Abstract

The present paper aims to describe other functionalities for an arrayed waveguide grating (AWG)-based device, showing that this widely used configuration can be designed not only to frequency multiplex/demultiplex wavelength division multiplexing (WDM) signals, but also to perform the discrete Fourier transform (DFT) and the discrete fractional Fourier transform (DFrFT) of a signal, in all-optical orthogonal frequency division multiplexing (OFDM) systems. In addition 1 × N and N × N phased array switches architectures are described, as well as a new configuration to perform polarization diversity demultiplexing. Finally, a general approach, based on an analogy with the finite impulse response (FIR) filter approach, is presented to design optical modulators for any modulation format, using either phase modulators (PM) or electro-absorption modulators (EAM).

© 2012 OSA

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  1. I. Tomkos, P. Zakynthinos, E. Palkopoulou, M. Angelou, D. Klonidis, and S. B. Ezra, “Enabling technologies for evolving flexible/elastic optical transmission and expected benefits from their introduction in the networks,” in Photonics in Switching (PS) 2012.
  2. W. Shieh and I. Djordjevic, OFDM for Optical Communications (Elsevier, 2010).
  3. V. Namias, “The fractional order Fourier transform and its application to quantum mechanics,” J. Inst. Math. Appl.25(3), 241–265 (1980).
    [CrossRef]
  4. L. Almeida, “The fractional Fourier transform and time-frequency representations,” Trans. Sig. Processing42(11), 3084–3091 (1994).
    [CrossRef]
  5. D. Mendlovic and H. Ozaktas, “Fractional Fourier transforms and their optical implementation: I,” J. Opt. Soc. Am.10(9), 1875–1881 (1993).
    [CrossRef]
  6. H. Ozaktas and D. Mendlovic, “Fractional Fourier transforms and their optical implementation. II,” J. Opt. Soc. Am.10(12), 2522–2531 (1993).
    [CrossRef]
  7. A. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am.10(10), 2181–2186 (1993).
    [CrossRef]
  8. H. M. Ozaktas, Z. Zalevsky, and M. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).
  9. M. Smit, “New focusing and dispersive planar component based on an optical phased array,” Electron. Lett.24(7), 385–386 (1988).
    [CrossRef]
  10. J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1988), Chap 5.
  11. C. Madsen and J. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach, Par. 4.4.2 (John Wiley & Sons, 1999).
  12. N. Kataoka, N. Wada, G. Cincotti, and K.-I. Kitayama, “2.56 Tbps (40-Gbps x 8-wavelengths 4-OC x 2-POL) asynchronous WDM-OCDMA-PON using a multi-port encoder/decoder,” in European Conference on Optical Communication (ECOC) postdeadline paper 2011.
  13. G. Cincotti, Naoya Wad, and K. Kitayama, “Characterization of a full encoder/decoder in the AWG configuration for code-based photonic routers-Part I: modeling and design,” J. Lightwave Technol.24(1), 103–112 (2006).
    [CrossRef]
  14. N. Wada, G. Cincotti, S. Yoshima, N. Kataoka, and K.-i. Kitayama, “Characterization of a full encoder/decoder in the AWG configuration for code-based photonic routers-Part II: experimental results,” J. Lightwave Technol.24(1), 113–121 (2006).
    [CrossRef]
  15. G. Cincotti, “Design of optical full encoders/decoders for code-based photonic routers,” J. Lightwave Technol.22(7), 1642–1650 (2004).
    [CrossRef]
  16. N. Kataoka, G. Cincotti, N. Wada, and K.-i. Kitayama, “Demonstration of asynchronous, 40 Gbps x 4-user DPSK-OCDMA transmission using a multi-port encoder/decoder,” Opt. Express19(26), B965–B970 (2011).
    [CrossRef] [PubMed]
  17. A. J. Lowery, “Design of arrayed-waveguide grating routers for use as optical OFDM demultiplexers,” Opt. Express18(13), 14129–14143 (2010).
    [CrossRef] [PubMed]
  18. S. Shimotsu, G. Cincotti, and N. Wada, “Demonstration of a 8x12.5 Gbit/s all-optical OFDM system with an arrayed waveguide grating and waveform reshaper,” in European Conference on Optical Communications (ECOC) 2012 Th.1.A.2.
  19. G. Cincotti, “Generalized fiber Fourier optics,” Opt. Lett.36(12), 2321–2323 (2011).
    [CrossRef] [PubMed]
  20. G. Cincotti, “Optical OFDM based on the fractional Fourier transform,” in Proc. SPIE Photonic West, 8284–08, 2012.
  21. H. Yamazaki, T. Yamada, T. Goh, and S. Mino, “Multilevel optical modulator with PLC and LiNbO3 hybrid integrated circuit,” in Optical Fiber Communication Conference and Exposition (OFC) 2011.
  22. C. Doerr, P. Winzer, L. Zhang, L. Buhl, and N. Sauer, “Monolithic InP 16-QAM modulator,” in Optical Fiber Communication Conference and Exposition (OFC) 2008 PDP20.
  23. C. Doerr and C. Dragone, “Proposed optical cross connect using a planar arrangement of beam steerers,” Photon Technol. Lett.11(2), 197–199 (1999).
    [CrossRef]
  24. T. Tanemura, M. Takenaka, A. Al Amin, K. Takeda, T. Shioda, M. Sugiyama, and Y. Nakano, “InP–InGaAsP integrated 1×5 optical switch using arrayed phase shifters,” Photon Technol. Lett.20(12), 1063–1065 (2008).
    [CrossRef]
  25. C. R. Doerr, G. Raybon, L. L. Liming Zhang, A. L. Buhl, J. H. Adamiecki, Sinsky, and N. J. Sauer, “Low-chirp 85-Gb/s duobinary modulator in InP using electroabsorption modulators,” Photon. Technol. Lett.21(17), 1199–1201 (2009).
    [CrossRef]
  26. G. Cincotti, “Polarization gratings: design and applications,” J. Quantum Electron.39(12), 1645–1652 (2003).
    [CrossRef]

2011 (2)

2010 (1)

2009 (1)

C. R. Doerr, G. Raybon, L. L. Liming Zhang, A. L. Buhl, J. H. Adamiecki, Sinsky, and N. J. Sauer, “Low-chirp 85-Gb/s duobinary modulator in InP using electroabsorption modulators,” Photon. Technol. Lett.21(17), 1199–1201 (2009).
[CrossRef]

2008 (1)

T. Tanemura, M. Takenaka, A. Al Amin, K. Takeda, T. Shioda, M. Sugiyama, and Y. Nakano, “InP–InGaAsP integrated 1×5 optical switch using arrayed phase shifters,” Photon Technol. Lett.20(12), 1063–1065 (2008).
[CrossRef]

2006 (2)

2004 (1)

2003 (1)

G. Cincotti, “Polarization gratings: design and applications,” J. Quantum Electron.39(12), 1645–1652 (2003).
[CrossRef]

1999 (1)

C. Doerr and C. Dragone, “Proposed optical cross connect using a planar arrangement of beam steerers,” Photon Technol. Lett.11(2), 197–199 (1999).
[CrossRef]

1994 (1)

L. Almeida, “The fractional Fourier transform and time-frequency representations,” Trans. Sig. Processing42(11), 3084–3091 (1994).
[CrossRef]

1993 (3)

D. Mendlovic and H. Ozaktas, “Fractional Fourier transforms and their optical implementation: I,” J. Opt. Soc. Am.10(9), 1875–1881 (1993).
[CrossRef]

H. Ozaktas and D. Mendlovic, “Fractional Fourier transforms and their optical implementation. II,” J. Opt. Soc. Am.10(12), 2522–2531 (1993).
[CrossRef]

A. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am.10(10), 2181–2186 (1993).
[CrossRef]

1988 (1)

M. Smit, “New focusing and dispersive planar component based on an optical phased array,” Electron. Lett.24(7), 385–386 (1988).
[CrossRef]

1980 (1)

V. Namias, “The fractional order Fourier transform and its application to quantum mechanics,” J. Inst. Math. Appl.25(3), 241–265 (1980).
[CrossRef]

Adamiecki, J. H.

C. R. Doerr, G. Raybon, L. L. Liming Zhang, A. L. Buhl, J. H. Adamiecki, Sinsky, and N. J. Sauer, “Low-chirp 85-Gb/s duobinary modulator in InP using electroabsorption modulators,” Photon. Technol. Lett.21(17), 1199–1201 (2009).
[CrossRef]

Al Amin, A.

T. Tanemura, M. Takenaka, A. Al Amin, K. Takeda, T. Shioda, M. Sugiyama, and Y. Nakano, “InP–InGaAsP integrated 1×5 optical switch using arrayed phase shifters,” Photon Technol. Lett.20(12), 1063–1065 (2008).
[CrossRef]

Almeida, L.

L. Almeida, “The fractional Fourier transform and time-frequency representations,” Trans. Sig. Processing42(11), 3084–3091 (1994).
[CrossRef]

Buhl, A. L.

C. R. Doerr, G. Raybon, L. L. Liming Zhang, A. L. Buhl, J. H. Adamiecki, Sinsky, and N. J. Sauer, “Low-chirp 85-Gb/s duobinary modulator in InP using electroabsorption modulators,” Photon. Technol. Lett.21(17), 1199–1201 (2009).
[CrossRef]

Cincotti, G.

Doerr, C.

C. Doerr and C. Dragone, “Proposed optical cross connect using a planar arrangement of beam steerers,” Photon Technol. Lett.11(2), 197–199 (1999).
[CrossRef]

Doerr, C. R.

C. R. Doerr, G. Raybon, L. L. Liming Zhang, A. L. Buhl, J. H. Adamiecki, Sinsky, and N. J. Sauer, “Low-chirp 85-Gb/s duobinary modulator in InP using electroabsorption modulators,” Photon. Technol. Lett.21(17), 1199–1201 (2009).
[CrossRef]

Dragone, C.

C. Doerr and C. Dragone, “Proposed optical cross connect using a planar arrangement of beam steerers,” Photon Technol. Lett.11(2), 197–199 (1999).
[CrossRef]

Kataoka, N.

Kitayama, K.

Kitayama, K.-i.

Liming Zhang, L. L.

C. R. Doerr, G. Raybon, L. L. Liming Zhang, A. L. Buhl, J. H. Adamiecki, Sinsky, and N. J. Sauer, “Low-chirp 85-Gb/s duobinary modulator in InP using electroabsorption modulators,” Photon. Technol. Lett.21(17), 1199–1201 (2009).
[CrossRef]

Lohmann, A.

A. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am.10(10), 2181–2186 (1993).
[CrossRef]

Lowery, A. J.

Mendlovic, D.

H. Ozaktas and D. Mendlovic, “Fractional Fourier transforms and their optical implementation. II,” J. Opt. Soc. Am.10(12), 2522–2531 (1993).
[CrossRef]

D. Mendlovic and H. Ozaktas, “Fractional Fourier transforms and their optical implementation: I,” J. Opt. Soc. Am.10(9), 1875–1881 (1993).
[CrossRef]

Nakano, Y.

T. Tanemura, M. Takenaka, A. Al Amin, K. Takeda, T. Shioda, M. Sugiyama, and Y. Nakano, “InP–InGaAsP integrated 1×5 optical switch using arrayed phase shifters,” Photon Technol. Lett.20(12), 1063–1065 (2008).
[CrossRef]

Namias, V.

V. Namias, “The fractional order Fourier transform and its application to quantum mechanics,” J. Inst. Math. Appl.25(3), 241–265 (1980).
[CrossRef]

Naoya Wad,

Ozaktas, H.

H. Ozaktas and D. Mendlovic, “Fractional Fourier transforms and their optical implementation. II,” J. Opt. Soc. Am.10(12), 2522–2531 (1993).
[CrossRef]

D. Mendlovic and H. Ozaktas, “Fractional Fourier transforms and their optical implementation: I,” J. Opt. Soc. Am.10(9), 1875–1881 (1993).
[CrossRef]

Raybon, G.

C. R. Doerr, G. Raybon, L. L. Liming Zhang, A. L. Buhl, J. H. Adamiecki, Sinsky, and N. J. Sauer, “Low-chirp 85-Gb/s duobinary modulator in InP using electroabsorption modulators,” Photon. Technol. Lett.21(17), 1199–1201 (2009).
[CrossRef]

Sauer, N. J.

C. R. Doerr, G. Raybon, L. L. Liming Zhang, A. L. Buhl, J. H. Adamiecki, Sinsky, and N. J. Sauer, “Low-chirp 85-Gb/s duobinary modulator in InP using electroabsorption modulators,” Photon. Technol. Lett.21(17), 1199–1201 (2009).
[CrossRef]

Shioda, T.

T. Tanemura, M. Takenaka, A. Al Amin, K. Takeda, T. Shioda, M. Sugiyama, and Y. Nakano, “InP–InGaAsP integrated 1×5 optical switch using arrayed phase shifters,” Photon Technol. Lett.20(12), 1063–1065 (2008).
[CrossRef]

Sinsky,

C. R. Doerr, G. Raybon, L. L. Liming Zhang, A. L. Buhl, J. H. Adamiecki, Sinsky, and N. J. Sauer, “Low-chirp 85-Gb/s duobinary modulator in InP using electroabsorption modulators,” Photon. Technol. Lett.21(17), 1199–1201 (2009).
[CrossRef]

Smit, M.

M. Smit, “New focusing and dispersive planar component based on an optical phased array,” Electron. Lett.24(7), 385–386 (1988).
[CrossRef]

Sugiyama, M.

T. Tanemura, M. Takenaka, A. Al Amin, K. Takeda, T. Shioda, M. Sugiyama, and Y. Nakano, “InP–InGaAsP integrated 1×5 optical switch using arrayed phase shifters,” Photon Technol. Lett.20(12), 1063–1065 (2008).
[CrossRef]

Takeda, K.

T. Tanemura, M. Takenaka, A. Al Amin, K. Takeda, T. Shioda, M. Sugiyama, and Y. Nakano, “InP–InGaAsP integrated 1×5 optical switch using arrayed phase shifters,” Photon Technol. Lett.20(12), 1063–1065 (2008).
[CrossRef]

Takenaka, M.

T. Tanemura, M. Takenaka, A. Al Amin, K. Takeda, T. Shioda, M. Sugiyama, and Y. Nakano, “InP–InGaAsP integrated 1×5 optical switch using arrayed phase shifters,” Photon Technol. Lett.20(12), 1063–1065 (2008).
[CrossRef]

Tanemura, T.

T. Tanemura, M. Takenaka, A. Al Amin, K. Takeda, T. Shioda, M. Sugiyama, and Y. Nakano, “InP–InGaAsP integrated 1×5 optical switch using arrayed phase shifters,” Photon Technol. Lett.20(12), 1063–1065 (2008).
[CrossRef]

Wada, N.

Yoshima, S.

Electron. Lett. (1)

M. Smit, “New focusing and dispersive planar component based on an optical phased array,” Electron. Lett.24(7), 385–386 (1988).
[CrossRef]

J. Inst. Math. Appl. (1)

V. Namias, “The fractional order Fourier transform and its application to quantum mechanics,” J. Inst. Math. Appl.25(3), 241–265 (1980).
[CrossRef]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. (3)

D. Mendlovic and H. Ozaktas, “Fractional Fourier transforms and their optical implementation: I,” J. Opt. Soc. Am.10(9), 1875–1881 (1993).
[CrossRef]

H. Ozaktas and D. Mendlovic, “Fractional Fourier transforms and their optical implementation. II,” J. Opt. Soc. Am.10(12), 2522–2531 (1993).
[CrossRef]

A. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am.10(10), 2181–2186 (1993).
[CrossRef]

J. Quantum Electron. (1)

G. Cincotti, “Polarization gratings: design and applications,” J. Quantum Electron.39(12), 1645–1652 (2003).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Photon Technol. Lett. (2)

C. Doerr and C. Dragone, “Proposed optical cross connect using a planar arrangement of beam steerers,” Photon Technol. Lett.11(2), 197–199 (1999).
[CrossRef]

T. Tanemura, M. Takenaka, A. Al Amin, K. Takeda, T. Shioda, M. Sugiyama, and Y. Nakano, “InP–InGaAsP integrated 1×5 optical switch using arrayed phase shifters,” Photon Technol. Lett.20(12), 1063–1065 (2008).
[CrossRef]

Photon. Technol. Lett. (1)

C. R. Doerr, G. Raybon, L. L. Liming Zhang, A. L. Buhl, J. H. Adamiecki, Sinsky, and N. J. Sauer, “Low-chirp 85-Gb/s duobinary modulator in InP using electroabsorption modulators,” Photon. Technol. Lett.21(17), 1199–1201 (2009).
[CrossRef]

Trans. Sig. Processing (1)

L. Almeida, “The fractional Fourier transform and time-frequency representations,” Trans. Sig. Processing42(11), 3084–3091 (1994).
[CrossRef]

Other (10)

I. Tomkos, P. Zakynthinos, E. Palkopoulou, M. Angelou, D. Klonidis, and S. B. Ezra, “Enabling technologies for evolving flexible/elastic optical transmission and expected benefits from their introduction in the networks,” in Photonics in Switching (PS) 2012.

W. Shieh and I. Djordjevic, OFDM for Optical Communications (Elsevier, 2010).

H. M. Ozaktas, Z. Zalevsky, and M. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1988), Chap 5.

C. Madsen and J. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach, Par. 4.4.2 (John Wiley & Sons, 1999).

N. Kataoka, N. Wada, G. Cincotti, and K.-I. Kitayama, “2.56 Tbps (40-Gbps x 8-wavelengths 4-OC x 2-POL) asynchronous WDM-OCDMA-PON using a multi-port encoder/decoder,” in European Conference on Optical Communication (ECOC) postdeadline paper 2011.

S. Shimotsu, G. Cincotti, and N. Wada, “Demonstration of a 8x12.5 Gbit/s all-optical OFDM system with an arrayed waveguide grating and waveform reshaper,” in European Conference on Optical Communications (ECOC) 2012 Th.1.A.2.

G. Cincotti, “Optical OFDM based on the fractional Fourier transform,” in Proc. SPIE Photonic West, 8284–08, 2012.

H. Yamazaki, T. Yamada, T. Goh, and S. Mino, “Multilevel optical modulator with PLC and LiNbO3 hybrid integrated circuit,” in Optical Fiber Communication Conference and Exposition (OFC) 2011.

C. Doerr, P. Winzer, L. Zhang, L. Buhl, and N. Sauer, “Monolithic InP 16-QAM modulator,” in Optical Fiber Communication Conference and Exposition (OFC) 2008 PDP20.

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Figures (8)

Fig. 1
Fig. 1

Time-frequency plane coordinates (FT) rotated of an angle pπ/2 (FrFT).

Fig. 2
Fig. 2

AWG configuration.

Fig. 3
Fig. 3

(a) Slab coupler: R is the curvature radius and l the slab length. (b) Bulk optics system composed of two lenses with focal length R placed at a distance l. (c) Slab coupler with input and output arrayed waveguides.

Fig. 4
Fig. 4

(a) Time waveform of the output signal from an AWG device that implements the DFT (N = 16, m = 0, τ = 5 ps); the input signal is a 2-ps Gaussian laser pulse. (b) Transfer function Hm(t) of an AWG device that implements the DFT. (c) Waveform hpm(t) of a FrFT sub-carrier (m = 0, p = 1/8). (d) Transfer function of an AWG device that implements the FrFT (N = 16, m = 0, τ = 5 ps, p = 1/8).

Fig. 5
Fig. 5

(a) Conventional 16-QAM modulator composed of two phase shifters and N = 4 MZIs driven by N = 4 complementary two-level electrical signals ± Vn (n = 0,1,..3). (b) 16-QAM modulator composed of a 90° hybrid and PMs driven by N = 4 two-level electrical signals Vn (n = 0,1,..3).

Fig. 6
Fig. 6

1 × N phased array switch composed of a hybrid and N = 8 PMs driven by N-level electrical signals. (b) N × N switch composed of two hybrids and N PMs.

Fig. 7
Fig. 7

8-PSK modulator composed of three hybrids and three EO switches driven by the electrical voltages Vn (n = 0,1,2).

Fig. 8
Fig. 8

Polarization diversity demultiplexer.

Equations (24)

Equations on this page are rendered with MathJax. Learn more.

S( f )=F{ s }( f )= s( t ) e j2πtf dt
S p ( u )= F p { s }( u )= 1 j tan( p π 2 ) s( t ) e jπ[ ( u 2 + t 2 )cot( p π 2 )2utcsc( p π 2 ) ] dt,
F p { F q { s } }= F p+q { s }.
b( x )= a( x' ) e j2π xx' λl dx'.
b m =b( m d o )= n=0 N1 a( n d i ) e j2π mn d o d i λl = n=0 N1 a n e j2π mn N ,
h m ( t )= n=( N1 )/2 ( N1 )/2 e j2π mn N δ( tnτ )
H m ( f )= n=( N1 )/2 ( N1 )/2 e j2πnτ( f+ m T ) = sin[ πT( f+ m T ) ] sin[ πτ( f+ m T ) ] ,
h m ( t )= n= δ( tnτ ) rec t T ( t ) e j2πm t T ,
H m ( f )= 1 τ n= δ ( f n τ )Tsinc[ T( f+ m T ) ]=N n= sinc ( Tf+mnN ).
h ¯ m ( t )= e j2πm t T ,
1 T 0 T h ¯ m ( t ) h ¯ m' * ( t )dt= δ mm' ,
h ¯ m p ( t )= e jπ[ ( t 2 T 2 + T 2 u m 2 )cot( p π 2 )2t u m csc( p π 2 ) ]
H ¯ m p ( f )= e jπ T 2 [ [ f u m csc( p π 2 ) ] 2 tan( p π 2 )+ u m 2 cot( p π 2 ) ] ,
u m = msin( p π 2 ) T ,
h m p ( t )= n=( N1 )/2 ( N1 )/2 e jπ[ n 2 N 2 + m 2 sin 2 ( p π 2 ) ]cot( p π 2 ) e j2π mn N δ ( tnτ )
H m p ( f )= e jπ[ ( f m T ) 2 T 2 tan( p π 2 )+ m 2 2 sin( pπ ) ] N n= sinc( Tf+nN ) ,
R= l 1+cos( πp 2 ) d i = 1 N λl sin( πp 2 ) d o = λlsin( πp 2 ) .
tan( p π 2 )= λ 2 DL T 2 c ,
H( z )= n=0 N1 a n z n ,
H( z )= n=0 N1 a n e j π 2 n = a 0 a 2 + a N2 +j( a 1 a 3 + a N1 ).
a n = j2π nm N ,
H( z )= n=1 N1 ( 1 z n + z n z n ) ,
h m ( t )=( e x + e y e j 2πm N ) n=( N1 )/2 ( N1 )/2 e j4π nm N δ( tnτ )
H( f )=( e x + e y e j 2πm N ) n= sinc [ πτ N 2 ( f 2m+nN Nτ ) ],

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