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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 6 — Mar. 17, 2008
  • pp: 3577–3582
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Increased pump acceptance bandwidth in spontaneous parametric downconversion process using Bragg reflection waveguides

Krishna Thyagarajan, Ritwick Das, Olivier Alibart, Marc de Micheli, Daniel B. Ostrowsky, and Sébastien Tanzilli  »View Author Affiliations


Optics Express, Vol. 16, Issue 6, pp. 3577-3582 (2008)
http://dx.doi.org/10.1364/OE.16.003577


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Abstract

In this paper we show that by suitably tailoring the dispersion characteristics of a Bragg reflection waveguide (BRW) mode, it is possible to achieve efficient photon pair generation over a large pump bandwidth while maintaining narrow signal bandwidth. The structure proposed consists of a high index core BRW with a periodically poled GaN core and periodically stratified cladding made up of alternate layers of Al0.02Ga0.98N and Al0.45Ga0.55N. Such photon-pair generators should find applications in realizing compact and stable sources for quantum information processing.

© 2008 Optical Society of America

1. Introduction

In the present work, we show that the use of Bragg reflection waveguides (BRWs) allows achieving narrow signal BW together with broad pump acceptance BW using a type-0 interaction with high efficiency in a GaN/AlxGa1-xN based nonlinear system. For quite sometime now, GaN has been investigated as an efficient nonlinear material due to its wide transparency range (365 nm–13.6 µm) and high nonlinear coefficient (d33 = 16.5 pm/V), comparable to LiNbO3 [13

13. J.L.P. Hughes, Y. Wang, and J.E. Sipe, “Calculation of linear and second-order optical response in wurtzite GaN and AlN,” Phys. Rev. B 55, 13630–13639, (1997). [CrossRef]

,14

14. S. Pezzagna, P. Vennegues, N. Grandjean, A.D. Wieck, and J. Massies, “Submicron periodic poling and chemical patterning of GaN,” Appl. Phys. Lett. 87, 062106 (2005). [CrossRef]

]. The use of epitaxially grown III-V semiconductors like GaN (and their ternary derivatives) for the design of optoelectronic devices is particularly advantageous because of the wide possibility of exploiting the mature fabrication technology for designing monolithically integrated components [14

14. S. Pezzagna, P. Vennegues, N. Grandjean, A.D. Wieck, and J. Massies, “Submicron periodic poling and chemical patterning of GaN,” Appl. Phys. Lett. 87, 062106 (2005). [CrossRef]

]. Exploiting the high second order nonlinearity of GaN, Chowdhury et al. [15

15. A. Chowdhury, Hock M. Ng, M. Bhardwaj, and N.G. Weimann, “Second-harmonic generation in periodically poled GaN,” Appl. Phys. Lett. 83, 1077–1079 (2003). [CrossRef]

] have experimentally demonstrated SHG in periodically poled GaN (PPGaN) but the nonlinear properties of GaN were not fully exploited due to the strong dispersion exhibited by bulk GaN in the visible region.

Fig. 1. Schematic of the proposed high index core BRW design for SPDC with PPGaN core and periodic cladding of Al0.02Ga0.98N (n1) and Al0.45Ga0.55N (n2) layers. The thicknesses of the layers corresponding to refractive indices nc, n1, n2 are labeled dc, d1, d2 respectively.

2. Results and analysis

We consider a high index core symmetric planar BRW with PPGaN core [14

14. S. Pezzagna, P. Vennegues, N. Grandjean, A.D. Wieck, and J. Massies, “Submicron periodic poling and chemical patterning of GaN,” Appl. Phys. Lett. 87, 062106 (2005). [CrossRef]

] and periodically stratified cladding made up of alternate layers of Al0.02Ga0.98N (n1) and Al0.45Ga0.55N (n2). These two particular alloys provide significant contrast in the refractive indices for better confinement of the modes as well as assisting in obtaining suitable dispersion characteristics [17

17. B.R. West and A.S. Helmy, “Dispersion tailoring of the quarter-wave Bragg reflection waveguide,” Opt. Express 14, 4073–4086 (2006). [CrossRef] [PubMed]

]. The epitaxial growth technique could lead to periodic poling of the upper cladding layers as well but this would have no effect on the argument presented here. The pump (λp = 800 nm) and signal (λs = 1550 nm) are taken to be total internal reflection (TIR) guided modes (x-polarized) in the high index core BRW (Fig. 1) and the idler (λi = 1653 nm) is taken to be a BRW mode (x- polarized) that satisfies the quarter wave condition [17

17. B.R. West and A.S. Helmy, “Dispersion tailoring of the quarter-wave Bragg reflection waveguide,” Opt. Express 14, 4073–4086 (2006). [CrossRef] [PubMed]

]. The analysis of the BRW modes is carried out by considering only the modes which have effective indices lower than those of the BRW materials (nc, n1 and n2), and falling within the stop band of the periodic cladding [16

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

]. The calculation of the effective indices for the BRW modes is described in [16

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

,17

17. B.R. West and A.S. Helmy, “Dispersion tailoring of the quarter-wave Bragg reflection waveguide,” Opt. Express 14, 4073–4086 (2006). [CrossRef] [PubMed]

]. Since, the guidance takes place via Bragg reflection; the BRW modes are highly dispersive essentially due to strong variation of the reflection coefficient of the periodic cladding with the wavelength [17

17. B.R. West and A.S. Helmy, “Dispersion tailoring of the quarter-wave Bragg reflection waveguide,” Opt. Express 14, 4073–4086 (2006). [CrossRef] [PubMed]

]. The TIR guided modes are analyzed using the standard transfer matrix method for leaky waves with 12 bilayers of the periodic cladding to achieve negligible leakage loss [18

18. A.K. Ghatak and K. Thyagarajan, “Introduction to Fiber Optics,” Cambridge University Press, Cambridge, U.K. (1998)

]. The refractive index and nonlinear coefficients of various components of the waveguiding structure is calculated using references [19

19. G.M. Laws, E.C. Larkins, I. Harrison, C. Molloy, and D. Somerford, “Improved refractive index formulas for the AlxGa1-xN and InyGa1-yN alloys,” J. Appl. Phys. 89, 1108–1115 (2001). [CrossRef]

] and [13

13. J.L.P. Hughes, Y. Wang, and J.E. Sipe, “Calculation of linear and second-order optical response in wurtzite GaN and AlN,” Phys. Rev. B 55, 13630–13639, (1997). [CrossRef]

], respectively. The proposed structure is designed such that the phase velocity dispersion slope of the idler (BRW) mode almost matches with that of the pump whereas it is significantly different from that of the signal. This can simultaneously lead to broad pump acceptance BW and narrow signal BW.

The quasi phase matching (QPM) condition is given by,

βp=βs+βi+K
(1)

where βp, βs and βi are the propagation constants of the mode at the pump, signal and idler wavelengths respectively and K represents the grating vector of the QPM grating. Now, for a fixed grating period, the change in signal wavelength due to a change in pump wavelength is given by,

dβsdλp=ddλp(βpβi)
(2)

Fig. 2. Plot showing the variation of the difference of the propagation constants of the pump (TIR-guided) and idler (BRW) modes, (βpi) as a function of the pump wavelength (λp) for dc = 582 nm and ΛQPM = 2.77 µm.
Fig. 3. Plot of the signal spectral power density as a function of pump wavelength (λp) with λs = 1550 nm for SPDC in the BRW structure (dashed curve) and in the conventional TIR based waveguide (solid curve).

In order to illustrate the idea, we have calculated the signal spectral power density variation with respect to pump wavelength (λp) for SPDC in the waveguide using the following equation [12

12. M. Fiorentino, S.M. Spillane, R.G. Beausoleil, T.D. Roberts, P. Battle, and M.W. Munro, “Spontaneous parametric down-conversion in periodically poled KTP waveguides and bulk crystals,” Opt. Express 15, 7479–7488 (2007). [CrossRef] [PubMed]

],

dPsdλs=16π3deff2l2cPpε0nsnpniλs4λiIov2sinc2(Δβl2)
(3)

where deff (=(2/π)d33) is the effective nonlinear coefficient for first order QPM, Δβ=βpsi-2π/ΛQPM is the phase mismatch parameter. ‘l’ is the interaction (waveguide) length, Pp is the input pump power per unit length in the y-direction (invariant) and ns, np and ni are the effective indices of signal (λs), pump (λp) and idler (λi) modes respectively. ‘Iov’ is the overlap integral given by [12

12. M. Fiorentino, S.M. Spillane, R.G. Beausoleil, T.D. Roberts, P. Battle, and M.W. Munro, “Spontaneous parametric down-conversion in periodically poled KTP waveguides and bulk crystals,” Opt. Express 15, 7479–7488 (2007). [CrossRef] [PubMed]

],

Iov=dxEx(p)Ex(s)Ex(i)
(4)

Fig. 4. Plot of variation of signal (λs) and idler (λi) wavelengths as function of pump wavelength (λp) for the BRW with dc = 582 nm and ΛQPM = 2.77 µm.
Fig. 5. Plot of the signal spectral power density as a function of signal wavelength (λs) with λp = 800 nm for SPDC in the BRW structure (solid curve) and in the conventional TIR based waveguide (dashed curve).

Keeping now the pump wavelength fixed at 800 nm, Fig. 5 shows the variation of signal spectral power density as a function of λs, for the designed BRW as well as the conventional TIR waveguide showing a signal BW of ΔλFWHM = 1.3 nm for l = 15 mm, which is much smaller for the designed BRW as compared to the conventional case (ΔλFWHM = 17.5 nm) for l = 15 mm. The reason for this narrow BW is that the dispersion characteristics of the signal (TIR guided) and idler (BRW mode) are so different that considerable phase mismatch (Δβ≠0) between the interacting modes results if λs changes (with λp remaining constant).

The expected number of photon pairs generated by the BRW as well as the conventional waveguide can be estimated by using Eq. (3). If we limit our detection window to 1 nm around central signal wavelength (λs = 1550 nm), we obtain the estimated pair flux to be ~6.67×108 pairs/s per mW/µm of pump for 15 mm long BRW whereas that for conventional waveguide, the estimated photon flux would be ~1.62×109 pairs/s per mW/µm of pump for identical length. Although, the estimated photon flux generation rate appears to be higher for a pump wavelength λp of 800 nm (corresponding to phase matched operation) for the conventional waveguide, the distinct advantage offered by our design is the tolerance to pump wavelength changes. Thus if the pump wavelength deviates from the central pump wavelength (λp = 800 nm) even by 0.5 nm, the efficiency of the photon flux generation for the conventional waveguide drops to almost zero (as shown in Fig. 3) while for the proposed design even for a deviation of pump wavelength by ~ 6 nm, the photon pair generation efficiency would still be appreciably large with a corresponding generation of a narrowband signal (~1 nm).

3. Discussion

The primary advantage offered by BRWs for efficient generation of entangled photon pairs is that we can tune the dispersive behaviour of a BRW mode to obtain suitable BW with respect to any wavelength of operation and for any material system within the constraints of transparency and nonlinearity of the constituent materials. This implies that depending upon the dispersion exhibited by the constituent materials and the BW targeted for the three-wave interaction, the BRW mode could be chosen appropriately and its waveguide dispersion could be tailored accordingly so as to counter the dispersion of other guided modes. By forcing the BRW mode to operate closer to the center of the bandgap, we can enhance the overlap in Eq. (4) but this leads to a trade-off between the target BW and spectral power density. Nevertheless, the freedom afforded by this design to accomplish type-0 interaction using any material system with high nonlinear coefficients can be exploited to achieve high spectral power density. Even though, this idea has been recently exploited using bulk birefringent crystals [21

21. P.J. Mosley, J.S. Lundeen, B.J. Smith, P. Wasylczyk, A.B. U’Ren, C. Silberhorn, and I.A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” arXiv:0711.1054.

], we believe the present work is the first proposition accomplishing this in a guided wave configuration that would lead to considerably higher efficiencies essentially due to longer interaction length and possibility of accessing the maximum nonlinear coefficient.

4. Conclusion

In conclusion, we have proposed a BRW design that can simultaneously achieve broad pump acceptance bandwidth and narrow signal bandwidth with only a small sacrifice of the efficiency. Due to the narrow signal BW, the idler spectrum would be broad if a broadband pump is used. Such a technique can be implemented for designing an unbalanced photon-pair source in terms of bandwidth, for which the narrowband photon would travel over long distance while the broadband one would be operated locally to prevent from decoherence due to dispersion. As an example, one could think of a heralded single photon source in which the broadband photon is detected, using an upconversion-based or a superconducting detector [22

22. T. Thew, S. Tanzilli, L. Krainer, S.C. Zeller, A. Rochas, I. Rech, S. Cova, H. Zbinden, and N. Gisin, “Low jitter upconversion detectors for telecom wavelength GHz QKD,” New J. Phys. 8, 32 (2006). [CrossRef]

,23

23. A. Verevkin, A. Pearlman, W. Slstrokysz, J. Zhang, M. Currie, A. Korneev, G. Chulkova, O. Okunev, P. Kouminov, K. Smirnov, B. Voronov, G.N. Gol’tsman, and Roman Sobolewski, “Ultrafast superconducting single-photon detectors for near-infrared-wavelength quantum communications,” J. Mod. Opt. 51, 1447–1458, (2004).

], in order to announce the arrival time of the associated narrowband signal photon at the end of the quantum communication channel [24

24. S. Fasel, O. Alibart, S. Tanzilli, P. Baldi, A. Beveratos, N. Gisin, and H. Zbinden, “High-quality asynchronous heralded single-photon source at telecom wavelength,” New J. Phys. 6, 163 (2004). [CrossRef]

].

Acknowledgments

References and Links

1.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum Cryptography,” Rev. Mod Phys. 74, 145–195 (2002). [CrossRef]

2.

C.H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W.K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993). [CrossRef] [PubMed]

3.

I. Marcikic, H. de Riedmatten, W. Tittel, H. Zbinden, and N. Gisin, “Long-distance teleportation of qubits at telecommunication wavelengths,” Nature 421, 509–513 (2003). [CrossRef] [PubMed]

4.

S. Lloyd, M.S. Shahriar, J.H. Shapiro, and P.R. Helmer, “Long distance, quantum teleportation to atomic states via complete Bell states measurement,” Phys. Rev. Lett. 87, 167903 (2001). [CrossRef] [PubMed]

5.

S. Tanzilli, W. Tittel, H. De Riedmatten, H. Zbinden, P. Baldi, M. De Micheli, D.B Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Europ. Phys. J. D 18, 155–160 (2002). [CrossRef]

6.

K. Banaszek, A. B. U’Ren, and I.A. Walmsley, “Generation of correlated photons in controlled spatial modes by downconversion in nonlinear waveguides,” Opt. Lett. 26, 1367–1369 (2001). [CrossRef]

7.

R.T. Thew, S. Tanzilli, W. Tittel, H. Zbinden, and N. Gisin, “Experimental investigation of the robustness of partially entangled qubits over 11 km,” Phys. Rev. A 66, 062304 (2002). [CrossRef]

8.

G. Fujii, N. Namekata, M. Motoya, S. Kurimura, and S. Inoue, “Bright narrowband source of photon pairs at optical telecommunication wavelengths using a type-II periodically poled lithium niobate waveguide,” Opt. Express 15, 12769–12776 (2007). [CrossRef] [PubMed]

9.

M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nature Phys. 3, 692–695 (2007). [CrossRef]

10.

E. Mason, M.A. Albota, F. König, and F.N.C. Wong, “Efficient generation of tunable photon pairs at 0.8 and 1.6 µm,” Opt. Lett. 27, 2115–2117 (2002). [CrossRef]

11.

I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, “Time-bin entangled qubits for quantum communication created by femtosecond pulses,” Phys. Rev. A 66, 062308 (2002). [CrossRef]

12.

M. Fiorentino, S.M. Spillane, R.G. Beausoleil, T.D. Roberts, P. Battle, and M.W. Munro, “Spontaneous parametric down-conversion in periodically poled KTP waveguides and bulk crystals,” Opt. Express 15, 7479–7488 (2007). [CrossRef] [PubMed]

13.

J.L.P. Hughes, Y. Wang, and J.E. Sipe, “Calculation of linear and second-order optical response in wurtzite GaN and AlN,” Phys. Rev. B 55, 13630–13639, (1997). [CrossRef]

14.

S. Pezzagna, P. Vennegues, N. Grandjean, A.D. Wieck, and J. Massies, “Submicron periodic poling and chemical patterning of GaN,” Appl. Phys. Lett. 87, 062106 (2005). [CrossRef]

15.

A. Chowdhury, Hock M. Ng, M. Bhardwaj, and N.G. Weimann, “Second-harmonic generation in periodically poled GaN,” Appl. Phys. Lett. 83, 1077–1079 (2003). [CrossRef]

16.

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

17.

B.R. West and A.S. Helmy, “Dispersion tailoring of the quarter-wave Bragg reflection waveguide,” Opt. Express 14, 4073–4086 (2006). [CrossRef] [PubMed]

18.

A.K. Ghatak and K. Thyagarajan, “Introduction to Fiber Optics,” Cambridge University Press, Cambridge, U.K. (1998)

19.

G.M. Laws, E.C. Larkins, I. Harrison, C. Molloy, and D. Somerford, “Improved refractive index formulas for the AlxGa1-xN and InyGa1-yN alloys,” J. Appl. Phys. 89, 1108–1115 (2001). [CrossRef]

20.

N.E. Yu, J.H. Ro, M. Cha, S. Kurimura, and T. Taira, “Broadband quasi-phase matched second-harmonic generation in MgO-doped periodically poled LiNbO3 at the communications band,” Opt. Lett. 27, 1046–1048 (2002). [CrossRef]

21.

P.J. Mosley, J.S. Lundeen, B.J. Smith, P. Wasylczyk, A.B. U’Ren, C. Silberhorn, and I.A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” arXiv:0711.1054.

22.

T. Thew, S. Tanzilli, L. Krainer, S.C. Zeller, A. Rochas, I. Rech, S. Cova, H. Zbinden, and N. Gisin, “Low jitter upconversion detectors for telecom wavelength GHz QKD,” New J. Phys. 8, 32 (2006). [CrossRef]

23.

A. Verevkin, A. Pearlman, W. Slstrokysz, J. Zhang, M. Currie, A. Korneev, G. Chulkova, O. Okunev, P. Kouminov, K. Smirnov, B. Voronov, G.N. Gol’tsman, and Roman Sobolewski, “Ultrafast superconducting single-photon detectors for near-infrared-wavelength quantum communications,” J. Mod. Opt. 51, 1447–1458, (2004).

24.

S. Fasel, O. Alibart, S. Tanzilli, P. Baldi, A. Beveratos, N. Gisin, and H. Zbinden, “High-quality asynchronous heralded single-photon source at telecom wavelength,” New J. Phys. 6, 163 (2004). [CrossRef]

OCIS Codes
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes
(190.4970) Nonlinear optics : Parametric oscillators and amplifiers
(230.1480) Optical devices : Bragg reflectors
(230.7390) Optical devices : Waveguides, planar

ToC Category:
Nonlinear Optics

History
Original Manuscript: November 14, 2007
Revised Manuscript: December 23, 2007
Manuscript Accepted: January 9, 2008
Published: March 3, 2008

Citation
Krishna Thyagarajan, Ritwick Das, Olivier Alibart, Marc d. Micheli, Daniel B. Ostrowsky, and Sébastien Tanzilli, "Increased pump acceptance bandwidth in spontaneous parametric downconversion process using Bragg reflection waveguides," Opt. Express 16, 3577-3582 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-6-3577


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References

  1. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, "Quantum Cryptography," Rev. Mod Phys. 74, 145-195 (2002). [CrossRef]
  2. C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W.K. Wootters, "Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels," Phys. Rev. Lett. 70, 1895-1899 (1993). [CrossRef] [PubMed]
  3. I. Marcikic, H. de Riedmatten, W. Tittel, H. Zbinden, and N. Gisin, "Long-distance teleportation of qubits at telecommunication wavelengths," Nature 421, 509-513 (2003). [CrossRef] [PubMed]
  4. S. Lloyd, M. S. Shahriar, J. H. Shapiro, and P. R. Helmer, "Long distance, quantum teleportation to atomic states via complete Bell states measurement," Phys. Rev. Lett. 87, 167903 (2001). [CrossRef] [PubMed]
  5. S. Tanzilli, W. Tittel, H. De Riedmatten, H. Zbinden, P. Baldi, M. De Micheli, D. B Ostrowsky, and N. Gisin, "PPLN waveguide for quantum communication," Europ. Phys. J. D 18, 155-160 (2002). [CrossRef]
  6. K. Banaszek, A. B. U’Ren, and I. A. Walmsley, "Generation of correlated photons in controlled spatial modes by downconversion in nonlinear waveguides," Opt. Lett. 26, 1367-1369 (2001). [CrossRef]
  7. R. T. Thew, S. Tanzilli, W. Tittel, H. Zbinden, and N. Gisin, "Experimental investigation of the robustness of partially entangled qubits over 11 km," Phys. Rev. A 66, 062304 (2002). [CrossRef]
  8. G. Fujii, N. Namekata, M. Motoya, S. Kurimura, and S. Inoue, "Bright narrowband source of photon pairs at optical telecommunication wavelengths using a type-II periodically poled lithium niobate waveguide," Opt. Express 15, 12769-12776 (2007). [CrossRef] [PubMed]
  9. M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, H. Zbinden, "Entangling independent photons by time measurement," Nature Phys. 3, 692-695 (2007). [CrossRef]
  10. E. Mason, M. A. Albota, F. König, and F. N. C. Wong, "Efficient generation of tunable photon pairs at 0.8 and 1.6 ?m," Opt. Lett. 27, 2115-2117 (2002). [CrossRef]
  11. I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, "Time-bin entangled qubits for quantum communication created by femtosecond pulses," Phys. Rev. A 66, 062308 (2002). [CrossRef]
  12. M. Fiorentino, S. M. Spillane, R. G. Beausoleil, T. D. Roberts, P. Battle, and M. W. Munro, "Spontaneous parametric down-conversion in periodically poled KTP waveguides and bulk crystals," Opt. Express 15, 7479-7488 (2007). [CrossRef] [PubMed]
  13. J. L. P. Hughes, Y. Wang, and J. E. Sipe, "Calculation of linear and second-order optical response in wurtzite GaN and AlN," Phys. Rev. B 55, 13630-13639, (1997). [CrossRef]
  14. S. Pezzagna, P. Vennegues, N. Grandjean, A. D. Wieck, and J. Massies, "Submicron periodic poling and chemical patterning of GaN," Appl. Phys. Lett. 87, 062106 (2005). [CrossRef]
  15. A. Chowdhury, HockM. Ng, M. Bhardwaj, and N.G. Weimann, "Second-harmonic generation in periodically poled GaN," Appl. Phys. Lett. 83, 1077-1079 (2003). [CrossRef]
  16. P. Yeh, and A. Yariv, " Bragg reflection waveguides," Opt. Commun. 19, 427-430 (1976). [CrossRef]
  17. B. R. West and A. S. Helmy, "Dispersion tailoring of the quarter-wave Bragg reflection waveguide," Opt. Express 14, 4073- 4086 (2006). [CrossRef] [PubMed]
  18. A. K. Ghatak and K. Thyagarajan, "Introduction to Fiber Optics," (Cambridge University Press, Cambridge, U.K. 1998)
  19. G. M. Laws, E. C. Larkins, I. Harrison, C. Molloy, and D. Somerford, "Improved refractive index formulas for the AlxGa1-xN and InyGa1-yN alloys," J. Appl. Phys. 89, 1108-1115 (2001). [CrossRef]
  20. N. E. Yu, J. H. Ro, M. Cha, S. Kurimura, and T. Taira, "Broadband quasi-phase matched second-harmonic generation in MgO-doped periodically poled LiNbO3 at the communications band," Opt. Lett. 27, 1046-1048 (2002). [CrossRef]
  21. P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, and I. A. Walmsley, "Heralded generation of ultrafast single photons in pure quantum states," arXiv:0711.1054.
  22. T. Thew, S. Tanzilli, L. Krainer, S. C. Zeller, A. Rochas, I. Rech, S. Cova, H. Zbinden, and N. Gisin, "Low jitter upconversion detectors for telecom wavelength GHz QKD," New J. Phys. 8, 32 (2006). [CrossRef]
  23. A. Verevkin, A. Pearlman, W. Slstrokysz, J. Zhang, M. Currie, A. Korneev, G. Chulkova, O. Okunev, P. Kouminov, K. Smirnov, B. Voronov, G.N. Gol'tsman, and R. Sobolewski, "Ultrafast superconducting single-photon detectors for near-infrared-wavelength quantum communications," J. Mod. Opt. 51, 1447-1458, (2004).
  24. S. Fasel, O. Alibart, S. Tanzilli, P. Baldi, A. Beveratos, N. Gisin, and H. Zbinden, "High-quality asynchronous heralded single-photon source at telecom wavelength," New J. Phys. 6, 163 (2004). [CrossRef]

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