## Design of DPSS based fiber bragg gratings and their application in all-optical encryption, OCDMA, optical steganography, and orthogonal-division multiplexing |

Optics Express, Vol. 22, Issue 9, pp. 10882-10897 (2014)

http://dx.doi.org/10.1364/OE.22.010882

Acrobat PDF (1216 KB)

### Abstract

The future information infrastructure will be affected by limited bandwidth of optical networks, high energy consumption, heterogeneity of network segments, and security issues. As a solution to all problems, we advocate the use of both electrical basis functions (orthogonal prolate spheroidal basis functions) and optical basis functions, implemented as FBGs with orthogonal impulse response in addition to spatial modes. We design the Bragg gratings with orthogonal impulse responses by means of discrete layer peeling algorithm. The target impulse responses belong to the class of discrete prolate spheroidal sequences, which are mutually orthogonal regardless of the sequence order, while occupying the fixed bandwidth. We then design the corresponding encoders and decoders suitable for all-optical encryption, optical CDMA, optical steganography, and orthogonal-division multiplexing (ODM). Finally, we propose the spectral multiplexing-ODM-spatial multiplexing scheme enabling beyond 10 Pb/s serial optical transport networks.

© 2014 Optical Society of America

## 1. Introduction

2. I. B. Djordjevic, “On the irregular nonbinary QC-LDPC-coded hybrid multidimensional OSCD-modulation enabling beyond 100 Tb/s optical transport,” J. Lightwave Technol. **31**(16), 2969–2975 (2013). [CrossRef]

## 2. Discrete prolate spheroidal sequences (DPSS) and discrete layer peeling algorithm for FBG design

### 2.1 Discrete prolate spheroidal sequences (DPSS)

### 2.2 Discrete layer peeling algorithm (DLPA) in DPSS-FBG design

8. J. Skaar, L. Wang, and T. Erdogan, “On the synthesis of fiber Bragg gratings by layer peeling,” IEEE J. Quantum Electron. **37**(2), 165–173 (2001). [CrossRef]

*J*complex uniform dielectric reflectors/layers, as illustrated in Fig. 1. In Fig. 1, for the

*j*-th layer both the forward (

*u*) and backward (

_{f}*u*) scattered signals are illustrated.

_{b}*t*= 0 depends only on the value of the reflection coefficient of the first reflector, the grating is “peeled off” layer by layer until all the required coupling coefficients for the resulting grating are calculated [8

8. J. Skaar, L. Wang, and T. Erdogan, “On the synthesis of fiber Bragg gratings by layer peeling,” IEEE J. Quantum Electron. **37**(2), 165–173 (2001). [CrossRef]

9. Y. Ouyang, Y. Sheng, M. Bernier, and G. Paul-Hus, “Iterative layer-peeling algorithm for designing fiber Bragg gratings with fabrication constraints,” J. Lightwave Technol. **23**(11), 3924–3930 (2005). [CrossRef]

*M*denotes the number of wavelengths observed. The

*r*(

*δ*) denotes the target complex reflection spectrum, obtained from corresponding DPSS. The ρ

*denotes the complex reflection coefficient of the*

_{j}*j*-th section, and

*δ*is the detuning coefficient defined as

*n*is the effective refractive index and

_{eff}*Λ*is the grating period. Finally, the

*q*denotes the coupling of the

_{j}*j*-th section with magnitude and phase determined as shown in Fig. 2. The evaluation starts by calculation of the reflection coefficient for the first layer, then the fields are propagated forward to find all required reflection coefficients until the end of all gratings, followed by the determination of the coupling coefficient.

*J*sections, each described by the transfer matrix

*T*

^{(}

^{j}^{)}. The elements of the transfer matrix of the

*j*-th section (

*j*= 1,2,…,

*J*) at the wavelength

10. B. Wu, Z. Wang, Y. Tian, M. P. Fok, B. J. Shastri, D. R. Kanoff, and P. R. Prucnal, “Optical steganography based on amplified spontaneous emission noise,” Opt. Express **21**(2), 2065–2071 (2013). [CrossRef] [PubMed]

### 2.3 Cardinality of DPSS-FBGs

9. Y. Ouyang, Y. Sheng, M. Bernier, and G. Paul-Hus, “Iterative layer-peeling algorithm for designing fiber Bragg gratings with fabrication constraints,” J. Lightwave Technol. **23**(11), 3924–3930 (2005). [CrossRef]

## 3. DPSS-FBGs in optical encryption, optical CDMA, optical steganography, and orthogonal-division multiplexing

### 3.1 All-optical encryption

2. I. B. Djordjevic, “On the irregular nonbinary QC-LDPC-coded hybrid multidimensional OSCD-modulation enabling beyond 100 Tb/s optical transport,” J. Lightwave Technol. **31**(16), 2969–2975 (2013). [CrossRef]

11. P. Pintus, F. Di Pasquale, and J. E. Bowers, “Integrated TE and TM optical circulators on ultra-low-loss silicon nitride platform,” Opt. Express **21**(4), 5041–5052 (2013). [CrossRef] [PubMed]

*K*optical switch is used to randomly select one out of

*K*available DPSS-FBGs to be used as an encryption device. On the other hand, an arbitrary sequence is used in masking stage to generate orthogonal noise sequence. This sequence is by MZ or phase modulator converted into optical domain. One of

*L*available DPSS-FBGs is selected at random by control input of 1:

*L*optical switch. Both DPSS-FBGs of encryption and masking sections are derived from the same class of DPS sequences of cardinality ≥

*L*+

*K*.

6. J. M. Castro, I. B. Djordjevic, and D. Geraghty, “Novel super-structured Bragg gratings for optical encryption,” J. Lightwave Technol. **24**(4), 1875–1885 (2006). [CrossRef]

6. J. M. Castro, I. B. Djordjevic, and D. Geraghty, “Novel super-structured Bragg gratings for optical encryption,” J. Lightwave Technol. **24**(4), 1875–1885 (2006). [CrossRef]

6. J. M. Castro, I. B. Djordjevic, and D. Geraghty, “Novel super-structured Bragg gratings for optical encryption,” J. Lightwave Technol. **24**(4), 1875–1885 (2006). [CrossRef]

^{−2}, the BER performance degradation even for different masking rates will be negligible.

### 3.2 Optical steganography

### 3.3 Optical CDMA (OCDMA)

14. A. Mendez, R. M. Gagliardi, V. J. Hernandez, C. V. Bennett, and W. J. Lennon, “High-performance optical CDMA system based on 2-D optical orthogonal codes,” J. Lightwave Technol. **22**(11), 2409–2419 (2004). [CrossRef]

17. T. H. Shake, “Security performance of optical CDMA against eavesdropping,” J. Lightwave Technol. **23**(2), 655–670 (2005). [CrossRef]

14. A. Mendez, R. M. Gagliardi, V. J. Hernandez, C. V. Bennett, and W. J. Lennon, “High-performance optical CDMA system based on 2-D optical orthogonal codes,” J. Lightwave Technol. **22**(11), 2409–2419 (2004). [CrossRef]

17. T. H. Shake, “Security performance of optical CDMA against eavesdropping,” J. Lightwave Technol. **23**(2), 655–670 (2005). [CrossRef]

### 3.4 Orthogonal-division multiplexing (ODM)

2. I. B. Djordjevic, “On the irregular nonbinary QC-LDPC-coded hybrid multidimensional OSCD-modulation enabling beyond 100 Tb/s optical transport,” J. Lightwave Technol. **31**(16), 2969–2975 (2013). [CrossRef]

*K*branches. Every branch is used as input of an electro-optical (E/O) modulator such as MZ, phase, or I/Q modulator. The output of the

*k*-th modulator (

*k*= 1,2,…,

*K*) is used as the input the

*k*-th DPSS-FBG, indicating that independent data streams are imposed on orthogonal impulse responses. The outputs of corresponding DPSS-FBGs are combined by

*K*:1 star coupler and transmitted to remote destination over either fiber-optics of free-space optical (FSO) system of interest. On receiver side, as shown in Fig. 14(b), the independent data streams are separated by corresponding conjugate DPSS-FBGs, whose outputs are used as inputs of corresponding coherent detectors. Notice that for FSO applications, the coherent detectors can be replaced by direct detectors. This scheme is applicable to any modulation format including on-off keying, M-PSK, M-QAM, to mention few. Since the orthogonal-division demultiplexing is performed in optical domain, both coherent and direct detections can be used. Finally, the system is compatible with both SMF and SDM fiber applications.

*m*×

_{i}*n*(

*i*∈{

*x*,

*y*}) block-interleaver [see Fig. 16(b)]. The

*m*bits from block-interleaver are taken column-wise and used to select the coordinates of 2

_{i}*M*-dimensional signal constellation (employing 2

*M*electrical basis functions). The configuration of corresponding 2

*M*-dimensional modulator can be found in [18

18. I. B. Djordjevic, A. Jovanovic, M. Cvijetic, and Z. H. Peric, “Multidimensional vector quantization-based signal constellation design enabling beyond 1 Pb/s serial optical transport networks,” IEEE Photon. J. **5**(4), 7901312 (2013). [CrossRef]

*M*-dimensional signal-constellation after up-sampling are passed through corresponding discrete-time (DT) pulse-shaping filters of impulse responses

*h*(

_{m}*n*) =

*Φ*(

_{m}*nT*), whose outputs are combined together into a single real (imaginary) data stream representing in-phase (quadrature) signal. After digital-to-analog conversion (DAC), the corresponding in-phase and quadrature signals are used as inputs to the I/Q modulator. The band selection within the band group is performed by complex multiplication with the exp(j2π

*f*)-term (

_{n}kT*T*is the sampling interval), as shown in Fig. 16(b), where

*f*is the center frequency of the

_{n}*n*-th band in band-group. Such obtained signals are initially spectrally-multiplexed to create the spectral band group. The spectral multiplexing can be achieved by the complex multiplication (to be performed in the electrical domain as shown in Fig. 16(b)) of corresponding 2

*M*-dimensional signals by exp[j2π(

*f*+

_{c}*f*)

_{n}*kT*], where

*f*is the central frequency of the

_{c}*c*-th spectral band group, and by combining them by a power coupler. Alternatively, the all-optical OFDM approach can be used for both spatial bands and spatial band groups multiplexing. The corresponding spectral band-group signals are then coupled into the orthogonal-division multiplexer, as shown in Fig. 16(a). The basic parameters of DPSS-FBG based ODM, corresponding to symbol rate of 31.25 GS/s are provided in Table 2. With LDPC code rate of 0.8, the information symbol rate would be 25 GS/s. To facilitate the demodulation process, both the central frequencies of bands within the band-group and frequencies among the band-groups are properly chosen so that principle of orthogonality is satisfied.

*M*-dimensional electrical signal. Two

*M*-dimensional projections (corresponding to x-/y-polarizations) are passed through analog-to-digital conversion (ADC) blocks and complex multiplier by exp[-j2π(

*f*+

_{c}*f*)

_{n}*kT*], and used as inputs to corresponding matched filters with impulse responses

*h*(

_{m}*n*) =

*Φ*(-

_{m}*nT*). For configuration of 2

*M*-dimensional demodulator please refer to [18

18. I. B. Djordjevic, A. Jovanovic, M. Cvijetic, and Z. H. Peric, “Multidimensional vector quantization-based signal constellation design enabling beyond 1 Pb/s serial optical transport networks,” IEEE Photon. J. **5**(4), 7901312 (2013). [CrossRef]

*a posteriori*probability (APP) demapper, which calculates symbol log-likelihood ratios (LLRs). We iterate the extrinsic information between LDPC decoders and APP demapper until convergence is achieved, or until pre-determined number of iterations has been reached. To compensate for the mode-coupling, optical MIMO detection principles described in [1] are used.

## 4. Concluding remarks

## Acknowledgments

## References and links

1. | M. Cvijetic, and I. B. Djordjevic, |

2. | I. B. Djordjevic, “On the irregular nonbinary QC-LDPC-coded hybrid multidimensional OSCD-modulation enabling beyond 100 Tb/s optical transport,” J. Lightwave Technol. |

3. | I. B. Djordjevic, |

4. | V. Annovazzi-Lodi, S. Donati, and A. Scire, “Synchronization of chaotic injected-laser systems and its application to optical cryptography,” IEEE J. Quantum Electron. |

5. | P. Torres, L. C. G. Valente, and M. C. R. Carvalho, “Security system for optical communication signals with fiber Bragg gratings,” IEEE Trans. Microw. Theory Tech. |

6. | J. M. Castro, I. B. Djordjevic, and D. Geraghty, “Novel super-structured Bragg gratings for optical encryption,” J. Lightwave Technol. |

7. | D. Slepian, “Prolate spheroidal wave functions, Fourier analysis, and uncertainty V: the discrete case,” Bell Syst. Tech. J. |

8. | J. Skaar, L. Wang, and T. Erdogan, “On the synthesis of fiber Bragg gratings by layer peeling,” IEEE J. Quantum Electron. |

9. | Y. Ouyang, Y. Sheng, M. Bernier, and G. Paul-Hus, “Iterative layer-peeling algorithm for designing fiber Bragg gratings with fabrication constraints,” J. Lightwave Technol. |

10. | B. Wu, Z. Wang, Y. Tian, M. P. Fok, B. J. Shastri, D. R. Kanoff, and P. R. Prucnal, “Optical steganography based on amplified spontaneous emission noise,” Opt. Express |

11. | P. Pintus, F. Di Pasquale, and J. E. Bowers, “Integrated TE and TM optical circulators on ultra-low-loss silicon nitride platform,” Opt. Express |

12. | M. P. Fok and P. R. Prucnal, “All-optical encryption based on interleaved waveband switching modulation for optical network security,” Opt. Lett. |

13. | P. R. Prucnal, M. P. Fok, Y. Deng, and Z. Wang, “Physical layer security in fiber-optic networks using optical signal processing,” in Proc. SPIE-OSA-IEEE Asia Communications and Photonics 7632, 6321M–1− 76321M–10 (2009), Shanghai, China. [CrossRef] |

14. | A. Mendez, R. M. Gagliardi, V. J. Hernandez, C. V. Bennett, and W. J. Lennon, “High-performance optical CDMA system based on 2-D optical orthogonal codes,” J. Lightwave Technol. |

15. | V V. J. Hernandez, W. Cong, J. Hu, C. Yang, N. K. Fontaine, R. P. Scott, Z. Ding, B. H. Kolner, J. P. Heritage, and S. J. B. Yoo, “A 320-Gb/s capacity (32-user× 10 Gb/s) SPECTS O-CDMA network testbed with enhanced spectral efficiency through forward error correction,” J. Lightwave Technol. |

16. | P. L. L. Bertarini, A. L. Sanches, and B.-H. V. Borges, “Optimal code set selection and security issues in spectral phase-encoded time spreading (SPECTS) OCDMA systems,” J. Lightwave Technol. |

17. | T. H. Shake, “Security performance of optical CDMA against eavesdropping,” J. Lightwave Technol. |

18. | I. B. Djordjevic, A. Jovanovic, M. Cvijetic, and Z. H. Peric, “Multidimensional vector quantization-based signal constellation design enabling beyond 1 Pb/s serial optical transport networks,” IEEE Photon. J. |

**OCIS Codes**

(060.0060) Fiber optics and optical communications : Fiber optics and optical communications

(060.4080) Fiber optics and optical communications : Modulation

(060.4230) Fiber optics and optical communications : Multiplexing

(060.3735) Fiber optics and optical communications : Fiber Bragg gratings

(060.4785) Fiber optics and optical communications : Optical security and encryption

**ToC Category:**

Fiber Optics

**History**

Original Manuscript: February 3, 2014

Revised Manuscript: April 23, 2014

Manuscript Accepted: April 23, 2014

Published: April 29, 2014

**Citation**

Ivan B. Djordjevic, Alaa H. Saleh, and Franko Küppers, "Design of DPSS based fiber bragg gratings and their application in all-optical encryption, OCDMA, optical steganography, and orthogonal-division multiplexing," Opt. Express **22**, 10882-10897 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-9-10882

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### References

- M. Cvijetic, and I. B. Djordjevic, Advanced optical communications and networks (Artech House, 2013).
- I. B. Djordjevic, “On the irregular nonbinary QC-LDPC-coded hybrid multidimensional OSCD-modulation enabling beyond 100 Tb/s optical transport,” J. Lightwave Technol. 31(16), 2969–2975 (2013). [CrossRef]
- I. B. Djordjevic, Quantum informationpProcessing and quantum error correction: an engineering approach (Elsevier/Academic Press, 2012).
- V. Annovazzi-Lodi, S. Donati, A. Scire, “Synchronization of chaotic injected-laser systems and its application to optical cryptography,” IEEE J. Quantum Electron. 32(6), 953–959 (1996). [CrossRef]
- P. Torres, L. C. G. Valente, M. C. R. Carvalho, “Security system for optical communication signals with fiber Bragg gratings,” IEEE Trans. Microw. Theory Tech. 50(1), 13–16 (2002). [CrossRef]
- J. M. Castro, I. B. Djordjevic, D. Geraghty, “Novel super-structured Bragg gratings for optical encryption,” J. Lightwave Technol. 24(4), 1875–1885 (2006). [CrossRef]
- D. Slepian, “Prolate spheroidal wave functions, Fourier analysis, and uncertainty V: the discrete case,” Bell Syst. Tech. J. 57(5), 1371–1430 (1978). [CrossRef]
- J. Skaar, L. Wang, T. Erdogan, “On the synthesis of fiber Bragg gratings by layer peeling,” IEEE J. Quantum Electron. 37(2), 165–173 (2001). [CrossRef]
- Y. Ouyang, Y. Sheng, M. Bernier, G. Paul-Hus, “Iterative layer-peeling algorithm for designing fiber Bragg gratings with fabrication constraints,” J. Lightwave Technol. 23(11), 3924–3930 (2005). [CrossRef]
- B. Wu, Z. Wang, Y. Tian, M. P. Fok, B. J. Shastri, D. R. Kanoff, P. R. Prucnal, “Optical steganography based on amplified spontaneous emission noise,” Opt. Express 21(2), 2065–2071 (2013). [CrossRef] [PubMed]
- P. Pintus, F. Di Pasquale, J. E. Bowers, “Integrated TE and TM optical circulators on ultra-low-loss silicon nitride platform,” Opt. Express 21(4), 5041–5052 (2013). [CrossRef] [PubMed]
- M. P. Fok, P. R. Prucnal, “All-optical encryption based on interleaved waveband switching modulation for optical network security,” Opt. Lett. 34(9), 1315–1317 (2009). [CrossRef] [PubMed]
- P. R. Prucnal, M. P. Fok, Y. Deng, and Z. Wang, “Physical layer security in fiber-optic networks using optical signal processing,” in Proc. SPIE-OSA-IEEE Asia Communications and Photonics 7632, 6321M–1− 76321M–10 (2009), Shanghai, China. [CrossRef]
- A. Mendez, R. M. Gagliardi, V. J. Hernandez, C. V. Bennett, W. J. Lennon, “High-performance optical CDMA system based on 2-D optical orthogonal codes,” J. Lightwave Technol. 22(11), 2409–2419 (2004). [CrossRef]
- V V. J. Hernandez, W. Cong, J. Hu, C. Yang, N. K. Fontaine, R. P. Scott, Z. Ding, B. H. Kolner, J. P. Heritage, S. J. B. Yoo, “A 320-Gb/s capacity (32-user× 10 Gb/s) SPECTS O-CDMA network testbed with enhanced spectral efficiency through forward error correction,” J. Lightwave Technol. 25(1), 79–86 (2007). [CrossRef]
- P. L. L. Bertarini, A. L. Sanches, B.-H. V. Borges, “Optimal code set selection and security issues in spectral phase-encoded time spreading (SPECTS) OCDMA systems,” J. Lightwave Technol. 30(12), 1882–1890 (2012). [CrossRef]
- T. H. Shake, “Security performance of optical CDMA against eavesdropping,” J. Lightwave Technol. 23(2), 655–670 (2005). [CrossRef]
- I. B. Djordjevic, A. Jovanovic, M. Cvijetic, Z. H. Peric, “Multidimensional vector quantization-based signal constellation design enabling beyond 1 Pb/s serial optical transport networks,” IEEE Photon. J. 5(4), 7901312 (2013). [CrossRef]

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