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Coherent Optical En/Decoding employing Discrete ProlateSpheroidal Sequences based Super Structured FBGs

Daniel Pastor(1)

, Cristian Triana(2)

, Roco Baos(1)

(1)Universidad Politcnica de Valencia, Camino de Vera s/n, Valencia, Espaa,dpastor@dcom.upv.es

(2)CMUN research group, Univ. Nacl. Colombia, Cra 30 #45-06, 111321 Bogot DC, Colombia

Abst ract We present the first experimental verification of the coherent optical en/decoding employing

Super-Structured Fibre Bragg Gratings performing Discrete Prolate Spheroidal Sequences (DPSS).

These devices present promising spectral and temporal characteristics for OCDMA networks and

optical encryption applications.

Introduction

Optical Coding and Decoding (OC) techniques

have been extensively proposed in order to

face the exponential data traffic growth at every

network level. These techniques have been

considered as a next natural step to be added toWDM and TDM in future heterogeneous optical

networks scenaries1. In the other hand, network

security is a very important issue, where

Quantum key distribution (QKD)2 and chaotic

cryptography3have been implemented. In order

to avoid the high cost and technical complexity

of these techniques, Super-Structured Fibre

Bragg Gratings (SSFBGs) have been proposed

as optical encryption devices4,5

. In this case the

security is provided by the transformation of the

transmitted signals into noise-like patterns in the

optical domain, hiding every data signal

structure to the non-authorized users. Djordjevic

et. al.5

have proposed SSFBGs whose impulse

responses belong to the class of Discrete

Prolate Spheroidal Sequences (DPSS), which

are mutually orthogonal regardless of the

sequence order, while occupying a fixed optical

bandwidth. They proposed these devices

theoretically and demonstrated numerically for

different applications such as: all-optical

encryption, OCDMA, optical steganography, and

orthogonal-division multiplexing (ODM).

In this paper we present for the first time, to our

knowledge, an experimental verification of theDPSS optical en/decoding where a set of 3

encoder and decoder couples from the N=128

family were fabricated and tested to validate

their autocorrelation and cross-correlation

features.

Devices design and fabrication

DPSS are simultaneously time-limited to a given

design value (i.e. symbol duration) and

bandwidth-limited to target optical band as

DWDM channelling. In a simplified description,

DPSS codes present an oscillating shape with

alternated positive and negative lobes in time(impulse response). The code generation is

computed straightforward numerically by fixing

the integer parameter N (number of orthogonal

codes) and the discrete frequency covering

range [- , ]. Each one of the N orthogonal

sequences (fixed ) can be obtained directly as

one of the N eigen-vectors of a three-diagonalmatrix with dimensions NxN as:

(1)

For the experimental verification we have

selected N=128 and . So we have 128

orthogonal codes of 128 chip length. A basic

parameter to be defined is the time sampling ( )

defined as the time separation between adjacentvalues of the discrete sequence. In our case we

fixed the separation between two consecutive

sequence values along the SSFBG to

so the sampling time was

. Fig. 1 shows the time and spectral

responses, according to the indicated , for the

code numbers = 10, 15 and 20. The encoders

are named c10, c15 and c20 and the respective

decoders c10*, c15* and c20*, which are the

time/space inverted version ( . The ordering

of the codes inside the family from = 1 to N

corresponds with the degree of concentration of

the energy in the spectral and temporal axis and

with the number of alternating lobes. More

specifically, codes present 10dB optical

bandwidth of , and

respectively, being the SSFBG`s total

length of ~22, ~26 and ~30 mm. Increasing

code number inside the N=128 family will

provide progressively wider sequences both in

time and spectrum covering the entire time

range 128* and frequency range

.This feature of variable time and spectral width

from one code to another can be exploited in

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encryption where a random switching of different

codes can be employed to generate a masking

signal and to hide the data structure to the

eavesdropper in both time and spectral-

domains5.

Fig. 1:Theoretical DPSS (c10, c15 & c20) (N=128, W=0.5).a) Discrete Sequence in time (ts=3.95ps), b) Spectrums; real

part(blue), imaginary part (red), amplitude (dotted black).

Other important feature of the DPSS sequences

as optical en/decoders for OCDMA applications

is their natural wavelength channelling, which

provides sharp lateral edges and very high out-

band rejection enabling good spectral efficiency

if employed in a WDM grid.

For the DPSS en/decoders design we employ

the Discrete Layer Peeling (DLP) synthesis

method, starting from the objective ideal spectral

response in Fig. 1 and fixing the maximum

reflectivity to 5%. Although the length of the

sequences is N=128 this information was

linearly interpolated after de DLP process to

obtain a complex (modulus and phase) index

perturbation profile sampled each 85.6

that was fabricated at this step basis. Each

discrete point was performed by a Ultra-Violet

(UV) laser beam exposition after a Phase

Mask(PM) to obtain the Bragg pattern. UV beam

was focused before the PM up to 40 .

The amplitude and phase control of each

sample of was achieved by a double UVexposition of (50mW UV beam) over the

same z-position, only changing the relative

phase of the Bragg period between them by the

proper displacement of the Bragg pattern. In this

way, the averaged UV flux is constant and the

averaged value of the refractive index remains

unaltered6-7

. After fabrication en/decoders were

spectrally characterised by a direct powerspectral measurement employing an Amplified

spontaneous emission (ASE) source and an

Optical Spectrum Analyser (OSA) with 10 pm

resolution. Fig. 2 shows the comparison

between the measured and theoretical spectra

with a very good agreement. Results in Fig. 2

are normalised to the maximum but measured

maximum reflectivities were between ~3-5%.

Fig. 2: Measured and theoretical en/decoders spectrums.

En/decoding experimental verification

The complete en/decoding process was verified

employing the experimental set up shown in

Fig. 3. We employ a fibre Mode Locking Laser

(MLL) generating ~10 ps pulses at 10 GHz

repetition rate. This signal was modulated by anElectro-Optical Modulator (EOM) reducing its

rate to 1.25GHz and providing an 800ps time

delay between pulses. Pulsed signal was

amplified by a 20dB flat gain Erbium Doped

Fibre Amplifier (EDFA) before being applied to

the encoder and the decoder.

Fig. 3:Measurement setup.

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No additional losses due to fibre length were

employed between encoder and decoder sets.

Finally we employed a variable EDFA with low

gain to preamplify the signal before detection.

For the correct en/decoding process an accurate

spectral alignment between devices is

mandatory. Spectral misalignments higher than~ 2-4 pm leads to the Auto-Correlation Peak

(ACP) suppression. This precise spectral

adjustment was carried out by active thermal

control packaging of the SSFBG en/decoders.

Fig. 4:Measured and theoretical encoded signals c10, c15and c20.

Fig. 4 shows the encoded signals at the encoder

set output (point A in Fig. 3) measured with an

80 GHz electrical bandwidth optical sampling

oscilloscope. The measured traces are

compared to the theoretical ones with a very

good agreement for all the codes. The complete

en/decoding process was verified carrying out

the different combinations of encoder-decoder

pairs, for example employing decoder c10* the

ACP signalis obtained connecting c10->c10*

(ACP1010), being the Cross-Correlation (XC)

signals c15->c10* (XC1510) and c20->c10*

(XC2010).

Fig. 5: Measured and theoretical ACP and XC signals

Fig. 5 shows the experimental results compared

to the theoretical simulations for decoder sets

c10* and c15*. ACP signals were normalized to

1 to easily read XC/ACP ratios, and XC traces

have been displaced down in Fig. 5 for clarity.

Notice that ACP signals are composed of the

peak and a pedestal area called the wings andXC is a reduced amplitude signal extended

twice the encoded signals (Fig. 4). Also the XC

signals presentalmost zero values in a certain

range around the center. This feature can be

very convenient in synchronous OCDMA

applications.

Conclusions

We have demonstrated experimentally the

encoding and decoding process employing

SSFBGs that reproduce the Discrete Prolate

Spheroidal Sequences. This family of codes

provide very interesting features in time andfrequency domain with very high cardinality for

encryption and OCDMA applications.

Acknowledgements

This work was supported from the Spanish

Government project TEC2013-42332-P.

References

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[3] V. Annovazzi-Lodi, et al., Synchronization of chaotic

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953 (1996).

[4] J. M. Castro et aI.,Novel super-structured Bragg

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[5] I. B. Djordjevic, et al., Design of DPSS based fiberbragg

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OCDMA, optical steganography, and orthogonal-divisionmultiplexing, Optics Express, Vol. 22, no. 9, p. 10882

(2014).

[6] R. Banos, et al., Rectangular Global Envelope Super

Structured FBGs for Multiband Coherent

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(2013).

[7] R. Banos, et al., Chromatic dispersin compensation

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no. 13, p 13966 (2012).

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