Abstract

Extending phased array techniques to optical frequencies is challenging because of the considerably smaller wavelengths and the difficulty of stabilizing the optical path lengths of multiple emitters to this level of precision. This is especially true under real-world conditions where thermal and vibrational disturbances cause path length variations that are considerable in relation to the wavelength. Earlier attempts have relied on an external mechanism to sense and compensate for any unwanted variations in the outgoing beams. Here we propose and demonstrate a method that does not rely on any external components. The method combines a pseudo-random noise phase modulation scheme together with conventional heterodyne interferometry to simultaneously measure phase variations between emitters. This information is then used to control the relative phases between the emitters and compensate for any unwanted disturbance. Experimental results are presented that support the viability of this design.

© 2013 Optical Society of America

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2012 (1)

2009 (1)

2007 (1)

2006 (1)

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wicham, Proc. SPIE 6102, 61020U (2006).

2005 (1)

2004 (1)

1996 (1)

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, Proc. IEEE 84, 268 (1996).
[CrossRef]

1994 (1)

1988 (1)

C. R. De Hainaut, K. P. Hentz, L. D. Weaver, and J. D. Gonglewski, Opt. Eng. 27, 279736 (1988).
[CrossRef]

Anderegg, J.

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wicham, Proc. SPIE 6102, 61020U (2006).

Augst, S. J.

Brosnan, S.

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wicham, Proc. SPIE 6102, 61020U (2006).

Bruesselbach, H.

Cheung, E.

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wicham, Proc. SPIE 6102, 61020U (2006).

Chua, S.

Corkum, D. L.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, Proc. IEEE 84, 268 (1996).
[CrossRef]

De Hainaut, C. R.

C. R. De Hainaut, K. P. Hentz, L. D. Weaver, and J. D. Gonglewski, Opt. Eng. 27, 279736 (1988).
[CrossRef]

de Vine, G.

Dorschner, T. A.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, Proc. IEEE 84, 268 (1996).
[CrossRef]

Epp, P.

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wicham, Proc. SPIE 6102, 61020U (2006).

Fan, T. Y.

Friedman, L. J.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, Proc. IEEE 84, 268 (1996).
[CrossRef]

Gonglewski, J. D.

C. R. De Hainaut, K. P. Hentz, L. D. Weaver, and J. D. Gonglewski, Opt. Eng. 27, 279736 (1988).
[CrossRef]

Goodno, G. D.

Halverson, P.

D. Shaddock, B. Ware, P. Halverson, R. E. Spero, and B. Klipstein, Proceedings 6th International LISA Symposium (American Institute of Physics, 2007), Vol. 873, pp. 654–660.

Hammons, D.

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wicham, Proc. SPIE 6102, 61020U (2006).

Hentz, K. P.

C. R. De Hainaut, K. P. Hentz, L. D. Weaver, and J. D. Gonglewski, Opt. Eng. 27, 279736 (1988).
[CrossRef]

Hobbs, D. S.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, Proc. IEEE 84, 268 (1996).
[CrossRef]

Holz, M.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, Proc. IEEE 84, 268 (1996).
[CrossRef]

Jones, D. C.

Klipstein, B.

D. Shaddock, B. Ware, P. Halverson, R. E. Spero, and B. Klipstein, Proceedings 6th International LISA Symposium (American Institute of Physics, 2007), Vol. 873, pp. 654–660.

Komine, H.

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wicham, Proc. SPIE 6102, 61020U (2006).

Kudielka, K. H.

Lam, T. Y.

Leeb, W. R.

Liberman, S.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, Proc. IEEE 84, 268 (1996).
[CrossRef]

Mangir, M.

McClelland, D. E.

McManamon, P. F.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, Proc. IEEE 84, 268 (1996).
[CrossRef]

Minden, M.

Neuberts, W. M.

Nguyen, H. Q.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, Proc. IEEE 84, 268 (1996).
[CrossRef]

Rabeling, D. S.

Resler, D. P.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, Proc. IEEE 84, 268 (1996).
[CrossRef]

Sanchez, A.

Scholtz, A. L.

Shaddock, D.

D. Shaddock, B. Ware, P. Halverson, R. E. Spero, and B. Klipstein, Proceedings 6th International LISA Symposium (American Institute of Physics, 2007), Vol. 873, pp. 654–660.

Shaddock, D. A.

Sharp, R. C.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, Proc. IEEE 84, 268 (1996).
[CrossRef]

Slagmolen, B. J.

Spero, R. E.

D. Shaddock, B. Ware, P. Halverson, R. E. Spero, and B. Klipstein, Proceedings 6th International LISA Symposium (American Institute of Physics, 2007), Vol. 873, pp. 654–660.

Wang, S.

Ware, B.

D. Shaddock, B. Ware, P. Halverson, R. E. Spero, and B. Klipstein, Proceedings 6th International LISA Symposium (American Institute of Physics, 2007), Vol. 873, pp. 654–660.

Watson, E. A.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, Proc. IEEE 84, 268 (1996).
[CrossRef]

Weaver, L. D.

C. R. De Hainaut, K. P. Hentz, L. D. Weaver, and J. D. Gonglewski, Opt. Eng. 27, 279736 (1988).
[CrossRef]

Weber, M.

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wicham, Proc. SPIE 6102, 61020U (2006).

Weiss, S. B.

Wicham, M.

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wicham, Proc. SPIE 6102, 61020U (2006).

Wuchenich, D. M.

Appl. Opt. (1)

J. Opt. Soc. Am. B (1)

Opt. Eng. (1)

C. R. De Hainaut, K. P. Hentz, L. D. Weaver, and J. D. Gonglewski, Opt. Eng. 27, 279736 (1988).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Proc. IEEE (1)

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, Proc. IEEE 84, 268 (1996).
[CrossRef]

Proc. SPIE (1)

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wicham, Proc. SPIE 6102, 61020U (2006).

Other (1)

D. Shaddock, B. Ware, P. Halverson, R. E. Spero, and B. Klipstein, Proceedings 6th International LISA Symposium (American Institute of Physics, 2007), Vol. 873, pp. 654–660.

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Figures (4)

Fig. 1.
Fig. 1.

Schematic of a three fiber, internally sensed OPA. Reflections from the reference flat are isolated by matching the digital delays to the optical delays of the different fibers. Parallel phasemeters monitor the phase of each reflection. EOM, electro-optic modulator; FC, fiber-coupler; LO, local oscillator; PRN, pseudorandom-noise.

Fig. 2.
Fig. 2.

Proposed DEHI-based OPA. Unlike other OPAs of this type no external components are needed to measure the phase of the outgoing beam.

Fig. 3.
Fig. 3.

Relative phase measurement. Blue (upper) and red (lower) curves show the measured phase of two fibers relative to the third (green line) as a function of time. With feedback applied the lines become indistinguishable.

Fig. 4.
Fig. 4.

(a) MATLAB model of expected results for 20 linear phase gradients from 0.5 to 0.5 cycles per emitter. (b) Measured results.

Equations (7)

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

Ep(t)=Eeiϕeiβ2(1+c(tτ)),
VACEcos(ϕ2πfhtβ2(1+c(tτ))),
SD=c(tτ)Ecos(ϕ2πfhtβ2(1+c(tτ))).
SD=c(tτ)E{cos(ϕ2πfht)cos(β2(1+c(tτ)))+sin(ϕ2πfht)·sin(β2(1+c(tτ)))}.
SD=c(tτ)E{cos(ϕ2πfht)+(β2(1+c(tτ)))sin(ϕ2πfht)},
SD=c(tτ)Ecos(ϕ2πfht)+Eβ2(c(tτ)+1)sin(ϕ2πfht).
SD=c(tτ)Ecos(ϕ2πfht)+c(tτ)Eβ2sin(ϕ2πfht)+Eβ2sin(ϕ2πfht).

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