PubMed]

].

The standard design of these HC-PBGF structures (for details see Ref. [2

2. P. St. J. Russell, “Photonic-crystal fibers,” J. Lightw. Technol. 24, 4729–4749 (2006). [CrossRef]

]), as shown in Fig. 1(a), consists of a stack of hollow capillaries with the 7 center capillaries missing, which forms the defect surrounded by a triangular array of air holes in silica. Light coupled into the defect site enters the bandgap region and is repeatedly scattered such that the light experiences destructive interference everywhere except in the defect site and is effectively guided down the fiber at wavelengths throughout the bandgap region. The spacing of the hollow capillaries (called pitch) and the index contrast determine the center wavelength and width of the bandgap. Early versions of HC-PBGFs had relatively high losses due to a strong coupling between the hollow-core modes and surface modes which are lossy and the absence of a full photonic bandgap. The use of long lengths of near-single-mode HC-PBGFs became practical only when the design and manufacturing process was sufficiently refined enough to achieve losses as low as 13 dB/km at 1550 nm [18

18. C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature (London) 424, 657–659 (2003). [CrossRef] [PubMed]

] [see Figure 1(b)]. Since then, a variety of low-loss hollow-core bandgap fibers have become available with bandgaps centered over a variety of different wavelength ranges. The lowest loss fiber (1.2 dB/km) was designed using a larger core formed by the removal of 19 cells [19

19. P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, D. P. Williams, L. Farr, M. W. Mason, A. Tomlinson, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express 13, 236–244 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-1-236. [CrossRef] [PubMed]

].

Fig. 1. Cross-sections of some hollow-core fibers. (a) The first fiber to demonstrate single-mode air guidance (Univ. of Bath) [17] (b) Low-loss hollow-core photonic bandgap fiber (Corning Inc.) [18].

3. Stimulated Raman scattering and four-wave mixing

Raman scattering is an inelastic scattering process in the presence of a pump beam in which a material makes a transition from one vibrational energy level to another through an intermediate state that is dipole coupled to both the initial and final states [20

20. R. W. Boyd, Nonlinear Optics (Academic, New York, 2003).

]. If the final state has higher (lower) energy than the initial state, the emitted photon is called the Stokes (anti-Stokes) photon and has a longer (shorter) wavelength than the pump photon. In the presence of a Stokes signal, this process can be stimulated and the signal wave is amplified. In addition to wavelength conversion, Raman scattering is useful for spectroscopically probing energy levels not directly dipole-connected with the ground state. The number of Stokes photons, ms, generated in the material varies with length z as [20

20. R. W. Boyd, Nonlinear Optics (Academic, New York, 2003).

],

dmsdz=Amp(ms+1)
(1)

where mp is the number of pump photons, and A is a constant including phase velocity and Raman gain coefficient. Maintaining a high confinement for pump and signal photons together over a long interaction length will significantly enhance the conversion rate. In fact, the first demonstration of the use of HC-PBGFs for nonlinear interactions was performed for Raman sideband generation [21

21. 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]

] in which different lengths of Kagome-structured fibers were filled with hydrogen at a pressure of 17 bar. A frequency-doubled Nd:YAG laser at 532 nm was coupled from one end to serve as the pump and with increasing pump powers, a vibrational Raman Stokes signal was observed at 683 nm. As shown in Fig. 2, a much weaker anti-Stokes signal at 435.2 nm was also observed at higher pump powers. The measured Raman threshold was 800 nJ (6-ns pulses) for Stokes and 3.4 µJ for the anti-Stokes signal, which represented values that were 2 orders of magnitude lower than that reported previously for the single-pass bulk configuration.

Fig. 2. Spectra showing evidence of stimulated Raman scattering in hollow-core fibers. Shown here is the pump at 532 nm, and with increasing pump powers, a Stokes line appears at 683 nm. At higher powers an anti-Stokes peak at 435 nm can also be seen [21].

An intriguing application of the bandgap nature of the HC-PBGFs is selectively enhancing the rotational Raman signal by supressing the vibrational transition, which by suitable choice of fiber, lies outside the bandgap. By launching the pump in circular polarization [22

22. F. Benabid, G. Bouwmans, J. C. Knight, P. St. J. Russell, and F. Couny, “Ultrahigh efficiency laser wavelength conversion in a gas-filled hollow core photonic crystal fiber by pure stimulated rotational Raman scattering in molecular hydrogen,” Phys. Rev. Lett. 93, 123903 (2004). [CrossRef] [PubMed]

] in a fiber filled with H2 at a pressure of 7 bar, almost 92% conversion efficiency to the rotational Stokes signal was achieved. The threshold was observed to be a function of the fiber length (3 nJ for 39 m and 20 nJ for 2.9 m for 0.8-ns pulses at 1.064 µm), which is 106 times lower than previously reported in bulk-geometries. Additionally, by changing the polarization and power in the pump, the power in various Stokes and anti-Stokes lines could be selectively controlled.

The use of lower-loss fibers allows longer lengths to be used, which can be especially useful for cascaded SRS processes in which the generated frequencies act as the pump fields for generating further sidebands. With sufficient bandwidth, it is possible to use this comb for ultrashort pulse generation. Using a low-loss fiber whose bandgap does not support vibrational Raman lines, it has been shown that a purely rotational Raman sideband comb spanning 80 THz can be generated [23

23. F. Benabid, G. Antonopoulos, J. C. Knight, and P. St. J. Russell, “Stokes amplification regimes in quasi-cw pumped hydrogen-filled hollow-core photonic crystal fiber,” Phys. Rev. Lett. 95, 213903 (2005). [CrossRef] [PubMed]

]. In this experiment, an 11-m long fiber with bandgap in the 900–1200 nm region (fiber attenuation: 67 dB/km) was filled with H2 at 10 bar and pumped at 1047 nm (100–300 nJ pulses) to generate this comb. The dependence of Raman threshold on pulsewidth was also studied in detail. In a recent striking result using a Kagome-structured fiber, generation of a comb spanning 325 to 2300 nm [24

24. F. Couny, F. Benabid, P. J. Roberts, P. S. Light, and M. G. Raymer, “Generation and photonic guidance of multioctave optical-frequency combs,” Science 318, 1118–1121 (2007). [CrossRef] [PubMed]

] was demonstrated. Figure 3 shows the generated Raman spectrum. Note that linear polarization excites the vibrational Raman spectrum with a spacing of 125 THz and circular polarization excites rotational and vibrational Raman spectrum, which has a spacing of 18 THz. In principle, it should be possible to generate sub-femtosecond pulses by properly adjusting the phases of these sidebands.

Fig. 3. (a) Vibrational Raman spectra generated in H2 with a comb spacing of 125 THz due to linearly polarized pump with the corresponding camera image of generated light viewed through a dispersive element. (b) Rotational and vibrational spectra due to circularly polarized pump showing comb lines separated by 18 GHz [24].

4. Applications to high-power pulse delivery and modelocked femtosecond fiber lasers

In a HC-PBGF, a large fraction (>92%) of the total light power is confined to the air core, which reduces the optical nonlinearities by as much as a factor of 1000 as compared to solid-core silica fibers. A detailed study on nonlinearities in HC-PBGFs due to silica-glass contribution has been recently published [29

29. C. J. Hensley, D. G. Ouzounov, A. L. Gaeta, N. Venkataraman, M. T. Gallagher, and K. W. Koch, “Silica-glass contribution to the effective nonlinearity of hollow-core photonic band-gap fibers,” Opt. Express 15, 3507–3512 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-6-3507. [CrossRef] [PubMed]

]. Since the material dispersion experienced by the light mode is that of air, the total dispersion is dominated by the waveguide dispersion. For all the hollow-core fibers fabricated till date, the group-velocity dispersion (GVD) across most of the bandgap is anomalous (See Fig. 4). The magnitude of the GVD can be substantially greater than that in conventional step-index silica fibers and the presence of anomalous GVD with nonlinearity can give rise to optical solitons [30

30. A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973). [CrossRef]

, 31

31. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980). [CrossRef]

]. For a medium in which the nonlinear refractive index n 2>0, the soliton condition in which nonlinearity and anomalous dispersion are balanced, occurs when the dispersion length Lds=τ 2 p/|β 2| is equal to the nonlinear length Lnl=λAeff/2πn 2 P where τp is the pulse duration, β 2 is the GVD coefficient, λ is the wavelength, Aeff is the effective mode area, and P is the peak pulse power. This condition yields the following expression for the peak power Psol of the soliton :

Psol=β2λAeff2πn2τp2
(2)

We note that for HC-PBGFs, since the n 2 is roughly 1000 times smaller, soliton pulses can propagate with peak powers 1000 times higher than in conventional single-mode fibers assuming the dispersion β 2 is comparable in both fibers.

Fig. 4. Experimentally measured dispersion parameter D is positive over most of the bandgap, indicating that the dispersion is anomalous [32].

Fig. 5. (a) After propagation through 2 m of hollow-core fiber filled with Xe gas, the input and output pulses are essentially identical in time demonstrating soliton propagation over ~30 dispersion lengths. (b) The corresponding spectra which shows pulse spectrum before and after it passed through the fiber which indicates the absence of Raman-induced red shift [32].

Ouzounov et al. [34

34. D. G. Ouzounov, C. J. Hensley, A. L. Gaeta, N. Venkateraman, M. T. Gallagher, and K. W. Koch, “Soliton pulse compression in photonic band-gap fibers,” Opt. Express 13, 6153–6159 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-16-6153. [CrossRef] [PubMed]

] further showed that by launching higher-order solitons in Xe gas, it is possible to compress 150-fs pulses by a factor of 2 (shown in Fig. 6) and the compression factor is limited by third-order dispersion in the fiber. They predict much higher compression ratios for longer pulses. Recently, Gérôme et al. [35

35. F. Gérôme, K. Cook, A. K. George, W. J. Wadsworth, and J. C. Knight, “Delivery of sub-100 fs pulses through 8 m of hollow-core fiber using soliton compression,” Opt. Express 15, 7126–7131 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-12-7126. [CrossRef] [PubMed]

] reported delivery of sub-100 fs pulses over 8 m of tapered hollow-core fiber using a similar compression scheme. Konorov et al. [36

36. S. O. Konorov, A. M. Zheltikov, P. Zhou, A. P. Tarasevitch, and D. von der Linde, “Self-channeling of subgigawatt femtosecond laser pulses in a ground-state waveguide induced in the hollow core of a photonic crystal fiber,” Opt. Lett. 29, 1521–1523 (2004). [CrossRef] [PubMed]

] demonstrated that sub-gigawatt pulses in a hollow-core fiber filled with various gases including air can undergo self-action due to nonlinearities of the gases that change the output beam profile as a function of power. Irrespective of the input beam profiles, the pulses coming out of the fiber had a clean circular mode suggesting the possible formation of a Townes profile [37

37. K. D. Moll, A. L. Gaeta, and G. Fibich, “Self-similar optical wave collapse: Observation of the Townes profile,” Phys. Rev. Lett. 90, 203902 (2003). [CrossRef] [PubMed]

]. Fedotov et al. [38

38. A. B. Fedotov, E. E. Serebryannikov, and A. M. Zheltikov, “Ionization-induced blueshift of high-peak-power guided-wave ultrashort laser pulses in hollow-core photonic-crystal fibers,” Phys. Rev. A 76, 053811 (2007). [CrossRef]

] have recently demonstrated a striking result whereby using ionization-induced blue-shift in Raman-active gases, they were able to control not only the overall rate of soliton selffrequency shift but also its sign for high-peak-power pulse delivery. Loss of pulse-energy to ionization and the limited anomalous GVD range limit the distance over which the blue-shift can be maintained and eventually the red-shift due to the Raman effect dominates at larger distances.

Fig. 6. (a) Measured autocorrelation traces for the input and output pulses for various input pulse energies which shows pulse compression. Pulse splitting is observed at the highest pulse energies. (b) Measured pulse widths plotted as a function of output pulse energy [34].

Femtosecond modelocked fiber lasers [39

39. J. C. Knight, “Photonic crystal fibers and fiber lasers (Invited),” J. Opt. Soc. Am. B 24, 1661–1668 (2007). [CrossRef]

] that operate in the soliton regime require an anomalous GVD fiber to complement the nonlinearity inside the cavity. Since silica fibers do not exhibit anomalous dispersion at wavelengths below 1.3 µm, prism pairs or gratings are typically used, which makes the lasers susceptible to mechanical and environmental instabilities. The large anomalous dispersion of HC-PBGFs along with their low effective nonlinearity provide a distinct advantage since large nonlinearities can distort the pulse quality and limit the power in the pulse [40

40. H. Lim, F. Ö. Ilday, and F.W. Wise, “Femtosecond ytterbium fiber laser with photonic crystal fiber for dispersion control,” Opt. Express 10, 1497–1502 (2002) http://www.opticsinfobase.org/abstract.cfm?URI=oe-10-25-1497. [PubMed]

]. Lim et al. [41

41. H. Lim and F. W. Wise, “Control of dispersion in a femtosecond ytterbium laser by use of hollow-core photonic bandgap fiber,” Opt. Express 12, 2231–2235 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-10-2231. [CrossRef] [PubMed]

] demonstrated a ytterbium fiber laser which used such a HC-PBGF for dispersion control to generate positively chirped pulses that yielded 160 fs pulses after post-compression. Lim et al. [42

42. H. Lim, A. Chong, and F. W. Wise, “Environmentally-stable femtosecond ytterbium fiber laser with birefringent photonic bandgap fiber,” Opt. Express 13, 3460–3464 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-9-3460. [CrossRef] [PubMed]

] also demonstrated polarization control using the inherent birefringence of a HC-PBGF to achieve higher environmental stability and generate 70-fs, 1-nJ pulses. Ortaç et al. [43

43. B. Ortaç, M. Plötner, T. Schreiber, J. Limpert, and A. Tünnermann, “Experimental and numerical study of pulse dynamics in positive net-cavity dispersion modelocked Yb-doped fiber lasers,” Opt. Express 1515595–15602 (2007) http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-23-15595. [CrossRef]

] demonstrated an all-fiber laser that used a HC-PBGF for post-compression of positively-chirped 15.4-ps pulses to 213-fs pulses.

5. Resonant optical interactions with atoms and molecules

Nonlinear optics at ultra-low light levels is critical for quantum information applications such as processing and cryptography [44

44. D. Bouwmeester, A. K. Ekert, and A. Zeilinger, The Physics of Quantum Information: Quantum Cryptography, Teleportation and Quantum Computation (Springer, New York, 2000).

, 45

45. M. D. Lukin, “Colloquium: Trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys. 75, 457–472 (2003). [CrossRef]

], which require single-photon manipulation [46

46. H. Schmidt and A. Imamoǧlu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21, 1936–1938 (1996). [CrossRef] [PubMed]

, 47

47. S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999). [CrossRef]

], generation, and storage [48

48. T. Chaneliére, D. N. Matsukevich, S. D. Jenkins, S. -Y. Lan, T. A. B. Kennedy, and A. Kuzmich, “Storage and retrieval of single photons transmitted between remote quantum memories,” Nature (London) 438, 833–836 (2005). [CrossRef] [PubMed]

]. Many applications utilize the phenomenon of electromagnetically-induced transparency (EIT) [49

49. K. -J. Boller, A. Imamoǧlu, and S. E. Harris “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991). [CrossRef] [PubMed]

], in which a strong control beam modifies the energy level structure of a medium, to not only eliminate the absorption for a weak resonant probe, but also enhance the nonlinearities of the medium. The strength of the nonlinear interaction depends both on the optical depth α=nσL, where n is the number density of absorbers (e.g., atoms),σ is the absorption cross-section, and L is the length over which the interaction occurs, and on the ratio of the guided light mode area and the scattering cross-section of the medium. Hollow-core PBGFs, with their ability to host atoms and molecules and to strongly confine light over very long interaction lengths provide an ideal geometry for performing such low-light nonlinear optics. These fiber-based devices can also be easily integrated into existing telecommunications networks. By similar arguments, the same geometry can be used for evoking a strong nonlinear response from materials with weak nonlinearities.

Ghosh et al. [50

50. S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005). [CrossRef] [PubMed]

] and Benabid et al. [52

52. F. Fenabid, P. S. Light, F. Couny, and P. St. J. Russell, “Electromagnetically-induced transparency grid in acetylene-filled hollow-core PCF,” Opt. Express 13, 5694–5703 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-15-5694. [CrossRef]

] demonstrated coherent interactions with molecules inside HC-PBGFs using acetylene. Acetylene is a linear symmetric molecule with clean rovibrational bands in the telecommunication wavelength regime, but it has a very weak transition dipole-moment (|µ|2~1×10-4 debye2) per absorption line [51

51. R. El Hachtouki and J. Vander Auwera, “Absolute line intensities in acetylene: The 1.5-µm region,” J. Mol. Spectrosc. 216, 355–362 (2002). [CrossRef]

]. Nevertheless, significant electromagnetically induced transparency (EIT) was observed in L-type interactions [50

50. S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005). [CrossRef] [PubMed]

] as shown in Fig. 7(b), with up to 40% depth (limited only by available pump powers). Pulse delays up to 800 ps with 20-ns probe pulses were also demonstrated at communication wavelengths using this system. Benabid et al. [52

52. F. Fenabid, P. S. Light, F. Couny, and P. St. J. Russell, “Electromagnetically-induced transparency grid in acetylene-filled hollow-core PCF,” Opt. Express 13, 5694–5703 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-15-5694. [CrossRef]

] observed EIT in both L and V schemes and were able to achieve transparencies as high as 70% by operating at higher pump powers. These observations of nonlinear effects from weakly nonlinear gases illustrate the ability of hollow-core fiber geometries to enhance the nonlinear response of the medium.

Fig. 7. (a) Absorption spectra for acetylene in Ref. [50] with theoretical fit. Energy level diagram shows levels used for EIT and (b) First demonstration of EIT in acetylene molecules. (c) Absorption spectra for acetylene in Ref. [52] and (d) corresponding EIT at higher powers.

Henningsen et al. [53

53. J. Henningsen, J. Hald, and J. C. Petersen, “Saturated absorption in acetylene and hydrogen cyanide in hollow-core photonic bandgap fibers,” Opt. Express 13, 10475–10482 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-26-10475. [CrossRef] [PubMed]

] reported saturated absorption spectroscopy with acetylene and 13C substituted hydrogen cyanide (HCN) with pump powers as low as 10 mW. They also studied gas-filling dynamics inside the core of the fiber and report fundamental differences in gasflow dynamics between acetylene and HCN due to the permanent dipole moment of HCN. Couny et al. [54

54. F. Couny, P. S. Light, F. Benabid, and P. St. J. Russell, “Electromagnetically induced transparency and saturable absorption in all-fiber devices based on 12C2H2-filled hollow-core photonic crystal fiber,” Opt. Commun. 263, 28–31 (2006). [CrossRef]

] fabricated all-fiber devices by splicing HC-PBGFs filled with acetylene to standard SMF fibers and demonstrated EIT at cryogenic temperatures. Hensley et al. [55

55. C. J. Hensley, D. H. Broaddus, C. B. Schaffer, and A. L. Gaeta, “Photonic band-gap fiber gas cell fabricated using femtosecond micromachining,” Opt. Express 15, 6690–6695 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-11-6690. [CrossRef] [PubMed]

] used femtosecond laser pulses to micromachine channels into the sides of HC-PBGFs and demonstrated variable pressure all-fiber gas cells. An improvement in the signal-to-noise ratio for the measurement made in Ref. [53

53. J. Henningsen, J. Hald, and J. C. Petersen, “Saturated absorption in acetylene and hydrogen cyanide in hollow-core photonic bandgap fibers,” Opt. Express 13, 10475–10482 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-26-10475. [CrossRef] [PubMed]

] was reported by Thapa et al. [56

56. R. Thapa, K. Knabe, M. Faheem, A. Naweed, O. L Weaver, and K. L. Corwin, “Saturated absorption spectroscopy of acetylene gas inside large-core photonic bandgap fiber,” Opt. Lett. 31, 2489–2491 (2006). [CrossRef] [PubMed]

] using large-core fibers to isolate core modes from surface modes. As a result of using thermal distribution of molecules at room temperature (υrms≃400m/s) in the small cores (~10 µm), the coherence time of the interaction of molecules with photons is limited by collisions between the molecules and the inner core walls [50

50. S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005). [CrossRef] [PubMed]

], which yields linewidths of the order of 30 - 40 MHz. Hald et al. [57

57. J. Hald, J. C. Petersen, and J. Henningsen, “Saturated optical absorption by slow molecules in hollow-core photonic band-gap fibers,” Phys. Rev. Lett. 98, 213902 (2007). [CrossRef] [PubMed]

] have shown that by properly choosing operational parameters like pressure and pump power, it is possible to achieve small linewidths and still maintain good spectral resolution.

Alkali atoms (e.g., Rubidium) interact strongly with resonant light due to their large transition dipole-moments (|µRb|2~1×102 debye2), which makes them good candidates for systems for performing low-light level nonlinear optics. Alkali atoms also have distinct hydrogen-like energy levels, and magnetic moment coupling between the electrons and nucleus gives rise to a distinct ground-state hyperfine doublet structure. As a result, the energy-level structure in which many energy levels are not directly dipole connected is ideal for setting up two-photon coherences through an intermediate level. This forms the basis of many schemes for storing quantum information that can be manipulated and retrieved. For these reasons alkali-atom systems are very attractive for use in quantum information systems.

The principal difficulty in working with alkali atoms is their chemical reactivity. Alkali atoms react readily with most substances and preventing interactions with glass cell walls is challenging. Furthermore, collisions with cell walls can cause transitions between the non-radiatively linked energy levels that can destroy the delicate coherences created in the atomic systems resulting in a loss of quantum coherence. In hollow-core PBGFs for which the core area is small, this problem is quite severe, and the atom-wall interactions make it difficult to load the fiber with a uniform vapor. Coating cell walls with paraffin has been shown to reduce the collisional decoherence as well as keep the atoms from reacting with bulk-cell walls [58

58. J. C. Camparo, “Alkali 〈I·S〉 wall relaxation in dichlorodimethylsilane coated resonance cells,” J. Chem. Phys. 86, 1533–1539 (1987). [CrossRef]

, 59

59. M. A. Bouchiat and J. Brossel, “Relaxation of optically pumped Rb atoms on paraffin-coated walls,” Phys. Rev. 147, 41–54 (1966). [CrossRef]

]. Ghosh et al. [60

60. S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, “Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber,” Phys. Rev. Lett. 97, 023603 (2006). [CrossRef] [PubMed]

] chemically coated the inner core walls of a HC-PBGF with a monolayer of organosilane (ODMS) to keep Rb atoms from reacting with the core wall. The Rb vapor was allowed to diffuse down the hollow-core and adsorb on the coating. They used light-induced atomic desorption to generate the vapor by desorbing atoms off the wall coatings using a second desorbing beam. Figure 8(a) shows the first demonstration of the generation of a metastable Rb vapor inside HC-PBGFs. By injecting a control beam into the fiber, EIT in Rb in the V-scheme (probe on D1 transition, pump on D2 transition) was demonstrated using pump powers as low as 10 nW, which is 1000 times lower than that used previously in bulk cells, which clearly demonstrated the potential of HC-PBGF geometries for low-light level nonlinear optics. More recently, Light et al. [61

61. P. S. Light, F. Benabid, F. Couny, M. Maric, and A. N. Luiten, “Electromagnetically induced transparency in Rb-filled coated hollow-core photonic crystal fiber,” Opt. Lett. 32, 1323–1325 (2007). [CrossRef] [PubMed]

] have demonstrated Λ-scheme EIT with EIT depths of 5% in a large-core kagome-structure fiber coated with a polymer - PDMS and claimed linewidths as narrow as 6 MHz.

6. Opto-mechanical effects in hollow-core photonic bandgap fibers

Light beams, through their electric field intensities, can exert physical forces on objects as demonstrated by Ashkin [62

62. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970). [CrossRef]

]. Electric fields induce temporary dipole moments in dielectrics, which induces a force that causes the dipole to be attracted towards the region of higher electric field. This effect is used in applications such as optical tweezers for handling small particles and for trapping of atoms with light [63

63. S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986). [CrossRef] [PubMed]

]. HC-PBGFs with light coupled in the core can be used for transporting and delivery of miniscule particles, atoms and biological materials over large distances regardless of bends. This was first demonstrated [64

64. F. Benabid, J. C. Knight, and P. St. J. Russell, “Particle levitation and guidance in hollow-core photonic crystal fiber,” Opt. Express 10, 1195–1203 (2002), http://www.opticsinfobase.org/abstract.cfm?URI=oe-10-21-1195. [PubMed]

] using a 80-µm-core hollow-core fiber that was positioned above a vibrating plate which held 5-µm polystyrene spheres. An Ar-ion beam (514 nm, 80 mW cw) is then coupled into the fiber, and the light coupled out from the other end forms a diverging light field as shown in Fig. 9(a) which accelerates the spheres towards the core in the direction of increasing light intensity. The force experienced by the particle depends on its distance from the fiber as shown in Fig. 9(b), and the authors reported particle transport over a 150-mm distance.

Fig. 8. (a) Absorption of Rb as measured through the fiber. After turning on the desorption beam, the absorption profile implies the generation of a very large atomic population. (b) EIT generated by a 361 nW control beam. Inset shows EIT in presence of optical pumping [60].
Fig. 9. (a) The particle in a diverging beam experiences a force towards the higher intensity region and (b) The force experienced by the particle at various distances from the fiber face. Solid circles represent experimental data while the solid curve denotes the calculated force from theory [64].

Mandal et al. [65

65. S. Mandal and D. Erickson, “Optofluidic transport in liquid core waveguiding structures,” Appl. Phys. Lett. 90, 184103 (2007). [CrossRef]

] have extended the result to demonstrate transport of polystyrene particles through liquid media. The core of a 19-cell HC-PBGF was selectively filled by collapsing the surrounding capillaries at one end and was then dipped into and filled with deionised water. Polystyrene particles were introduced into the deionised water reservoir and a 488-nm laser (210 mW) was coupled into the fiber from the other end to demonstrate transport of particles over a distance of 2 cm. This technique also demonstrated optically induced separation of particles into distinct bands which has potential applications to separation of particles based on size and mass.

In a recent experiment [66

66. T. Takekoshi and R. J. Knize, “Optical guiding of atoms through a hollow-core photonic band-gap fiber,” Phys. Rev. Lett. 98, 210404 (2007). [CrossRef] [PubMed]

], transport of Rb atoms through a HC-PBGF was demonstrated. A beam of Rb atoms is generated using an oven and collimator slits. This beam is incident on a fiber through which light is coupled from the other side. The light is suitably red-detuned from resonance generating an attractive dipole potential for the Rb atoms. The transported atoms were recorded on the other side using a channeltron, and atom fluxes as high as 300 atoms/s were demonstrated.

7. Perspective

The unique HC-PBGF goemetry has opened new doors for pushing the limits of nonlinear optics. The required threshold power for processes such as SRS has been considerably lowered, and the demonstrated conversion eficiencies have been greatly improved. The SRS technique has applications in generation of sub-femtosecond pulses, and numerous groups are working towards using the gas-filled hollow-core fibers as high-gain media for making efficient Raman laser oscillators.

HC-PBGFs can facilitate numerous quantum optical applications. The scheme outlined in Ref. [46

46. H. Schmidt and A. Imamoǧlu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21, 1936–1938 (1996). [CrossRef] [PubMed]

] can be potentially realised down to single-photon levels in HC-PBGF geometries where it is possible to have strong atom-photon coupling. One of the main obstacles is the sizable decoherence that arises due to atom-wall collisions in the core. A solution would be to generate cold-atoms either inside the fiber core or outside the core and then transport them into the core. By controlling the transverse motion of atoms optically to control the collisional decoherence, several groups are trying to realise sensitive quantum-optical effects. By confining atoms and the light mode to volumes with transverse areas approaching the atomic scattering cross-sections, effects seen with high-Q cavities such as photon-blockade [67

67. K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, “Photon blockade in an optical cavity with one trapped atom,” Nature (London) 436, 87–90 (2005). [CrossRef] [PubMed]

] can be studied. This system can also be used to store and interact quantum information by storing multiple light pulses along the fiber length. Using the recently developed fiber micromachining techniques [55

55. C. J. Hensley, D. H. Broaddus, C. B. Schaffer, and A. L. Gaeta, “Photonic band-gap fiber gas cell fabricated using femtosecond micromachining,” Opt. Express 15, 6690–6695 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-11-6690. [CrossRef] [PubMed]

], it might be possible to write electromagnetic cavities into hollow-core fibers by altering the refractive index of the fiber walls, thus improving the atom-photon interaction by orders of magnitude.

These fibers can be used to greatly enhance the nonlinearities for weakly nonlinear materials and can be implemented in many sensitive gas and liquid phase spectroscopic applications. Hollow-core PBGFs may find applications in high harmonic generation (HHG) [68

68. A. L’Huillier, K. J. Schafer, and K. C. Kulander, “Higher-order harmonic generation in xenon at 1064 nm: The role of phase matching,” Phys. Rev. Lett. 66, 2200–2203 (1991). [CrossRef] [PubMed]

, 69

69. P. B. Corkum, “Plasma perspective on strong-field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993). [CrossRef] [PubMed]

]. By filling a hollow-core PBGF with suitable non-Raman-active gases like the noble gases, the conversion efficiency of HHG can be greatly enhanced due to the long interaction lengths [70

70. E. E. Serebryannikov, D. von der Linde, and A. M. Zheltikov, “Phase-matching solutions for high-order harmonic generation in hollow-core photonic-crystal fibers,” Phys. Rev. E , 70, 066619 (2004). [CrossRef]

]. By preparing a resonant medium like Rb vapor using a weak cw beam [71

71. P. M. Paul, T. O. Clatterbuck, C. Lyngå, P. Colosimo, L. F. DiMauro, P. Agostini, and K. C. Kulander, “Enhanced high harmonic generation from an optically prepared excited medium,” Phys. Rev. Lett. 94, 113906 (2005). [CrossRef] [PubMed]

], it might be possible to demonstrate HHG with very high efficiency inside hollow-core PBGFs.

Physical transport of particles along hollow-core fibers can also have uses in biological applications. Atom transport inside HC-PBGFs can be applied to perform Sagnac atom-interferometry along closed loops which can be used for applications such as highly sensitive gyroscopes and accelerometers.

Acknowledgements

The authors gratefully acknowledge support by the Center for Nanoscale Systems, supported by the NSF under grant No. EEC-0117770, the Air Force Office of Scientific Research under contract No. F49620-03-0223, and DARPA under the Slow-Light program.

References and links

1.

P. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003). [CrossRef] [PubMed]

2.

P. St. J. Russell, “Photonic-crystal fibers,” J. Lightw. Technol. 24, 4729–4749 (2006). [CrossRef]

3.

G. P. Agrawal, Fiber-Optic Communication Systems (Wiley, New York, 1992).

4.

K. Nagayama, T. Saitoh, M. Kakui, K. Kawasaki, M. Matsui, H. Takamizawa, H. Miyaki, Y. Ooga, I. Tsuchiya, and Y. Chigusa, “Ultra low loss (0.151 dB/km) fiber and its impact on submarine transmission systems,” OFC2002, Paper FA10-1.

5.

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

6.

T. Abel, J. Hirsch, and J. A. Harrington, “Hollow glass waveguides for broadband infrared transmission,” Opt. Lett. 19, 1034–1036 (1994). [CrossRef] [PubMed]

7.

E. Yablonovitch, “Photonic band-gap structures,” J. Opt. Soc. Am. B 10, 283–295 (1993). [CrossRef]

8.

P. Lodahl, A. Floris van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelberg, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature (London) 430, 654–657 (2004). [CrossRef] [PubMed]

9.

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109, 1492–1505 (1958). [CrossRef]

10.

N. F. Mott, “Electrons in disordered structures,” Adv. Phys. 16, 49–144 (1967). [CrossRef]

11.

P. Yeh and A. Yariv, “Bragg reflection waveguides,” Opt. Commun. 19, 427–430 (1976). [CrossRef]

12.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987). [CrossRef] [PubMed]

13.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987). [CrossRef] [PubMed]

14.

P. R. Villeneuve and M. Piché, “Photonic band gaps in two-dimensional square and hexagonal lattices,” Phys. Rev. B 46, 4969–4972 (1992). [CrossRef]

15.

A. A. Maradudin and A. R. McGurn, “Out of plane propagation of electromagnetic waves in a two-dimensional periodic dielectric medium,” J. Mod. Opt. 41, 275–284 (1994). [CrossRef]

16.

T. A. Birks, P. J. Roberts, P. St. J. Russell, D. M. Atkin, and T. J. Shepherd, “Full 2-D photonic bandgaps in silica/air structures,” Electron. Lett. 31, 1941–1943 (1995). [CrossRef]

17.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999). [CrossRef] [PubMed]

18.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature (London) 424, 657–659 (2003). [CrossRef] [PubMed]

19.

P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, D. P. Williams, L. Farr, M. W. Mason, A. Tomlinson, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express 13, 236–244 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-1-236. [CrossRef] [PubMed]

20.

R. W. Boyd, Nonlinear Optics (Academic, New York, 2003).

21.

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]

22.

F. Benabid, G. Bouwmans, J. C. Knight, P. St. J. Russell, and F. Couny, “Ultrahigh efficiency laser wavelength conversion in a gas-filled hollow core photonic crystal fiber by pure stimulated rotational Raman scattering in molecular hydrogen,” Phys. Rev. Lett. 93, 123903 (2004). [CrossRef] [PubMed]

23.

F. Benabid, G. Antonopoulos, J. C. Knight, and P. St. J. Russell, “Stokes amplification regimes in quasi-cw pumped hydrogen-filled hollow-core photonic crystal fiber,” Phys. Rev. Lett. 95, 213903 (2005). [CrossRef] [PubMed]

24.

F. Couny, F. Benabid, P. J. Roberts, P. S. Light, and M. G. Raymer, “Generation and photonic guidance of multioctave optical-frequency combs,” Science 318, 1118–1121 (2007). [CrossRef] [PubMed]

25.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge, Cambridge, 1997).

26.

S. O. Konorov, A. B. Fedotov, and A. M. Zheltikov, “Enhanced four-wave mixing in a hollow-core photonic-crystal fiber,” Opt. Lett. 28, 1448–1450 (2003). [CrossRef] [PubMed]

27.

A. B. Fedotov, S. O. Konorov, V. P. Mitrokhin, E. E. Serebryannikov, and A. M. Zheltikov, “Coherent anti-Stokes Raman scattering in isolated air-guided modes of a hollow-core photonic-crystal fiber,” Phys. Rev. A 70, 045802 (2004). [CrossRef]

28.

S. O. Konorov, A. B. Fedotov, A. M. Zheltikov, and R. B. Miles, “Phase-matched four-wave mixing and sensing of water molecules by coherent anti-Stokes Raman scattering in large-core-area hollow photonic-crystal fibers,” J. Opt. Soc. Am. B 22, 2049–2053 (2005). [CrossRef]

29.

C. J. Hensley, D. G. Ouzounov, A. L. Gaeta, N. Venkataraman, M. T. Gallagher, and K. W. Koch, “Silica-glass contribution to the effective nonlinearity of hollow-core photonic band-gap fibers,” Opt. Express 15, 3507–3512 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-6-3507. [CrossRef] [PubMed]

30.

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973). [CrossRef]

31.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980). [CrossRef]

32.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704 (2003). [CrossRef] [PubMed]

33.

F. Luan, J. C. Knight, P. St. J. Russell, S. Campbell, D. Xiao, D. T. Reid, B. J. Mangan, D. P. Williams, and P. J. Roberts, “Femtosecond soliton pulse delivery at 800 nm wavelength in hollow-core photonic bandgap fibers,” Opt. Express 12, 835–840 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-5-835. [CrossRef] [PubMed]

34.

D. G. Ouzounov, C. J. Hensley, A. L. Gaeta, N. Venkateraman, M. T. Gallagher, and K. W. Koch, “Soliton pulse compression in photonic band-gap fibers,” Opt. Express 13, 6153–6159 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-16-6153. [CrossRef] [PubMed]

35.

F. Gérôme, K. Cook, A. K. George, W. J. Wadsworth, and J. C. Knight, “Delivery of sub-100 fs pulses through 8 m of hollow-core fiber using soliton compression,” Opt. Express 15, 7126–7131 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-12-7126. [CrossRef] [PubMed]

36.

S. O. Konorov, A. M. Zheltikov, P. Zhou, A. P. Tarasevitch, and D. von der Linde, “Self-channeling of subgigawatt femtosecond laser pulses in a ground-state waveguide induced in the hollow core of a photonic crystal fiber,” Opt. Lett. 29, 1521–1523 (2004). [CrossRef] [PubMed]

37.

K. D. Moll, A. L. Gaeta, and G. Fibich, “Self-similar optical wave collapse: Observation of the Townes profile,” Phys. Rev. Lett. 90, 203902 (2003). [CrossRef] [PubMed]

38.

A. B. Fedotov, E. E. Serebryannikov, and A. M. Zheltikov, “Ionization-induced blueshift of high-peak-power guided-wave ultrashort laser pulses in hollow-core photonic-crystal fibers,” Phys. Rev. A 76, 053811 (2007). [CrossRef]

39.

J. C. Knight, “Photonic crystal fibers and fiber lasers (Invited),” J. Opt. Soc. Am. B 24, 1661–1668 (2007). [CrossRef]

40.

H. Lim, F. Ö. Ilday, and F.W. Wise, “Femtosecond ytterbium fiber laser with photonic crystal fiber for dispersion control,” Opt. Express 10, 1497–1502 (2002) http://www.opticsinfobase.org/abstract.cfm?URI=oe-10-25-1497. [PubMed]

41.

H. Lim and F. W. Wise, “Control of dispersion in a femtosecond ytterbium laser by use of hollow-core photonic bandgap fiber,” Opt. Express 12, 2231–2235 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-10-2231. [CrossRef] [PubMed]

42.

H. Lim, A. Chong, and F. W. Wise, “Environmentally-stable femtosecond ytterbium fiber laser with birefringent photonic bandgap fiber,” Opt. Express 13, 3460–3464 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-9-3460. [CrossRef] [PubMed]

43.

B. Ortaç, M. Plötner, T. Schreiber, J. Limpert, and A. Tünnermann, “Experimental and numerical study of pulse dynamics in positive net-cavity dispersion modelocked Yb-doped fiber lasers,” Opt. Express 1515595–15602 (2007) http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-23-15595. [CrossRef]

44.

D. Bouwmeester, A. K. Ekert, and A. Zeilinger, The Physics of Quantum Information: Quantum Cryptography, Teleportation and Quantum Computation (Springer, New York, 2000).

45.

M. D. Lukin, “Colloquium: Trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys. 75, 457–472 (2003). [CrossRef]

46.

H. Schmidt and A. Imamoǧlu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21, 1936–1938 (1996). [CrossRef] [PubMed]

47.

S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999). [CrossRef]

48.

T. Chaneliére, D. N. Matsukevich, S. D. Jenkins, S. -Y. Lan, T. A. B. Kennedy, and A. Kuzmich, “Storage and retrieval of single photons transmitted between remote quantum memories,” Nature (London) 438, 833–836 (2005). [CrossRef] [PubMed]

49.

K. -J. Boller, A. Imamoǧlu, and S. E. Harris “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991). [CrossRef] [PubMed]

50.

S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005). [CrossRef] [PubMed]

51.

R. El Hachtouki and J. Vander Auwera, “Absolute line intensities in acetylene: The 1.5-µm region,” J. Mol. Spectrosc. 216, 355–362 (2002). [CrossRef]

52.

F. Fenabid, P. S. Light, F. Couny, and P. St. J. Russell, “Electromagnetically-induced transparency grid in acetylene-filled hollow-core PCF,” Opt. Express 13, 5694–5703 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-15-5694. [CrossRef]

53.

J. Henningsen, J. Hald, and J. C. Petersen, “Saturated absorption in acetylene and hydrogen cyanide in hollow-core photonic bandgap fibers,” Opt. Express 13, 10475–10482 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-26-10475. [CrossRef] [PubMed]

54.

F. Couny, P. S. Light, F. Benabid, and P. St. J. Russell, “Electromagnetically induced transparency and saturable absorption in all-fiber devices based on 12C2H2-filled hollow-core photonic crystal fiber,” Opt. Commun. 263, 28–31 (2006). [CrossRef]

55.

C. J. Hensley, D. H. Broaddus, C. B. Schaffer, and A. L. Gaeta, “Photonic band-gap fiber gas cell fabricated using femtosecond micromachining,” Opt. Express 15, 6690–6695 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-11-6690. [CrossRef] [PubMed]

56.

R. Thapa, K. Knabe, M. Faheem, A. Naweed, O. L Weaver, and K. L. Corwin, “Saturated absorption spectroscopy of acetylene gas inside large-core photonic bandgap fiber,” Opt. Lett. 31, 2489–2491 (2006). [CrossRef] [PubMed]

57.

J. Hald, J. C. Petersen, and J. Henningsen, “Saturated optical absorption by slow molecules in hollow-core photonic band-gap fibers,” Phys. Rev. Lett. 98, 213902 (2007). [CrossRef] [PubMed]

58.

J. C. Camparo, “Alkali 〈I·S〉 wall relaxation in dichlorodimethylsilane coated resonance cells,” J. Chem. Phys. 86, 1533–1539 (1987). [CrossRef]

59.

M. A. Bouchiat and J. Brossel, “Relaxation of optically pumped Rb atoms on paraffin-coated walls,” Phys. Rev. 147, 41–54 (1966). [CrossRef]

60.

S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, “Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber,” Phys. Rev. Lett. 97, 023603 (2006). [CrossRef] [PubMed]

61.

P. S. Light, F. Benabid, F. Couny, M. Maric, and A. N. Luiten, “Electromagnetically induced transparency in Rb-filled coated hollow-core photonic crystal fiber,” Opt. Lett. 32, 1323–1325 (2007). [CrossRef] [PubMed]

62.

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970). [CrossRef]

63.

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986). [CrossRef] [PubMed]

64.

F. Benabid, J. C. Knight, and P. St. J. Russell, “Particle levitation and guidance in hollow-core photonic crystal fiber,” Opt. Express 10, 1195–1203 (2002), http://www.opticsinfobase.org/abstract.cfm?URI=oe-10-21-1195. [PubMed]

65.

S. Mandal and D. Erickson, “Optofluidic transport in liquid core waveguiding structures,” Appl. Phys. Lett. 90, 184103 (2007). [CrossRef]

66.

T. Takekoshi and R. J. Knize, “Optical guiding of atoms through a hollow-core photonic band-gap fiber,” Phys. Rev. Lett. 98, 210404 (2007). [CrossRef] [PubMed]

67.

K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, “Photon blockade in an optical cavity with one trapped atom,” Nature (London) 436, 87–90 (2005). [CrossRef] [PubMed]

68.

A. L’Huillier, K. J. Schafer, and K. C. Kulander, “Higher-order harmonic generation in xenon at 1064 nm: The role of phase matching,” Phys. Rev. Lett. 66, 2200–2203 (1991). [CrossRef] [PubMed]

69.

P. B. Corkum, “Plasma perspective on strong-field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993). [CrossRef] [PubMed]

70.

E. E. Serebryannikov, D. von der Linde, and A. M. Zheltikov, “Phase-matching solutions for high-order harmonic generation in hollow-core photonic-crystal fibers,” Phys. Rev. E , 70, 066619 (2004). [CrossRef]

71.

P. M. Paul, T. O. Clatterbuck, C. Lyngå, P. Colosimo, L. F. DiMauro, P. Agostini, and K. C. Kulander, “Enhanced high harmonic generation from an optically prepared excited medium,” Phys. Rev. Lett. 94, 113906 (2005). [CrossRef] [PubMed]

OCIS Codes
(190.4370) Nonlinear optics : Nonlinear optics, fibers
(350.4238) Other areas of optics : Nanophotonics and photonic crystals

ToC Category:
Nonlinear Optics in Novel Media and Materials

History
Original Manuscript: January 28, 2008
Revised Manuscript: March 21, 2008
Manuscript Accepted: March 22, 2008
Published: March 28, 2008

Virtual Issues
Focus Serial: Frontiers of Nonlinear Optics (2007) Optics Express

Citation
Amar R. Bhagwat and Alexander L. Gaeta, "Nonlinear optics in hollow-core photonic bandgap fibers," Opt. Express 16, 5035-5047 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-7-5035


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. P. Russell, "Photonic crystal fibers," Science 299, 358-362 (2003). [CrossRef] [PubMed]
  2. P. St. J. Russell, "Photonic-crystal fibers," J. Lightw. Technol. 24, 4729-4749 (2006). [CrossRef]
  3. G. P. Agrawal, Fiber-Optic Communication Systems (Wiley, New York, 1992).
  4. K. Nagayama, T. Saitoh, M. Kakui, K. Kawasaki, M. Matsui, H. Takamizawa, H. Miyaki, Y. Ooga, I. Tsuchiya, and Y. Chigusa, "Ultra low loss (0.151 dB/km) fiber and its impact on submarine transmission systems," OFC2002, Paper FA10-1.
  5. G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 2001).
  6. T. Abel, J. Hirsch, and J. A. Harrington, "Hollow glass waveguides for broadband infrared transmission," Opt. Lett. 19, 1034-1036 (1994). [CrossRef] [PubMed]
  7. E. Yablonovitch, "Photonic band-gap structures," J. Opt. Soc. Am. B 10, 283-295 (1993). [CrossRef]
  8. P. Lodahl, A. Floris van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelberg, and W. L. Vos, "Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals," Nature (London) 430, 654-657 (2004). [CrossRef] [PubMed]
  9. P. W. Anderson, "Absence of diffusion in certain random lattices," Phys. Rev. 109, 1492-1505 (1958). [CrossRef]
  10. N. F. Mott, "Electrons in disordered structures," Adv. Phys. 16, 49-144 (1967). [CrossRef]
  11. P. Yeh and A. Yariv, "Bragg reflection waveguides," Opt. Commun. 19, 427-430 (1976). [CrossRef]
  12. E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987). [CrossRef] [PubMed]
  13. S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486- 2489 (1987). [CrossRef] [PubMed]
  14. P. R. Villeneuve and M. Piche, "Photonic band gaps in two-dimensional square and hexagonal lattices," Phys. Rev. B 46, 4969-4972 (1992). [CrossRef]
  15. A. A. Maradudin and A. R. McGurn, "Out of plane propagation of electromagnetic waves in a two-dimensional periodic dielectric medium," J. Mod. Opt. 41, 275-284 (1994). [CrossRef]
  16. T. A. Birks, P. J. Roberts, P. St. J. Russell, D. M. Atkin, and T. J. Shepherd, "Full 2-D photonic bandgaps in silica/air structures," Electron. Lett. 31, 1941-1943 (1995). [CrossRef]
  17. R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999). [CrossRef] [PubMed]
  18. C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature (London) 424, 657-659 (2003). [CrossRef] [PubMed]
  19. P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, D. P. Williams, L. Farr, M. W. Mason, A. Tomlinson, T. A. Birks, J. C. Knight, and P. St. J. Russell, "Ultimate low loss of hollow-core photonic crystal fibres," Opt. Express 13, 236-244 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-1-236. [CrossRef] [PubMed]
  20. R. W. Boyd, Nonlinear Optics (Academic, New York, 2003).
  21. 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]
  22. F. Benabid, G. Bouwmans, J. C. Knight, P. St. J. Russell, and F. Couny, "Ultrahigh efficiency laser wavelength conversion in a gas-filled hollow core photonic crystal fiber by pure stimulated rotational Raman scattering in molecular hydrogen," Phys. Rev. Lett. 93, 123903 (2004). [CrossRef] [PubMed]
  23. F. Benabid, G. Antonopoulos, J. C. Knight, and P. St. J. Russell, "Stokes amplification regimes in quasi-cw pumped hydrogen-filled hollow-core photonic crystal fiber," Phys. Rev. Lett. 95, 213903 (2005). [CrossRef] [PubMed]
  24. F. Couny, F. Benabid, P. J. Roberts, P. S. Light, and M. G. Raymer, "Generation and photonic guidance of multioctave optical-frequency combs," Science 318, 1118-1121 (2007). [CrossRef] [PubMed]
  25. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge, Cambridge, 1997).
  26. S. O. Konorov, A. B. Fedotov, and A. M. Zheltikov, "Enhanced four-wave mixing in a hollow-core photoniccrystal fiber," Opt. Lett. 28, 1448-1450 (2003). [CrossRef] [PubMed]
  27. A. B. Fedotov, S. O. Konorov, V. P. Mitrokhin, E. E. Serebryannikov, and A. M. Zheltikov, "Coherent anti-Stokes Raman scattering in isolated air-guided modes of a hollow-core photonic-crystal fiber," Phys. Rev. A 70, 045802 (2004). [CrossRef]
  28. S. O. Konorov, A. B. Fedotov, A. M. Zheltikov, and R. B. Miles, "Phase-matched four-wave mixing and sensing of water molecules by coherent anti-Stokes Raman scattering in large-core-area hollow photonic-crystal fibers," J. Opt. Soc. Am. B 22, 2049-2053 (2005). [CrossRef]
  29. C. J. Hensley, D. G. Ouzounov, A. L. Gaeta, N. Venkataraman, M. T. Gallagher, and K. W. Koch, "Silica-glass contribution to the effective nonlinearity of hollow-core photonic band-gap fibers," Opt. Express 15, 3507-3512 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-6-3507. [CrossRef] [PubMed]
  30. A. Hasegawa and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion," Appl. Phys. Lett. 23, 142-144 (1973). [CrossRef]
  31. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, "Experimental observation of picosecond pulse narrowing and solitons in optical fibers," Phys. Rev. Lett. 45, 1095-1098 (1980). [CrossRef]
  32. D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, "Generation of megawatt optical solitons in hollow-core photonic band-gap fibers," Science 301, 1702-1704 (2003). [CrossRef] [PubMed]
  33. F. Luan, J. C. Knight, P. St. J. Russell, S. Campbell, D. Xiao, D. T. Reid, B. J. Mangan, D. P. Williams, and P. J. Roberts, "Femtosecond soliton pulse delivery at 800 nm wavelength in hollow-core photonic bandgap fibers," Opt. Express 12, 835-840 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-5-835. [CrossRef] [PubMed]
  34. D. G. Ouzounov, C. J. Hensley, A. L. Gaeta, N. Venkateraman, M. T. Gallagher, and K. W. Koch, "Soliton pulse compression in photonic band-gap fibers," Opt. Express 13, 6153-6159 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-16-6153. [CrossRef] [PubMed]
  35. F. Gerome, K. Cook, A. K. George, W. J. Wadsworth, and J. C. Knight, "Delivery of sub-100 fs pulses through 8 m of hollow-core fiber using soliton compression," Opt. Express 15, 7126-7131 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-12-7126. [CrossRef] [PubMed]
  36. S. O. Konorov, A. M. Zheltikov, P. Zhou, A. P. Tarasevitch, and D. von der Linde, "Self-channeling of subgigawatt femtosecond laser pulses in a ground-state waveguide induced in the hollow core of a photonic crystal fiber," Opt. Lett. 29, 1521-1523 (2004). [CrossRef] [PubMed]
  37. K. D. Moll, A. L. Gaeta, and G. Fibich, "Self-similar optical wave collapse: Observation of the Townes profile," Phys. Rev. Lett. 90, 203902 (2003). [CrossRef] [PubMed]
  38. A. B. Fedotov, E. E. Serebryannikov, and A. M. Zheltikov, "Ionization-induced blueshift of high-peak-power guided-wave ultrashort laser pulses in hollow-core photonic-crystal fibers," Phys. Rev. A 76, 053811 (2007). [CrossRef]
  39. J. C. Knight, "Photonic crystal fibers and fiber lasers (Invited)," J. Opt. Soc. Am. B 24, 1661-1668 (2007). [CrossRef]
  40. H. Lim, F. O. Ilday, and F. W. Wise, "Femtosecond ytterbium fiber laser with photonic crystal fiber for dispersion control," Opt. Express 10, 1497-1502 (2002). http://www.opticsinfobase.org/abstract.cfm?URI=oe-10-25-1497. [PubMed]
  41. H. Lim and F. W. Wise, "Control of dispersion in a femtosecond ytterbium laser by use of hollow-core photonic bandgap fiber," Opt. Express 12, 2231-2235 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-10-2231. [CrossRef] [PubMed]
  42. H. Lim, A. Chong, and F. W. Wise, "Environmentally-stable femtosecond ytterbium fiber laser with birefringent photonic bandgap fiber," Opt. Express 13, 3460-3464 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-9-3460. [CrossRef] [PubMed]
  43. B. Ortac¸, M. Plotner, T. Schreiber, J. Limpert, and A. Tunnermann, "Experimental and numerical study of pulse dynamics in positive net-cavity dispersion modelocked Yb-doped fiber lasers," Opt. Express 1515595-15602 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-23-15595. [CrossRef]
  44. D. Bouwmeester, A. K. Ekert, and A. Zeilinger, The Physics of Quantum Information: Quantum Cryptography, Teleportation and Quantum Computation (Springer, New York, 2000).
  45. M. D. Lukin, "Colloquium: Trapping and manipulating photon states in atomic ensembles," Rev. Mod. Phys. 75, 457-472 (2003). [CrossRef]
  46. H. Schmidt and A. Imamoglu, "Giant Kerr nonlinearities obtained by electromagnetically induced transparency," Opt. Lett. 21, 1936-1938 (1996). [CrossRef] [PubMed]
  47. S. E. Harris and L. V. Hau, "Nonlinear optics at low light levels," Phys. Rev. Lett. 82, 4611-4614 (1999). [CrossRef]
  48. T. Chaneliere, D. N. Matsukevich, S. D. Jenkins, S. -Y. Lan, T. A. B. Kennedy, and A. Kuzmich, "Storage and retrieval of single photons transmitted between remote quantum memories," Nature (London) 438, 833-836 (2005). [CrossRef] [PubMed]
  49. K. -J. Boller, A. Imamoglu, and S. E. Harris "Observation of electromagnetically induced transparency," Phys. Rev. Lett. 66, 2593-2596 (1991). [CrossRef] [PubMed]
  50. S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, "Resonant optical interactions with molecules confined in photonic band-gap fibers," Phys. Rev. Lett. 94, 093902 (2005). [CrossRef] [PubMed]
  51. R. El Hachtouki and J. Vander Auwera, "Absolute line intensities in acetylene: The 1.5-μm region," J. Mol. Spectrosc. 216, 355-362 (2002). [CrossRef]
  52. F. Fenabid, P. S. Light, F. Couny, and P. St. J. Russell, "Electromagnetically-induced transparency grid in acetylene-filled hollow-core PCF," Opt. Express 13, 5694-5703 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-15-5694. [CrossRef]
  53. J. Henningsen, J. Hald, and J. C. Petersen, "Saturated absorption in acetylene and hydrogen cyanide in hollow-core photonic bandgap fibers," Opt. Express 13, 10475-10482 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-26-10475. [CrossRef] [PubMed]
  54. F. Couny, P. S. Light, F. Benabid, and P. St. J. Russell, "Electromagnetically induced transparency and saturable absorption in all-fiber devices based on 12C2H2-filled hollow-core photonic crystal fiber," Opt. Commun. 263, 28-31 (2006). [CrossRef]
  55. C. J. Hensley, D. H. Broaddus, C. B. Schaffer, and A. L. Gaeta, "Photonic band-gap fiber gas cell fabricated using femtosecond micromachining," Opt. Express 15, 6690-6695 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-11-6690. [CrossRef] [PubMed]
  56. R. Thapa, K. Knabe, M. Faheem, A. Naweed, O. L. Weaver, and K. L. Corwin, "Saturated absorption spectroscopy of acetylene gas inside large-core photonic bandgap fiber," Opt. Lett. 31, 2489-2491 (2006). [CrossRef] [PubMed]
  57. J. Hald, J. C. Petersen, and J. Henningsen, "Saturated optical absorption by slow molecules in hollow-core photonic band-gap fibers," Phys. Rev. Lett. 98, 213902 (2007). [CrossRef] [PubMed]
  58. J. C. Camparo, "Alkali hI·Si wall relaxation in dichlorodimethylsilane coated resonance cells," J. Chem. Phys. 86, 1533-1539 (1987). [CrossRef]
  59. M. A. Bouchiat and J. Brossel, "Relaxation of optically pumped Rb atoms on paraffin-coated walls," Phys. Rev. 147, 41-54 (1966). [CrossRef]
  60. S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, "Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber," Phys. Rev. Lett. 97, 023603 (2006). [CrossRef] [PubMed]
  61. P. S. Light, F. Benabid, F. Couny, M. Maric, and A. N. Luiten, "Electromagnetically induced transparency in Rb-filled coated hollow-core photonic crystal fiber," Opt. Lett. 32, 1323-1325 (2007). [CrossRef] [PubMed]
  62. A. Ashkin, "Acceleration and trapping of particles by radiation pressure," Phys. Rev. Lett. 24, 156-159 (1970). [CrossRef]
  63. S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, "Experimental observation of optically trapped atoms," Phys. Rev. Lett. 57, 314-317 (1986). [CrossRef] [PubMed]
  64. F. Benabid, J. C. Knight, and P. St. J. Russell, "Particle levitation and guidance in hollow-core photonic crystal fiber," Opt. Express 10, 1195-1203 (2002), http://www.opticsinfobase.org/abstract.cfm?URI=oe-10-21-1195. [PubMed]
  65. S. Mandal and D. Erickson, "Optofluidic transport in liquid core waveguiding structures," Appl. Phys. Lett. 90, 184103 (2007). [CrossRef]
  66. T. Takekoshi and R. J. Knize, "Optical guiding of atoms through a hollow-core photonic band-gap fiber," Phys. Rev. Lett. 98, 210404 (2007). [CrossRef] [PubMed]
  67. K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, "Photon blockade in an optical cavity with one trapped atom," Nature (London) 436, 87-90 (2005). [CrossRef] [PubMed]
  68. A. L’Huillier, K. J. Schafer, and K. C. Kulander, "Higher-order harmonic generation in xenon at 1064 nm: The role of phase matching," Phys. Rev. Lett. 66, 2200-2203 (1991). [CrossRef] [PubMed]
  69. P. B. Corkum, "Plasma perspective on strong-field multiphoton ionization," Phys. Rev. Lett. 71, 1994-1997 (1993). [CrossRef] [PubMed]
  70. E. E. Serebryannikov, D. von der Linde, and A. M. Zheltikov, " Phase-matching solutions for high-order harmonic generation in hollow-core photonic-crystal fibers," Phys. Rev. E,  70, 066619 (2004). [CrossRef]
  71. P. M. Paul, T. O. Clatterbuck, C. Lynga, P. Colosimo, L. F. DiMauro, P. Agostini and K. C. Kulander, "Enhanced high harmonic generation from an optically prepared excited medium," Phys. Rev. Lett. 94, 113906 (2005). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited