Abstract

This paper investigates the power penalty from optical phased arrays used for wide-angle beam steering of optical communication signals. The analysis studies the effect of aperture size, data rate, modulation format, and diffraction angle on digital lightwave signals. The results show increasing power penalties for larger angles, aperture sizes, and data rates. At a 10° steering angle, 10-cm aperture, and for both on-off keying (OOK) and differential phase-shift keying (DPSK) the 2.5-Gb/s power penalty is approximately 1.0 dB, while at 10 Gb/s the penalty increases to 7.7 dB for OOK and 7.8 dB for DPSK.

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References

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  1. P. F. McManamon et al.," Optical Phased array technology," Proc. IEEE 84, 268-298 (1996).
    [CrossRef]
  2. A. Polishuk and S. Arnon, "Communication performance analysis of microsatellites using an optical phased array antenna," Opt. Eng. 42, 2015-2024 (2003).
    [CrossRef]
  3. A. A. Oliner and G. H. Knittel, Phased Array Antennas (Artech House, Massachusetts, 1972) pp. 243-253.
  4. M. Born and E. Wolf, Principle of Optics (University Press, Cambridge, 7th ed., 2002) p. 428, Eqn. (36).
  5. M. Born and E. Wolf, Principle of Optics (University Press, Cambridge, 7th ed., 2002) p. 448.
  6. T.K. Gaylord and M.G. Moharam, "Analysis of optical diffraction by gratings," Proc. IEEE 73, 894-937 (1985).
    [CrossRef]
  7. B. Sklar, Digital Communications Fundamentals and Applications (Prentice Hall PTR, New Jersey, 2nd ed., 2004) pp. 194-204.
  8. L. G. Kazovsky and O. K. Tonguz "Sensitivity of direct-detection lightwave receivers using optical preampli- fiers," IEEE Photon. Technol. Lett. 3, 53-55 (1991).
    [CrossRef]
  9. P. A. Humblet andM. Azizoglu,"On the bit error rate of lightwave systems with optical amplifiers," J. Lightwave Technol. 9, 1576-1584 (1991).
    [CrossRef]

2003

A. Polishuk and S. Arnon, "Communication performance analysis of microsatellites using an optical phased array antenna," Opt. Eng. 42, 2015-2024 (2003).
[CrossRef]

1996

P. F. McManamon et al.," Optical Phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

1991

L. G. Kazovsky and O. K. Tonguz "Sensitivity of direct-detection lightwave receivers using optical preampli- fiers," IEEE Photon. Technol. Lett. 3, 53-55 (1991).
[CrossRef]

P. A. Humblet andM. Azizoglu,"On the bit error rate of lightwave systems with optical amplifiers," J. Lightwave Technol. 9, 1576-1584 (1991).
[CrossRef]

1985

T.K. Gaylord and M.G. Moharam, "Analysis of optical diffraction by gratings," Proc. IEEE 73, 894-937 (1985).
[CrossRef]

Arnon, S.

A. Polishuk and S. Arnon, "Communication performance analysis of microsatellites using an optical phased array antenna," Opt. Eng. 42, 2015-2024 (2003).
[CrossRef]

Azizoglu, M.

P. A. Humblet andM. Azizoglu,"On the bit error rate of lightwave systems with optical amplifiers," J. Lightwave Technol. 9, 1576-1584 (1991).
[CrossRef]

Gaylord, T.K.

T.K. Gaylord and M.G. Moharam, "Analysis of optical diffraction by gratings," Proc. IEEE 73, 894-937 (1985).
[CrossRef]

Humblet, P. A.

P. A. Humblet andM. Azizoglu,"On the bit error rate of lightwave systems with optical amplifiers," J. Lightwave Technol. 9, 1576-1584 (1991).
[CrossRef]

Kazovsky, L. G.

L. G. Kazovsky and O. K. Tonguz "Sensitivity of direct-detection lightwave receivers using optical preampli- fiers," IEEE Photon. Technol. Lett. 3, 53-55 (1991).
[CrossRef]

McManamon, P. F.

P. F. McManamon et al.," Optical Phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Moharam, M.G.

T.K. Gaylord and M.G. Moharam, "Analysis of optical diffraction by gratings," Proc. IEEE 73, 894-937 (1985).
[CrossRef]

Polishuk, A.

A. Polishuk and S. Arnon, "Communication performance analysis of microsatellites using an optical phased array antenna," Opt. Eng. 42, 2015-2024 (2003).
[CrossRef]

Tonguz, O. K.

L. G. Kazovsky and O. K. Tonguz "Sensitivity of direct-detection lightwave receivers using optical preampli- fiers," IEEE Photon. Technol. Lett. 3, 53-55 (1991).
[CrossRef]

IEEE Photon. Technol. Lett.

L. G. Kazovsky and O. K. Tonguz "Sensitivity of direct-detection lightwave receivers using optical preampli- fiers," IEEE Photon. Technol. Lett. 3, 53-55 (1991).
[CrossRef]

J. Lightwave Technol.

P. A. Humblet andM. Azizoglu,"On the bit error rate of lightwave systems with optical amplifiers," J. Lightwave Technol. 9, 1576-1584 (1991).
[CrossRef]

Opt. Eng.

A. Polishuk and S. Arnon, "Communication performance analysis of microsatellites using an optical phased array antenna," Opt. Eng. 42, 2015-2024 (2003).
[CrossRef]

Proc. IEEE

T.K. Gaylord and M.G. Moharam, "Analysis of optical diffraction by gratings," Proc. IEEE 73, 894-937 (1985).
[CrossRef]

P. F. McManamon et al.," Optical Phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Other

B. Sklar, Digital Communications Fundamentals and Applications (Prentice Hall PTR, New Jersey, 2nd ed., 2004) pp. 194-204.

A. A. Oliner and G. H. Knittel, Phased Array Antennas (Artech House, Massachusetts, 1972) pp. 243-253.

M. Born and E. Wolf, Principle of Optics (University Press, Cambridge, 7th ed., 2002) p. 428, Eqn. (36).

M. Born and E. Wolf, Principle of Optics (University Press, Cambridge, 7th ed., 2002) p. 448.

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Figures (9)

Fig. 1.
Fig. 1.

Diffraction through a general aperture.

Fig. 2.
Fig. 2.

Diffraction grating (a) and diffraction angles (b)

Fig. 3.
Fig. 3.

Phase function of OPA

Fig. 4.
Fig. 4.

Treatment used to approximate Gaussian beam profiles

Fig. 5.
Fig. 5.

The frequency response as a function of λ. For different angles of incidence and a fixed OPA aperture Dopa = 1 cm.

Fig. 6.
Fig. 6.

The frequency response as a function of λ. For different angles of incidence and a fixed OPA aperture Dopa = 10 cm

Fig. 7.
Fig. 7.

Configuration for the network simulation

Fig. 8.
Fig. 8.

Bit error rate of OPA for 2.5-Gb/s simulations: OOK (a), DPSK (b)

Fig. 9.
Fig. 9.

Bit error rate of OPA for 10-Gb/s simulations: OOK (a), DPSK (b)

Tables (1)

Tables Icon

Table 1. OPA: Number of Apertures and the value of d

Equations (24)

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l o = x o r s , l = x r o ; m o = y o r s , m = y r o
U ̂ p q = C A e ik ( + ) d ξ
U ̂ p q = C n e ik ( p ξ n + q η n ) A e ik ( p ξ + q η ) d ξ d η .
U ( p ) = U ̂ p 0 = 1 e iNkdp 1 e ikdp U o ( p )
where , U o ( p ) = C A T ( ξ ) e ikpξ d ξ
I ( p ) = U ( p ) 2 = 1 cos ( Nkdp ) 1 cos ( kdp ) I o ( p )
I ( p ) = ( sin ( Nkdp 2 ) sin ( kdp 2 ) ) 2 I o ( p ) .
p = 2 kd = d ,
sin θ m sin θ i = m λ d
U o ( m λ d ) = 1 d d 2 d 2 T ( ξ ) e i 2 π m d ξ
ζ ( ξ ) = { h ξ d 0 ξ d h ξ d d + h d d d d ξ d
T ( ξ ) = e ( ξ ) = { e i 2 π ( n 1 ) h λ ξ d 0 ξ d e i 2 π ( n 1 ) h λ [ ξ d d d d d ] d ξ d
U o ( OPA ) ( m λ d ) = 1 d [ 0 d e i 2 π [ m d ( n 1 ) h λ d ] ξ d ξ + e i 2 π ( n 1 ) hd λ ( d d ) d d e i 2 π [ m d + ( n 1 ) λ ( d d ) ] ξ d ξ ]
= 1 d [ e i 2 π [ md d ( n 1 ) h λ ] 1 i 2 π [ m d ( n 1 ) h λ d ] + e i 2 π m e i 2 π [ md d ( n 1 ) h λ ] i 2 π [ m d + ( n 1 ) h λ ( d d ) ] ] ,
U o ( OPA ) ( m λ d ) = a [ e i 2 π [ am ( n 1 ) h λ ] 1 i 2 π [ am ( n 1 ) h λ ] + e i 2 π m e i 2 π [ am ( n 1 ) h λ ] i 2 π [ am + ( n 1 ) ha λ ( 1 a ) ] ] .
I ( OPA ) ( m λ d ) = ( sin ( N m λ k 2 ) sin ( m λ k 2 ) ) U o ( OPA ) ( m λ d ) 2
U o ( b ) ( m λ d ) = sin π [ m ( n 1 ) h λ ] π ( m ( n 1 ) h λ ) ,
I o ( b ) ( m λ d ) = ( sin ( N M λ k 2 ) sin ( m λ k 2 ) ) U o ( b ) ( m λ d ) 2 .
h = m λ n 1 .
I ( b ) ( λ ) = ( sin ( N π m λ o λ ) sin ( π md λ o λ ) ) 2 U o ( b ) ( λ ) 2
U o ( b ) ( λ ) = sin ( π ( 1 λ o λ ) ) π ( 1 λ o λ )
U ( b ) ( λ ) = C n j = 1 N [ e i n j 2 π λ o λ × U o ( b ) ( λ ) × U G ( n j ) ] ,
U G ( n j ) = e ( n j N 2 w d ) 2
σ 2 = 2 × n sp × h × f × B o × ( G 1 ) ,

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