Abstract

In this paper, a theoretical model for an Interleave-Chirped Arrayed Waveguide Grating (IC-AWG) is presented. The model describes the operation of the device by means of a field (amplitude and phase) transfer response. The validation of the model is accomplished by means of simulations, using parameters from previously fabricated devices. A novel design procedure is derived from the model, and it is later on employed to demonstrate the design of colorless universal IC-AWGs. The model can be readily applied to the analysis and design of future multi-wavelength optical coherent communications receivers and optical waveform analyzers.

© 2013 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. Kikuchi, “Coherent optical communications: historical perspectives and future directions,” in High Spectral Density Optical Communication Technology, M. Nakazawa, K. Kikuchi, and T. Miyazaki, eds (Springer, 2010), Chap. 2.
    [CrossRef]
  2. R. Nagarajan, e.a., “Terabit/s class InP photonic integrated circuits,” Semicond. Sci. Tech.27, 094003 (2012).
    [CrossRef]
  3. J. T. Rahn, e.a., “250 Gb/s real-time PIC-based super-channel transmission over a gridless 6000 km terrestrial link,” in Proc. Opt. Fiber Comm. conference paper PDP5D.5 (2012).
  4. L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol.4, 615–627 (1995).
    [CrossRef]
  5. M. Bachmann, P. Besse, and H. Melchior, “General self-imaging properties in N × N multimode interference couplers including phase relations,” Appl. Opt.33, 3905–3911 (1994).
    [CrossRef] [PubMed]
  6. J. M. Heaton and R. M. Jenkins, “General matrix theory of self-imaging in multimode interference (MMI) couplers,” IEEE Photon. Technol. Lett.11, 212–214 (1999).
    [CrossRef]
  7. J. Van Roey, J. van der Donk, and P. Lagasse, “Beam-propagation method: analysis and assessment,” J. Opt. Soc. Am.71, 803–810 (1981).
    [CrossRef]
  8. C. R. Doerr, L. Zhang, and P. J. Winzer, “Monolithic InP multiwavelength coherent receiver using a chirped arrayed waveguide grating,” J. Lightwave Technol.29, 536–541 (2011).
    [CrossRef]
  9. P. Muñoz, D. Pastor, and J. Capmany, “Modeling and design of arrayed waveguide gratings,” J. Lightwave Technol.20, 661–674 (2002).
    [CrossRef]
  10. H. Takahashi, K. Oda, H. Toba, and Y. Inoue, “Transmission characteristics of arrayed waveguide N × N wavelength multiplexer,” J. Lightwave Technol.13, 447–455 (1995).
    [CrossRef]
  11. Y. Wan and R. Hui, “Design of WDM cross connect based on interleaved AWG (IAWG) and a phase shifter array,” J. Lightwave Technol.25, 1390–1400 (2007).
    [CrossRef]
  12. J. W. Goodman, “Introduction to Fourier optics,” in Classic Textbook Reissue Series, W. Stephen, ed. (New York: McGraw-Hill, 1988), Chap. 5, pp. 83–90.
  13. L. H. Spiekman, M. R. Amersfoort, A. H. de Vreede, F. P. G. M. van Ham, A. Kuntze, J. W. Pedersen, P. Demeester, and M. K. Smit, “Design and realization of polarization independent phased array wavelength demultiplexers using different array orders for TE and TM,” J. Lightwave Technol.14, 991–995 (1996).
    [CrossRef]
  14. C. R. Doerr, L. Zhang, L. Buhl, V. I. Kopp, D. Neugroschl, and G. Weiner, “Tapered dual-core fiber for efficient and robust coupling to InP photonic integrated circuits,” Proc. OFC paper OThN5 (2009).
  15. M. Lohmeyer, “Wave-matching-method for mode analysis of dielectric waveguides,” Opt. Quantum Electron.29, 907–922 (1997).
    [CrossRef]
  16. FieldDesigner™, PhoeniX Software, http://www.phoenixbv.com .
  17. M. K. Smit and C. van Dam, “PHASAR-based WDM-devices: Principles, design and applications,” IEEE J. Sel. Top. Quant.2, 236–250 (1996).
    [CrossRef]
  18. N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics4, 248–254 (2010).
    [CrossRef]
  19. S. T. S. Cheung, B. Guan, S. S. Djordjevic, K. Okamoto, and S. J. B. Yoo, “Low-loss and high contrast Silicon-on-Insulator (SOI) arrayed waveguide grating,” in CLEO: Science and Innovations, OSA Technical Digest (online) (Optical Society of America, 2012), paper CM4A.5.
  20. P. Bernasconi, C. Doerr, C. Dragone, M. Cappuzzo, E. Laskowski, and A. Paunescu, “Large N×N waveguide grating routers,” J. Lightwave Technol.18, 985–991 (2000).
    [CrossRef]

2012 (1)

R. Nagarajan, e.a., “Terabit/s class InP photonic integrated circuits,” Semicond. Sci. Tech.27, 094003 (2012).
[CrossRef]

2011 (1)

2010 (1)

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics4, 248–254 (2010).
[CrossRef]

2007 (1)

2002 (1)

2000 (1)

1999 (1)

J. M. Heaton and R. M. Jenkins, “General matrix theory of self-imaging in multimode interference (MMI) couplers,” IEEE Photon. Technol. Lett.11, 212–214 (1999).
[CrossRef]

1997 (1)

M. Lohmeyer, “Wave-matching-method for mode analysis of dielectric waveguides,” Opt. Quantum Electron.29, 907–922 (1997).
[CrossRef]

1996 (2)

M. K. Smit and C. van Dam, “PHASAR-based WDM-devices: Principles, design and applications,” IEEE J. Sel. Top. Quant.2, 236–250 (1996).
[CrossRef]

L. H. Spiekman, M. R. Amersfoort, A. H. de Vreede, F. P. G. M. van Ham, A. Kuntze, J. W. Pedersen, P. Demeester, and M. K. Smit, “Design and realization of polarization independent phased array wavelength demultiplexers using different array orders for TE and TM,” J. Lightwave Technol.14, 991–995 (1996).
[CrossRef]

1995 (2)

H. Takahashi, K. Oda, H. Toba, and Y. Inoue, “Transmission characteristics of arrayed waveguide N × N wavelength multiplexer,” J. Lightwave Technol.13, 447–455 (1995).
[CrossRef]

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol.4, 615–627 (1995).
[CrossRef]

1994 (1)

1981 (1)

Amersfoort, M. R.

L. H. Spiekman, M. R. Amersfoort, A. H. de Vreede, F. P. G. M. van Ham, A. Kuntze, J. W. Pedersen, P. Demeester, and M. K. Smit, “Design and realization of polarization independent phased array wavelength demultiplexers using different array orders for TE and TM,” J. Lightwave Technol.14, 991–995 (1996).
[CrossRef]

Bachmann, M.

Bernasconi, P.

Besse, P.

Buhl, L.

C. R. Doerr, L. Zhang, L. Buhl, V. I. Kopp, D. Neugroschl, and G. Weiner, “Tapered dual-core fiber for efficient and robust coupling to InP photonic integrated circuits,” Proc. OFC paper OThN5 (2009).

Capmany, J.

Cappuzzo, M.

Cheung, S. T. S.

S. T. S. Cheung, B. Guan, S. S. Djordjevic, K. Okamoto, and S. J. B. Yoo, “Low-loss and high contrast Silicon-on-Insulator (SOI) arrayed waveguide grating,” in CLEO: Science and Innovations, OSA Technical Digest (online) (Optical Society of America, 2012), paper CM4A.5.

de Vreede, A. H.

L. H. Spiekman, M. R. Amersfoort, A. H. de Vreede, F. P. G. M. van Ham, A. Kuntze, J. W. Pedersen, P. Demeester, and M. K. Smit, “Design and realization of polarization independent phased array wavelength demultiplexers using different array orders for TE and TM,” J. Lightwave Technol.14, 991–995 (1996).
[CrossRef]

Demeester, P.

L. H. Spiekman, M. R. Amersfoort, A. H. de Vreede, F. P. G. M. van Ham, A. Kuntze, J. W. Pedersen, P. Demeester, and M. K. Smit, “Design and realization of polarization independent phased array wavelength demultiplexers using different array orders for TE and TM,” J. Lightwave Technol.14, 991–995 (1996).
[CrossRef]

Djordjevic, S. S.

S. T. S. Cheung, B. Guan, S. S. Djordjevic, K. Okamoto, and S. J. B. Yoo, “Low-loss and high contrast Silicon-on-Insulator (SOI) arrayed waveguide grating,” in CLEO: Science and Innovations, OSA Technical Digest (online) (Optical Society of America, 2012), paper CM4A.5.

Doerr, C.

Doerr, C. R.

C. R. Doerr, L. Zhang, and P. J. Winzer, “Monolithic InP multiwavelength coherent receiver using a chirped arrayed waveguide grating,” J. Lightwave Technol.29, 536–541 (2011).
[CrossRef]

C. R. Doerr, L. Zhang, L. Buhl, V. I. Kopp, D. Neugroschl, and G. Weiner, “Tapered dual-core fiber for efficient and robust coupling to InP photonic integrated circuits,” Proc. OFC paper OThN5 (2009).

Dragone, C.

Fontaine, N. K.

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics4, 248–254 (2010).
[CrossRef]

Goodman, J. W.

J. W. Goodman, “Introduction to Fourier optics,” in Classic Textbook Reissue Series, W. Stephen, ed. (New York: McGraw-Hill, 1988), Chap. 5, pp. 83–90.

Guan, B.

S. T. S. Cheung, B. Guan, S. S. Djordjevic, K. Okamoto, and S. J. B. Yoo, “Low-loss and high contrast Silicon-on-Insulator (SOI) arrayed waveguide grating,” in CLEO: Science and Innovations, OSA Technical Digest (online) (Optical Society of America, 2012), paper CM4A.5.

Heaton, J. M.

J. M. Heaton and R. M. Jenkins, “General matrix theory of self-imaging in multimode interference (MMI) couplers,” IEEE Photon. Technol. Lett.11, 212–214 (1999).
[CrossRef]

Heritage, J. P.

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics4, 248–254 (2010).
[CrossRef]

Hui, R.

Inoue, Y.

H. Takahashi, K. Oda, H. Toba, and Y. Inoue, “Transmission characteristics of arrayed waveguide N × N wavelength multiplexer,” J. Lightwave Technol.13, 447–455 (1995).
[CrossRef]

Jenkins, R. M.

J. M. Heaton and R. M. Jenkins, “General matrix theory of self-imaging in multimode interference (MMI) couplers,” IEEE Photon. Technol. Lett.11, 212–214 (1999).
[CrossRef]

Kikuchi, K.

K. Kikuchi, “Coherent optical communications: historical perspectives and future directions,” in High Spectral Density Optical Communication Technology, M. Nakazawa, K. Kikuchi, and T. Miyazaki, eds (Springer, 2010), Chap. 2.
[CrossRef]

Kopp, V. I.

C. R. Doerr, L. Zhang, L. Buhl, V. I. Kopp, D. Neugroschl, and G. Weiner, “Tapered dual-core fiber for efficient and robust coupling to InP photonic integrated circuits,” Proc. OFC paper OThN5 (2009).

Kuntze, A.

L. H. Spiekman, M. R. Amersfoort, A. H. de Vreede, F. P. G. M. van Ham, A. Kuntze, J. W. Pedersen, P. Demeester, and M. K. Smit, “Design and realization of polarization independent phased array wavelength demultiplexers using different array orders for TE and TM,” J. Lightwave Technol.14, 991–995 (1996).
[CrossRef]

Lagasse, P.

Laskowski, E.

Lohmeyer, M.

M. Lohmeyer, “Wave-matching-method for mode analysis of dielectric waveguides,” Opt. Quantum Electron.29, 907–922 (1997).
[CrossRef]

Melchior, H.

Muñoz, P.

Nagarajan, R.

R. Nagarajan, e.a., “Terabit/s class InP photonic integrated circuits,” Semicond. Sci. Tech.27, 094003 (2012).
[CrossRef]

Neugroschl, D.

C. R. Doerr, L. Zhang, L. Buhl, V. I. Kopp, D. Neugroschl, and G. Weiner, “Tapered dual-core fiber for efficient and robust coupling to InP photonic integrated circuits,” Proc. OFC paper OThN5 (2009).

Oda, K.

H. Takahashi, K. Oda, H. Toba, and Y. Inoue, “Transmission characteristics of arrayed waveguide N × N wavelength multiplexer,” J. Lightwave Technol.13, 447–455 (1995).
[CrossRef]

Okamoto, K.

S. T. S. Cheung, B. Guan, S. S. Djordjevic, K. Okamoto, and S. J. B. Yoo, “Low-loss and high contrast Silicon-on-Insulator (SOI) arrayed waveguide grating,” in CLEO: Science and Innovations, OSA Technical Digest (online) (Optical Society of America, 2012), paper CM4A.5.

Pastor, D.

Paunescu, A.

Pedersen, J. W.

L. H. Spiekman, M. R. Amersfoort, A. H. de Vreede, F. P. G. M. van Ham, A. Kuntze, J. W. Pedersen, P. Demeester, and M. K. Smit, “Design and realization of polarization independent phased array wavelength demultiplexers using different array orders for TE and TM,” J. Lightwave Technol.14, 991–995 (1996).
[CrossRef]

Pennings, E. C. M.

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol.4, 615–627 (1995).
[CrossRef]

Rahn, J. T.

J. T. Rahn, e.a., “250 Gb/s real-time PIC-based super-channel transmission over a gridless 6000 km terrestrial link,” in Proc. Opt. Fiber Comm. conference paper PDP5D.5 (2012).

Scott, R. P.

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics4, 248–254 (2010).
[CrossRef]

Smit, M. K.

L. H. Spiekman, M. R. Amersfoort, A. H. de Vreede, F. P. G. M. van Ham, A. Kuntze, J. W. Pedersen, P. Demeester, and M. K. Smit, “Design and realization of polarization independent phased array wavelength demultiplexers using different array orders for TE and TM,” J. Lightwave Technol.14, 991–995 (1996).
[CrossRef]

M. K. Smit and C. van Dam, “PHASAR-based WDM-devices: Principles, design and applications,” IEEE J. Sel. Top. Quant.2, 236–250 (1996).
[CrossRef]

Soares, F. M.

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics4, 248–254 (2010).
[CrossRef]

Soldano, L. B.

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol.4, 615–627 (1995).
[CrossRef]

Spiekman, L. H.

L. H. Spiekman, M. R. Amersfoort, A. H. de Vreede, F. P. G. M. van Ham, A. Kuntze, J. W. Pedersen, P. Demeester, and M. K. Smit, “Design and realization of polarization independent phased array wavelength demultiplexers using different array orders for TE and TM,” J. Lightwave Technol.14, 991–995 (1996).
[CrossRef]

Takahashi, H.

H. Takahashi, K. Oda, H. Toba, and Y. Inoue, “Transmission characteristics of arrayed waveguide N × N wavelength multiplexer,” J. Lightwave Technol.13, 447–455 (1995).
[CrossRef]

Toba, H.

H. Takahashi, K. Oda, H. Toba, and Y. Inoue, “Transmission characteristics of arrayed waveguide N × N wavelength multiplexer,” J. Lightwave Technol.13, 447–455 (1995).
[CrossRef]

van Dam, C.

M. K. Smit and C. van Dam, “PHASAR-based WDM-devices: Principles, design and applications,” IEEE J. Sel. Top. Quant.2, 236–250 (1996).
[CrossRef]

van der Donk, J.

van Ham, F. P. G. M.

L. H. Spiekman, M. R. Amersfoort, A. H. de Vreede, F. P. G. M. van Ham, A. Kuntze, J. W. Pedersen, P. Demeester, and M. K. Smit, “Design and realization of polarization independent phased array wavelength demultiplexers using different array orders for TE and TM,” J. Lightwave Technol.14, 991–995 (1996).
[CrossRef]

Van Roey, J.

Wan, Y.

Weiner, G.

C. R. Doerr, L. Zhang, L. Buhl, V. I. Kopp, D. Neugroschl, and G. Weiner, “Tapered dual-core fiber for efficient and robust coupling to InP photonic integrated circuits,” Proc. OFC paper OThN5 (2009).

Winzer, P. J.

Yoo, S. J. B.

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics4, 248–254 (2010).
[CrossRef]

S. T. S. Cheung, B. Guan, S. S. Djordjevic, K. Okamoto, and S. J. B. Yoo, “Low-loss and high contrast Silicon-on-Insulator (SOI) arrayed waveguide grating,” in CLEO: Science and Innovations, OSA Technical Digest (online) (Optical Society of America, 2012), paper CM4A.5.

Zhang, L.

C. R. Doerr, L. Zhang, and P. J. Winzer, “Monolithic InP multiwavelength coherent receiver using a chirped arrayed waveguide grating,” J. Lightwave Technol.29, 536–541 (2011).
[CrossRef]

C. R. Doerr, L. Zhang, L. Buhl, V. I. Kopp, D. Neugroschl, and G. Weiner, “Tapered dual-core fiber for efficient and robust coupling to InP photonic integrated circuits,” Proc. OFC paper OThN5 (2009).

Zhou, L.

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics4, 248–254 (2010).
[CrossRef]

Appl. Opt. (1)

IEEE J. Sel. Top. Quant. (1)

M. K. Smit and C. van Dam, “PHASAR-based WDM-devices: Principles, design and applications,” IEEE J. Sel. Top. Quant.2, 236–250 (1996).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

J. M. Heaton and R. M. Jenkins, “General matrix theory of self-imaging in multimode interference (MMI) couplers,” IEEE Photon. Technol. Lett.11, 212–214 (1999).
[CrossRef]

J. Lightwave Technol. (7)

L. H. Spiekman, M. R. Amersfoort, A. H. de Vreede, F. P. G. M. van Ham, A. Kuntze, J. W. Pedersen, P. Demeester, and M. K. Smit, “Design and realization of polarization independent phased array wavelength demultiplexers using different array orders for TE and TM,” J. Lightwave Technol.14, 991–995 (1996).
[CrossRef]

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol.4, 615–627 (1995).
[CrossRef]

C. R. Doerr, L. Zhang, and P. J. Winzer, “Monolithic InP multiwavelength coherent receiver using a chirped arrayed waveguide grating,” J. Lightwave Technol.29, 536–541 (2011).
[CrossRef]

P. Muñoz, D. Pastor, and J. Capmany, “Modeling and design of arrayed waveguide gratings,” J. Lightwave Technol.20, 661–674 (2002).
[CrossRef]

H. Takahashi, K. Oda, H. Toba, and Y. Inoue, “Transmission characteristics of arrayed waveguide N × N wavelength multiplexer,” J. Lightwave Technol.13, 447–455 (1995).
[CrossRef]

Y. Wan and R. Hui, “Design of WDM cross connect based on interleaved AWG (IAWG) and a phase shifter array,” J. Lightwave Technol.25, 1390–1400 (2007).
[CrossRef]

P. Bernasconi, C. Doerr, C. Dragone, M. Cappuzzo, E. Laskowski, and A. Paunescu, “Large N×N waveguide grating routers,” J. Lightwave Technol.18, 985–991 (2000).
[CrossRef]

J. Opt. Soc. Am. (1)

Nat. Photonics (1)

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics4, 248–254 (2010).
[CrossRef]

Opt. Quantum Electron. (1)

M. Lohmeyer, “Wave-matching-method for mode analysis of dielectric waveguides,” Opt. Quantum Electron.29, 907–922 (1997).
[CrossRef]

Semicond. Sci. Tech. (1)

R. Nagarajan, e.a., “Terabit/s class InP photonic integrated circuits,” Semicond. Sci. Tech.27, 094003 (2012).
[CrossRef]

Other (6)

J. T. Rahn, e.a., “250 Gb/s real-time PIC-based super-channel transmission over a gridless 6000 km terrestrial link,” in Proc. Opt. Fiber Comm. conference paper PDP5D.5 (2012).

K. Kikuchi, “Coherent optical communications: historical perspectives and future directions,” in High Spectral Density Optical Communication Technology, M. Nakazawa, K. Kikuchi, and T. Miyazaki, eds (Springer, 2010), Chap. 2.
[CrossRef]

J. W. Goodman, “Introduction to Fourier optics,” in Classic Textbook Reissue Series, W. Stephen, ed. (New York: McGraw-Hill, 1988), Chap. 5, pp. 83–90.

FieldDesigner™, PhoeniX Software, http://www.phoenixbv.com .

S. T. S. Cheung, B. Guan, S. S. Djordjevic, K. Okamoto, and S. J. B. Yoo, “Low-loss and high contrast Silicon-on-Insulator (SOI) arrayed waveguide grating,” in CLEO: Science and Innovations, OSA Technical Digest (online) (Optical Society of America, 2012), paper CM4A.5.

C. R. Doerr, L. Zhang, L. Buhl, V. I. Kopp, D. Neugroschl, and G. Weiner, “Tapered dual-core fiber for efficient and robust coupling to InP photonic integrated circuits,” Proc. OFC paper OThN5 (2009).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

(a) IC-AWG layout. (b) Field focusing points without and (c) with chirp. Abbreviations: subscripts i, w and o stand for input, arrayed and output waveguides, respectively; ω: waveguide width; d: waveguide spacing; Lf : focal length; FPR: free propagation region; l0: shortest AW length; Δl: incremental length; λ: wavelength; nc: AW effective index; BZ: Brillouin Zone.

Fig. 2
Fig. 2

f3 (x3, λ) using input waveguide 1 for each wavelength channel and polarization.

Fig. 3
Fig. 3

Transfer function tp,q (λ) for input waveguide p = 1 at (a) output waveguides 1 to 4 at TE polarization and (b) output waveguides 5 to 8 at TM polarization.

Fig. 4
Fig. 4

Power and phase transfer functions tp,q (λ) for input waveguides p = 0, 1 and output waveguides (a) 1, (b) 9, (c) 17 and (d) 25 for TE polarization.

Fig. 5
Fig. 5

Vectorial representation of the field at the output waveguides

Fig. 6
Fig. 6

Field at the output plane x3 using input waveguide 1 for each channel and polarization

Fig. 7
Fig. 7

Transfer function at (a) output waveguides 1 to 4 at TE polarization and (b) output waveguides 5 to 8 at TM polarization

Fig. 8
Fig. 8

Schematic of IC-AWG with (a) two input waveguides, obtaining at the output waveguides response for each polarization in two channels per OW, and with (b) four input waveguides, obtaining at the output waveguides response in two channels but at the same polarization state.

Fig. 9
Fig. 9

(a) Schematic of a coherent detector using a four input waveguides IC-AWG with optical switches. (b) Schematic of a coherent detector using a two input waveguides IC-AWG with polarization splitter. Abbreviations: LO, local oscillator; PD array, photodetector array; Pol splitter, polarization splitter.

Tables (3)

Tables Icon

Table 1 Summary of the variables used in the formulation. Subscripts i, g and o stand for input, arrayed and output waveguides, respectively.

Tables Icon

Table 2 Number of the output waveguide for each phase shift, channel and polarization

Tables Icon

Table 3 Summary of the IAWG design example parameters. Subscripts i, g and o stand for input, arrayed and output waveguides, respectively.

Equations (33)

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

b i ( x 0 ) = 2 π ω i 2 4 e ( x 0 ω i ) 2
B i ( x 1 ) = { b i ( x 0 ) } | u = x 1 α = 2 π ω i 2 α 2 4 e ( π ω i ( x 1 α ) ) 2
α = c L f n s ν
f 1 ( x 1 ) = 2 π ω g 2 4 k = 0 M 1 [ r B i ( M r d ω + k d ω ) b g ( x 1 M r d ω k d ω ) ]
f 1 ( x 1 ) = 2 π ω g 2 4 k = 0 M 1 [ Π ( x 1 N d ω ) B i ( x 1 ) r = + δ ( x 1 M r d ω k d ω ) ] b g ( x 1 )
Π ( x 1 N d ω ) = { 1 , if | x | N d ω 2 0 , otherwise
l r , k = l c , k + Δ l ( r + N 2 M )
Δ l = m λ 0 n c
ϕ r , k ( ν ) = e j β l r , k = e j β ( l c , k + Δ l ( r + N 2 M ) )
β = 2 π n c ν c
f 2 ( x 2 , ν ) = 2 π ω g 2 4 k = 0 M 1 { Π ( x 2 N d ω ) B i ( x 2 ) ϕ k ( x 2 , ν ) δ ω , k ( x 2 ) e j β Δ l k M } b g ( x 2 )
δ ω , k ( x 2 ) = r = + δ ( x 2 M r d ω k d ω )
ϕ k ( x 2 , ν ) = ψ k ( ν ) e j β Δ l x 2 M d ω
ψ k ( ν ) = e j β ( l c , k + Δ l N 2 M )
f 3 ( x 3 , ν ) = 2 π ω g 2 4 B g ( x 3 ) k = 0 M 1 [ sinc ( N d ω x 3 α ) b i ( x 3 ) Φ k ( x 3 , ν ) Δ ω , k ( x 3 ) e j β Δ l k M ]
Φ k ( x 3 , ν ) = { ψ k ( ν ) e j β Δ l x 2 M d ω } | u = x 3 α = ψ k ( ν ) δ ( x 3 + n c ν Δ l α c M d ω )
Δ ω , k ( x 3 ) = { r = + δ ( x 2 M r d ω k d ω ) } | u = x 3 α = 1 M r = + e j 2 π k d ω x 3 α δ ( x 3 r α M d ω )
f 3 ( x 3 , ν ) = 2 π ω g 2 α 2 4 B g ( x 3 ) 1 M k = 0 M 1 [ ψ k ( ν ) e j β Δ l k M r = + e j 2 π r k M f M ( x 3 r α M d ω + n c ν Δ l α c M d ω ) ]
f M ( x 3 ) = sinc ( N d ω x 3 α ) b i ( x 3 )
γ = c M d ω n c Δ l α = ν 0 d ω α m
t 0 , q ( ν ) = + f 3 ( x 3 , ν ) b 0 ( x 3 q d 0 ) x 3
b i , p ( x 0 ) = 2 π ω i 2 4 e ( x 0 p d i ω i ) 2 = b i , p ( x 0 p d i )
f 3 ( x 3 , ν ) = 2 π ω g 2 α 2 4 B g ( x 3 ) 1 M k = 0 M 1 [ ψ k ( ν ) e j β Δ l k M r = + e j 2 π r k M f M ( x 3 r α M d ω + n c ν Δ l α c M d ω + p d i ) ]
t p , q ( ν ) = + f 3 , p ( x 3 , ν ) b 0 ( x 3 q d 0 ) x 3
Δ x pol = m d ω ( α T M ( ν ) n c , T M ( ν ) α T M ( ν ) ν n c , T E ( ν 0 ) ν 0 α T E ( ν ) + n c , T E ( ν ) α T E ( ν ) ν n c , T E ( ν 0 ) ν 0 )
Δ ν pol = n c , T E ( ν o ) ν o n c , T M ( ν + Δ ν pol ) ν α T E ( ν ) n c , T E ( ν o ) ν o n c , T M ( ν + Δ ν pol ) α T M ( ν + Δ ν pol ) + α T E ( ν ) n c , T E ( ν ) ν n c , T M ( ν + Δ ν pol ) α T M ( ν + Δ ν pol )
Δ ν pol = n c , T E ( ν 0 ) ν 0 n c , T M ( ν 0 + Δ ν pol ) ν 0
Δ x F S R = α M d ω
m = 1 2 M n s , T M ( ν 0 ) n s , T E ( ν 0 ) n c , T E ( ν 0 ) n c , T E ( ν 0 ) n c , T M ( ν 0 )
L u ( dB ) = 20 log 10 ( B g ( 0 ) B g ( Δ x L u ) )
L u ( dB ) = 20 log 10 ( 1 e ( π ω g M 1 M d ω ) 2 )
Δ ν b w = 2 γ ω 0 2 ln ( 10 3 / 20 )
L f = ν 0 n s n g d 0 Δ f c h d ω Δ l

Metrics