Abstract

A scheme is proposed to enhance the cascaded four-wave mixing (CFWM) generation, by introducing an optical feedback to the input port. Experimental and numerical results show that more efficient CFWM generation can be obtained by the scheme. The number of CFWM products is increased, as well as the powers of most CFWM products are improved.

©2012 Optical Society of America

1. Introduction

Cascaded four-wave mixing (CFWM) generated in highly-nonlinear fiber (HNLF) is extensively investigated recently [1, 2], due to its wide potential applications as multi-wavelength source for dense wavelength-division multiplexing system, all-optical wavelength multicasting [3], high repetition rate pulse source [4], frequency combs for astrophysical spectrometer calibration and metrology [5], etc. For those applications, efficient CFWM, i.e. lots of frequency components with high power, is desired. To meet this requirement, very short (about a few meters) dispersion flattened fiber [1] or dispersion-managed fibers [6, 7] are proposed as nonlinear media. Three-pump technique with carefully tuned pump wavelength spacing was also proposed to generate frequency combs efficiently [8].

In this paper, a scheme to enhance the generation of CFWM products via optical feedback is proposed and demonstrated. Experiments validate that the number of CFWM products and the power of most CFWM products can be increased utilizing this scheme. Simulation further confirms that significant improvement of CFWM generation can be achieved by optical feedback. The paper is organized as follows. The second section describes the proposed scheme and the experimental settings. Experimental results and analysis is reported in the third section. Numerical demonstration of the scheme is shown in the fourth section. The fifth section presents the discussion and conclusion.

2. Illustration of the scheme and the experimental settings

The proposed scheme to enhance the CFWM generation is illustrated in Fig. 1(a) , where part of the output from HNLF is fed back to the input port. The scheme and mechanism are somewhat similar to optical parametric oscillator (OPO) [9], which is usually used to wavelength-conversion of a single pump.

 

Fig. 1 (a) Illustration of the scheme to improve the cascaded four-wave mixing via optical feedback. (b) Experimental setup. HNLF: high nonlinear fiber, CW: continues wave, EDFA: Erbium doped fiber amplifier, PC: polarization controller, OSA: optical spectrum analyzer, PM: phase modulation, ISO: isolator.

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Experiments are carried out to validate the proposed scheme. The experimental setup is shown in Fig. 1(b). Two continuous waves as dual-pump were injected into a 1-km long HNLF, the nonlinear coefficient, zero dispersion wavelength (ZDW), and the dispersion slope of which are 10.5 W−1km−1, 1543 nm, and 0.019 ps/(nm2km), respectively. A phase modulator is used to suppress the stimulated Brillouin scattering effects of pumps in HNLF. New frequency components are generated as sidebands through CFWM in the HNLF. An optical feedback structure constituted by two couplers and an isolator is constructed. The feedback ratio [Pfeedback/Pinput labeled in Fig. 1(b)] can be tuned by use of different couplers. For example, if the coupling ratio of couplers 2 and 3 are both 90:10, feedback ratio is 9%, and if the coupling ratio of couplers 2 and 3 are 70:30 and 90:10, respectively, the feedback ratio is 27%.

3. Experimental results and analysis

With the feedback structure, broader CFWM bandwidth with more FWM products is obtained compared to conventional scheme (i.e. CFWM without optical feedback, by disconnecting the fiber at Point A in our experiment), as shown in Fig. 2 as a typical result. As can be observed, more frequency components are generated. Meanwhile, the powers of those frequency components, which are generated in both experiments with and without optical feedback, are increased by feedback.

 

Fig. 2 A typical output with and without feedback observed by OSA. Lower curve (black): without feedback, upper curve (green): with feedback.

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The enhancement of CFWM process induced by the optical feedback is investigated in detail, with adjusting the wavelength spacing of pumps, the feedback ratio, and the input pump power [Pinput labeled in Fig. 1(b)]. Only one of the three parameters above is adjusted each time, and the other two are fixed. When fixed, the three parameters are set as wavelength spacing 2 nm (wavelengths of pumps 1 and 2 are 1546 and 1548 nm, respectively), 9%, and 23 dBm (the power of each pump is about 20 dBm), respectively. When feedback ratio is 9% and pump power is 20 dBm, the EDFA output is about 26 dBm. For the experiments investigating the effect of feedback ratio, the EDFA output is tuned to keep Pinput constant for different feedback ratio.

Two specific frequency components, the −2nd and 3rd order idlers (labeled in Fig. 2), are inspected firstly. The results ruled by power increments of the −2nd and 3rd order idlers induced by feedback are shown in Fig. 3 . The improvement of idler power with the wavelength of pump 2 increasing from 1540 to 1555 nm is given in Fig. 3(a), which shows that the −2nd and 3rd order idlers are enhanced for all the wavelength spacing of pumps. The power increment (in dB) of the 3rd idler is usually larger than that of the −2nd idler, since the power (in dBm) of the 3rd idler is usually much smaller than that of the −2nd idler in our experiment. The power improvement is significantly reduced for wavelength of pump 2 around 1552 nm. We believe it is resulting from the difference of phase mismatch parameter, which is determined by the pump wavelengths.

 

Fig. 3 The power enhancement of −2nd and 3rd order CFWM products via optical feedback versus (a) wavelength of pump 2, (b) feedback ratio, and (c) EDFA output power.

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The increment of idler power with the feedback ratio increasing from 1% to 27% is show in Fig. 3(b), which indicates that the power of idler will increase rapidly for large feedback ratio. Simulations show, for larger feedback ratio, the idler power improvement will be larger. But in the experiment, the feedback ratio is limited by the coupling ratio of the optical couplers using in the fiber loop.

The power increment of idler with EDFA output power increasing from 20 to 30 dBm is shown in Fig. 3(c). It should be noted that for high pump power (e.g. EDFA output power is higher than 28 dBm), the power increment of −2nd and 3rd order idlers are little. However, more CFWM products with wavelength farther from pumps are generated or enhanced for the case of higher pump power. It is experimentally observed that, for high pump power, the number of CFWM products (the bandwidth) and the powers of most CFWM products are both increased by the optical feedback, though the power of a few frequency components near the pumps may be a little decreased. This phenomenon can be also observed in the numerical result shown in section 4, where the pump power is much higher. For high pump power, the frequency components near the pumps (e.g. the −2nd/3rd order idler) served as pumps to generate or amplify the idlers far away from input pumps, thus the energy of −2nd/3rd order idler will transfer to other components. However, the power decrease only occurs in a few CFWM products (which usually with high power), and the overall effect of optical feedback on the CFWM generation is good, as described in the following.

In order to estimate the overall effect of optical feedback on CFWM generation, another quantitative measurement, which considers both the power improvement and the increasing amount of the frequency components, is adopted. The number of CFWM products with a power enhancement more than 2 dB through feedback, n2dB, is counted, as shown in Table 1 . For the new frequency components only generated in the case with feedback, we set the corresponding idler powers be zero for the case without feedback.

Tables Icon

Table 1. Number of CFWM products with a power enhancement more than 2 dB induced by the optical feedback (n2dB) in different conditions.

Table 1 shows that, for all the cases with different pump power, wavelength spacing and feedback ratio, more efficient CFWM is obtained by optical feedback. Especially, it shows that, the enhancement effect is better when the inject pump power or the feedback ratio is larger.

4. Numerical demonstration

Recently, CFWM with bandwidths as large as 300 nm have been demonstrated by use of short and dispersion flattened HNLF [1]. Our simulation results, one of which is given in Fig. 4 , show that, for broadband conventional CFWM, it can be improved by the proposed method, i.e. through an optical feedback. The parameters of simulation are: the powers of pumps (1555 and 1563 nm) are both 10 W, the feedback ratio is 0.25%, the signal-to-noise ratio is of 80 dB, the length of HNLF is 30 m with γ = 10 W−1km−1, ZDW is 1550 nm, and the dispersion coefficients at ZDW are S0 = 0.00075 ps/nm2/km, β4 = 10−7 ps4/m. Split-step-Fourier-method is used for the numerical simulation to solve the nonlinear Schrödinger equation [1]. As can be seen, most of the components have gotten a power gain through feedback and a large number of new frequency components are generated, i.e. the CFWM efficiency is enhanced greatly by the optical feedback.

 

Fig. 4 Numerical results of output CFWM products for the cases with and without feedback in a short and dispersion flattened HNLF.

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5. Discussion and conclusion

The mechanism of the proposed scheme to improve the dual-pump CFWM generation is similar to single-pump FOPO. Instead of generating signal/idler from the parametric noise in traditional scheme, the optical feedback will provide some seed which is much helpful to increase the conversion efficiency. Even if the feedback ratio is small, Figs. 4 and 5 show that CFWM generation with feedback is better than that with the same (or even much higher) pump power but without feedback.

 

Fig. 5 Numerical results of output CFWM products for the cases with feedback and without feedback but with larger incident pump power. The simulation parameters are the same as Fig. 4.

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In our experiments, taking the feedback energy into account, the total energy of the case with feedback (Ptotal = Pinput + Pfeedback) will be higher than that without feedback (Ptotal = Pinput). With lots of numerical simulations (e.g. Fig. 5) and experiments, it is confirmed that, the CFWM generation with feedback is better than that with the same (or even larger) total incident pump energy but without feedback.

In conclusion, optical feedback is proposed to achieve more efficient CFWM generation in this paper. Firstly, the effect of feedback on the power of the idlers near pumps is investigated experimentally. Then the overall effect of optical feedback on the CFWM generation is discussed. Experiments and numerical simulations show that more CFWM products can be generated and the powers of most CFWM products can be increased by the proposed technique. Larger feedback ratio corresponds to better enhancement. For high pump power, the improvement of CFWM by feedback is significant, even if the feedback ratio is small.

Acknowledgments

Portions of this work were supported by the National Science Foundation of China (NSFC 61177046 and 60907028) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20090002120009).

References and Links

1. A. Cerqueira Sodre Jr, J. M. Boggio, A. A. Rieznik, H. E. Hernandez-Figueroa, H. L. Fragnito, and J. C. Knight, “Highly efficient generation of broadband cascaded four-wave mixing products,” Opt. Express 16(4), 2816–2828 (2008). [CrossRef]   [PubMed]  

2. C. J. McKinstrie and M. G. Raymer, “Four-wave-mixing cascades near the zero-dispersion frequency,” Opt. Express 14(21), 9600–9610 (2006). [CrossRef]   [PubMed]  

3. S. Gao and X. Xiao, “All-optical wavelength multicasting based on cascaded four-wave mixing with a single pump in highly nonlinear fibers,” Opt. Commun. 285(5), 784–789 (2012). [CrossRef]  

4. G. M. Macfarlane, A. S. Bell, E. Riis, and A. I. Ferguson, “Optical comb generator as an efficient short-pulse source,” Opt. Lett. 21(7), 534–536 (1996). [CrossRef]   [PubMed]  

5. F. C. Cruz, “Optical frequency combs generated by four-wave mixing in optical fibers for astrophysical spectrometer calibration and metrology,” Opt. Express 16(17), 13267–13275 (2008). [CrossRef]   [PubMed]  

6. J. Boggio, S. Moro, N. Alic, M. Karlsson, J. Bland-Hawthorn, and S. Radic, “Nearly octave-spanning cascaded four-wave-mixing generation in low dispersion highly nonlinear fiber,” in Proceedings of European Conference on Optical Communication (ECOC 2009), paper 9.1.2.

7. E. Myslivets, B. P. Kuo, N. Alic, and S. Radic, “Generation of wideband frequency combs by continuous-wave seeding of multistage mixers with synthesized dispersion,” Opt. Express 20(3), 3331–3344 (2012). [CrossRef]   [PubMed]  

8. C. Arismar, J. D. Marconi, H. E. Hernandez-Figueroa, and H. L. Fragnito, “Broadband cascaded four-wave mixing by using a three-pump technique in optical fibers,” Opt. Commun. 282(22), 4436–4439 (2009). [CrossRef]  

9. M. E. Marhic, K. K.-Y. Wong, L. G. Kazovsky, and T. E. Tsai, “Continuous-wave fiber optical parametric oscillator,” Opt. Lett. 27(16), 1439–1441 (2002). [CrossRef]   [PubMed]  

References

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  1. A. Cerqueira Sodre, J. M. Boggio, A. A. Rieznik, H. E. Hernandez-Figueroa, H. L. Fragnito, and J. C. Knight, “Highly efficient generation of broadband cascaded four-wave mixing products,” Opt. Express 16(4), 2816–2828 (2008).
    [Crossref] [PubMed]
  2. C. J. McKinstrie and M. G. Raymer, “Four-wave-mixing cascades near the zero-dispersion frequency,” Opt. Express 14(21), 9600–9610 (2006).
    [Crossref] [PubMed]
  3. S. Gao and X. Xiao, “All-optical wavelength multicasting based on cascaded four-wave mixing with a single pump in highly nonlinear fibers,” Opt. Commun. 285(5), 784–789 (2012).
    [Crossref]
  4. G. M. Macfarlane, A. S. Bell, E. Riis, and A. I. Ferguson, “Optical comb generator as an efficient short-pulse source,” Opt. Lett. 21(7), 534–536 (1996).
    [Crossref] [PubMed]
  5. F. C. Cruz, “Optical frequency combs generated by four-wave mixing in optical fibers for astrophysical spectrometer calibration and metrology,” Opt. Express 16(17), 13267–13275 (2008).
    [Crossref] [PubMed]
  6. J. Boggio, S. Moro, N. Alic, M. Karlsson, J. Bland-Hawthorn, and S. Radic, “Nearly octave-spanning cascaded four-wave-mixing generation in low dispersion highly nonlinear fiber,” in Proceedings of European Conference on Optical Communication (ECOC 2009), paper 9.1.2.
  7. E. Myslivets, B. P. Kuo, N. Alic, and S. Radic, “Generation of wideband frequency combs by continuous-wave seeding of multistage mixers with synthesized dispersion,” Opt. Express 20(3), 3331–3344 (2012).
    [Crossref] [PubMed]
  8. C. Arismar, J. D. Marconi, H. E. Hernandez-Figueroa, and H. L. Fragnito, “Broadband cascaded four-wave mixing by using a three-pump technique in optical fibers,” Opt. Commun. 282(22), 4436–4439 (2009).
    [Crossref]
  9. M. E. Marhic, K. K.-Y. Wong, L. G. Kazovsky, and T. E. Tsai, “Continuous-wave fiber optical parametric oscillator,” Opt. Lett. 27(16), 1439–1441 (2002).
    [Crossref] [PubMed]

2012 (2)

S. Gao and X. Xiao, “All-optical wavelength multicasting based on cascaded four-wave mixing with a single pump in highly nonlinear fibers,” Opt. Commun. 285(5), 784–789 (2012).
[Crossref]

E. Myslivets, B. P. Kuo, N. Alic, and S. Radic, “Generation of wideband frequency combs by continuous-wave seeding of multistage mixers with synthesized dispersion,” Opt. Express 20(3), 3331–3344 (2012).
[Crossref] [PubMed]

2009 (1)

C. Arismar, J. D. Marconi, H. E. Hernandez-Figueroa, and H. L. Fragnito, “Broadband cascaded four-wave mixing by using a three-pump technique in optical fibers,” Opt. Commun. 282(22), 4436–4439 (2009).
[Crossref]

2008 (2)

2006 (1)

2002 (1)

1996 (1)

Alic, N.

Arismar, C.

C. Arismar, J. D. Marconi, H. E. Hernandez-Figueroa, and H. L. Fragnito, “Broadband cascaded four-wave mixing by using a three-pump technique in optical fibers,” Opt. Commun. 282(22), 4436–4439 (2009).
[Crossref]

Bell, A. S.

Boggio, J. M.

Cerqueira Sodre, A.

Cruz, F. C.

Ferguson, A. I.

Fragnito, H. L.

C. Arismar, J. D. Marconi, H. E. Hernandez-Figueroa, and H. L. Fragnito, “Broadband cascaded four-wave mixing by using a three-pump technique in optical fibers,” Opt. Commun. 282(22), 4436–4439 (2009).
[Crossref]

A. Cerqueira Sodre, J. M. Boggio, A. A. Rieznik, H. E. Hernandez-Figueroa, H. L. Fragnito, and J. C. Knight, “Highly efficient generation of broadband cascaded four-wave mixing products,” Opt. Express 16(4), 2816–2828 (2008).
[Crossref] [PubMed]

Gao, S.

S. Gao and X. Xiao, “All-optical wavelength multicasting based on cascaded four-wave mixing with a single pump in highly nonlinear fibers,” Opt. Commun. 285(5), 784–789 (2012).
[Crossref]

Hernandez-Figueroa, H. E.

C. Arismar, J. D. Marconi, H. E. Hernandez-Figueroa, and H. L. Fragnito, “Broadband cascaded four-wave mixing by using a three-pump technique in optical fibers,” Opt. Commun. 282(22), 4436–4439 (2009).
[Crossref]

A. Cerqueira Sodre, J. M. Boggio, A. A. Rieznik, H. E. Hernandez-Figueroa, H. L. Fragnito, and J. C. Knight, “Highly efficient generation of broadband cascaded four-wave mixing products,” Opt. Express 16(4), 2816–2828 (2008).
[Crossref] [PubMed]

Kazovsky, L. G.

Knight, J. C.

Kuo, B. P.

Macfarlane, G. M.

Marconi, J. D.

C. Arismar, J. D. Marconi, H. E. Hernandez-Figueroa, and H. L. Fragnito, “Broadband cascaded four-wave mixing by using a three-pump technique in optical fibers,” Opt. Commun. 282(22), 4436–4439 (2009).
[Crossref]

Marhic, M. E.

McKinstrie, C. J.

Myslivets, E.

Radic, S.

Raymer, M. G.

Rieznik, A. A.

Riis, E.

Tsai, T. E.

Wong, K. K.-Y.

Xiao, X.

S. Gao and X. Xiao, “All-optical wavelength multicasting based on cascaded four-wave mixing with a single pump in highly nonlinear fibers,” Opt. Commun. 285(5), 784–789 (2012).
[Crossref]

Opt. Commun. (2)

S. Gao and X. Xiao, “All-optical wavelength multicasting based on cascaded four-wave mixing with a single pump in highly nonlinear fibers,” Opt. Commun. 285(5), 784–789 (2012).
[Crossref]

C. Arismar, J. D. Marconi, H. E. Hernandez-Figueroa, and H. L. Fragnito, “Broadband cascaded four-wave mixing by using a three-pump technique in optical fibers,” Opt. Commun. 282(22), 4436–4439 (2009).
[Crossref]

Opt. Express (4)

Opt. Lett. (2)

Other (1)

J. Boggio, S. Moro, N. Alic, M. Karlsson, J. Bland-Hawthorn, and S. Radic, “Nearly octave-spanning cascaded four-wave-mixing generation in low dispersion highly nonlinear fiber,” in Proceedings of European Conference on Optical Communication (ECOC 2009), paper 9.1.2.

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Figures (5)

Fig. 1
Fig. 1 (a) Illustration of the scheme to improve the cascaded four-wave mixing via optical feedback. (b) Experimental setup. HNLF: high nonlinear fiber, CW: continues wave, EDFA: Erbium doped fiber amplifier, PC: polarization controller, OSA: optical spectrum analyzer, PM: phase modulation, ISO: isolator.
Fig. 2
Fig. 2 A typical output with and without feedback observed by OSA. Lower curve (black): without feedback, upper curve (green): with feedback.
Fig. 3
Fig. 3 The power enhancement of −2nd and 3rd order CFWM products via optical feedback versus (a) wavelength of pump 2, (b) feedback ratio, and (c) EDFA output power.
Fig. 4
Fig. 4 Numerical results of output CFWM products for the cases with and without feedback in a short and dispersion flattened HNLF.
Fig. 5
Fig. 5 Numerical results of output CFWM products for the cases with feedback and without feedback but with larger incident pump power. The simulation parameters are the same as Fig. 4.

Tables (1)

Tables Icon

Table 1 Number of CFWM products with a power enhancement more than 2 dB induced by the optical feedback (n2dB) in different conditions.

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