Abstract

All-optical wavelength-selective single- and dual-channel wavelength conversion and tuning has been demonstrated in a periodically poled Ti:LiNbO3 waveguide that has two second-harmonic phase-matching peaks by cascaded sum and difference frequency generation (cSFG/DFG). The wavelength conversion efficiency was measured to be -7 dB with coupled pump power of 233 mW.

©2004 Optical Society of America

1. Introduction

All-optical wavelength converters are key elements of future wavelength-division-multiplexed (WDM) optical networks. They make it possibile to increase both the flexibility and the efficiency of optical networks using a dynamic reallocation of optical channels in a WDM system [1]. Moreover, tunability of a wavelength converter can further enhance the flexibility of network systems by facilitating reconfigurable dynamic wavelength routing. Among various wavelength converters [2, 3, 4], the periodically poled LiNbO 3 (PPLN) is most promising because it has several good properties in wavelength conversion such as strict transparency, independence of bit rate and data format, low noise level, and a high efficiency [5]. Recently, the spatially deflected simultaneous wavelength interchange based on difference frequency generation (DFG) was performed in a two-dimensional nonlinear lattice, fabricated in LiNbO 3 [6, 7]. However, in the case of cascaded difference frequency generation (cDFG) in a PPLN waveguide, it is practically impossible to reconfigure the device for a different converted wavelength because of slow temperature-tuning speed of the phase-matching wavelength. To overcome the restriction of optical wavelength tunability, cascaded sum and difference frequency generation (cSFG/DFG) was proposed [8, 9]. However, all-optical wavelength-selective single- and dual-channel wavelength conversion and tuning of the converted wavelength in a PPLN waveguide have not been demonstrated. In this letter, we demonstrate, for what we believe is the first time, selective one-channel wavelength conversion and simultaneous two-channel wavelength conversion on the basis of cSFG/DFG in a Ti:PPLN waveguide that has two second-harmonic (SH) phase-matching peaks. The converting channel (one of two channels or simultaneous two channels) can be selected by tuning the wavelength of the first pump wave, which produces SFG with the signal channel. The wavelength tuning of the converted wave can be achieved by the tuning of the wavelength of the second pump wave, which produces DFG with generated SF.

2. Characteristics of Ti:PPLN

The SH curve of an 80-mm-long Ti:PPLN waveguide of 16.6-µm microdomain period is shown in Fig. 1. The propagation loss of waveguide at 1.53-µm wavelength (TM-polarization)was determined by the Fabry-Perot method [10] to be 0.12 dB/cm. After characterizing the Ti:PPLN waveguide, we added antireflection coating to the endfaces of the sample not only to avoid the Fabry-Perot interference effect but also to get more coupling efficiency between the fiber and the Ti waveguide. One side of the sample was angle polished to avoid internal multiple reflection of waves. The wavelengths of the two peaks in Fig. 1 are 1530.24 and 1530.5 nm at room temperature. The double- or multiple-SH peaks have been frequently observed in the Ti:PPLN waveguide owing to unexpected fabrication faults such as nonuniform periodicity of quasi-phase-matched (QPM) grating and inhomogeneity of refractive index along the waveguide [11]. Those peaks are also observable in intentionally engineered non-uniform QPM grating [12], phase-modulated domain structure [13], and uniform QPM grating, which has the temperature gradient [14]. The different power levels of two SH peaks in Fig. 1 may come from random fabrication errors. To produce more symmetric power levels of SH peaks, QPM engineered gratings can be applied [12, 13].

 

Fig. 1. SHG curve at room temperature. The conversion efficiency of the two high peaks are 319%/W and 291%/W, respectively.

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3. Operational principle and experimental setup

The experimental setup to demonstrate all-optical channel-selective wavelength conversion is shown in Fig. 2. The external cavity laser (ECL:1555.88 nm) was combined in a fiber-optic 3-dB power splitter with the 1556.44 nm of a distributed-feedback (DFB1) laser. Both waves were used for two signal channels. Two other DFB lasers, DFB2 and DFB3, were coupled by a second fiber-optic 3-dB power splitter and boosted by a high-power erbium-doped fiber amplifier (HP-EDFA). The DFB2 and DFB3 lasers served as pumps to generate SFG and DFG, respectively. The signals and the pumps were combined by a third fiber-optic 3-dB splitter and simultaneously coupled to the wavelength converter (Ti:PPLN waveguide) operated at 157 °C. The wavelength conversions were observed with an optical spectrum analyzer (OSA). The polarizations of all four waves were controlled by fiber-optic polarization controllers (PC1–PC4).

All-optical wavelength conversion based on cSFG/DFG offers a broad tuning range, low spontaneous emission noise, and ultrafast operation speed. Moreover, the SFG process in a Ti:PPLN waveguide that has double or multiple peaks of SH characteristic curve can offer wavelength-selective one-channel dropping as well as simultaneous dropping of several channels by use of tuning of pump wavelengths. The operation principle of the one-channel and simultaneous two-channel dropping on the basis of SFG with one pump wave is shown in Fig. 3. If a Ti:PPLN waveguide has two phase-matching curves (SH peaks), such as in Fig. 3, one pump wave can interact with two signals at two different phase-matching conditions and make sum frequency (SF); pump 1 interacts with signal 1 in the second phase-matching condition (second phase-matching curve) and signal 2 in the first phase-matching condition (first phase-matching curve). However, signal 1 can also can interact with pump 1 ′ in the first phase-matching condition. In the same way, signal 2 and pump 1 ″ interact with each other in the second phase-matching condition. Therefore, if we coupled pump 1 ′ or pump 1″ in the Ti:PPLN waveguide, we could make selective one-channel (signal 1 or signal 2) dropping, or simultaneous two-channel dropping can be achieved by pump 1. Details of wavelength-selective one-channel and simultaneous two-channel dropping were discussed elsewhere [15].

 

Fig. 2. Experimental setup to demonstrate all-optical channel-selective wavelength conversion by cSFG/DFG; ECL: extended cavity semiconductor laser, DFB: distributed feedback laser, HP-EDFA: high power erbium-doped fiber amplifer, OSA: optical spectrum analyzer, (PC1, PC2, PC3, PC4): polarization controller.

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Fig. 3. Phase-matching characteristics for channel dropping by SFG. Vertical arrow lines indicate energy conservations.

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Fig. 4. Optical spectra of wavelength conversion on the basis of the cSFG/DFG process (in the case of signal 1 conversion). In our case, the spacing between signal 1 and signal 2 is greater than 0.3 nm where the cross talk between channels becomes significant.

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In Fig. 2, SFG was achieved by tuning of pump 1 (DFB2) wavelength. At the same time, pump 2 interacts with the SF wave(s) to generate the idler(s) by the DFG process. This process is slightly phase mismatched, yet it obeys energy conservation as described in detail in Refs. [8, 9, 16].

4. Results and discussion

The optical spectra of wavelength-conversion experiments are shown in Figs. 4, 5, and 6. The channel-selective wavelength conversion is shown in Figs. 4 and 5. Simultaneous dual-channel wavelength conversion is shown in Fig. 6. The coupled power levels of pump 1 and pump 2 waves were 116 and 233 mW, respectively, and both coupled signals were 0.7 mW. The conversion efficiency from the signal to the generated idler was measured to be approximately -7 dB. When the wavelength of pump 2 was varied from 1559.73 to 1559.14 nm, the idler wavelength was tuned from 1540.72 to 1541.31 nm almost linearly (see the dotted curve in Fig. 5). More information about the tunability of the idler wavelength was reported in Ref. [8]. The lower power levels of signal 1 compared with signal 2 in Fig. 4 and signal 2 compared with signal 1 in Fig. 5 show the power depletion of the signal channels by the corresponding SFG process. More coupled pump power (~325 mW) for SFG can make full signal depletion (≤-17dB). Details about signal depletion with SFG as a function of the coupled pump power was discussed in Ref. [15].

 

Fig. 5. Optical spectra of wavelength conversion based on cSFG/DFG process (in the case of signal 2 conversion).

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5. Conclusion

We have demonstrated, for what we believe is the first time, selective one-channel wavelength conversion and simultaneous two-channel wavelength conversion on the basis of cSFG/DFG in a Ti:PPLN waveguide, that has two SH phase-matching peaks. The converting channel (one of two channels or simultaneous two channels) can be selected by tuning the wavelength of the first pump wave, which produces SFG with the signal channel. The wavelength tuning of the converted wave can be achieved by tuning the second pump, which produces DFG with generated SF. The conversion efficiency of the signal to the idler was approximately -7 dB with the first pump power of 116mWand the second pump power of 233mW. Further research using pulse signals is underway for applications in optical communication networking and optical computing. We believe that this selective channel wavelength conversion could be a useful technology for future all-optical communication networks.

 

Fig. 6. Optical spectra of wavelength conversion based on cSFG/DFG process (in the case of the conversion of both signals).

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Acknowledgment

This study was supported by the Ministry of Science and Technology of Korea through the Strategic National R&D Program (M10330000001-03B3700-00110).

References and links

1. A. Schiffini, A. Paoletti, D. Caccioli, P. Minzioni, P. Griggio, G. Lorenzetto, S. Cascelli, M. Guglielmucci, F. Materia, G. Tosi-Beleffi, H. Suche, Y. Lee, V. Quiring, and W. Sohler, “Field demonstration of all optical in line wavelength conversion in a WDM 40 Gbit/s dispersion managed link using a polarization insensitive Ti:PPLN converter,” OFC ’03, Atlanta, GA/USA, March 2003, 291–293.

2. K. Inoue, “Tunable and selective wavelength conversion using fiber four-wave mixing with two pump lights,” IEEE Photon. Technol. Lett. 6, 1451–1453 (1994). [CrossRef]  

3. F. Ratovelomanana, N. Vodjdani, A. Enard, G. Glastre, D. Rondi, R. Blondeau, C. Joergensen, T. Durhuus, B. Mikkelsen, K. E. Stubkjaer, A. Jourdan, and G. Soulage, “An all-optical wavelength-converter with semiconductor optical amplifiers monolithically integrated in a asymmetric passive Mach-Zehnder interferometer,” IEEE Photon. Technol. Lett.6, 992–994 (1994).

4. M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, “1.5-µm-Band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 11, 653–655 (1999). [CrossRef]  

5. G. Schreiber, H. Suche, Y. L. Lee, W. Grundkötter, V. Quiring, R. Ricken, and W. Sohler, “Efficient cascaded difference frequency conversion in periodically poled Ti:LiNbO3 waveguides using pulsed and cw pumping,” Appl. Phys. B 73, 501–504 (2001). [CrossRef]  

6. A. Chowdhury, S. Hagness, and L. McCaughan, “Simultaneous optical wavelength interchange with a two-dimensional second-order nonlinear photonic crystal,” Opt. Lett. 25, 832–834 (2000). [CrossRef]  

7. A. Chowdhury, C. Staus, B. Boland, T. Kuech, and L. McCaughan, “Experimental demonstration of 1535–1555-nm simultaneous optical wavelength interchange with a nonlinear photonic crystal,” Opt. Lett. 26, 1353–1355 (2001). [CrossRef]  

8. Y. H. Min, J. H. Lee, Y. L. Lee, W. Grundköter, V. Quiring, and W. Sohler, “Tunable all-optical wavelength conversion of 5-ps pulses by cascaded sum- and difference frequency generation (cSFG/DFG) in a Ti:PPNL waveguide,” OFC ’03, Atlanta, GA/USA, March 2003, 767–768.

9. Y. H. Min, W. Grundköter, J. H. Lee, Y. L. Lee, V. Quiring, and W. Sohler, “Efficient, all-optical wavelength conversion and tuning of ps-pulses in a Ti:PPLN channel waveguide,” Proc. Conference Lasers and Electro-Optics (CLEO/Europe ’03), Munich/Germany, paper CE5-1-THU.

10. R. Regener and W. Sohler, “Loss in low-finesse Ti:LiNbO3 optical waveguide resonators,” Appl. Phys. B 36,143–147 (1985). [CrossRef]  

11. S. Helmfrid and G. Arvidsson, “Influence of randomly varying domain lengths and nonuniform effective index on second-harmonic generation in quasi-phase-matching waveguides,” J. Opt. Soc. Am. B 8, 797–804 (1991). [CrossRef]  

12. M. H. Chou, K. R. Parameswaran, and M. M. Fejer, “Multi-channel wavelength conversion by use of engineered quasi-phase-matching structures in LiNbO3 waveguides,” Opt. Lett. 24, 1157–1159 (1999). [CrossRef]  

13. M. Asobe, O. Tadanage, H. Miyazawa, Y. Nishida, and H. Suzuki, “Multiple quasi-phase-matched LiNbO3 wavelength converter with a continuously phase-modulated domain structure,” Opt. Lett. 28, 558–560 (2003). [CrossRef]   [PubMed]  

14. Y. L. Lee, Y. Noh, C. Jung, T. J. Yu, D.-K. Ko, and J. Lee, “Broadening of the second-harmonic phase-matching bandwidth in a temperature gradient controlled periodically poled Ti:LiNbO3 channel waveguide,” Opt. Express 11, 2813–2816 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2813. [CrossRef]   [PubMed]  

15. Y. L. Lee, C. Jung, Y.-C. Noh, I. W. Choi, D.-K. Ko, J. Lee, H. Y. Lee, and H. Suche, “Wavelength selective single and dual-channel dropping in a periodically poled Ti:LiNbO3 waveguide,” Opt. Express 12, 701–707 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-701. [CrossRef]   [PubMed]  

16. B. Chen and C. Xu, “Analysis of novel cascaded χ(2) (SFG+DFG) wavelength conversions in quasi- phase-matched waveguides,” IEEE J. Quantum. Electron. 40, 256–261 (2004). [CrossRef]  

References

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  1. A. Schiffini, A. Paoletti, D. Caccioli, P. Minzioni, P. Griggio, G. Lorenzetto, S. Cascelli, M. Guglielmucci, F. Materia, G. Tosi-Beleffi, H. Suche, Y. Lee, V. Quiring, and W. Sohler, “Field demonstration of all optical in line wavelength conversion in a WDM 40 Gbit/s dispersion managed link using a polarization insensitive Ti:PPLN converter,” OFC ’03, Atlanta, GA/USA, March 2003, 291–293.
  2. K. Inoue, “Tunable and selective wavelength conversion using fiber four-wave mixing with two pump lights,” IEEE Photon. Technol. Lett. 6, 1451–1453 (1994).
    [Crossref]
  3. F. Ratovelomanana, N. Vodjdani, A. Enard, G. Glastre, D. Rondi, R. Blondeau, C. Joergensen, T. Durhuus, B. Mikkelsen, K. E. Stubkjaer, A. Jourdan, and G. Soulage, “An all-optical wavelength-converter with semiconductor optical amplifiers monolithically integrated in a asymmetric passive Mach-Zehnder interferometer,” IEEE Photon. Technol. Lett.6, 992–994 (1994).
  4. M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, “1.5-µm-Band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 11, 653–655 (1999).
    [Crossref]
  5. G. Schreiber, H. Suche, Y. L. Lee, W. Grundkötter, V. Quiring, R. Ricken, and W. Sohler, “Efficient cascaded difference frequency conversion in periodically poled Ti:LiNbO3 waveguides using pulsed and cw pumping,” Appl. Phys. B 73, 501–504 (2001).
    [Crossref]
  6. A. Chowdhury, S. Hagness, and L. McCaughan, “Simultaneous optical wavelength interchange with a two-dimensional second-order nonlinear photonic crystal,” Opt. Lett. 25, 832–834 (2000).
    [Crossref]
  7. A. Chowdhury, C. Staus, B. Boland, T. Kuech, and L. McCaughan, “Experimental demonstration of 1535–1555-nm simultaneous optical wavelength interchange with a nonlinear photonic crystal,” Opt. Lett. 26, 1353–1355 (2001).
    [Crossref]
  8. Y. H. Min, J. H. Lee, Y. L. Lee, W. Grundköter, V. Quiring, and W. Sohler, “Tunable all-optical wavelength conversion of 5-ps pulses by cascaded sum- and difference frequency generation (cSFG/DFG) in a Ti:PPNL waveguide,” OFC ’03, Atlanta, GA/USA, March 2003, 767–768.
  9. Y. H. Min, W. Grundköter, J. H. Lee, Y. L. Lee, V. Quiring, and W. Sohler, “Efficient, all-optical wavelength conversion and tuning of ps-pulses in a Ti:PPLN channel waveguide,” Proc. Conference Lasers and Electro-Optics (CLEO/Europe ’03), Munich/Germany, paper CE5-1-THU.
  10. R. Regener and W. Sohler, “Loss in low-finesse Ti:LiNbO3 optical waveguide resonators,” Appl. Phys. B 36,143–147 (1985).
    [Crossref]
  11. S. Helmfrid and G. Arvidsson, “Influence of randomly varying domain lengths and nonuniform effective index on second-harmonic generation in quasi-phase-matching waveguides,” J. Opt. Soc. Am. B 8, 797–804 (1991).
    [Crossref]
  12. M. H. Chou, K. R. Parameswaran, and M. M. Fejer, “Multi-channel wavelength conversion by use of engineered quasi-phase-matching structures in LiNbO3 waveguides,” Opt. Lett. 24, 1157–1159 (1999).
    [Crossref]
  13. M. Asobe, O. Tadanage, H. Miyazawa, Y. Nishida, and H. Suzuki, “Multiple quasi-phase-matched LiNbO3 wavelength converter with a continuously phase-modulated domain structure,” Opt. Lett. 28, 558–560 (2003).
    [Crossref] [PubMed]
  14. Y. L. Lee, Y. Noh, C. Jung, T. J. Yu, D.-K. Ko, and J. Lee, “Broadening of the second-harmonic phase-matching bandwidth in a temperature gradient controlled periodically poled Ti:LiNbO3 channel waveguide,” Opt. Express 11, 2813–2816 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2813.
    [Crossref] [PubMed]
  15. Y. L. Lee, C. Jung, Y.-C. Noh, I. W. Choi, D.-K. Ko, J. Lee, H. Y. Lee, and H. Suche, “Wavelength selective single and dual-channel dropping in a periodically poled Ti:LiNbO3 waveguide,” Opt. Express 12, 701–707 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-701.
    [Crossref] [PubMed]
  16. B. Chen and C. Xu, “Analysis of novel cascaded χ(2) (SFG+DFG) wavelength conversions in quasi- phase-matched waveguides,” IEEE J. Quantum. Electron. 40, 256–261 (2004).
    [Crossref]

2004 (2)

2003 (2)

2001 (2)

G. Schreiber, H. Suche, Y. L. Lee, W. Grundkötter, V. Quiring, R. Ricken, and W. Sohler, “Efficient cascaded difference frequency conversion in periodically poled Ti:LiNbO3 waveguides using pulsed and cw pumping,” Appl. Phys. B 73, 501–504 (2001).
[Crossref]

A. Chowdhury, C. Staus, B. Boland, T. Kuech, and L. McCaughan, “Experimental demonstration of 1535–1555-nm simultaneous optical wavelength interchange with a nonlinear photonic crystal,” Opt. Lett. 26, 1353–1355 (2001).
[Crossref]

2000 (1)

1999 (2)

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, “1.5-µm-Band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 11, 653–655 (1999).
[Crossref]

M. H. Chou, K. R. Parameswaran, and M. M. Fejer, “Multi-channel wavelength conversion by use of engineered quasi-phase-matching structures in LiNbO3 waveguides,” Opt. Lett. 24, 1157–1159 (1999).
[Crossref]

1994 (1)

K. Inoue, “Tunable and selective wavelength conversion using fiber four-wave mixing with two pump lights,” IEEE Photon. Technol. Lett. 6, 1451–1453 (1994).
[Crossref]

1991 (1)

1985 (1)

R. Regener and W. Sohler, “Loss in low-finesse Ti:LiNbO3 optical waveguide resonators,” Appl. Phys. B 36,143–147 (1985).
[Crossref]

Arvidsson, G.

Asobe, M.

Blondeau, R.

F. Ratovelomanana, N. Vodjdani, A. Enard, G. Glastre, D. Rondi, R. Blondeau, C. Joergensen, T. Durhuus, B. Mikkelsen, K. E. Stubkjaer, A. Jourdan, and G. Soulage, “An all-optical wavelength-converter with semiconductor optical amplifiers monolithically integrated in a asymmetric passive Mach-Zehnder interferometer,” IEEE Photon. Technol. Lett.6, 992–994 (1994).

Boland, B.

Brener, I.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, “1.5-µm-Band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 11, 653–655 (1999).
[Crossref]

Caccioli, D.

A. Schiffini, A. Paoletti, D. Caccioli, P. Minzioni, P. Griggio, G. Lorenzetto, S. Cascelli, M. Guglielmucci, F. Materia, G. Tosi-Beleffi, H. Suche, Y. Lee, V. Quiring, and W. Sohler, “Field demonstration of all optical in line wavelength conversion in a WDM 40 Gbit/s dispersion managed link using a polarization insensitive Ti:PPLN converter,” OFC ’03, Atlanta, GA/USA, March 2003, 291–293.

Cascelli, S.

A. Schiffini, A. Paoletti, D. Caccioli, P. Minzioni, P. Griggio, G. Lorenzetto, S. Cascelli, M. Guglielmucci, F. Materia, G. Tosi-Beleffi, H. Suche, Y. Lee, V. Quiring, and W. Sohler, “Field demonstration of all optical in line wavelength conversion in a WDM 40 Gbit/s dispersion managed link using a polarization insensitive Ti:PPLN converter,” OFC ’03, Atlanta, GA/USA, March 2003, 291–293.

Chaban, E. E.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, “1.5-µm-Band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 11, 653–655 (1999).
[Crossref]

Chen, B.

B. Chen and C. Xu, “Analysis of novel cascaded χ(2) (SFG+DFG) wavelength conversions in quasi- phase-matched waveguides,” IEEE J. Quantum. Electron. 40, 256–261 (2004).
[Crossref]

Choi, I. W.

Chou, M. H.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, “1.5-µm-Band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 11, 653–655 (1999).
[Crossref]

M. H. Chou, K. R. Parameswaran, and M. M. Fejer, “Multi-channel wavelength conversion by use of engineered quasi-phase-matching structures in LiNbO3 waveguides,” Opt. Lett. 24, 1157–1159 (1999).
[Crossref]

Chowdhury, A.

Christman, S. B.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, “1.5-µm-Band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 11, 653–655 (1999).
[Crossref]

Durhuus, T.

F. Ratovelomanana, N. Vodjdani, A. Enard, G. Glastre, D. Rondi, R. Blondeau, C. Joergensen, T. Durhuus, B. Mikkelsen, K. E. Stubkjaer, A. Jourdan, and G. Soulage, “An all-optical wavelength-converter with semiconductor optical amplifiers monolithically integrated in a asymmetric passive Mach-Zehnder interferometer,” IEEE Photon. Technol. Lett.6, 992–994 (1994).

Enard, A.

F. Ratovelomanana, N. Vodjdani, A. Enard, G. Glastre, D. Rondi, R. Blondeau, C. Joergensen, T. Durhuus, B. Mikkelsen, K. E. Stubkjaer, A. Jourdan, and G. Soulage, “An all-optical wavelength-converter with semiconductor optical amplifiers monolithically integrated in a asymmetric passive Mach-Zehnder interferometer,” IEEE Photon. Technol. Lett.6, 992–994 (1994).

Fejer, M. M.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, “1.5-µm-Band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 11, 653–655 (1999).
[Crossref]

M. H. Chou, K. R. Parameswaran, and M. M. Fejer, “Multi-channel wavelength conversion by use of engineered quasi-phase-matching structures in LiNbO3 waveguides,” Opt. Lett. 24, 1157–1159 (1999).
[Crossref]

Glastre, G.

F. Ratovelomanana, N. Vodjdani, A. Enard, G. Glastre, D. Rondi, R. Blondeau, C. Joergensen, T. Durhuus, B. Mikkelsen, K. E. Stubkjaer, A. Jourdan, and G. Soulage, “An all-optical wavelength-converter with semiconductor optical amplifiers monolithically integrated in a asymmetric passive Mach-Zehnder interferometer,” IEEE Photon. Technol. Lett.6, 992–994 (1994).

Griggio, P.

A. Schiffini, A. Paoletti, D. Caccioli, P. Minzioni, P. Griggio, G. Lorenzetto, S. Cascelli, M. Guglielmucci, F. Materia, G. Tosi-Beleffi, H. Suche, Y. Lee, V. Quiring, and W. Sohler, “Field demonstration of all optical in line wavelength conversion in a WDM 40 Gbit/s dispersion managed link using a polarization insensitive Ti:PPLN converter,” OFC ’03, Atlanta, GA/USA, March 2003, 291–293.

Grundköter, W.

Y. H. Min, W. Grundköter, J. H. Lee, Y. L. Lee, V. Quiring, and W. Sohler, “Efficient, all-optical wavelength conversion and tuning of ps-pulses in a Ti:PPLN channel waveguide,” Proc. Conference Lasers and Electro-Optics (CLEO/Europe ’03), Munich/Germany, paper CE5-1-THU.

Y. H. Min, J. H. Lee, Y. L. Lee, W. Grundköter, V. Quiring, and W. Sohler, “Tunable all-optical wavelength conversion of 5-ps pulses by cascaded sum- and difference frequency generation (cSFG/DFG) in a Ti:PPNL waveguide,” OFC ’03, Atlanta, GA/USA, March 2003, 767–768.

Grundkötter, W.

G. Schreiber, H. Suche, Y. L. Lee, W. Grundkötter, V. Quiring, R. Ricken, and W. Sohler, “Efficient cascaded difference frequency conversion in periodically poled Ti:LiNbO3 waveguides using pulsed and cw pumping,” Appl. Phys. B 73, 501–504 (2001).
[Crossref]

Guglielmucci, M.

A. Schiffini, A. Paoletti, D. Caccioli, P. Minzioni, P. Griggio, G. Lorenzetto, S. Cascelli, M. Guglielmucci, F. Materia, G. Tosi-Beleffi, H. Suche, Y. Lee, V. Quiring, and W. Sohler, “Field demonstration of all optical in line wavelength conversion in a WDM 40 Gbit/s dispersion managed link using a polarization insensitive Ti:PPLN converter,” OFC ’03, Atlanta, GA/USA, March 2003, 291–293.

Hagness, S.

Helmfrid, S.

Inoue, K.

K. Inoue, “Tunable and selective wavelength conversion using fiber four-wave mixing with two pump lights,” IEEE Photon. Technol. Lett. 6, 1451–1453 (1994).
[Crossref]

Joergensen, C.

F. Ratovelomanana, N. Vodjdani, A. Enard, G. Glastre, D. Rondi, R. Blondeau, C. Joergensen, T. Durhuus, B. Mikkelsen, K. E. Stubkjaer, A. Jourdan, and G. Soulage, “An all-optical wavelength-converter with semiconductor optical amplifiers monolithically integrated in a asymmetric passive Mach-Zehnder interferometer,” IEEE Photon. Technol. Lett.6, 992–994 (1994).

Jourdan, A.

F. Ratovelomanana, N. Vodjdani, A. Enard, G. Glastre, D. Rondi, R. Blondeau, C. Joergensen, T. Durhuus, B. Mikkelsen, K. E. Stubkjaer, A. Jourdan, and G. Soulage, “An all-optical wavelength-converter with semiconductor optical amplifiers monolithically integrated in a asymmetric passive Mach-Zehnder interferometer,” IEEE Photon. Technol. Lett.6, 992–994 (1994).

Jung, C.

Ko, D.-K.

Kuech, T.

Lee, H. Y.

Lee, J.

Lee, J. H.

Y. H. Min, J. H. Lee, Y. L. Lee, W. Grundköter, V. Quiring, and W. Sohler, “Tunable all-optical wavelength conversion of 5-ps pulses by cascaded sum- and difference frequency generation (cSFG/DFG) in a Ti:PPNL waveguide,” OFC ’03, Atlanta, GA/USA, March 2003, 767–768.

Y. H. Min, W. Grundköter, J. H. Lee, Y. L. Lee, V. Quiring, and W. Sohler, “Efficient, all-optical wavelength conversion and tuning of ps-pulses in a Ti:PPLN channel waveguide,” Proc. Conference Lasers and Electro-Optics (CLEO/Europe ’03), Munich/Germany, paper CE5-1-THU.

Lee, Y.

A. Schiffini, A. Paoletti, D. Caccioli, P. Minzioni, P. Griggio, G. Lorenzetto, S. Cascelli, M. Guglielmucci, F. Materia, G. Tosi-Beleffi, H. Suche, Y. Lee, V. Quiring, and W. Sohler, “Field demonstration of all optical in line wavelength conversion in a WDM 40 Gbit/s dispersion managed link using a polarization insensitive Ti:PPLN converter,” OFC ’03, Atlanta, GA/USA, March 2003, 291–293.

Lee, Y. L.

Y. L. Lee, C. Jung, Y.-C. Noh, I. W. Choi, D.-K. Ko, J. Lee, H. Y. Lee, and H. Suche, “Wavelength selective single and dual-channel dropping in a periodically poled Ti:LiNbO3 waveguide,” Opt. Express 12, 701–707 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-701.
[Crossref] [PubMed]

Y. L. Lee, Y. Noh, C. Jung, T. J. Yu, D.-K. Ko, and J. Lee, “Broadening of the second-harmonic phase-matching bandwidth in a temperature gradient controlled periodically poled Ti:LiNbO3 channel waveguide,” Opt. Express 11, 2813–2816 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2813.
[Crossref] [PubMed]

G. Schreiber, H. Suche, Y. L. Lee, W. Grundkötter, V. Quiring, R. Ricken, and W. Sohler, “Efficient cascaded difference frequency conversion in periodically poled Ti:LiNbO3 waveguides using pulsed and cw pumping,” Appl. Phys. B 73, 501–504 (2001).
[Crossref]

Y. H. Min, J. H. Lee, Y. L. Lee, W. Grundköter, V. Quiring, and W. Sohler, “Tunable all-optical wavelength conversion of 5-ps pulses by cascaded sum- and difference frequency generation (cSFG/DFG) in a Ti:PPNL waveguide,” OFC ’03, Atlanta, GA/USA, March 2003, 767–768.

Y. H. Min, W. Grundköter, J. H. Lee, Y. L. Lee, V. Quiring, and W. Sohler, “Efficient, all-optical wavelength conversion and tuning of ps-pulses in a Ti:PPLN channel waveguide,” Proc. Conference Lasers and Electro-Optics (CLEO/Europe ’03), Munich/Germany, paper CE5-1-THU.

Lorenzetto, G.

A. Schiffini, A. Paoletti, D. Caccioli, P. Minzioni, P. Griggio, G. Lorenzetto, S. Cascelli, M. Guglielmucci, F. Materia, G. Tosi-Beleffi, H. Suche, Y. Lee, V. Quiring, and W. Sohler, “Field demonstration of all optical in line wavelength conversion in a WDM 40 Gbit/s dispersion managed link using a polarization insensitive Ti:PPLN converter,” OFC ’03, Atlanta, GA/USA, March 2003, 291–293.

Materia, F.

A. Schiffini, A. Paoletti, D. Caccioli, P. Minzioni, P. Griggio, G. Lorenzetto, S. Cascelli, M. Guglielmucci, F. Materia, G. Tosi-Beleffi, H. Suche, Y. Lee, V. Quiring, and W. Sohler, “Field demonstration of all optical in line wavelength conversion in a WDM 40 Gbit/s dispersion managed link using a polarization insensitive Ti:PPLN converter,” OFC ’03, Atlanta, GA/USA, March 2003, 291–293.

McCaughan, L.

Mikkelsen, B.

F. Ratovelomanana, N. Vodjdani, A. Enard, G. Glastre, D. Rondi, R. Blondeau, C. Joergensen, T. Durhuus, B. Mikkelsen, K. E. Stubkjaer, A. Jourdan, and G. Soulage, “An all-optical wavelength-converter with semiconductor optical amplifiers monolithically integrated in a asymmetric passive Mach-Zehnder interferometer,” IEEE Photon. Technol. Lett.6, 992–994 (1994).

Min, Y. H.

Y. H. Min, J. H. Lee, Y. L. Lee, W. Grundköter, V. Quiring, and W. Sohler, “Tunable all-optical wavelength conversion of 5-ps pulses by cascaded sum- and difference frequency generation (cSFG/DFG) in a Ti:PPNL waveguide,” OFC ’03, Atlanta, GA/USA, March 2003, 767–768.

Y. H. Min, W. Grundköter, J. H. Lee, Y. L. Lee, V. Quiring, and W. Sohler, “Efficient, all-optical wavelength conversion and tuning of ps-pulses in a Ti:PPLN channel waveguide,” Proc. Conference Lasers and Electro-Optics (CLEO/Europe ’03), Munich/Germany, paper CE5-1-THU.

Minzioni, P.

A. Schiffini, A. Paoletti, D. Caccioli, P. Minzioni, P. Griggio, G. Lorenzetto, S. Cascelli, M. Guglielmucci, F. Materia, G. Tosi-Beleffi, H. Suche, Y. Lee, V. Quiring, and W. Sohler, “Field demonstration of all optical in line wavelength conversion in a WDM 40 Gbit/s dispersion managed link using a polarization insensitive Ti:PPLN converter,” OFC ’03, Atlanta, GA/USA, March 2003, 291–293.

Miyazawa, H.

Nishida, Y.

Noh, Y.

Noh, Y.-C.

Paoletti, A.

A. Schiffini, A. Paoletti, D. Caccioli, P. Minzioni, P. Griggio, G. Lorenzetto, S. Cascelli, M. Guglielmucci, F. Materia, G. Tosi-Beleffi, H. Suche, Y. Lee, V. Quiring, and W. Sohler, “Field demonstration of all optical in line wavelength conversion in a WDM 40 Gbit/s dispersion managed link using a polarization insensitive Ti:PPLN converter,” OFC ’03, Atlanta, GA/USA, March 2003, 291–293.

Parameswaran, K. R.

Quiring, V.

G. Schreiber, H. Suche, Y. L. Lee, W. Grundkötter, V. Quiring, R. Ricken, and W. Sohler, “Efficient cascaded difference frequency conversion in periodically poled Ti:LiNbO3 waveguides using pulsed and cw pumping,” Appl. Phys. B 73, 501–504 (2001).
[Crossref]

A. Schiffini, A. Paoletti, D. Caccioli, P. Minzioni, P. Griggio, G. Lorenzetto, S. Cascelli, M. Guglielmucci, F. Materia, G. Tosi-Beleffi, H. Suche, Y. Lee, V. Quiring, and W. Sohler, “Field demonstration of all optical in line wavelength conversion in a WDM 40 Gbit/s dispersion managed link using a polarization insensitive Ti:PPLN converter,” OFC ’03, Atlanta, GA/USA, March 2003, 291–293.

Y. H. Min, W. Grundköter, J. H. Lee, Y. L. Lee, V. Quiring, and W. Sohler, “Efficient, all-optical wavelength conversion and tuning of ps-pulses in a Ti:PPLN channel waveguide,” Proc. Conference Lasers and Electro-Optics (CLEO/Europe ’03), Munich/Germany, paper CE5-1-THU.

Y. H. Min, J. H. Lee, Y. L. Lee, W. Grundköter, V. Quiring, and W. Sohler, “Tunable all-optical wavelength conversion of 5-ps pulses by cascaded sum- and difference frequency generation (cSFG/DFG) in a Ti:PPNL waveguide,” OFC ’03, Atlanta, GA/USA, March 2003, 767–768.

Ratovelomanana, F.

F. Ratovelomanana, N. Vodjdani, A. Enard, G. Glastre, D. Rondi, R. Blondeau, C. Joergensen, T. Durhuus, B. Mikkelsen, K. E. Stubkjaer, A. Jourdan, and G. Soulage, “An all-optical wavelength-converter with semiconductor optical amplifiers monolithically integrated in a asymmetric passive Mach-Zehnder interferometer,” IEEE Photon. Technol. Lett.6, 992–994 (1994).

Regener, R.

R. Regener and W. Sohler, “Loss in low-finesse Ti:LiNbO3 optical waveguide resonators,” Appl. Phys. B 36,143–147 (1985).
[Crossref]

Ricken, R.

G. Schreiber, H. Suche, Y. L. Lee, W. Grundkötter, V. Quiring, R. Ricken, and W. Sohler, “Efficient cascaded difference frequency conversion in periodically poled Ti:LiNbO3 waveguides using pulsed and cw pumping,” Appl. Phys. B 73, 501–504 (2001).
[Crossref]

Rondi, D.

F. Ratovelomanana, N. Vodjdani, A. Enard, G. Glastre, D. Rondi, R. Blondeau, C. Joergensen, T. Durhuus, B. Mikkelsen, K. E. Stubkjaer, A. Jourdan, and G. Soulage, “An all-optical wavelength-converter with semiconductor optical amplifiers monolithically integrated in a asymmetric passive Mach-Zehnder interferometer,” IEEE Photon. Technol. Lett.6, 992–994 (1994).

Schiffini, A.

A. Schiffini, A. Paoletti, D. Caccioli, P. Minzioni, P. Griggio, G. Lorenzetto, S. Cascelli, M. Guglielmucci, F. Materia, G. Tosi-Beleffi, H. Suche, Y. Lee, V. Quiring, and W. Sohler, “Field demonstration of all optical in line wavelength conversion in a WDM 40 Gbit/s dispersion managed link using a polarization insensitive Ti:PPLN converter,” OFC ’03, Atlanta, GA/USA, March 2003, 291–293.

Schreiber, G.

G. Schreiber, H. Suche, Y. L. Lee, W. Grundkötter, V. Quiring, R. Ricken, and W. Sohler, “Efficient cascaded difference frequency conversion in periodically poled Ti:LiNbO3 waveguides using pulsed and cw pumping,” Appl. Phys. B 73, 501–504 (2001).
[Crossref]

Sohler, W.

G. Schreiber, H. Suche, Y. L. Lee, W. Grundkötter, V. Quiring, R. Ricken, and W. Sohler, “Efficient cascaded difference frequency conversion in periodically poled Ti:LiNbO3 waveguides using pulsed and cw pumping,” Appl. Phys. B 73, 501–504 (2001).
[Crossref]

R. Regener and W. Sohler, “Loss in low-finesse Ti:LiNbO3 optical waveguide resonators,” Appl. Phys. B 36,143–147 (1985).
[Crossref]

Y. H. Min, W. Grundköter, J. H. Lee, Y. L. Lee, V. Quiring, and W. Sohler, “Efficient, all-optical wavelength conversion and tuning of ps-pulses in a Ti:PPLN channel waveguide,” Proc. Conference Lasers and Electro-Optics (CLEO/Europe ’03), Munich/Germany, paper CE5-1-THU.

Y. H. Min, J. H. Lee, Y. L. Lee, W. Grundköter, V. Quiring, and W. Sohler, “Tunable all-optical wavelength conversion of 5-ps pulses by cascaded sum- and difference frequency generation (cSFG/DFG) in a Ti:PPNL waveguide,” OFC ’03, Atlanta, GA/USA, March 2003, 767–768.

A. Schiffini, A. Paoletti, D. Caccioli, P. Minzioni, P. Griggio, G. Lorenzetto, S. Cascelli, M. Guglielmucci, F. Materia, G. Tosi-Beleffi, H. Suche, Y. Lee, V. Quiring, and W. Sohler, “Field demonstration of all optical in line wavelength conversion in a WDM 40 Gbit/s dispersion managed link using a polarization insensitive Ti:PPLN converter,” OFC ’03, Atlanta, GA/USA, March 2003, 291–293.

Soulage, G.

F. Ratovelomanana, N. Vodjdani, A. Enard, G. Glastre, D. Rondi, R. Blondeau, C. Joergensen, T. Durhuus, B. Mikkelsen, K. E. Stubkjaer, A. Jourdan, and G. Soulage, “An all-optical wavelength-converter with semiconductor optical amplifiers monolithically integrated in a asymmetric passive Mach-Zehnder interferometer,” IEEE Photon. Technol. Lett.6, 992–994 (1994).

Staus, C.

Stubkjaer, K. E.

F. Ratovelomanana, N. Vodjdani, A. Enard, G. Glastre, D. Rondi, R. Blondeau, C. Joergensen, T. Durhuus, B. Mikkelsen, K. E. Stubkjaer, A. Jourdan, and G. Soulage, “An all-optical wavelength-converter with semiconductor optical amplifiers monolithically integrated in a asymmetric passive Mach-Zehnder interferometer,” IEEE Photon. Technol. Lett.6, 992–994 (1994).

Suche, H.

Y. L. Lee, C. Jung, Y.-C. Noh, I. W. Choi, D.-K. Ko, J. Lee, H. Y. Lee, and H. Suche, “Wavelength selective single and dual-channel dropping in a periodically poled Ti:LiNbO3 waveguide,” Opt. Express 12, 701–707 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-701.
[Crossref] [PubMed]

G. Schreiber, H. Suche, Y. L. Lee, W. Grundkötter, V. Quiring, R. Ricken, and W. Sohler, “Efficient cascaded difference frequency conversion in periodically poled Ti:LiNbO3 waveguides using pulsed and cw pumping,” Appl. Phys. B 73, 501–504 (2001).
[Crossref]

A. Schiffini, A. Paoletti, D. Caccioli, P. Minzioni, P. Griggio, G. Lorenzetto, S. Cascelli, M. Guglielmucci, F. Materia, G. Tosi-Beleffi, H. Suche, Y. Lee, V. Quiring, and W. Sohler, “Field demonstration of all optical in line wavelength conversion in a WDM 40 Gbit/s dispersion managed link using a polarization insensitive Ti:PPLN converter,” OFC ’03, Atlanta, GA/USA, March 2003, 291–293.

Suzuki, H.

Tadanage, O.

Tosi-Beleffi, G.

A. Schiffini, A. Paoletti, D. Caccioli, P. Minzioni, P. Griggio, G. Lorenzetto, S. Cascelli, M. Guglielmucci, F. Materia, G. Tosi-Beleffi, H. Suche, Y. Lee, V. Quiring, and W. Sohler, “Field demonstration of all optical in line wavelength conversion in a WDM 40 Gbit/s dispersion managed link using a polarization insensitive Ti:PPLN converter,” OFC ’03, Atlanta, GA/USA, March 2003, 291–293.

Vodjdani, N.

F. Ratovelomanana, N. Vodjdani, A. Enard, G. Glastre, D. Rondi, R. Blondeau, C. Joergensen, T. Durhuus, B. Mikkelsen, K. E. Stubkjaer, A. Jourdan, and G. Soulage, “An all-optical wavelength-converter with semiconductor optical amplifiers monolithically integrated in a asymmetric passive Mach-Zehnder interferometer,” IEEE Photon. Technol. Lett.6, 992–994 (1994).

Xu, C.

B. Chen and C. Xu, “Analysis of novel cascaded χ(2) (SFG+DFG) wavelength conversions in quasi- phase-matched waveguides,” IEEE J. Quantum. Electron. 40, 256–261 (2004).
[Crossref]

Yu, T. J.

Appl. Phys. B (2)

G. Schreiber, H. Suche, Y. L. Lee, W. Grundkötter, V. Quiring, R. Ricken, and W. Sohler, “Efficient cascaded difference frequency conversion in periodically poled Ti:LiNbO3 waveguides using pulsed and cw pumping,” Appl. Phys. B 73, 501–504 (2001).
[Crossref]

R. Regener and W. Sohler, “Loss in low-finesse Ti:LiNbO3 optical waveguide resonators,” Appl. Phys. B 36,143–147 (1985).
[Crossref]

IEEE J. Quantum. Electron. (1)

B. Chen and C. Xu, “Analysis of novel cascaded χ(2) (SFG+DFG) wavelength conversions in quasi- phase-matched waveguides,” IEEE J. Quantum. Electron. 40, 256–261 (2004).
[Crossref]

IEEE Photon. Technol. Lett. (2)

K. Inoue, “Tunable and selective wavelength conversion using fiber four-wave mixing with two pump lights,” IEEE Photon. Technol. Lett. 6, 1451–1453 (1994).
[Crossref]

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, “1.5-µm-Band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 11, 653–655 (1999).
[Crossref]

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

Opt. Express (2)

Opt. Lett. (4)

Other (4)

Y. H. Min, J. H. Lee, Y. L. Lee, W. Grundköter, V. Quiring, and W. Sohler, “Tunable all-optical wavelength conversion of 5-ps pulses by cascaded sum- and difference frequency generation (cSFG/DFG) in a Ti:PPNL waveguide,” OFC ’03, Atlanta, GA/USA, March 2003, 767–768.

Y. H. Min, W. Grundköter, J. H. Lee, Y. L. Lee, V. Quiring, and W. Sohler, “Efficient, all-optical wavelength conversion and tuning of ps-pulses in a Ti:PPLN channel waveguide,” Proc. Conference Lasers and Electro-Optics (CLEO/Europe ’03), Munich/Germany, paper CE5-1-THU.

A. Schiffini, A. Paoletti, D. Caccioli, P. Minzioni, P. Griggio, G. Lorenzetto, S. Cascelli, M. Guglielmucci, F. Materia, G. Tosi-Beleffi, H. Suche, Y. Lee, V. Quiring, and W. Sohler, “Field demonstration of all optical in line wavelength conversion in a WDM 40 Gbit/s dispersion managed link using a polarization insensitive Ti:PPLN converter,” OFC ’03, Atlanta, GA/USA, March 2003, 291–293.

F. Ratovelomanana, N. Vodjdani, A. Enard, G. Glastre, D. Rondi, R. Blondeau, C. Joergensen, T. Durhuus, B. Mikkelsen, K. E. Stubkjaer, A. Jourdan, and G. Soulage, “An all-optical wavelength-converter with semiconductor optical amplifiers monolithically integrated in a asymmetric passive Mach-Zehnder interferometer,” IEEE Photon. Technol. Lett.6, 992–994 (1994).

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Figures (6)

Fig. 1.
Fig. 1. SHG curve at room temperature. The conversion efficiency of the two high peaks are 319%/W and 291%/W, respectively.
Fig. 2.
Fig. 2. Experimental setup to demonstrate all-optical channel-selective wavelength conversion by cSFG/DFG; ECL: extended cavity semiconductor laser, DFB: distributed feedback laser, HP-EDFA: high power erbium-doped fiber amplifer, OSA: optical spectrum analyzer, (PC1, PC2, PC3, PC4): polarization controller.
Fig. 3.
Fig. 3. Phase-matching characteristics for channel dropping by SFG. Vertical arrow lines indicate energy conservations.
Fig. 4.
Fig. 4. Optical spectra of wavelength conversion on the basis of the cSFG/DFG process (in the case of signal 1 conversion). In our case, the spacing between signal 1 and signal 2 is greater than 0.3 nm where the cross talk between channels becomes significant.
Fig. 5.
Fig. 5. Optical spectra of wavelength conversion based on cSFG/DFG process (in the case of signal 2 conversion).
Fig. 6.
Fig. 6. Optical spectra of wavelength conversion based on cSFG/DFG process (in the case of the conversion of both signals).

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