## Simple nonlinear interferometer-based all-optical thresholder and its applications for optical CDMA

Optics Express, Vol. 15, Issue 20, pp. 13114-13122 (2007)

http://dx.doi.org/10.1364/OE.15.013114

Acrobat PDF (247 KB)

### Abstract

We present an experimental demonstration of an ultrafast all-optical thresholder based on a nonlinear Sagnac interferometer. The proposed design is intended for operation at very small nonlinear phase shifts. Therefore, it requires an in-loop nonlinearity lower than for the classical nonlinear loop mirror scheme. Only 15 meters of conventional (non-holey) silica-based fiber is used as a nonlinear element. The proposed thresholder is polarization insensitive and is good for multi-wavelength operation, meeting all the requirements for autocorrelation detection in various optical CDMA communication systems. The observed cubic transfer function is superior to the quadratic transfer function of second harmonic generation-based thresholders.

© 2007 Optical Society of America

## 1. Introduction

01. K.-L. Deng, I. Glesk, K. I. Kang, and P. R. Prucnal, “Unbalanced TOAD for Optical Data and Clock Separation in Self-Clocked Transparent OTDM Networks,” IEEE Photon. Technol. Lett. **9**, 830–832 (1997). [CrossRef]

02. J.H. Lee, P. C. Teh, Z. Yusoff, M. Ibsen, W. Belardi, T. M. Monro, and D. J. Richardson, “A holey fiber-based nonlinear thresholding device for optical CDMA receiver performance enhancement,” IEEE Photon. Technol. Lett. **14**, 876–878 (2002). [CrossRef]

03. X. Wang, T. Hamanaka, N. Wada, and K. Kitayama, “Dispersion-flattened-fiber based optical thresholder for multiple-access-interference suppression in OCDMA system,” Optics Express **13**, 5499–5505 (2005). [CrossRef] [PubMed]

04. Z. Jiang, D. S. Seo, S.-D. Yang, D. E. Leaird, R. V. Roussev, C. Langrock, M. M. Fejer, and A. M. Weiner, “Low-power high-contrast coded waveform discrimination at 10 GHz via nonlinear processing,” IEEE Photon. Technol. Lett. **16**, 1778–1780 (2004). [CrossRef]

05. N. J. Doran and D. Wood, “Non-linear optical loop mirror,” Opt. Lett. **13**, 56–58 (1988). [CrossRef] [PubMed]

06. M. E. Fermann, F. Haberl, M. Hofer, and H. Hochreiter, “Nonlinear amplifying loop mirror,” Opt. Lett. **15**, 752–754 (1990). [CrossRef] [PubMed]

07. A. G. Striegler, M. Meissner, K. Cvecek, K. Sponsel, G. Leuchs, and B. Schmauss, “NOLM-based RZ-DPSK signal regeneration,” IEEE Photon. Technol. Lett. **17**, 639–641 (2005). [CrossRef]

## 2. Theoretical background

08. D. J. Richardson, R. I. Laming, and D. N. Payne, “Switching and passive mode-locking of fibre lasers using nonlinear loop mirrors,” Proceedings of SPIE **1581**, 26–39 (1991). [CrossRef]

*T*— the ratio of output power to the launched power:

*T*=

*P*/

_{out}*P*. This effect causes the thresholder to behave nonlinearly with input power. To achieve effective thresholding, we would like to have complete destructive interference of the counterpropagating waves at the output port. This means that the waves’ amplitudes at the output port must be equal, and their phases opposite, if there is no nonlinear phase shift. To be more realistic, we assume that there are small errors in both phase and amplitude. Assume that one wave would give output power

_{in}*kP*in the absence of another wave (without interference), and the other wave — (

_{in}*k*+δ)

*P*so δ is the amplitude mismatch. The phase difference between these two waves is equal to φ = π + φ

_{in}_{e}+ φ

_{NL}, where φ

_{e}is the initial phase error and φ

_{NL}= Γ

*P*is a nonlinear phase shift proportional to the input power. When two waves interfere, the output power takes the form

_{in}*k*, and small nonlinear and error phases, i.e. φ

_{e},φ

_{NL}≪ 1. Finding the Taylor series expansion up to the first non-vanishing term, the resulting expression for the output power is

_{NL}the output of the thresholder is described by three terms which are linear, quadratic, and cubic with input power. Simple analysis shows that the linear term dominates at

*T*does not depend on the launched power because of the phase and amplitude errors, which allows some non-zero transmittance. So in this regime the output power is proportional to the input power, i.e. the device behaves just as a linear attenuator. When the nonlinear phase shift becomes strong enough to overcome both phase and amplitude mismatches (φ

_{e}and δ), we may neglect these two parameters. In that case the ratio of output and input amplitudes is proportional to the nonlinear phase shift. So the ratio of powers, i.e.

*T*, grows as a square of phase shift, resulting in a cubic transfer characteristic. In most situations, the cubic curve is steep enough to eliminate small signals and pass through big ones, that is, to perform thresholding. For example, thresholders based on a second harmonic generation in PPLN have only a quadratic transfer curve, which is inferior to the cubic one observed in our study.

## 3. Experimental demonstration

### 3.1. Device description

*n*= 0.043. The measured nonlinear coefficient at λ = 1550nm is γ= (9±1)W

^{-1}km

^{-1}. The fiber loss at the same wavelength is 2dB/km and can be neglected. The resulting nonlinear coefficient of NOLM, after taking into account the splitting ratio of the coupler and splice losses, is a quite modest value of Γ = 0.1W

^{-1}. The measured chromatic dispersion of the nonlinear fiber is

*D*= (-55 ± 5)ps/nm ∙ km, i.e. it is in the region of normal dispersion.

^{2}pulse profile. In all experiments we used an Erbium-Doped Fiber Amplifier (EDFA) with a maximum output power of about 300mW, directly connected to the input of the thresholder. All power measurements were conducted in points “in” and “out” (Fig. 1) with a standard average power meter.

### 3.2. Thresholder transfer function

_{NL}= 2π and touches the in-phase interference line at φ

_{NL}= π as follows from Eq.(1). The experimentally observed dependence does not reach these points, but still shows similar behavior. We found the point of the maximum measured transmittance and ascribed a nonlinear phase shift of π to it. Also, from the known nonlinear coefficient of the fiber used in the setup we calculated the required input CW power which would produce the same nonlinear phase shift of π and called it the effective peak power for this particular point of maximum transmittance. This procedure defined the normalization constant, which is the ratio between measured mean power and effective pulse power. The same value was used for normalization of all other data points. For the higher repetition rate of MLL this constant was scaled proportional to the rate (16 times), since the same procedure could not be used again due to insufficient peak power at higher repetition rate. The fact that after such normalization the data is in agreement with our measurements conducted with CW light (see later in text) justifies this normalization method.

^{2}intensity profile. The actual peak power appears to be 1.7 times higher than the effective peak power defined above. This is reasonable because an effective power includes an overall nonlinear response for the whole pulse. Such an integral response is weaker than the maximal peak response, corresponding to the actual peak power. Also, the deviations from the ideal sech

^{2}pulse profile may contribute to this peak-to-effective power ratio.

08. D. J. Richardson, R. I. Laming, and D. N. Payne, “Switching and passive mode-locking of fibre lasers using nonlinear loop mirrors,” Proceedings of SPIE **1581**, 26–39 (1991). [CrossRef]

_{NL}smaller than 0.05 it grows linearly with the input power, and at φ

_{NL}≳ 0.1 the cubic dependence is observed up to φ

_{NL}≈ 1.

_{NL}operation. Nevertheless, as will be shown later in the applications section, the thresholder performs satisfactory even for broad spectral widths of the order of 10 nm.

### 3.3. Applications

09. J. A. Salehi, A. M. Weiner, and J. P. Heritage, “Coherent ultrashort light pulse code-division multiple access communication systems,” J. Lightwave Technol. **8**, 478–491 (1990). [CrossRef]

^{-11}) measured with the 2

^{15}-1 pseudo-random bit sequence indicates error-free transmission. It should be said that a much faster electronic receiver with bandwidth of more than 12GHz can detect the initial signal as well, which is also demonstrated in experiment and is consistent with the discussion above.

## 4. Discussion

05. N. J. Doran and D. Wood, “Non-linear optical loop mirror,” Opt. Lett. **13**, 56–58 (1988). [CrossRef] [PubMed]

07. A. G. Striegler, M. Meissner, K. Cvecek, K. Sponsel, G. Leuchs, and B. Schmauss, “NOLM-based RZ-DPSK signal regeneration,” IEEE Photon. Technol. Lett. **17**, 639–641 (2005). [CrossRef]

^{-20}m

^{2}/W, [11

11. A. Boskovic, S. V. Chernikov, J. R. Taylor, L. Gruner-Nielsen, and O. A. Levring, “Direct continuous-wave measurement of n2 in various types of telecommunication fiber at 1.55 μm,” Opt. Lett. **21**, 1966–1968 (1996). [CrossRef] [PubMed]

*n*

_{2}≈ 2 × 10

^{-19}m

^{2}/W, [12

12. M. A. Newhouse, D. L. Weidman, and D. W. Hall, “Enhanced-nonlinearity single-mode lead silicate optical fiber,” Opt. Lett. **15**, 1185–1187 (1990). [CrossRef] [PubMed]

_{2}S

_{3}-based (

*n*

_{2}≈ 4 × 10

^{-18}m

^{2}/W, [13

13. M. Asobe, T. Kanamori, and K. Kubodera, “Applications of highly nonlinear chalcogenide glass fibers inultrafast all-optical switches,” IEEE J. Quantum Electron. **29**, 2325–2333 (1993). [CrossRef]

*n*

_{2}≈ 1.1 × 10

^{-18}m

^{2}/W, [14]). Therefore, non-silica based fibers can potentially be used in the proposed thresholder scheme to increase the in-loop nonlinearity.

## 5. Conclusion

## References and links

01. | K.-L. Deng, I. Glesk, K. I. Kang, and P. R. Prucnal, “Unbalanced TOAD for Optical Data and Clock Separation in Self-Clocked Transparent OTDM Networks,” IEEE Photon. Technol. Lett. |

02. | J.H. Lee, P. C. Teh, Z. Yusoff, M. Ibsen, W. Belardi, T. M. Monro, and D. J. Richardson, “A holey fiber-based nonlinear thresholding device for optical CDMA receiver performance enhancement,” IEEE Photon. Technol. Lett. |

03. | X. Wang, T. Hamanaka, N. Wada, and K. Kitayama, “Dispersion-flattened-fiber based optical thresholder for multiple-access-interference suppression in OCDMA system,” Optics Express |

04. | Z. Jiang, D. S. Seo, S.-D. Yang, D. E. Leaird, R. V. Roussev, C. Langrock, M. M. Fejer, and A. M. Weiner, “Low-power high-contrast coded waveform discrimination at 10 GHz via nonlinear processing,” IEEE Photon. Technol. Lett. |

05. | N. J. Doran and D. Wood, “Non-linear optical loop mirror,” Opt. Lett. |

06. | M. E. Fermann, F. Haberl, M. Hofer, and H. Hochreiter, “Nonlinear amplifying loop mirror,” Opt. Lett. |

07. | A. G. Striegler, M. Meissner, K. Cvecek, K. Sponsel, G. Leuchs, and B. Schmauss, “NOLM-based RZ-DPSK signal regeneration,” IEEE Photon. Technol. Lett. |

08. | D. J. Richardson, R. I. Laming, and D. N. Payne, “Switching and passive mode-locking of fibre lasers using nonlinear loop mirrors,” Proceedings of SPIE |

09. | J. A. Salehi, A. M. Weiner, and J. P. Heritage, “Coherent ultrashort light pulse code-division multiple access communication systems,” J. Lightwave Technol. |

10. | I. Glesk, V. Baby, C.-S. Bres, L. Xu, D. Rand, and P. R. Prucnal, “Experimental demonstration of 2.5 Gbit/s incoherent two-dimensional optical code division multiple access system,” Acta Physica Slovaca |

11. | A. Boskovic, S. V. Chernikov, J. R. Taylor, L. Gruner-Nielsen, and O. A. Levring, “Direct continuous-wave measurement of n2 in various types of telecommunication fiber at 1.55 μm,” Opt. Lett. |

12. | M. A. Newhouse, D. L. Weidman, and D. W. Hall, “Enhanced-nonlinearity single-mode lead silicate optical fiber,” Opt. Lett. |

13. | M. Asobe, T. Kanamori, and K. Kubodera, “Applications of highly nonlinear chalcogenide glass fibers inultrafast all-optical switches,” IEEE J. Quantum Electron. |

14. | N. Sugimoto, T. Nagashima, T. Hasegawa, S. Ohara, K. Taira, and K. Kikuchi, “Bismuth-based optical fiber with nonlinear coefficient of 1360 W-1km-1,” in |

**OCIS Codes**

(060.1810) Fiber optics and optical communications : Buffers, couplers, routers, switches, and multiplexers

(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: July 2, 2007

Revised Manuscript: September 17, 2007

Manuscript Accepted: September 20, 2007

Published: September 26, 2007

**Citation**

Konstantin Kravtsov, Paul R. Prucnal, and Mikhail M. Bubnov, "Simple nonlinear interferometer-based all-optical thresholder and its applications for optical CDMA," Opt. Express **15**, 13114-13122 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-20-13114

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### References

- K.-L. Deng, I. Glesk, K. I. Kang, and P. R. Prucnal, "Unbalanced TOAD for Optical Data and Clock Separation in Self-Clocked Transparent OTDM Networks," IEEE Photon. Technol. Lett. 9, 830-832 (1997). [CrossRef]
- J. H. Lee, P. C. Teh, Z. Yusoff, M. Ibsen, W. Belardi, T. M. Monro, and D. J. Richardson, "A holey fiber-based nonlinear thresholding device for optical CDMA receiver performance enhancement," IEEE Photon. Technol. Lett. 14, 876-878 (2002). [CrossRef]
- X. Wang, T. Hamanaka, N. Wada, and K. Kitayama, "Dispersion-flattened-fiber based optical thresholder for multiple-access-interference suppression in OCDMA system," Optics Express 13, 5499-5505 (2005). [CrossRef] [PubMed]
- Z. Jiang, D. S. Seo, S.-D. Yang, D. E. Leaird, R. V. Roussev, C. Langrock, M. M. Fejer, and A. M. Weiner, "Low-power high-contrast coded waveform discrimination at 10 GHz via nonlinear processing," IEEE Photon. Technol. Lett. 16, 1778-1780 (2004). [CrossRef]
- N. J. Doran and D. Wood, "Non-linear optical loop mirror," Opt. Lett. 13, 56-58 (1988). [CrossRef] [PubMed]
- M. E. Fermann, F. Haberl, M. Hofer, and H. Hochreiter, "Nonlinear amplifying loop mirror," Opt. Lett. 15, 752-754 (1990). [CrossRef] [PubMed]
- A. G. Striegler, M. Meissner, K. Cvecek, K. Sponsel, G. Leuchs, and B. Schmauss, "NOLM-based RZ-DPSK signal regeneration," IEEE Photon. Technol. Lett. 17, 639-641 (2005). [CrossRef]
- D. J. Richardson, R. I. Laming, and D. N. Payne, "Switching and passive mode-locking of fibre lasers using nonlinear loop mirrors," Proceedings of SPIE 1581, 26-39 (1991). [CrossRef]
- J. A. Salehi, A. M. Weiner, and J. P. Heritage, "Coherent ultrashort light pulse code-division multiple access communication systems," J. Lightwave Technol. 8, 478-491 (1990). [CrossRef]
- I. Glesk, V. Baby, C.-S. Bres, L. Xu, D. Rand, and P. R. Prucnal, "Experimental demonstration of 2.5 Gbit/s incoherent two-dimensional optical code division multiple access system," Acta Physica Slovaca 54, 245-250 (2004).Q1
- A. Boskovic, S. V. Chernikov, J. R. Taylor, L. Gruner-Nielsen, and O. A. Levring, "Direct continuous-wave measurement of n2 in various types of telecommunication fiber at 1.55 m," Opt. Lett. 21, 1966-1968 (1996). [CrossRef] [PubMed]
- M. A. Newhouse, D. L. Weidman, and D. W. Hall, "Enhanced-nonlinearity single-mode lead silicate optical fiber," Opt. Lett. 15, 1185-1187 (1990). [CrossRef] [PubMed]
- M. Asobe, T. Kanamori, and K. Kubodera, "Applications of highly nonlinear chalcogenide glass fibers inultrafast all-optical switches," IEEE J. Quantum Electron. 29, 2325-2333 (1993). [CrossRef]
- N. Sugimoto, T. Nagashima, T. Hasegawa, S. Ohara, K. Taira, and K. Kikuchi, "Bismuth-based optical fiber with nonlinear coefficient of 1360 W-1km-1," in OFC2004 PDP26 (Los Angeles, CA, 2004).

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