Abstract

A mathematical method of finding a surface that focuses a finite size source has been developed. We show its use solving two particularly simple cases in which we compare the energy efficiency of the new surface to the classical elliptical cavities. In the examples given, the new designs are frequently advantageous.

© 1990 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. B. Schuldt, B. L. Aagard, “An Analysis of Radiation Transfer by Means of Elliptical Cylinder Reflectors,” Appl. Opt. 2, 509–513 (1963).
    [CrossRef]
  2. C. Bowness, “On the Efficiency of Single and Multiple Elliptical Laser Cavities,” Appl. Opt. 4, 103–107 (1965).
    [CrossRef]
  3. D. R. Skinner, J. Tregellas-Williams, “Total Energy and Energy Distribution in a Laser Crystal Due to Optical Pumping, as Calculated by the Monte Carlo Method,” Aust. J. Phys. 19, 1–18 (1966).
  4. K. K. Tetsuokano, H. Matsuzawa, “Optimum Design of Spherical and Ellipsoidal Pumping Chambers for Lasers,” Proc. IEEE 55, 1630–1631 (1967).
    [CrossRef]
  5. C. H. Church, I. Liberman, “The Spherical Reflector for Use in the Optical Pumping of Lasers,” Appl. Opt. 6, 1966–1968 (1967).
    [CrossRef] [PubMed]
  6. F. Docchio, “The Rod Image: A New Method for the Calculation of Pump Efficienc in Reflecting Close-Coupled Cavities,” Appl. Opt. 24, 3746–3751 (1985).
    [CrossRef] [PubMed]
  7. F. Docchio, L. Pallaro, O. Svelto, “Pump Cavities for Compact Pulsed Nd:YAG Lasers: A Comparative Study,” Appl. Opt. 24, 3752–3755 (1985).
    [CrossRef] [PubMed]
  8. T. Li, S. D. Sims, “Observations on the Pump Light Intensity Distribution of a Ruby Optical Maser with Different Pumping Schemes,” Proc. IRE 50, 464–465 (1962).
  9. H. F. Mahlein, G. Zeidler, “Pump Light Distribution in a Laser Rod Pumped Exfocally in a Rotational Ellipsoid,” Appl. Opt. 110, 872–879 (1971).
    [CrossRef]

1985

1971

H. F. Mahlein, G. Zeidler, “Pump Light Distribution in a Laser Rod Pumped Exfocally in a Rotational Ellipsoid,” Appl. Opt. 110, 872–879 (1971).
[CrossRef]

1967

K. K. Tetsuokano, H. Matsuzawa, “Optimum Design of Spherical and Ellipsoidal Pumping Chambers for Lasers,” Proc. IEEE 55, 1630–1631 (1967).
[CrossRef]

C. H. Church, I. Liberman, “The Spherical Reflector for Use in the Optical Pumping of Lasers,” Appl. Opt. 6, 1966–1968 (1967).
[CrossRef] [PubMed]

1966

D. R. Skinner, J. Tregellas-Williams, “Total Energy and Energy Distribution in a Laser Crystal Due to Optical Pumping, as Calculated by the Monte Carlo Method,” Aust. J. Phys. 19, 1–18 (1966).

1965

1963

1962

T. Li, S. D. Sims, “Observations on the Pump Light Intensity Distribution of a Ruby Optical Maser with Different Pumping Schemes,” Proc. IRE 50, 464–465 (1962).

Aagard, B. L.

Bowness, C.

Church, C. H.

Docchio, F.

Li, T.

T. Li, S. D. Sims, “Observations on the Pump Light Intensity Distribution of a Ruby Optical Maser with Different Pumping Schemes,” Proc. IRE 50, 464–465 (1962).

Liberman, I.

Mahlein, H. F.

H. F. Mahlein, G. Zeidler, “Pump Light Distribution in a Laser Rod Pumped Exfocally in a Rotational Ellipsoid,” Appl. Opt. 110, 872–879 (1971).
[CrossRef]

Matsuzawa, H.

K. K. Tetsuokano, H. Matsuzawa, “Optimum Design of Spherical and Ellipsoidal Pumping Chambers for Lasers,” Proc. IEEE 55, 1630–1631 (1967).
[CrossRef]

Pallaro, L.

Schuldt, S. B.

Sims, S. D.

T. Li, S. D. Sims, “Observations on the Pump Light Intensity Distribution of a Ruby Optical Maser with Different Pumping Schemes,” Proc. IRE 50, 464–465 (1962).

Skinner, D. R.

D. R. Skinner, J. Tregellas-Williams, “Total Energy and Energy Distribution in a Laser Crystal Due to Optical Pumping, as Calculated by the Monte Carlo Method,” Aust. J. Phys. 19, 1–18 (1966).

Svelto, O.

Tetsuokano, K. K.

K. K. Tetsuokano, H. Matsuzawa, “Optimum Design of Spherical and Ellipsoidal Pumping Chambers for Lasers,” Proc. IEEE 55, 1630–1631 (1967).
[CrossRef]

Tregellas-Williams, J.

D. R. Skinner, J. Tregellas-Williams, “Total Energy and Energy Distribution in a Laser Crystal Due to Optical Pumping, as Calculated by the Monte Carlo Method,” Aust. J. Phys. 19, 1–18 (1966).

Zeidler, G.

H. F. Mahlein, G. Zeidler, “Pump Light Distribution in a Laser Rod Pumped Exfocally in a Rotational Ellipsoid,” Appl. Opt. 110, 872–879 (1971).
[CrossRef]

Appl. Opt.

Aust. J. Phys.

D. R. Skinner, J. Tregellas-Williams, “Total Energy and Energy Distribution in a Laser Crystal Due to Optical Pumping, as Calculated by the Monte Carlo Method,” Aust. J. Phys. 19, 1–18 (1966).

Proc. IEEE

K. K. Tetsuokano, H. Matsuzawa, “Optimum Design of Spherical and Ellipsoidal Pumping Chambers for Lasers,” Proc. IEEE 55, 1630–1631 (1967).
[CrossRef]

Proc. IRE

T. Li, S. D. Sims, “Observations on the Pump Light Intensity Distribution of a Ruby Optical Maser with Different Pumping Schemes,” Proc. IRE 50, 464–465 (1962).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Example of the construction of one of the possible envelope cavities for a circular cross-section lamp. The foci of the ellipses shown are marked with dots.

Fig. 2
Fig. 2

General procedure for constructing the envelope surface: O1, target point; O2, center of the emitting source; (x*,y*), point on the surface of the emitting source; ϑ,ϑ′,α, angles shown in the figure; c(t), semidistance between foci O1–(x*,y*), respectively, of a certain ellipse in the family.

Fig. 3
Fig. 3

Example of a parabola–ellipse composite cavity for c/a = 0.8, rl/a = 0.5.

Tables (7)

Tables Icon

Table I Energy Efficiencies of Elliptical Cavities (Upper Number) Compared with Those of Elliptical Envelope Cavities (Lower Number) for c/a = 0.2

Tables Icon

Table II Energy Efficiencies of Eillptical Cavities (Upper Number) Compared with Those of Elliptical Envelope Cavities (Lower Number) for c/a = 0.4

Tables Icon

Table III Energy Efficiencies of Elliptical Cavities (Upper Number) Compared with Those of Elliptical Envelope Cavities (Lower Number) for c/a = 0.6

Tables Icon

Table IV Energy Efficiencies of Elliptical Cavities (Upper Number) Compared with Those of Parabola–Ellipse Composite Cavities (Lower Number) for c/a = 0.2

Tables Icon

Table V Energy Efficiencies of Elliptical Cavities (Upper Number) Compared with Those of Parabola–Ellipse Composite Cavities (Lower Number) for c/a = 0.4

Tables Icon

Table VI Energy Efficiencies of Elliptical Cavities (Upper Number) Compared with Those of Parabola–Ellipse Composite Cavities (Lower Number) for c/a = 0.6

Tables Icon

Table VII Energy Efficiencies of Elliptical Cavities (Upper Number) Compared with Those of Parabola–Ellipse Composite Cavities (Lower Number) for c/a = 0.8

Equations (14)

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

x * = x * ( t ) , y * = y * ( t ) ,
r = a 2 ( t ) - c 2 ( t ) a ( t ) - c ( t ) cos ( ϑ ) .
cos ( ϑ ) = cos ( ϑ - α ) = cos ( ϑ ) cos ( α ) + sin ( ϑ ) sin ( α ) , sin ( α ) = y * ( t ) 2 c ( t ) ;             cos ( α ) = x * ( t ) 2 c ( t ) , [ 2 c ( t ) ] 2 = x * ( t ) 2 + y * ( t ) 2 .
r { a ( t ) - 1 / 2 [ x * ( t ) cos ( ϑ ) + y * ( t ) sin ( ϑ ) ] } - a 2 ( t ) + ¼ [ x * ( t ) 2 + y * ( t ) 2 ] = 0 ,
d ( 2 ) d t = r { d a ( t ) d t - 1 / 2 [ d x * ( t ) d t cos ( ϑ ) + d y * ( t ) d t sin ( ϑ ) ] } - 2 a ( t ) d a ( t ) d t + 1 / 2 [ x * ( t ) d x * ( t ) d t + y * ( t ) d y * ( t ) d t ] = 0.
c 1 r 2 + c 2 r + c 3 = 0 ,
c 1 = [ 2 a + 2 c cos ( ϑ ) ] 2 - r l 2 , c 2 = [ 4 a + 4 c cos ( ϑ ) ] ( - 2 a + 0.5 r l + 2 c ) 2 - 4 r l 2 c cos ( ϑ ) , c 3 = ( - 2 a 2 + 0.5 r l 2 + 2 c 2 ) 2 - 4 c 2 r l 2 ,
r = ( a - r l / 2 ) 2 - c 2 a - r l / 2 - c cos ( ϑ )             internal ,
r = ( a + r l / 2 ) 2 - c 2 a + r l / 2 - c cos ( ϑ )             external .
r l / a = 0.01 , 0.05 , 0.1 , 0.15 , 0.2 , 0.3 , r t / r l = 0.1 , 0.3 , 0.5 , 0.8 , 1.0 , 1.2 , c / a = 0.2 , 0.4 , 0.6 ,
x * ( t ) = 2 c , y * ( t ) = t ,             t [ - r l , r l ] .
r = 2 ( a + c ) 1 + cos ( ϑ )             ϑ [ - π / 2 , π / 2 ] ,
r = 2 ( a - c ) 1 - cos ( ϑ )             ϑ [ π / 2 , - π / 2 ]
r l / a = 0.01 , 0.05 , 0.1 , 0.15 , 0.2 , 0.3 , 0.6 , 0.9 ; r t / r l = 0.1 , 0.3 , 0.5 , 0.8 , 1.0 , 1.2 ; c / a = 0.2 , 0.4 , 0.6 , 0.8.

Metrics