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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 1 — Jan. 3, 2011
  • pp: 380–386
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Polarization independent quasi-phase-matched sum frequency generation for single photon detection

Xiao-shi Song, Zi-yan Yu, Qin Wang, Fei Xu, and Yan-qing Lu  »View Author Affiliations


Optics Express, Vol. 19, Issue 1, pp. 380-386 (2011)
http://dx.doi.org/10.1364/OE.19.000380


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Abstract

Polarization independent sum frequency generation (SFG) is proposed in an electro-optic (EO) tunable periodically poled Lithium Niobate (PPLN). The PPLN consists of four sections. External electric field could be selectively applied to them to induce polarization rotation between the ordinary and extraordinary waves. If the domain structure is well designed, the signal wave with an arbitrary polarization state could realize efficient frequency up-conversion as long as a z-polarized pump wave is selected. The applications in single photon detection and optical communications are discussed.

© 2010 OSA

1. Introduction

2. Theory and simulation

Figure 1
Fig. 1 Schematic diagram of a four-section PPLN. External electric fields are applied along the y-axis at the second and the third sections, representing with EO1 and EO2 in the figure.
shows the schematic diagram of a polarization independent PPLN containing four sections. The first and the fourth sections are identical whose period is designed just for QPM SFG. However, the periods in the second and third sections are different; they are designed only for polarization rotation of the signal wave and the SFW, respectively [9

9. Y. Q. Lu, Z. L. Wan, Q. Wang, Y. X. Xi, and N. B. Ming, “Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications,” Appl. Phys. Lett. 77(23), 3719 (2000). [CrossRef]

]. External DC electrical fields are applied at the y-surfaces of the second and third sections. With a suitable electric field, the second and third sections could just act as 90° polarization rotators for signal wave and SFW, respectively. In order to utilize the largest nonlinear coefficient d33 of LiNbO3, the lights should propagate along the crystal’s x-axis and the escorting pump wave should be z-polarized. Because the wavelength bandwidths for polarization rotation in the second and third sections are very sharp [9

9. Y. Q. Lu, Z. L. Wan, Q. Wang, Y. X. Xi, and N. B. Ming, “Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications,” Appl. Phys. Lett. 77(23), 3719 (2000). [CrossRef]

], the polarization state of the pump wave is not affected inside the sample.

When a z-polarized signal wave is propagated through the sample, the signal wave will be converted to the z-polarized SFW basically in the first section and then the generated z-polarized SFW is further totally converted to a y-polarized SFW in the third section. At last the SFW passes through the last section without nonlinear frequency conversion. On the other hand, when a y-polarized signal wave is injected, it passes through the first section without SFG. Then it is converted to a z-polarized signal wave in the second section. Because the third section has no impact to it, the generated z-polarized signal wave is further frequency up-converted to a z-polarized SFW after it enters the fourth section. In a word, a y-polarized signal wave generates a z-polarized SFW while a z-polarized signal wave induces a y-polarized SFW. As long as the first and the last sections have the same length, the PPLN may have the same frequency up-conversion capability for y- and z- polarized signal waves. Because all normally-incident lights could be divided into y- and z- polarized components, polarization independent frequency up-conversion thus could be expected.

To analysis the above processes in detail and obtain the numerical results, the corresponding coupling equations can be deduced under the plane-wave approximation with consideration of both SFG and electro-optic (EO) interactions [10

10. A. Yariv, and P. Yeh, Optical Waves in Crystals (John Wiley and Sons, New York, 1984), Chap. 12.

,11

11. Y. Kong, X. F. Chen, and Y. Xia, “Competition of frequency conversion and polarization coupling in periodically poled lithium niobate,” Appl. Phys. B 91(3-4), 479–482 (2008). [CrossRef]

].
{dEsydx=iωsnsycε23(s)(x)EszeiΔk2x,dEszdx=iωsnszc[ε23(s)(x)EsyeiΔk2x+d33(x)EpzEozeiΔk1x],dEpzdx=iωpnpzcd33(x)Esz*EozeiΔk1x,dEoydx=iωonoycε23(o)(x)EozeiΔk3x,dEozdx=iωonozc[ε23(o)(x)EoyeiΔk3x+d33(x)EszEpzeiΔk1x].
(1)
Where Ejξ, ωjξ, kjξ and njξ (the subscript j = s, p, o refer to the signal wave, the pump wave and the SFW respectively, and ξ=y,zrepresent the polarizations) are the external field amplitudes, the angular frequencies, the wave-vectors and the refractive indices, respectively. c is the speed of light in vacuum. The converted wave is generated at frequency ωo=ωs+ωp. d33(x) = d33f(x) is the modulated nonlinear coefficient. ε23(s)(x)=nsy2nsz2γ51(x)E for the signal wave and ε23(o)(x)=noy2noz2γ51(x)E for the SFW, where γ51(x)=γ51f(x) is the modulated EO coefficient in PPLN and E refers to the external DC electric field. As no electric field is applied to the first and the fourth section, the corresponding E is 0. Δk1=kozkszkpz, Δk2=ksyksz, Δk3=koykoz are the wave vector mismatch for SFG and polarization rotation of the signal wave and the SFW, respectively. The asterisk denotes complex conjugation.

In a PPLN, the structure function f(x) changes its sign form + 1 to −1 periodically in different domains. It can be expanded as Fourier series, f(x)=mgmexp(iGmx) where Gm are the reciprocal vectors and gm are the amplitudes of the reciprocal vectors. Without loss of generality, the reciprocal vector G1 (the subscript 1 is ignored hereinafter) is adopted to compensate the wave vector mismatch for efficient conversion. For example, in the first and fourth section, G1, 4 (here the second subscript denotes which section the reciprocal vector is in) is adopted as Δk1=kozkszkpz=G1,4 to compensate the nonlinear phase mismatch for SFG and the wave vector mismatch becomes Δk1=kozkszkpzG1,4=0. In the same way, G2 in the second section is adopted to compensate the phase mismatch for the signal wave’s polarization rotation as Δk2=ksyksz=G2 (i.e., Δk2=ksykszG2=0). And G3 in the third section is adopted to compensate the phase mismatch for SFW’s polarization rotation as Δk3=koykoz=G3 (Δk3=koykozG3=0). In this case, the coupling Eqs. (1) can be simplified as:
{dAsydx=iK2AszeiΔk2x,dAszdx=iK2AsyeiΔk2xiK1ApzAozeiΔk1x,dApzdx=iK1Asz*AozeiΔk1x,dAoydx=iK3AozeiΔk3x,dAozdx=iK3AoyeiΔk3xiK1*AszApzeiΔk1x.
(2)
with Aj=njωjEj, K1=d33g1cωszωpzωoznsznpznoz, K2=iγ51g1ωsE2cnsy3nsz3, K3=iγ51g1ωoE2cnoy3noz3. Ki (i = 1, 2, 3) represents the coupling coefficients for SFG and EO effect.

Numerical solutions to Eqs. (2) have been done to verify our design. A 1064 nm pump wave is employed and the injected signal wave has the wavelength of 1550 nm. In order to convert the signal wave to the SFW completely, we set the intensity of the signal wave at 0.2 MW/cm2, which is far weaker than the intensity of the pump wave at 10 MW/cm2. The PPLN period in the first and fourth section is designed at Λ = 11.62 μm to satisfy the SFG QPM condition at room temperature 25 °C. The corresponding periods of these two sections are 500 for complete up-conversion. Λ = 20.48 μm in the second section and Λ = 7.27 μm in the third section are selected for polarization rotation of the signal wave and the SFW, respectively. d33 = 25.2 pm/V and γ = 32.6 pm/V are used for simulation. To realize the complete conversion between the ordinary and extraordinary waves, we set the electric field at 710 V/mm and the periods of the second and the third sections at 250 and 260 respectively. The sample length is about 18.6 mm.

Figures 2
Fig. 2 The light intensity at different positions inside the four-section PPLN when the signal wave is y-polarized (a) or z-polarized (b). Solid, dotted, dash-dotted and dashed curves represent y-polarized signal wave, z-polarized signal wave, y-polarized SFW and z-polarized SFW, respectively. The unit of the intensity is MW/cm2.
and 3
Fig. 3 The light intensity versus the wavelength when the signal wave is y-polarized ((a) and (b) correspond to the signal wave and SFW respectively) or z-polarized ((c) and (d) correspond to the signal wave and SFW respectively). The unit of the intensity is MW/cm2.
show the numerical simulation results. Figure 2 describes the light intensity evolution of the signal wave and the SFW inside our devised PPLN. It can be seen that no matter with what kind of polarization states, the injected signal wave is almost totally converted to SFW. The light intensity of the SFW remains about 0.5 MW/cm2 for the y-polarized (Fig. 2(a)) and z-polarized (Fig. 2(b)) signal waves. Figure 3 shows the spectral response. Figures 3(a) and 3(b) correspond to the results when a y-polarized signal wave is injected. Figures 3(c) and 3(d) correspond to the results when a z-polarized signal wave is injected. For example, when a y-polarized signal wave is injected, the light intensity of the generated z-polarized SFW reaches the highest and the light intensity of the y- and z- polarized signal wave vanishes if the phase matching condition is satisfied in accordance with Fig. 2. In addition, the light intensity of the z-polarized signal wave shows double peaks at the wavelength which has a slight offset from the phase matching point. The results are consistent when a z-polarized signal wave is injected but the light intensity of the z-polarized signal wave has small fluctuations near the phase matching point. On the other hand, the y-polarized SFW is negligible at side wavelengths when a y-polarized signal wave is injected. This is because when a y-polarized signal wave near the phase matching point is injected, the z-polarized SFW will not be generated in the first section so that there is no y-polarized SFW being converted in the third section. As a result, the y-polarized sum-frequency wave will not be observed at the side wavelengths. However, when a z-polarized signal wave at side wavelengths is injected, the signal wave will not be fully converted into the z-polarized SFW in the first section and the left signal wave will not be totally converted into the y-polarized signal wave. The remaining z-polarized signal wave is partly frequency up-converted into SFW in the forth section so we observe a non-negligible generation of z-polarized SFW at side wavelengths. Because the total energy of involved lights should be conserved and there are some z-polarized SFWs at side wavelengths, the light intensity of the z-polarized signal wave thus shows small side fluctuations (e.g., double peaks) at corresponding wavelengths.

3. Discussion

In addition to bulk PPLN, Lithium niobate waveguide also has been utilized in many optical devices and applications. In comparison with bulk crystal, the waveguide has non-uniform mode distribution while with high field confinement. Efficient fiber to waveguide coupling has been realized for years so that a PPLN waveguide could be well compatible with most optical communication devices. Although our simulation above is based on the plane-wave approximation, the key coupling equations, i.e., Eqs. (2), still can be used in the waveguide case with minor revision about the coupling coefficients and wave vector mismatches. The overlap integral of the mode fields also should be added in the coupling coefficients. The propagation constants and effective refractive indices take place of the wave vectors and bulk wave’s refractive indices, respectively. We take a typical Ti-diffused PPLN waveguide as an example.

In the first and fourth sections for frequency up-conversion, the coupling coefficient K1 in Eqs. (2) should be modified by an overlap factor ~esf(y,z)es*(y,z)ep*(y,z)dydz [12

12. P. F. Hu, T. C. Chong, L. P. Shi, and W. X. Hou, “Theoretical analysis of optimal quasi-phase matched second harmonic generation waveguide structure in LiTaO3 substrates,” Opt. Quantum Electron. 31(4), 337–349 (1999). [CrossRef]

], where esf (y, z), es* (y,z) and ep* (y, z) are the normalized field profiles of the SFW, signal wave and pump wave, respectively. This modification may result in a decrease of the coupling coefficient, so the power density of the input light should be elevated accordingly to compensate the coupling coefficient reduction. As a result, the conversion efficiency in these two sections still may be kept in a desired level. On the other hand, the TE/TM mode conversion realizes in the second and the third sections, which correspond to the polarization rotation in a bulk PPLN. In this case, the coupling coefficients K2 and K3 should be multiplied by the overlap factors of the involved mode fields and the applied electric field [13

13. C. Y. Huang, C. H. Lin, Y. H. Chen, and Y. C. Huang, “Electro-optic Ti:PPLN waveguide as efficient optical wavelength filter and polarization mode converter,” Opt. Express 15(5), 2548–2554 (2007). [CrossRef] [PubMed]

]. We take K2 for the second section as an example. It changes to K2=iγ51g1ωsE2cnsy,eff3nsz,eff3ν. Different from the original coefficients in Eqs. (2), the refractive indices of the ordinary and extraordinary signal waves are replaced by the effective counterparts of the TE and TM modes respectively. An overlap factor of the mode fields and the modulating field is added, defined by ν=eo*(y,z)ey(y,z)ee(y,z)dydz, where eo (y, z), ee (y,z) and ey (y, z) are the normalized field profiles of the ordinary wave, extraordinary wave and the applied electric field, respectively. As the overlap factor is less than 1 so that the mode conversion efficiency will be affected. Unlike the SFG in the first and fourth sections, the TE/TM mode conversion is a linear process so it is not influenced by the light intensity. However, a 100% mode conversion is still easily achievable by extending the length of the corresponding second section or just simply increasing the applied field. In the third section, the situation is similar for the mode conversion of the SFW. A word, same results could be obtained in all four PPLN sections, thus the simulation curves shown in Fig. 24 should also be valid in PPLN waveguides.

Unlike the bulk PPLN with negligible inherent loss, the waveguide normally has some propagation loss that has to be taken into account. For a typical Ti-diffused PPLN waveguide, the propagation losses of SFW and signal waves are ~0.2 dB/cm and ~0.1 dB/cm, respectively [14

14. L. G. Sheu, C. T. Lee, and H. C. Lee, “Nondestructive measurement of loss performance in channel waveguide devices with phase modulator,” Opt. Rev. 3(3), 192–196 (1996). [CrossRef]

,15

15. E. Pomarico, B. Sanguinetti, N. Gisin, R. Thew, H. Zbinden, G. Schreiber, A. Thomas, and W. Sohler, “Waveguide-based OPO source of entangled photon pairs,” N. J. Phys. 11(11), 113042 (2009). [CrossRef]

]. Even if these losses are considered, the SFG photon to photon quantum efficiency still could reaches ~94%. Because the commercial detectors in telecom wavelength only has 1/3~1/4 single photon detection probability than that in visible band, our up-conversion scheme are still very favorable for single photon detection operating at infrared wavelengths [1

1. R. V. Roussev, C. Langrock, J. R. Kurz, and M. M. Fejer, “Periodically poled lithium niobate waveguide sum-frequency generator for efficient single-photon detection at communication wavelengths,” Opt. Lett. 29(13), 1518–1520 (2004). [CrossRef] [PubMed]

].

4. Conclusion

Acknowledgements

This work is supported by National 973 program under contract No. 2011CBA00205 and 2010CB327803, and the National Science Foundation of China (NSFC) program No. 60977039 and 10874080. The authors also acknowledge the support from New Century Excellent Talents Program and the Specialized Research Fund for the Doctoral Program of Higher Education.

References and links

1.

R. V. Roussev, C. Langrock, J. R. Kurz, and M. M. Fejer, “Periodically poled lithium niobate waveguide sum-frequency generator for efficient single-photon detection at communication wavelengths,” Opt. Lett. 29(13), 1518–1520 (2004). [CrossRef] [PubMed]

2.

X. R. Gu, K. Huang, Y. Li, H. F. Pan, E. Wu, and H. P. Zeng, “Temporal and spectral control of single-photon frequency upconversion for pulsed radiation,” Appl. Phys. Lett. 96(13), 131111 (2010). [CrossRef]

3.

A. P. Vandevender and P. G. Kwiat, “High efficiency single photon detection via frequency up-conversion,” J. Mod. Opt. 51, 1433 (2004).

4.

M. A. Albota, F. N. C. Wong, and J. H. Shapiro, “Polarization-independent frequency conversion for quantum optical communication,” J. Opt. Soc. Am. B 23(5), 918 (2006). [CrossRef]

5.

S. Yu and W. Y. Gu, “Wavelength conversions in quasi-phase-matched LiNbO3 waveguide based on double-pass cascaded χ(2) SFG+DFG interactions,” IEEE J. Quantum Electron. 40(12), 1744 (2004). [CrossRef]

6.

J. Wang, J. Q. Sun, and Q. Z. Sun, “Experimental observation of a 1.5 μm band wavelength conversion and logic NOT gate at 40 Gbits/s based on sum-frequency generation,” Opt. Lett. 31(11), 1711–1713 (2006). [CrossRef] [PubMed]

7.

T. Suhara and H. Ishizuki, “Integrated QPM sum-frequency generation interferometer device for ultrafast optical switching,” IEEE Photon. Technol. Lett. 13(11), 1203–1205 (2001). [CrossRef]

8.

Y. L. Lee, B. A. Yu, T. J. Eom, W. Shin, C. Jung, Y. C. Noh, J. Lee, D. K. Ko, and K. Oh, “All-optical AND and NAND gates based on cascaded second-order nonlinear processes in a Ti-diffused periodically poled LiNbO(3) waveguide,” Opt. Express 14(7), 2776–2782 (2006). [CrossRef] [PubMed]

9.

Y. Q. Lu, Z. L. Wan, Q. Wang, Y. X. Xi, and N. B. Ming, “Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications,” Appl. Phys. Lett. 77(23), 3719 (2000). [CrossRef]

10.

A. Yariv, and P. Yeh, Optical Waves in Crystals (John Wiley and Sons, New York, 1984), Chap. 12.

11.

Y. Kong, X. F. Chen, and Y. Xia, “Competition of frequency conversion and polarization coupling in periodically poled lithium niobate,” Appl. Phys. B 91(3-4), 479–482 (2008). [CrossRef]

12.

P. F. Hu, T. C. Chong, L. P. Shi, and W. X. Hou, “Theoretical analysis of optimal quasi-phase matched second harmonic generation waveguide structure in LiTaO3 substrates,” Opt. Quantum Electron. 31(4), 337–349 (1999). [CrossRef]

13.

C. Y. Huang, C. H. Lin, Y. H. Chen, and Y. C. Huang, “Electro-optic Ti:PPLN waveguide as efficient optical wavelength filter and polarization mode converter,” Opt. Express 15(5), 2548–2554 (2007). [CrossRef] [PubMed]

14.

L. G. Sheu, C. T. Lee, and H. C. Lee, “Nondestructive measurement of loss performance in channel waveguide devices with phase modulator,” Opt. Rev. 3(3), 192–196 (1996). [CrossRef]

15.

E. Pomarico, B. Sanguinetti, N. Gisin, R. Thew, H. Zbinden, G. Schreiber, A. Thomas, and W. Sohler, “Waveguide-based OPO source of entangled photon pairs,” N. J. Phys. 11(11), 113042 (2009). [CrossRef]

OCIS Codes
(160.3730) Materials : Lithium niobate
(190.7220) Nonlinear optics : Upconversion

ToC Category:
Nonlinear Optics

History
Original Manuscript: October 13, 2010
Revised Manuscript: November 29, 2010
Manuscript Accepted: November 29, 2010
Published: December 24, 2010

Citation
Xiao-shi Song, Zi-yan Yu, Qin Wang, Fei Xu, and Yan-qing Lu, "Polarization independent quasi-phase-matched sum frequency generation for single photon detection," Opt. Express 19, 380-386 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-1-380


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References

  1. R. V. Roussev, C. Langrock, J. R. Kurz, and M. M. Fejer, “Periodically poled lithium niobate waveguide sum-frequency generator for efficient single-photon detection at communication wavelengths,” Opt. Lett. 29(13), 1518–1520 (2004). [CrossRef] [PubMed]
  2. X. R. Gu, K. Huang, Y. Li, H. F. Pan, E. Wu, and H. P. Zeng, “Temporal and spectral control of single-photon frequency upconversion for pulsed radiation,” Appl. Phys. Lett. 96(13), 131111 (2010). [CrossRef]
  3. A. P. Vandevender and P. G. Kwiat, “High efficiency single photon detection via frequency up-conversion,” J. Mod. Opt. 51, 1433 (2004).
  4. M. A. Albota, F. N. C. Wong, and J. H. Shapiro, “Polarization-independent frequency conversion for quantum optical communication,” J. Opt. Soc. Am. B 23(5), 918 (2006). [CrossRef]
  5. S. Yu and W. Y. Gu, “Wavelength conversions in quasi-phase-matched LiNbO3 waveguide based on double-pass cascaded χ(2) SFG+DFG interactions,” IEEE J. Quantum Electron. 40(12), 1744 (2004). [CrossRef]
  6. J. Wang, J. Q. Sun, and Q. Z. Sun, “Experimental observation of a 1.5 μm band wavelength conversion and logic NOT gate at 40 Gbits/s based on sum-frequency generation,” Opt. Lett. 31(11), 1711–1713 (2006). [CrossRef] [PubMed]
  7. T. Suhara and H. Ishizuki, “Integrated QPM sum-frequency generation interferometer device for ultrafast optical switching,” IEEE Photon. Technol. Lett. 13(11), 1203–1205 (2001). [CrossRef]
  8. Y. L. Lee, B. A. Yu, T. J. Eom, W. Shin, C. Jung, Y. C. Noh, J. Lee, D. K. Ko, and K. Oh, “All-optical AND and NAND gates based on cascaded second-order nonlinear processes in a Ti-diffused periodically poled LiNbO(3) waveguide,” Opt. Express 14(7), 2776–2782 (2006). [CrossRef] [PubMed]
  9. Y. Q. Lu, Z. L. Wan, Q. Wang, Y. X. Xi, and N. B. Ming, “Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications,” Appl. Phys. Lett. 77(23), 3719 (2000). [CrossRef]
  10. A. Yariv, and P. Yeh, Optical Waves in Crystals (John Wiley and Sons, New York, 1984), Chap. 12.
  11. Y. Kong, X. F. Chen, and Y. Xia, “Competition of frequency conversion and polarization coupling in periodically poled lithium niobate,” Appl. Phys. B 91(3-4), 479–482 (2008). [CrossRef]
  12. P. F. Hu, T. C. Chong, L. P. Shi, and W. X. Hou, “Theoretical analysis of optimal quasi-phase matched second harmonic generation waveguide structure in LiTaO3 substrates,” Opt. Quantum Electron. 31(4), 337–349 (1999). [CrossRef]
  13. C. Y. Huang, C. H. Lin, Y. H. Chen, and Y. C. Huang, “Electro-optic Ti:PPLN waveguide as efficient optical wavelength filter and polarization mode converter,” Opt. Express 15(5), 2548–2554 (2007). [CrossRef] [PubMed]
  14. L. G. Sheu, C. T. Lee, and H. C. Lee, “Nondestructive measurement of loss performance in channel waveguide devices with phase modulator,” Opt. Rev. 3(3), 192–196 (1996). [CrossRef]
  15. E. Pomarico, B. Sanguinetti, N. Gisin, R. Thew, H. Zbinden, G. Schreiber, A. Thomas, and W. Sohler, “Waveguide-based OPO source of entangled photon pairs,” N. J. Phys. 11(11), 113042 (2009). [CrossRef]

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