Abstract

The aberration sensitivity of unstable-cavity geometries is studied by incorporating the change of the ray path by the intra-cavity aberrations in geometric-optic approximation. The first order non-linear correction in a positive branch, confocal unstable cavity is obtained analytically. In particular, as the optic field passes through an aberration plane in which the higher order aberrations are presented, more higher order aberrations are induced on the wavefront of optic field, and the original transverse modes are mixed. This mode mixing is studied by introducing non-constant propagation matrices. Similar to the linear results, we find that the non-linear corrections to aberration sensitivity decreases when geometric magnification or aberration orders increase.

©2008 Optical Society of America

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References

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  1. G. Albercht, S. Sutton, V. George, W. Sooy, and W. Krupke, “Solid state heat capacity disk laser,” Laser and particle beam,  16, 605 (1998).
    [Crossref]
  2. K. N. Lafortune, R. L. Hurd, E. M. Johansson, C. B. Dane, S. N. Fochs, and J. M. Brase, “Intracavity, Adaptive Correction of a High-Average-Power, Solid-State, Heat-Capacity Laser,” UCRL-PROC-208886 (2004).
  3. Yu.A. Anan’ev, N. A. Sventsitskaya, and V. E. Sherstobitov, “Properties of a Laser with an Unstable Cavity,” Sov. Phys. JETP 28, 69–74 (1969).
  4. Yu.A. Anan’ev. “Unstable Resonators and Their Applications,” Sov. J. Quantum Electron. 1, 565–586 (1972).
    [Crossref]
  5. K. E. Oughstun, “Aberration sensitivity of unstable-cavity geometries,” J. Opt. Soc. Am. A 3, 1113–1141 (1986).
    [Crossref]
  6. K. E. Oughstun, “Intracavity adaptive optic compensation of phase aberrations. I: Analysis,” J. Opt. Soc. Am. 71, 863–872 (1981).
  7. K. E. Oughstun, “Intracavity adaptive optic compensation of phase aberrations. I: Passive cavity study for a small Neq resonator,” J. Opt. Soc. Am. 71, 863–872 (1981).
    [Crossref]

1998 (1)

G. Albercht, S. Sutton, V. George, W. Sooy, and W. Krupke, “Solid state heat capacity disk laser,” Laser and particle beam,  16, 605 (1998).
[Crossref]

1986 (1)

1981 (2)

K. E. Oughstun, “Intracavity adaptive optic compensation of phase aberrations. I: Analysis,” J. Opt. Soc. Am. 71, 863–872 (1981).

K. E. Oughstun, “Intracavity adaptive optic compensation of phase aberrations. I: Passive cavity study for a small Neq resonator,” J. Opt. Soc. Am. 71, 863–872 (1981).
[Crossref]

1972 (1)

Yu.A. Anan’ev. “Unstable Resonators and Their Applications,” Sov. J. Quantum Electron. 1, 565–586 (1972).
[Crossref]

1969 (1)

Yu.A. Anan’ev, N. A. Sventsitskaya, and V. E. Sherstobitov, “Properties of a Laser with an Unstable Cavity,” Sov. Phys. JETP 28, 69–74 (1969).

Albercht, G.

G. Albercht, S. Sutton, V. George, W. Sooy, and W. Krupke, “Solid state heat capacity disk laser,” Laser and particle beam,  16, 605 (1998).
[Crossref]

Anan’ev, Yu.A.

Yu.A. Anan’ev, N. A. Sventsitskaya, and V. E. Sherstobitov, “Properties of a Laser with an Unstable Cavity,” Sov. Phys. JETP 28, 69–74 (1969).

Anan’ev., Yu.A.

Yu.A. Anan’ev. “Unstable Resonators and Their Applications,” Sov. J. Quantum Electron. 1, 565–586 (1972).
[Crossref]

Brase, J. M.

K. N. Lafortune, R. L. Hurd, E. M. Johansson, C. B. Dane, S. N. Fochs, and J. M. Brase, “Intracavity, Adaptive Correction of a High-Average-Power, Solid-State, Heat-Capacity Laser,” UCRL-PROC-208886 (2004).

Dane, C. B.

K. N. Lafortune, R. L. Hurd, E. M. Johansson, C. B. Dane, S. N. Fochs, and J. M. Brase, “Intracavity, Adaptive Correction of a High-Average-Power, Solid-State, Heat-Capacity Laser,” UCRL-PROC-208886 (2004).

Fochs, S. N.

K. N. Lafortune, R. L. Hurd, E. M. Johansson, C. B. Dane, S. N. Fochs, and J. M. Brase, “Intracavity, Adaptive Correction of a High-Average-Power, Solid-State, Heat-Capacity Laser,” UCRL-PROC-208886 (2004).

George, V.

G. Albercht, S. Sutton, V. George, W. Sooy, and W. Krupke, “Solid state heat capacity disk laser,” Laser and particle beam,  16, 605 (1998).
[Crossref]

Hurd, R. L.

K. N. Lafortune, R. L. Hurd, E. M. Johansson, C. B. Dane, S. N. Fochs, and J. M. Brase, “Intracavity, Adaptive Correction of a High-Average-Power, Solid-State, Heat-Capacity Laser,” UCRL-PROC-208886 (2004).

Johansson, E. M.

K. N. Lafortune, R. L. Hurd, E. M. Johansson, C. B. Dane, S. N. Fochs, and J. M. Brase, “Intracavity, Adaptive Correction of a High-Average-Power, Solid-State, Heat-Capacity Laser,” UCRL-PROC-208886 (2004).

Krupke, W.

G. Albercht, S. Sutton, V. George, W. Sooy, and W. Krupke, “Solid state heat capacity disk laser,” Laser and particle beam,  16, 605 (1998).
[Crossref]

Lafortune, K. N.

K. N. Lafortune, R. L. Hurd, E. M. Johansson, C. B. Dane, S. N. Fochs, and J. M. Brase, “Intracavity, Adaptive Correction of a High-Average-Power, Solid-State, Heat-Capacity Laser,” UCRL-PROC-208886 (2004).

Oughstun, K. E.

K. E. Oughstun, “Aberration sensitivity of unstable-cavity geometries,” J. Opt. Soc. Am. A 3, 1113–1141 (1986).
[Crossref]

K. E. Oughstun, “Intracavity adaptive optic compensation of phase aberrations. I: Analysis,” J. Opt. Soc. Am. 71, 863–872 (1981).

K. E. Oughstun, “Intracavity adaptive optic compensation of phase aberrations. I: Passive cavity study for a small Neq resonator,” J. Opt. Soc. Am. 71, 863–872 (1981).
[Crossref]

Sherstobitov, V. E.

Yu.A. Anan’ev, N. A. Sventsitskaya, and V. E. Sherstobitov, “Properties of a Laser with an Unstable Cavity,” Sov. Phys. JETP 28, 69–74 (1969).

Sooy, W.

G. Albercht, S. Sutton, V. George, W. Sooy, and W. Krupke, “Solid state heat capacity disk laser,” Laser and particle beam,  16, 605 (1998).
[Crossref]

Sutton, S.

G. Albercht, S. Sutton, V. George, W. Sooy, and W. Krupke, “Solid state heat capacity disk laser,” Laser and particle beam,  16, 605 (1998).
[Crossref]

Sventsitskaya, N. A.

Yu.A. Anan’ev, N. A. Sventsitskaya, and V. E. Sherstobitov, “Properties of a Laser with an Unstable Cavity,” Sov. Phys. JETP 28, 69–74 (1969).

J. Opt. Soc. Am. (2)

K. E. Oughstun, “Intracavity adaptive optic compensation of phase aberrations. I: Analysis,” J. Opt. Soc. Am. 71, 863–872 (1981).

K. E. Oughstun, “Intracavity adaptive optic compensation of phase aberrations. I: Passive cavity study for a small Neq resonator,” J. Opt. Soc. Am. 71, 863–872 (1981).
[Crossref]

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

Laser and particle beam (1)

G. Albercht, S. Sutton, V. George, W. Sooy, and W. Krupke, “Solid state heat capacity disk laser,” Laser and particle beam,  16, 605 (1998).
[Crossref]

Sov. J. Quantum Electron. (1)

Yu.A. Anan’ev. “Unstable Resonators and Their Applications,” Sov. J. Quantum Electron. 1, 565–586 (1972).
[Crossref]

Sov. Phys. JETP (1)

Yu.A. Anan’ev, N. A. Sventsitskaya, and V. E. Sherstobitov, “Properties of a Laser with an Unstable Cavity,” Sov. Phys. JETP 28, 69–74 (1969).

Other (1)

K. N. Lafortune, R. L. Hurd, E. M. Johansson, C. B. Dane, S. N. Fochs, and J. M. Brase, “Intracavity, Adaptive Correction of a High-Average-Power, Solid-State, Heat-Capacity Laser,” UCRL-PROC-208886 (2004).

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Figures (5)

Fig. 1.
Fig. 1. Ray propagates in an confocal unstable cavity in positive branch with intra-cavity aberration.
Fig. 2.
Fig. 2. Sensitivity coefficients of phase curvature vs magnification M.
Fig. 3.
Fig. 3. The linear coefficient (dash line) and quadratic coefficient (solid line) in Eq. (23) vs magnification M.
Fig. 4.
Fig. 4. Coefficients ak in Eq. (33) vs magnification M.
Fig. 5.
Fig. 5. Coefficients bk in Eq. (33) vs magnification M.

Equations (47)

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ϕ in ( x , z i ) = j = 0 α j in ( z j ) x j .
ϕ out ( x ) = j = 0 α j out x j .
α j out = i = 0 m ν ¯ j ( z i ) α j in ( z i ) ,
α j out = i = 0 m 2 k j ν jk ( z i , α k in ) α k in ( z i ) ,
ν jk ( α k in ) = ν ¯ j δ jk + c 1 jk α k in + c 2 jk ( α k in ) 2 +
ϕ out N = j = 1 p = 0 N k = 1 m α jk [ ( β pk L ) j + ( β pk R ) j ] x j ,
x = lim N β N R x .
K i = ( 1 0 δ i 1 ) ,
T k L = i = k 1 ( K i P i ) R 2 = ( A k B k C k D k ) .
A k 1 + i = 1 k ( z k z i ) δ i + M 1 L B k ,
B k z k + i = 1 k z i ( z k z i ) δ i ,
C k i = 1 k δ i + M 1 L D k , D k 1 + i = 1 k z i δ i ,
( x pk L θ pk L ) = T k L Q p ( x 0 ) , ( x pk R θ pk R ) = ( T k L ) 1 Q p + 1 ( x 0 ) ,
Q = P 1 i = 1 m ( K i P i + 1 ) R 1 P m + 1 j = m 1 ( K j P j ) R 2
= ( M + Δ + ϒ + ( 2 M 1 ) Ω + Δ 2 ϒ M L ( 1 + 1 M ) + 2 ϒ L M + 2 Ω L ϒ ML ( M 2 2 M + 2 ) + M 2 + 1 ML Δ + M 1 L Ω 1 + Δ M + Δ + Ω ϒ ) ,
Δ = L i = 1 m δ i , Ω = i = 1 m z i δ i , ϒ = i = 1 m z i ( 1 z i L ) δ i .
β pk R = λ 1 p + 1 D k s ( λ 1 p + 1 λ 2 p + 1 ) L + ( M 1 ) z k L ( M 1 ) + O ( δ 2 ) ,
β pk L = λ 1 p A k s λ 1 p λ 2 p M 1 + O ( δ 2 ) ,
λ 1 = M ( 1 + 2 Ω + 2 Δ M 1 ) , λ 2 = 1 M ( 1 2 ϒ 2 Δ M 1 ) ,
s = M 2 + 1 M 2 1 Δ + M M + 1 Ω M 2 M + 1 ϒ .
ϕ out ( x ) = j k = 1 m α jk in x j λ 1 j 1 { ( A k ) j + λ 1 j ( D k ) j jsM M 1
( 1 + ( M 1 ) z k L ) j 1 js M 1 Mjs z k L } + O ( δ 2 ) .
ϕ out ( x ) = j k = 1 m α jk in x j M j 1 { M j + ( 1 + ( M 1 ) z k L ) j } .
α out = 1 f ( a + b L f ) + O ( L 2 f 2 ) ,
a = 13 M 2 + 4 M + 3 5 ( M 2 1 ) ,
b = 46 M 4 + 3066 M 3 + 3767 M 2 + 666 M + 546 125 ( M + 1 ) ( M 1 ) 3 .
λ 1 > 1 L f < ( M 1 ) 2 4 M ( M + 1 ) .
α out = 1 f ( a + b L f ) 1 f ( a + b L f ' ) cL f f .
L f = a a L f ( b a + a 2 b a 3 ac a 2 ) L 2 f 2 + O ( L 3 f 3 ) .
L f = L a R c ( b a 3 c a a 2 ) L 2 R c 2 + O ( L 3 R c 3 ) .
λ 1 p = M [ 1 + 2 M j ( p 1 ) x ' j ω + O ( κ 2 ) ] ,
λ 2 p = M [ 1 2 M j ( p 1 ) x ' j ω ˜ + O ( κ 2 ) ] ,
ω = Ω 0 + Δ 0 M 1 , ω ˜ = ϒ 0 + Δ 0 M 1 ,
Δ 0 = 2 L i = 1 m σ i , Ω 0 = 2 i = 1 m z i σ i , ϒ 0 = 2 i = 1 m z i ( 1 z i L ) σ i .
A pk = t k + 2 M jp x j i = 1 k t i ( z k z i ) σ i , D pk = 1 + 2 M jp x j i = 1 k z i σ i ,
t k = 1 + M 1 L z k .
β pk L = A pk i = 1 p λ 1 i s 0 x j M ( j + 1 ) p M + 1 M j + 2 1 ,
β pk L = D pk i = 1 p λ 1 i s 0 x j t k M ( j + 1 ) ( p + 1 ) M + 1 M j + 2 1 ,
x = x [ lim N i = 1 N λ 1 i ] 1 ,
ϕ out ( x ) = x j + 2 k = 1 m σ k ( a k + ( j + 2 ) b k x j ) + O ( σ 3 ) ,
b k = t k j + 2 + M j + 2 M j + 2 1 ω + t k j + 2 + M j + 3 M j + 3 1 ω + 2 M 2 ( j + 1 ) 1 i = 1 k σ i [ t k j + 1 t i ( z k z i ) + M 2 ( j + 1 ) z i ]
s 0 t k ( M + 1 ) ( M 2 ( j + 1 ) 1 ) ( M j + 2 1 ) ( t k j + M 2 ( j + 1 ) ) .
ϕ in ( x , L 2 ) = k = 3 σ k x k .
ϕ out ( x ) = k = 3 σ k ( a k x k + L b k σ k x 2 ( k 1 ) ) + O ( σ 3 ) ,
b k = 2 k ( M 1 ) ( M k + 1 1 ) ( 1 M k ) ( M 1 ) ( 1 + [ ( M + 1 ) 2 ] k )
+ k M 2 ( k 1 ) 1 { M 2 ( k 1 ) ( M + 1 ) k 1 2 k 5 M 2 + M + 2 M k 1 [ 1 M + 1 + 1 2 M 2 ( k 1 ) ] } .
ϕ k out ( x ) ~ λ ( a k x k + M 2 N f b k ) + O ( 1 N f 2 ) ,

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