Abstract

We investigate the general characteristics of Herriott-type multipass cavities (MPC) for femtosecond lasers. MPCs can be used to increase the laser pulse energy by extending the laser cavity path length and decreasing the repetition rate, as well as to make standard repetition rate lasers more compact. We present an analytical design condition for MPCs which preserve the Gaussian beam q parameter, enabling the laser path length to be extended while leaving the Kerr-lens modelocking operating point of the cavity invariant. As a specific example, we analyze q preserving MPCs consisting of a flat and curved mirror to obtain analytical expressions for the cavity length. This predicts the optimum MPC designs that minimize the pulse repetition rate for given specifications. These design conditions should prove useful for designing a wide range of high pulse energy or compact femtosecond lasers.

© 2003 Optical Society of America

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References

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Appl. Opt.

Opt. Lett.

Other

A.R. Libertun, R. Shelton H.C. Kapteyn, and M. M. Murnane, �??A 36nJ-15.5 MHz extended-cavity Ti:sapphire oscillator,�?? in CLEO�??99 Technical Digest, (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 469-470.

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Figures (5)

Fig. 1.
Fig. 1.

A schematic of a general multi-pass cavity. One round trip is represented by the ABCD matrix.

Fig. 2.
Fig. 2.

The spot pattern formed by the beams upon successive transits will in general be elliptical at a given reference plane in the cavity. A circular spot pattern is obtained at the input reference plane when the position and tilt of the incident ray is adjusted according to Eq. 8.

Fig. 3.
Fig. 3.

Spot patterns corresponding some possible q preserving configurations for the case where m=1,2,3,4,5 and n=9.

Fig. 4.
Fig. 4.

A sketch of the MPC consisting of a flat and a curved mirror with radius R or focal length f=R/2, separated by a distance L0. This cavity can be analyzed to calculate the optimum configuration which minimizes the repetition rate or maximizes the beam path length for a given cavity size.

Fig. 5.
Fig. 5.

Calculated variation of (a) the pulse repetition rate and (b) the corresponding mirror separation for the q preserving configurations of the multi-pass cavity for different values of m for the flat - curved MPC case.

Tables (1)

Tables Icon

Table 1. Calculated values of nopt, the achievable minimum repetition rate fmin, and the corresponding MPC separation Lopt for different values of m for the flat-curved MPC.

Equations (17)

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M T = [ A B C D ] .
r i = [ r 0 r 0 ] .
r n = M T n r i .
A + D 2 1 .
λ 1 = e i θ , v 1 = 1 B ( B C ) [ B ( A e i θ ) ]
λ 2 = e i θ , v 2 = 1 B ( B C ) [ B ( A e i θ ) ] .
M T n = [ A D 2 sin n θ sin θ + cos n θ B sin n θ sin θ C sin n θ sin θ D A 2 sin n θ sin θ + cos n θ ] .
x n = x 0 cos n θ + ( x o ( A D ) + 2 B x 0 ' 2 sin θ ) sin n θ
y n = y 0 cos n θ + ( y o ( A D ) + 2 B y 0 ' 2 sin θ ) sin n θ ,
y 0 = 0
y 0 ' = x 0 sin θ B ,
x 0 ' = x 0 2 B ( D A )
n θ = m π .
M T = [ 1 2 L 0 R 2 L 0 ( 1 L 0 R ) 2 R 1 2 L R ] ,
cos θ = 1 2 L 0 R .
f rep = c 2 n R ( 1 cos ( m π n ) ) ,
1 = cos ( m π n opt ) + m π n opt sin ( m π n opt ) .

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