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

Design of DPSS based fiber bragg gratings and their application in all-optical encryption, OCDMA, optical steganography, and orthogonal-division multiplexing Ivan B. Djordjevic,1,2,* Alaa H. Saleh,2 and Franko Küppers2 1

University of Arizona, Depart. Electrical & Computer Eng., 1230 E. Speedway Blvd., Tucson, Arizona 85721, USA 2 Institute for Microwave Engineering and Photonics at TU Darmstadt, 64283 Darmstadt, Germany * [email protected]

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 OCIS codes: (060.0060) Fiber optics and optical communications; (060.3735) Fiber Bragg gratings; (060.4785) Optical security and encryption; (060.4080) Modulation; (060.4230) Multiplexing.

References and links 1. 2.

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). 3. I. B. Djordjevic, Quantum informationpProcessing and quantum error correction: an engineering approach (Elsevier/Academic Press, 2012). 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. 32(6), 953–959 (1996). 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. 50(1), 13–16 (2002). 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). 7. D. Slepian, “Prolate spheroidal wave functions, Fourier analysis, and uncertainty V: the discrete case,” Bell Syst. Tech. J. 57(5), 1371–1430 (1978). 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). 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). 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). 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). 12. M. P. Fok and P. R. Prucnal, “All-optical encryption based on interleaved waveband switching modulation for optical network security,” Opt. Lett. 34(9), 1315–1317 (2009).

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Received 3 Feb 2014; revised 23 Apr 2014; accepted 23 Apr 2014; published 29 Apr 2014 5 May 2014 | Vol. 22, No. 9 | DOI:10.1364/OE.22.010882 | OPTICS EXPRESS 10882

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. 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). 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. 25(1), 79–86 (2007). 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. 30(12), 1882–1890 (2012). 17. T. H. Shake, “Security performance of optical CDMA against eavesdropping,” J. Lightwave Technol. 23(2), 655–670 (2005). 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).

1. Introduction The exponential internet traffic growth projections place enormous transmission rate demands on the underlying information infrastructure at every level, ranging from the core to access networks [1]. The 100 Gb/s Ethernet (100 GbE) standard has been adopted recently (IEEE 802.3ba), and 400 GbE and 1 Tb/s Ethernet (1 TbE) are considered by many authors as next natural steps. Terabit optical Ethernet technologies will be affected not only by limited bandwidth of information-infrastructure, but also by its energy consumption [2]. Additionally, future optical networks will be heterogeneous in nature. Another interesting problem not sufficiently addressed in current literature is related to security of the dense wavelength division multiplexing (DWDM) networks. To address the security issues of optical communication systems, the quantum key distribution (QKD) [3] and chaotic cryptography [4] have been proposed recently. Most research efforts today in QKD have focused on two-dimensional QKD, such as the polarization state of photons. Moreover, the data rates for quantum key exchange are very low, and transmission distance is limited. On the other hand, in chaos cryptography the dynamics of the laser is prescribed to follow a given trajectory depending on the information to be transmitted. To decode the prescribed trajectory, the synchronism between transmitter and receiver is required. To avoid the high cost of QKD, the properly designed fiber Bragg gratings (FBGs) as optical encryption devices have been advocated in [5,6]. In particular, in [6] a super-structured Bragg gratings (SSBGs) approach to all-optical encryption was proposed. The security has been provided by the transformation of the transmitted signal into noise-like patterns in the optical domain, hiding any data signal structure to the nonauthorized users. However, since the impulse responses of these encoders are quasiorthogonal, while the designed method is heuristic, these systems suffer from limited cardinality of corresponding optical encryption signal set. The purpose of this paper is to address all four problems of the next generation optical networks; namely, limited bandwidth of information infrastructure, high power consumption, heterogeneity, and security problems; in a simultaneous manner. The key idea of the paper is to design the Bragg gratings to have 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 orthogonaldivision multiplexing (ODM). To solve for the limited bandwidth infrastructure and high energy consumption problems, we advocate the use of both electrical basis functions (orthogonal prolate spheroidal basis functions) and optical basis functions (ODM and spatial modes), in similar fashion as described in [2]. The paper is organized as follows. In subsection 2.1, we describe the discrete prolate spheroidal sequences (DPSS), which are used as impulse responses for target fiber Bragg grating design. The corresponding FBG design by discrete layer peeling algorithm is described in subsection 2.2. Given that the impulse responses of designed FBGs #205901 - $15.00 USD (C) 2014 OSA


corresponding to DPSS are strongly dependent on the pulse laser emitted signal pulsewidth, we discuss the cardinality of basis functions set as the function of cross-correlation coefficient in subsection 2.3. In Section 3, we describe different applications of proposed DPSS-FBG family including optical encryption, optical CDMA, optical steganography, and orthogonaldivision multiplexing. Finally, some important concluding remarks are provided in Section 4. 2. Discrete prolate spheroidal sequences (DPSS) and discrete layer peeling algorithm for FBG design 2.1 Discrete prolate spheroidal sequences (DPSS) As we mentioned in Introduction, for optical encryption applications and related fields, it is of high importance to ensure that impulse responses of corresponding encoders are orthogonal to each other. As indicated in [2], the modified orthogonal polynomials can be used as impulse responses for encoders. Unfortunately, the modified orthogonal polynomials offer a limited flexibility in terms of time × bandwidth product. On the other hand, the orthogonal prolate spheroidal wave (OPSW) functions are simultaneously time-limited to symbol duration and bandwidth-limited to target band and as such are extremely suitable for optical communication. Here we are restrict our attention to their discrete version, known as discrete prolate spheroidal sequences (DPSS) [7], which are a frequency band-limited sequences to [W, W], while at the same time almost entirely time-limited to length N. The DPS sequences

{u( ) ( N ,W )} j

n

of the j-th order are determined as a real-valued solution to the following

system of discrete equations [7]: N −1



sin 2π ( n − i )

i =0

π (n − i)

ui( j ) ( N , W ) = μ j ( N , W ) un( j ) ( N , W ) ; n = 0, ±1, ±2,

(1)

where i and n denote the particular sample in each DPSS, while j = 0,1,2, …. denotes the order of particular DPSS out of the set of sequences. N denotes the sequence length of each DPSS, W is a discrete bandwidth, and the shaping factors μ j ( N , W ) are ordered eigenvalues of the system of Eq. (1) corresponding to the concentration of each DPSS within the desired time interval of length N. Therefore, the eigenvalues fall within the range 0 < μ j ≤ 1 , with 1 corresponding to the case when the sequence energy is entirely included in the desired time interval. The small values of μ j imply that most of the sequence energy is outside the desired time interval. After this introduction of DPSS, we turn our attention to the use of these sequences as impulse responses of corresponding Bragg gratings to be employed as encoders for optical encryption and other areas. 2.2 Discrete layer peeling algorithm (DLPA) in DPSS-FBG design

Discrete layer peeling algorithm was proven to be efficient tool for designing fiber Bragg gratings with a desired transfer function [8]. The basic idea is to divide the grating to a series of J complex uniform dielectric reflectors/layers, as illustrated in Fig. 1. In Fig. 1, for the j-th layer both the forward (uf) and backward (ub) scattered signals are illustrated. By using the causality argument, i.e. the fact that the FBG impulse response at 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 [8,9]. The corresponding algorithm is described by flow-chart shown in Fig. 2, where M denotes the number of wavelengths observed. The r(δ) denotes the target complex reflection spectrum, obtained from corresponding DPSS. The ρj denotes the complex reflection coefficient of the j-th section, and δ is the detuning coefficient defined as δ ( λ ) = (2π / λ )neff − π / Λ, where neff is the effective refractive index and Λ is the grating

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period. Finally, the qj denotes the coupling of the 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. The j-th section

ρj

uf ub

Forward wave Backward wave

Fig. 1. Illustrating the DPSS-FBG design. The ρj is the complex reflection coefficient of the jth section and Δ denotes the section length. First discrete, complex reflection coefficient

r (δ )

ρ1 =

realizable complex reflection spectrum

Transfer fields to next section & peeling off current section

Δ

π

Δ / 2π



r1 ( δ ) d δ

− Δ / 2π

r j +1 (δ ) = exp(− 2iδΔ )

rj (δ ) − ρ j 1 − ρ j rj (δ ) *

coupling coefficient

| q1 |= − tanh − 1 (| ρ 1 |) / Δ phase ( q1 ) = − phase ( ρ 1 )

No

Structure is determined?

Yes

End

ρ j +1 =

1 M

M

r k =1

j +1

(k )

reflection coefficient

| q j +1 |= − tanh −1 (| ρ j +1 |) / Δ phase(q j +1 ) = − phase( ρ j +1 ) coupling coefficient

Fig. 2. Flow-chart illustrating the discrete layer peeling algorithm.

The transfer matrix method is used to analyze the synthesized gratings’ spectra of corresponding encoders. For simplicity of implementation, we assume that the number of sections in the layer peeling algorithm is the same as the number of reflectors previously chosen in the design. In Fig. 3, we provide the flow-chart illustrating that overall grating can be considered as a concatenation of 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 λk , k = 1, 2, , M are given as follows:  q2 − δ 2 ( λ )L   q 2 − δ 2 ( λ )L  δ ( λk ) m k m k    −j sin h  T11 ( λk ) = cos h 2 2     J J q − δ λ ( ) m k     (2) 2 2  q − δ ( λ )L  qm m k m) m) m) m) ( m) ( ( ( (  , T22 = T11 , T21 = −T12 . sin h  T12 ( λk ) = − j   J qm2 − δ 2 ( λk )   ( m)

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As an illustration, the transfer functions corresponding to both theoretical DPS sequence and design result are shown in the Fig. 4. Transfer matrix of the first layer

T (1) T (1)  T (1) (λ) =  11(1) 12(1)  T21 T22 

q coupling coefficient Transfer matrix of the j-th layer

T ( j ) T ( j )  T ( j ) (λ) =  11( j ) 12( j )  T21 T22 

No

Yes

Last layer?

r (λ ) = −

M

T ( λ ) = ∏ T ( k ) (λ ) k =1

T21 T11

reflection

matrix of M consecutive layers

Fig. 3. Flow chart illustrating the applied transfer matrix method.

-10

Reflectivity,R [dB]

-20 -30 -40 Target Design Result

-50 -60 -70 1.547

1.548

1.549

1.55 1.551 Wavelength, λ [μm]

1.552

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(a) Target Design Result

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Reflectivity,R [dB]

-20 -30 -40 -50 -60 -70 -80 1.544

1.546

1.548

1.55 Wavelength, λ [μm]

1.552

1.554

(b)

Fig. 4. Spectra of the target transfer functions and those obtained by the layer peeling algorithm for: (a) the 10-th order of DPSS and (b) the 100-th order DPSS.

The set of DPS sequences used as prototype is generated up to the order of 197, and the length of grating was set to 1 cm (corresponding to 10 Gb/s rate). Two particular transfer function instances, corresponding to the 10-th and 100-th orders are shown in the Fig. 4. In the wavelength region of interest, pretty much nice agreement between the target and actual #205901 - $15.00 USD (C) 2014 OSA


transfer functions have been obtained. The comparison of corresponding impulse responses is provided in Fig. 5. The discrepancy comes from the fact that the narrow Gaussian pulse of width 1 ps has been observed as the input to the grating instead of the unit-sample (delta) function. Notice that the bandwidth occupied is dictated by the number of DPS sequences and target symbol rate, while the central wavelength can be located to be in the wavelength region different from commercially available FBGs, including the wavelength region considered in reference [10]. 0.25 Design Result Target

0.2

Impulse Response, h(t)

0.15 0.1 0.05 0 -0.05 -0.1 -0.15 -0.2 -0.25 0

20

40 60 Time, t [ps]

80

100

Fig. 5. Impulse responses of the target transfer functions and result obtained by the layer peeling algorithm for the 10-th order of DPSS.

2.3 Cardinality of DPSS-FBGs

Since the narrow Gaussian pulse has been used as the input to the grating instead of unitsample (delta) function, the impulse responses orthogonality of DPSS-FBGs will be violated. This restriction has been dictated by currently existing pulse lasers and fabrication limitations. In order to investigate the reduction of cardinality of DPSS set due to practical restrictions, we study the cardinality as the function of maximum tolerable cross-correlation among the impulse responses in the actual set. The corresponding results are summarized in Figs. 6 and 7. 160 Pulsewidth: 0.1 ps 1 ps 120 5 ps 10 ps 100

Cardinality, C

140

80 60 40 20 0 0

0.1

0.2 0.3 Cross-correlation, ρ

0.4

Fig. 6. Cardinality of the actual Bragg gratings’ designs for the target 150 DPSS set of FBGs found for 10-Gb/s rate as a function of the normalized cross-correlation (with different input pulsewidths).

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160 140

Cardinality, C

120 Pulsewidth:

100

0.1 ps 1 ps 5 ps 10 ps

80 60 40 20 0 0

0.05

0.1

0.15 0.2 0.25 0.3 Cross-correlation, ρ

0.35

0.4

Fig. 7. Cardinality of the theoretical DPS sequences corresponding to the target of 150 for 10Gb/s rate as a function of the normalized cross-correlation (with different input pulsewidths).

Clearly, for theoretical DPS sequences, the full set of 150 is obtained when input Gaussian pulse width is smaller than or equal to 0.1 ps. Otherwise, for 10% of tolerable crosscorrelation, the cardinality drops down to about 60 for 1 ps pulsewidths. On the other hand, for the designs obtained by DLPA, for 1 ps pulse widths the cardinality drops down to 51 for the same level of cross-correlation (10%). This additional degradation is contributed to the DLPA suboptimal design along with the practical fabrication constraints [9]. Since the proposed DPSS-based FBGs can be described using the transfer matrix method given by Eq. (2) and Fig. 3, conventional FBG fabrication methods, including ultra-violet laser writing, are applicable here. 3. DPSS-FBGs in optical encryption, optical CDMA, optical steganography, and orthogonal-division multiplexing

Given the description of proposed DPSS-FBGs, in this section we study the different applications of interest including all-optical encryption, optical CDMA, optical steganography, orthogonal-division multiplexing, to name few. 3.1 All-optical encryption

In our information centric society Internet became the cornerstone of the universal information exchange. By year 2015, internet traffic in the United States alone is projected to be 50 times larger than its 2008 level with an exponential growth trend that will continue in upcoming decades. Although there are many proposals how to cope with the incoming bandwidth crunch [1,2], the security of future optical networks appears to fall well behind. Given the fact that by tapping out the portion of DWDM signal, the huge amount of data can be compromised, the security is becoming one of the major issues for future optical networks to be addressed sooner rather than later. In this section, we describe how the DPSS-FBGs can be used in all-optical encryption, which represents an interesting solution to enhance security of existing optical networks. Here we are concerned with encoders/decoders for optical encryption that can potentially be implemented on a single-chip in integrated optics. Given the fact that the basic building blocks are Bragg gratings and optical circulators, which are already fabricated on a singlechip [11], the proposed design represents a promising low-cost solution to all-optical encryption. The encoders and decoders for all optical encryption are shown in Fig. 8. The encoder for all-optical encryption is composed of two stages: encryption stage, the upper section of the encoder, and the masking stage, the lower section of the encoder. The same pulse laser is used for both stages. The PRBS sequence is by means of either Mach-Zehnder (MZ) or phase #205901 - $15.00 USD (C) 2014 OSA


modulator converted into optical domain. The 1: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. On the receiver side, the conjugate DPSS-FBGs have been used to decipher the transmitted sequence. When the transmitter and receiver use complementary DPSS-FBGs strong autocorrelation peak get generated at every signaling interval, while zero autocorrelation is obtained after non-matched DPSS-FBGs. The decision circuit selects the branch with strongest cross-correlation peak at every symbol interval. Since the masking sequence has been generated by randomly selected DPSS-FBG, generated from the same set of DPS sequences as for the encryption portion of the transmitter there is no need to use demasking at the receiver side. Therefore, the masking is used to hide any data structure to the eavesdropper in both time- and spectral-domains. As an illustration, in Fig. 9(a), we provide the output of encoder observed at different time intervals. Clearly, the regular structure of the data sequence is not visible to the eavesdropper, as the output appears as Gaussian noise to the eavesdropper. On the other hand, at the receiver side as shown in Fig. 9(b), the transmitted sequence 1 0 0 0 1 1 0 0 1 0 1 0 can easily be detected by simple threshold receiver. Given the fact that proposed DPSS-based FBGs are particular instances of FBGs, as they satisfy Eq. (2), various methods already in use to tune FBGs, including piezoelectric and thermal tunings, are applicable in tuning DPSS-FBGs as well. This tunability property can be used to simplify the encoder and decoder configurations, described in Fig. 8. Random selection of the output Encryption stage DPSS-FBG 1 MachZehnder modulator

1:K optical switch

…

… DPSS-FBG K

K:1 star coupler

User data Power combiner

Pulsed laser

To optical system of interest

DPSS-FBG 1’ (noise source 1) MachZehnder modulator

1:L optical switch

…

… DPSS-FBG L (noise source L)

Random sequence

L:1 star coupler

Masking stage

Randomly select the output

(a) Conjugate DPSS-FBG 1

Received signal

1:K star coupler

…

…

Decision circuit

To destination node

Conjugate DPSS-FBG K

(b) Fig. 8. Encoder/decoder configurations for DPSS-FBGs’ based all-optical encryption: (a) encoder configuration and (b) decoder configuration.

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Regarding the security, it is dictated by the cardinality of the DPSS set, as discussed in [6]. Since the pseudo-orthogonal impulse responses have been used in [6], while orthogonal ones in this paper, the cardinality of proposed DPSS set is higher, which leads to better security compared to scheme introduced in [6]. To improve the security further, we propose to use the masking sequences at data rates different from transmitted sequence, as illustrated in Fig. 10. In this particular example, the masking sequences of the same rate, half rate, and twice higher rates than transmitted sequence have been used. The parameters of corresponding DPSS-FGBs for nominal transmitted sequence rate of 10 Gb/s are provided in Table 1. The BER performance of proposed scheme are evaluated in Fig. 11. Clearly, when the same masking rate is used as transmitted data rate there is no any performance degradation compared to the case without encoding. On the other hand, as we increase the number of masks of different rates, there is certain performance degradation. Given the fact that in modern optical communication systems either turbo-product or LDPC codes have been used, for moderate BER threshold rates of 10−2, the BER performance degradation even for different masking rates will be negligible. 1 0 -1

0

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0.8

0.6

0.4

0.2

0 0

0.2

0.4

0.6 Time, t [ns]

0.8

1

1.2

(b)

Fig. 9. Illustration of encoding and decoding in proposed all-optical encryption scheme: (a) the outputs of encoder at different time intervals, and (b) the output of matched DPSS-FBG.

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Data symbol duration Mask 3, Half Rate Mask 2 Double Rate

Mask 2 Double Rate

Mask 2 Double Rate

Mask 2 Double Rate

Mask 1 the same rate

Mask 1 the same rate

Data rate

Data rate

0

Time, t

Fig. 10. Improving the security of proposed scheme by using masking sequences with data rates different from the transmitted sequence. Table 1. Parameters of DPSS-FBGs Corresponding to Different Data Rates Parameter (10 Gb/s) Total length Number of segments Index Max cross correlation Number of generated codes Parameter (20 Gb/s) Total length Number of segments Index Max cross correlation Parameter (5 Gb/s) Total length Number of segments Index Max cross correlation 10

Bit error rate, BER

10

10

10

10

10

Value 1.037 cm 200 1.446 0.05 40 out of 150 set Value 0.54 cm 100 (keep segment length equal) 1.4 0.01 Value 2.083 cm 400 (keep segment length equal) 1.44 0.01

0

Back-to-back with masks 1,2,3 Back-to-back with masks 1,2 Back-to-back with mask 1 Before masking Before encryption

-2

-4

-6

-8

-10

0

5

10 15 Q-Factor, 20log10(Q) [dB]

20

25

Fig. 11. BER performance of the proposed encryption system with several masks of rates different from transmitted sequence data rate (10 Gb/s). The laser pulse width is set to 1ps.

3.2 Optical steganography

Another interesting application of the proposed DPSS-FBGs technology is the optical steganography [10,12,13]. In general, the encrypted data can be recorded by eavesdropper

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regardless of its degree of encryption, so at least the information of ‘data existence’ on line will be leaked, even when the advanced masking proposed in this paper is used. This will allow the eavesdropper to “store and wait” for chosen channels till new technologies emerge for cracking them. On the other hand, the optical steganography will provide the possibility of hiding data within the public channel, by using so called “stealth channels” that are only visible to the authorized recipients. The proposed DPSS-FBGs can also be used for optical steganography applications. In Fig. 12, we provide the BER performance of stealth channels and compare them against the BER performance of the public channel. The masking data rate is the same as transmitted data rate. Clearly, there is no any performance degradation even for five stealth channels compared to the performance of the public channel. 10

Bit error rate, BER

10

10

10

10

0

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1 Public channel alone 1 Public channel with 3 hidden streams 3 Public channels with 5 hidden streams

-8

0

5

10 15 Q-Factor, 20log10(Q) [dB]

20

Fig. 12. BER performance of stealth channels against that of the public channel. The laser pulse width is set to 1 ps and data rate to 10 Gb/s.

3.3 Optical CDMA (OCDMA)

The optical code division multiple access (OCDMA) has been a hot research topic during the past two decades [14-17]. The advantages are optical CDMA numerous including privacy and inherent security in transmission, simplified network control (there is no need for the centralized network control), scalability of the network, support to multimedia applications, provision for quality of service (QoS), to mention few. The proposed DPSS-FBGs can also be used in OCDMA. In Fig. 13, we provide the BER results corresponding to different numbers of users, ranging from 1 to 36. In simulations, the laser pulse width is set to 1 ps and data rate of individual users to 10 Gb/s.

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Bit error rate, BER

10

0

1 user 8 users 36 users

10

-2

10

-4

10

-6

10

-8

10

-10

0

5 10 15 Q-Factor, 20log10(Q) [dB]

20

Fig. 13. BER performance of proposed OCDMA system for different number of users. The laser pulse width is set to 1 ps and data rate to 10 Gb/s.

The DPSS-FBGs, used in simulations are the same as in Table 1, corresponding to 10 Gb/s. Clearly, there is no any degradation when 36 users are used compared to a single user. This represents a key advantage of the proposed scheme, based on orthogonal impulse responses, compared to conventional OCDMA approaches based on pseudo-orthogonal impulse responses. Although the BPSK is used in this example, arbitrary complex signal constellations are applicable as the decoding is performed in optical domain, which represents another key advantage of the proposed scheme compared to conventional OCDMA techniques [14-17]. 3.4 Orthogonal-division multiplexing (ODM)

As a solution to limited bandwidth of information infrastructure, high energy consumption, and heterogeneity problems, the use of all available degrees of freedom for conveyance of the information over fibers supporting spatial-division multiplexing (SDM); such as few-mode fibers (FMFs), few-core fibers (FCFs) or few-core-few-mode fibers (FCFMFs); has been advocated in [2]. The optical degrees of freedom include the polarization and spatial modes in FMFs and FCFs. The electrical degrees of freedom include orthogonal prolate spheroidal wave (OPSW) functions. These degrees of freedom are used as the basis functions for multidimensional signaling. Given the orthogonality of impulse response of proposed DPSSFBGs, they can be used to provide an additional degree of freedom, in so called ODM, whose principles are illustrated in Fig. 14. Clearly, this scheme represents the generalization of OCDMA scheme discussed in previous section. The pulse laser output is split into 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 orthogonaldivision 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.

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Now we describe how the orthogonal-division multiplexing can be used to enable beyond 10 Pb/s serial optical transport, which represents the generalization of the scheme proposed in [18]. The signal frame shown in Fig. 15 is flexible and envisioned to support bit rates of up to 10 Pb/s. It is organized into 10 band-groups with center frequencies being orthogonal to each other. Each spectral component caries 1 Tb/s Ethernet (1 TbE), while each spectral band group carries 10 TbE traffic. We employ a four-step hierarchical architecture with a building block being 1 Tb/s supperchannel signal. Next, 1 TbE spectral slots are arranged in spectral band-groups to enable up to 10 TbE. By combining two (four) spectral band-groups, the scheme can enable 20 TbE (40 TbE). The second layer is related to spectral-division multiplexing, resulting in 100 Tb/s aggregate data rate per spatial mode, corresponding to 100 TbE. By combining two/four/ten such obtained signals by using the orthogonal-division multiplexer shown in Fig. 14(a), the scheme is compatible with 200 Tb/s/400 Tb/s/1 Pb/s. Finally, the fiber link layer is implemented by combining the signals from spatial modes to achieve 10 Pb/s serial optical transport. The adaptive software-defined LDPC-coded multiband OFDM with spectral multiplexing, ODM, and SDM that we have proposed is shown in Figs. 16(a). For easier explanation, only a single polarization state is shown, with no details with respect to synchronization and clock recovery circuits. The independent adaptive regular/irregular LDPC-coded data streams are written into mi × n (i∈{x,y}) block-interleaver [see Fig. 16(b)]. The mi bits from blockinterleaver are taken column-wise and used to select the coordinates of 2M-dimensional signal constellation (employing 2M electrical basis functions). The configuration of corresponding 2M-dimensional modulator can be found in [18]. The even (odd) coordinates of 2M-dimensional signal-constellation after up-sampling are passed through corresponding discrete-time (DT) pulse-shaping filters of impulse responses hm(n) = Φm(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(j2πfnkT)-term (T is the sampling interval), as shown in Fig. 16(b), where fn is the center frequency of the 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 2M-dimensional signals by exp[j2π(fc + fn)kT], where fc is the central frequency of the 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.

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Orthogonal-division multiplexer E/O modulator 1

1:K star coupler

…

…

Pulsed laser

DPSS-FBG 1

E/O modulator k

DPSS-FBG k

To optical system

…

…

K:1 star coupler

E/O modulator K

of interest

DPSS-FBG K

(a) Orthogonal-division demultiplexer

… Conjugate DPSS-FBG K

channel 1

Detected channel k

…

of interest

Coherent detector k

Conjugate DPSS-FBG k K:1 star coupler

…

From optical system

Detected

…

Coherent detector 1

Conjugate DPSS-FBG 1

Coherent detector K

Detected channel K

(b)

Fig. 14. The principles of orthogonal-division multiplexing: (a) transmitter configuration and (b) receiver configuration. E/O modulator: electro-optical modulator (MZ modulator, phase modulator, or I/Q modulator).

On the receiver side, see Fig. 16(c), after mode-demultiplexing, followed by orthogonaldivision demultiplexing, every mode/ODM projection is forwarded to the conventional polarization-diversity receiver, which provides the projections along the basis functions in both polarizations (and in-phase/quadrature channels). Each projection (in-phase/quadrature in either polarization) represents 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(fc + fn)kT], and used as inputs to corresponding matched filters with impulse responses hm(n) = Φm(-nT). For configuration of 2M-dimensional demodulator please refer to [18]. Finally, the re-sampled outputs represent projections along the corresponding basis functions, and these projections are used as inputs to the multidimensional 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.

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Spectral Multiplexing

Spectral band group # 1 Band # 10

Band Band #1 #2

Spectral band group # 2 Band # 20

Band Band # 11 # 12

Spectral band group # 3

…

… 1 TbE

Band # 30

Band Band # 21 # 22


…

…

10 Tb/s


Band # 40

Band Band # 31 # 32

Band # 100

Band Band # 91 # 92

…

… Bit rate

20 Tb/s 40 Tb/s

Orthogonal-Division Multiplexing

Spectral content of a signal incident to the orthogonal-division multiplexer (100 Tb/s) ODM signal # 1

ODM signal # 2

ODM Signal # 4

ODM Signal # 10

… 100 TbE

200 TbE

Bit rate

400 TbE 1 Pb/s Spatial Band # 1

Spatial Multiplexing

ODM Signal # 3

Spatial Band # 2

Spatial Band # 3

Spatial Band # 4

Spatial Band # 10

… 1 Pb/s

2 Pb/s

Bit rate

4 Pb/s 10 Pb/s

Fig. 15. Conceptual scheme of spectral-ODM-spatial processing enabling up to 10 Pb/s serial optical transport networking. ODM: orthogonal-division multiplexing. Table 2. Parameters of DPSS-FBGs to be Used in Proposed ODM Scheme (for Symbol Rate of 31.25 Gb/s and LDPC Code Rate of 0.8) Parameter (31.25 Gb/s) Total length Number of segments Index Max cross correlation Number of generated codes

Value 0.33 cm 100 1.446 0.05 32 out of 150 set

4. Concluding remarks

As the response to never ending high rate demands, 100 GbE standard has been adopted recently (IEEE 802.3ba), and 400 GbE/1 TbE and beyond Ethernet technologies have been intensively studied. It has become evident that terabit optical Ethernet technologies will be affected not only by limited bandwidth of information-infrastructure, but also by its energy consumption, heterogeneity of network segments, and security issues. As a solution to all problems, in this paper, we have advocated the use of both electrical basis functions and optical basis functions, implemented as FBGs with orthogonal impulse response in addition to spatial modes. We have designed the Bragg gratings with orthogonal impulse responses by means of the discrete layer peeling algorithm. The target impulse responses have been derived from the class of discrete prolate spheroidal sequences, which are mutually orthogonal regardless of the sequence order. We have designed the corresponding encoders/decoders and studied their application in all-optical encryption, OCDMA, optical steganography, and orthogonal-division multiplexing. Finally, we have proposed the spectral multiplexing-ODM-spatial multiplexing scheme enabling beyond 10 Pb/s serial optical transport. The future research topics include the fabrication of DPSS-based FBGs, their experimental evaluation, the demonstration of tunability, and proof-of-concept experimental demonstration of various applications that have been proposed in this paper. However, these topics are out of scope of this paper, and will be addressed in a follow-up publication.

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Content of spatial mode 1 Supperchannel 1

Spectral band group 1 LDPC-coded 2M-dim. mod. 1

I/Q Mod. Spectral multiplexing

…

Supperchannel N1

LDPC-coded I/Q 2M-dim. mod. N1 Mod. Spectral multiplexing

…

Source channels (spectral band group)

Content of spectral band group N2

Content of ODM signal 1

SDM fiber

Modemultiplexer

…

ODM

…

Content of ODM signal N3

Content of spatial mode N4

(a)

…

…

LDPC encoder (R=k / n)

…

…

Source 1 channels (i-th spectral band) mi

2M-dim. symbols Interleaver mi ×n

mi

2M-dim. mapper

…

2M-dim. mod.

Complex multiplier

LDPC encoder (R=k / n)

DAC

LPF

DAC

LPF

I/Q modulator

LDPC-coded 2M-dimensional modulator

to spectralmultiplexer

(b) 2M-dim. demodulator

LDPC decoders

…

Modedemux + orthogonaldivision demux

…

SDM fiber

Spectral demultiplexing + pol. div. Rx

Spectral demultiplexing + pol. div. Rx

2M-dim. demodulator

LDPC decoders

(c)

Fig. 16. (a) Block diagram of a transmitter for the software-defined coded multiband opticalOFDM with spectral-ODM-spatial multiplexing. (b) Details of the LDPC-coded 2Mdimensional modulator. (c) Details of the receiver. N1 denotes the number of bands (supperchannels) within the spectral band group; N2 denotes the number of spectral band groups; N3 denotes the number of ODM inputs; N4 denotes the number of spatial modes; and 2M denotes the number of electrical basis functions.

Acknowledgments

This work was supported by TU Darmstadt Fellowship supporting Dr. Djordjevic sabbatical (during 2013). This work was also supported in part by the NSF under Grant CCF-0952711.

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