Abstract

Abstract

We introduce a previously unreported laser cavity configuration, using a diffractive optical element (DOE) in place of the output coupler. Such a configuration allows the DOE to work both in reflection, as a mode shaping element, and in transmission as a beam shaper. Employing dual wavelength DOE optimization techniques and phase delays greater than 2π, allows the two functions to be designed independently. Thus, an arbitrary output beam profile can be combined with a mode shape which maximizes energy extraction from the gain medium. Devices are designed and their performance modeled for a 1m cavity with 5mm diameter mirrors and a wavelength of 632.8nm. An element with 32 quantization levels and a maximum phase delay of 8π in transmission produces high quality results.

© 2007 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. A. G. Fox, and T. Li, "Resonant modes in a maser interferometer," Bell. Syst. Tech. J. 40,453-488 (1961).
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    [CrossRef]

2006 (2)

J-S. Liu, A. J. Caley, andM. R. Taghizadeh, "Symmetrical iterative Fourier-transform algorithm using both phase and amplitude freedoms," Opt. Commun. 67,347-355 (2006).
[CrossRef]

A. J. Caley, and M. R. Taghizadeh. "Analysis of the effects of bias phase and wavelength choice on the design of dual-wavelength diffractive optical elements," J. Opt. Soc. Am. A 23, 193-198, (2006).
[CrossRef]

2005 (1)

A. J. Caley, A. J. Waddie and M. R. Taghizadeh. "A novel algorithm for designing diffractive optical elements for two colour far-field pattern formation," J. Opt. A-Pure Appl. Opt. 7, S276-S279, (2005).
[CrossRef]

2004 (1)

V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H-P. Herzig, "Diffractive elements designed to suppress unwanted zeroth order due to surface depth error," J. Mod. Opt. 512111-2123 (2004).
[CrossRef]

2003 (2)

M. J. Thomson andM. R. Taghizadeh, "Diffractive elements for high-power fibre coupling applications," J.Mod. Opt. 50, 1691-1699 (2003).

J.-S. Liu and M.R. Taghizadeh, "Design and simulated performance of transmissive phase elements for intracavity beam shaping," J. Opt. A-Pure Appl. Opt. 5216-220 (2003).
[CrossRef]

2002 (1)

M. R. Taghizadeh and A. J. Waddie, "Micro-optical and optoelectronic components for optical interconnection applications," ACTA PHYSICA POLONICA SERIES A 101,175-188 (2002).

1995 (1)

1994 (1)

1993 (1)

1992 (1)

1991 (1)

1978 (1)

1961 (1)

A. G. Fox, and T. Li, "Resonant modes in a maser interferometer," Bell. Syst. Tech. J. 40,453-488 (1961).

Belanger, P. A.

Caley, A. J.

J-S. Liu, A. J. Caley, andM. R. Taghizadeh, "Symmetrical iterative Fourier-transform algorithm using both phase and amplitude freedoms," Opt. Commun. 67,347-355 (2006).
[CrossRef]

A. J. Caley, and M. R. Taghizadeh. "Analysis of the effects of bias phase and wavelength choice on the design of dual-wavelength diffractive optical elements," J. Opt. Soc. Am. A 23, 193-198, (2006).
[CrossRef]

A. J. Caley, A. J. Waddie and M. R. Taghizadeh. "A novel algorithm for designing diffractive optical elements for two colour far-field pattern formation," J. Opt. A-Pure Appl. Opt. 7, S276-S279, (2005).
[CrossRef]

Chen, D.

Colombeau, B.

Dammann, H.

Dohnalik, T.

Farn, M. W.

Fox, A. G.

A. G. Fox, and T. Li, "Resonant modes in a maser interferometer," Bell. Syst. Tech. J. 40,453-488 (1961).

Froehy, C.

Herzig, H-P.

V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H-P. Herzig, "Diffractive elements designed to suppress unwanted zeroth order due to surface depth error," J. Mod. Opt. 512111-2123 (2004).
[CrossRef]

Jefimovs, K.

V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H-P. Herzig, "Diffractive elements designed to suppress unwanted zeroth order due to surface depth error," J. Mod. Opt. 512111-2123 (2004).
[CrossRef]

Kermene, V.

Kettunen, V.

V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H-P. Herzig, "Diffractive elements designed to suppress unwanted zeroth order due to surface depth error," J. Mod. Opt. 512111-2123 (2004).
[CrossRef]

Kuittinen, M.

V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H-P. Herzig, "Diffractive elements designed to suppress unwanted zeroth order due to surface depth error," J. Mod. Opt. 512111-2123 (2004).
[CrossRef]

Leger, J. R.

Li, T.

A. G. Fox, and T. Li, "Resonant modes in a maser interferometer," Bell. Syst. Tech. J. 40,453-488 (1961).

Liu, J.-S.

J.-S. Liu and M.R. Taghizadeh, "Design and simulated performance of transmissive phase elements for intracavity beam shaping," J. Opt. A-Pure Appl. Opt. 5216-220 (2003).
[CrossRef]

Liu, J-S.

J-S. Liu, A. J. Caley, andM. R. Taghizadeh, "Symmetrical iterative Fourier-transform algorithm using both phase and amplitude freedoms," Opt. Commun. 67,347-355 (2006).
[CrossRef]

Medeiros, S. S.

Mowry, G.

Pare, C.

Ripoll, O.

V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H-P. Herzig, "Diffractive elements designed to suppress unwanted zeroth order due to surface depth error," J. Mod. Opt. 512111-2123 (2004).
[CrossRef]

Saviot, A.

Simonen, J.

V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H-P. Herzig, "Diffractive elements designed to suppress unwanted zeroth order due to surface depth error," J. Mod. Opt. 512111-2123 (2004).
[CrossRef]

Stern, M. B.

Taghizadeh, M. R.

A. J. Caley, and M. R. Taghizadeh. "Analysis of the effects of bias phase and wavelength choice on the design of dual-wavelength diffractive optical elements," J. Opt. Soc. Am. A 23, 193-198, (2006).
[CrossRef]

A. J. Caley, A. J. Waddie and M. R. Taghizadeh. "A novel algorithm for designing diffractive optical elements for two colour far-field pattern formation," J. Opt. A-Pure Appl. Opt. 7, S276-S279, (2005).
[CrossRef]

M. J. Thomson andM. R. Taghizadeh, "Diffractive elements for high-power fibre coupling applications," J.Mod. Opt. 50, 1691-1699 (2003).

M. R. Taghizadeh and A. J. Waddie, "Micro-optical and optoelectronic components for optical interconnection applications," ACTA PHYSICA POLONICA SERIES A 101,175-188 (2002).

Taghizadeh, M.R.

J.-S. Liu and M.R. Taghizadeh, "Design and simulated performance of transmissive phase elements for intracavity beam shaping," J. Opt. A-Pure Appl. Opt. 5216-220 (2003).
[CrossRef]

Thomson, M. J.

M. J. Thomson andM. R. Taghizadeh, "Diffractive elements for high-power fibre coupling applications," J.Mod. Opt. 50, 1691-1699 (2003).

Vampouille, M.

Veldkamp, W. B.

Waddie, A. J.

A. J. Caley, A. J. Waddie and M. R. Taghizadeh. "A novel algorithm for designing diffractive optical elements for two colour far-field pattern formation," J. Opt. A-Pure Appl. Opt. 7, S276-S279, (2005).
[CrossRef]

M. R. Taghizadeh and A. J. Waddie, "Micro-optical and optoelectronic components for optical interconnection applications," ACTA PHYSICA POLONICA SERIES A 101,175-188 (2002).

Wang, Z.

ACTA PHYSICA POLONICA SERIES A (1)

M. R. Taghizadeh and A. J. Waddie, "Micro-optical and optoelectronic components for optical interconnection applications," ACTA PHYSICA POLONICA SERIES A 101,175-188 (2002).

Appl. Opt. (2)

Bell. Syst. Tech. J. (1)

A. G. Fox, and T. Li, "Resonant modes in a maser interferometer," Bell. Syst. Tech. J. 40,453-488 (1961).

J. Mod. Opt. (1)

V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H-P. Herzig, "Diffractive elements designed to suppress unwanted zeroth order due to surface depth error," J. Mod. Opt. 512111-2123 (2004).
[CrossRef]

J. Opt. A-Pure Appl. Opt. (2)

J.-S. Liu and M.R. Taghizadeh, "Design and simulated performance of transmissive phase elements for intracavity beam shaping," J. Opt. A-Pure Appl. Opt. 5216-220 (2003).
[CrossRef]

A. J. Caley, A. J. Waddie and M. R. Taghizadeh. "A novel algorithm for designing diffractive optical elements for two colour far-field pattern formation," J. Opt. A-Pure Appl. Opt. 7, S276-S279, (2005).
[CrossRef]

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

J.Mod. Opt. (1)

M. J. Thomson andM. R. Taghizadeh, "Diffractive elements for high-power fibre coupling applications," J.Mod. Opt. 50, 1691-1699 (2003).

Opt. Commun. (1)

J-S. Liu, A. J. Caley, andM. R. Taghizadeh, "Symmetrical iterative Fourier-transform algorithm using both phase and amplitude freedoms," Opt. Commun. 67,347-355 (2006).
[CrossRef]

Opt. Lett. (4)

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Figures (6)

Fig. 1.
Fig. 1.

Schematic of proposed cavity configuration.

Fig. 2.
Fig. 2.

Illustration of the quantization process.

Fig. 3.
Fig. 3.

Fundamental mode generated by the bare cavity.

Fig. 4.
Fig. 4.

(a) Fundamental mode generated by unquantized MSE and (b) output at 500mm using unquantized beam shaping DOE.

Fig. 5.
Fig. 5.

Fundamental mode generated by elements quantized to (a) 16 levels with a maximum phase in transmission of 2π, (b) 32 levels with a maximum phase in transmission of 4π, (c) 32 levels with a maximum phase in transmission of 8π and (d) 64 levels with a maximum phase in transmission of 8π.

Fig. 6.
Fig. 6.

Resulting output beam shape generated by elements quantized to (a) 16 levels with a maximum phase in transmission of 2π, (b) 32 levels with a maximum phase in transmission of 4π, (c) 32 levels with a maximum phase in transmission of 8π and (d) 64 levels with a maximum phase in transmission of 8π.

Equations (5)

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exp [ ikl ( L ( λ u ) 2 ( λ v ) 2 ) 1 2 ] ,
ϕ R ( x , y ) = A * ( x , y ) A ( x , y )
h 1 = ϕ T λ 2 π ( n 1 )
h 2 = ϕ R λ 4 π
U ( x , y ) = e ( x ω 0 ) 20 ( y ω 0 ) 20

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