Abstract

We show that the second-order coherent-mode representation of a stationary quasi-monochromatic scalar light beam can be experimentally characterized by dual-mode holographic interference using an arbitrary basis. Analysis of the laser beam emitted from a stable spherical mirror cavity, using a mismatched Hermite–Gaussian basis, recovered the profiles and powers of a set of cavity modes with the expected spot size, including a hybrid of frequency degenerate modes. Observed near- and far-field irradiance transverse profiles and associated M2 parameter measures confirmed the results.

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2012

2011

2010

2009

2007

2002

2000

1998

S. Withington and J. A. Murphy, IEEE Trans. Antennas Propag. 46, 1651 (1998).
[CrossRef]

1995

1989

J. Turunen, E. Tervonen, and A. T. Friberg, Opt. Lett. 14, 627 (1989).
[CrossRef]

E. Tervonen, J. Turunen, and A. T. Friberg, Appl. Phys. B 49, 409 (1989).
[CrossRef]

1983

H. O. Bartelt, A. W. Lohmann, W. Freude, and G. K. Grau, Electron. Lett. 19, 247 (1983).
[CrossRef]

Anderson, B. L.

Bartelt, H. O.

H. O. Bartelt, A. W. Lohmann, W. Freude, and G. K. Grau, Electron. Lett. 19, 247 (1983).
[CrossRef]

Belsley, M. S.

Brüning, R.

Campos, J.

Davidson, N.

Duparré, M.

Ferreira, F. P.

Flamm, D.

Forbes, A.

Freude, W.

H. O. Bartelt, A. W. Lohmann, W. Freude, and G. K. Grau, Electron. Lett. 19, 247 (1983).
[CrossRef]

Friberg, A. T.

E. Tervonen, J. Turunen, and A. T. Friberg, Appl. Phys. B 49, 409 (1989).
[CrossRef]

J. Turunen, E. Tervonen, and A. T. Friberg, Opt. Lett. 14, 627 (1989).
[CrossRef]

Friesem, A. A.

Golub, M.

V. Soifer and M. Golub, Laser Beam Mode Selection by Computer Generated Holograms (CRC Press, 1994).

Golub, M. A.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (International Society for Optics and Photonics, 1996).

Grau, G. K.

H. O. Bartelt, A. W. Lohmann, W. Freude, and G. K. Grau, Electron. Lett. 19, 247 (1983).
[CrossRef]

Gureyev, T. E.

Kaiser, T.

Klein, C. A.

Lohmann, A. W.

H. O. Bartelt, A. W. Lohmann, W. Freude, and G. K. Grau, Electron. Lett. 19, 247 (1983).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Murphy, J. A.

S. Withington and J. A. Murphy, IEEE Trans. Antennas Propag. 46, 1651 (1998).
[CrossRef]

Naidoo, D.

Ngcobo, S.

Nicolás, J.

Nugent, K. A.

Roberts, A.

Schmidt, O. A.

Schröter, S.

Schulze, C.

Shimshi, L.

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1986).

Soifer, V.

V. Soifer and M. Golub, Laser Beam Mode Selection by Computer Generated Holograms (CRC Press, 1994).

Tervonen, E.

J. Turunen, E. Tervonen, and A. T. Friberg, Opt. Lett. 14, 627 (1989).
[CrossRef]

E. Tervonen, J. Turunen, and A. T. Friberg, Appl. Phys. B 49, 409 (1989).
[CrossRef]

Turunen, J.

E. Tervonen, J. Turunen, and A. T. Friberg, Appl. Phys. B 49, 409 (1989).
[CrossRef]

J. Turunen, E. Tervonen, and A. T. Friberg, Opt. Lett. 14, 627 (1989).
[CrossRef]

Warnky, C. M.

Withington, S.

S. Withington and J. A. Murphy, IEEE Trans. Antennas Propag. 46, 1651 (1998).
[CrossRef]

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Yzuel, M. J.

Appl. Opt.

Appl. Phys. B

E. Tervonen, J. Turunen, and A. T. Friberg, Appl. Phys. B 49, 409 (1989).
[CrossRef]

Electron. Lett.

H. O. Bartelt, A. W. Lohmann, W. Freude, and G. K. Grau, Electron. Lett. 19, 247 (1983).
[CrossRef]

IEEE Trans. Antennas Propag.

S. Withington and J. A. Murphy, IEEE Trans. Antennas Propag. 46, 1651 (1998).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Express

Opt. Lett.

Other

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

V. Soifer and M. Golub, Laser Beam Mode Selection by Computer Generated Holograms (CRC Press, 1994).

J. W. Goodman, Introduction to Fourier Optics (International Society for Optics and Photonics, 1996).

A. E. Siegman, Lasers (University Science Books, 1986).

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Figures (3)

Fig. 1.
Fig. 1.

Scheme of the setup. A spatial light modulator, based on a TN-LCD, acted as a dynamic hologram. Mostly amplitude modulation was achieved by previous calibration of elliptical polarization (EP) states. Fourier patterns appearing at the back focal plane of L1 were magnified by lens L3. The near-field irradiance profile (at the TN-LCD plane) was imaged through L1-L2.

Fig. 2.
Fig. 2.

Field distributions of the coherent modes obtained by diagonalization of the correlation matrix J and corresponding fits to HG cavity modes (see text for details). Mode 1 (51% of total power) fitted a HG10; Mode 2 (26% of total power) fitted a hybrid mode HG11*, with m+n=2; Mode 3 (13% of total power) fitted a purely Gaussian HG00. Plots 1 and 3 are fits to the integrals of modal amplitudes (essentially real) along its principle directions. “Amp.” = Field amplitude.

Fig. 3.
Fig. 3.

Contour plots of the observed irradiance distribution at the near-field and the corresponding distribution reconstructed by modal analysis. The last was calculated as the sum of the intensities of all found coherent modes, weighted by their respective relative powers. (Notice the absence of an axis of symmetry, which is explained by the presence of mode HG11*.)

Equations (9)

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

J(ρ,ρ)E*(ρ,t)E(ρ,t)¯.
J(ρ,ρ)=nλnϕn*(ρ)ϕn(ρ).
d2ρJ(ρ,ρ)ϕn(ρ)=λnϕn(ρ).
ψk|J|ψl=ψk|EE|ψl¯.
ψk|J|ψl=nλnψk|ϕnϕn|ψl.
lψk|J|ψlψl|ϕm=λmψk|ϕm.
tk(ρ)=|exp(ik0θx)+exp(iΔk)ψk(ρ)|2.
E˜(θ/λ,0)ψk|E+exp(ΔlΔk)ψl|E.
Ikl=Jkk+Jll+2|Jkl|cos[Arg(Jkl)+ΔlΔk].

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