Abstract

The plane-wave theory for the transmittance and absorbtance of a perfectly aligned Michelson coupler with a dielectric slab beam splitter is presented. It is shown that the transmittance and absorbtance vary sinusoidally and in quadrature. As a result of this quadrature relationship, the maximum transmittance occurs at a setting of the translatable coupler mirror at which the absorbtance is not at an extremum, and so the curve of output power as a function ofcoupler setting is asymmetrical with respect to the setting yielding maximum transmittance. Experimental measurements of the output power of a far-infrared HCN laser as a function of the coupler setting confirm this asymmetry, which seems to have been overlooked or ignored in previous studies.

© 1996 Optical Society of America

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References

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  1. R. Ulrich, T. J. Bridges, M. A. Pollack, “Variable metal mesh coupler for far infrared lasers,” Appl. Opt. 9, 2511–2516 (1970).
  2. K. M. Evenson, J. S. Wells, L. M. Matarrese, D. A. Jennings, “Variable output-coupling far-infrared Michelson laser,” J. Appl. Phys. 42, 1233–1234 (1971).
  3. S. R. Kumar, R. J. Tansy, J. Waldman, “Optically pumped submillimeter wave laser with Michelson interferometric output coupling,” IEEE J. Quantum Electron. QE-13, 30–33 (1977).
  4. C. O. Weiss, “Optically pumped FIR-laser with variable Fabry–Perot output coupler,” Appl. Phys. 13, 383–385 (1977).
  5. G. Duxbury, H. Herman, “CW optically pumped far-infrared waveguide laser with variable-output Michelson coupler,” J. Phys. E 11, 419–420 (1978).
  6. Yu. E. Kamenev, E. M. Kuleshov, “Waveguide HCN laser with controlled coupling,” Sov. J. Quantum Electron. 20, 48–49 (1990).
  7. J. J. Degnan, H. E. Walker, J. H. McElroy, N. McAvoy, “Gain and saturation intensity measurements in a waveguide CO2 laser,” IEEE J. Quantum Electron. QE-9, 489–491 (1973).
  8. B. S. Patel, “Determination of gain, saturation intensity, and internal losses of a laser using an intracavity rotatable reflector,” IEEE J. Quantum Electron. QE-9, 1150–1151 (1973).
  9. P. Woskoboinikow, W. C. Jennings, “The measurement of far-infrared laser gain and loss using a Michelson coupler,” IEEE J. Quantum Electron. QE-12, 613–615 (1976).
  10. J. L. Bruneau, P. Belland, T. Lebertre, D. Veron, “CW HCN laser gain in a hollow dielectric rectangular cross-section discharge tube,” Appl. Phys. 19, 359–361 (1979).
  11. P. A. Stimson, L. B. Whitbourn, “GLAYERS: A program for the IBM PC which calculates the properties of metal grids in dielectric stacks,” Tech. Memo. no. 61 (Commonwealth Scientific and Industrial Research Organization Divisionof Applied Physics, Lindfield, Australia, 1989). Built into the program are optical constants for materials commonly used at far-infrared wavelengths.
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  13. M. Born, E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1965).

1990 (1)

Yu. E. Kamenev, E. M. Kuleshov, “Waveguide HCN laser with controlled coupling,” Sov. J. Quantum Electron. 20, 48–49 (1990).

1980 (1)

1979 (1)

J. L. Bruneau, P. Belland, T. Lebertre, D. Veron, “CW HCN laser gain in a hollow dielectric rectangular cross-section discharge tube,” Appl. Phys. 19, 359–361 (1979).

1978 (1)

G. Duxbury, H. Herman, “CW optically pumped far-infrared waveguide laser with variable-output Michelson coupler,” J. Phys. E 11, 419–420 (1978).

1977 (2)

S. R. Kumar, R. J. Tansy, J. Waldman, “Optically pumped submillimeter wave laser with Michelson interferometric output coupling,” IEEE J. Quantum Electron. QE-13, 30–33 (1977).

C. O. Weiss, “Optically pumped FIR-laser with variable Fabry–Perot output coupler,” Appl. Phys. 13, 383–385 (1977).

1976 (1)

P. Woskoboinikow, W. C. Jennings, “The measurement of far-infrared laser gain and loss using a Michelson coupler,” IEEE J. Quantum Electron. QE-12, 613–615 (1976).

1973 (2)

J. J. Degnan, H. E. Walker, J. H. McElroy, N. McAvoy, “Gain and saturation intensity measurements in a waveguide CO2 laser,” IEEE J. Quantum Electron. QE-9, 489–491 (1973).

B. S. Patel, “Determination of gain, saturation intensity, and internal losses of a laser using an intracavity rotatable reflector,” IEEE J. Quantum Electron. QE-9, 1150–1151 (1973).

1971 (1)

K. M. Evenson, J. S. Wells, L. M. Matarrese, D. A. Jennings, “Variable output-coupling far-infrared Michelson laser,” J. Appl. Phys. 42, 1233–1234 (1971).

1970 (1)

Belland, P.

J. L. Bruneau, P. Belland, T. Lebertre, D. Veron, “CW HCN laser gain in a hollow dielectric rectangular cross-section discharge tube,” Appl. Phys. 19, 359–361 (1979).

Born, M.

M. Born, E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1965).

Bridges, T. J.

Bruneau, J. L.

J. L. Bruneau, P. Belland, T. Lebertre, D. Veron, “CW HCN laser gain in a hollow dielectric rectangular cross-section discharge tube,” Appl. Phys. 19, 359–361 (1979).

Casperson, L. W.

Degnan, J. J.

J. J. Degnan, H. E. Walker, J. H. McElroy, N. McAvoy, “Gain and saturation intensity measurements in a waveguide CO2 laser,” IEEE J. Quantum Electron. QE-9, 489–491 (1973).

Duxbury, G.

G. Duxbury, H. Herman, “CW optically pumped far-infrared waveguide laser with variable-output Michelson coupler,” J. Phys. E 11, 419–420 (1978).

Evenson, K. M.

K. M. Evenson, J. S. Wells, L. M. Matarrese, D. A. Jennings, “Variable output-coupling far-infrared Michelson laser,” J. Appl. Phys. 42, 1233–1234 (1971).

Herman, H.

G. Duxbury, H. Herman, “CW optically pumped far-infrared waveguide laser with variable-output Michelson coupler,” J. Phys. E 11, 419–420 (1978).

Jennings, D. A.

K. M. Evenson, J. S. Wells, L. M. Matarrese, D. A. Jennings, “Variable output-coupling far-infrared Michelson laser,” J. Appl. Phys. 42, 1233–1234 (1971).

Jennings, W. C.

P. Woskoboinikow, W. C. Jennings, “The measurement of far-infrared laser gain and loss using a Michelson coupler,” IEEE J. Quantum Electron. QE-12, 613–615 (1976).

Kamenev, Yu. E.

Yu. E. Kamenev, E. M. Kuleshov, “Waveguide HCN laser with controlled coupling,” Sov. J. Quantum Electron. 20, 48–49 (1990).

Kuleshov, E. M.

Yu. E. Kamenev, E. M. Kuleshov, “Waveguide HCN laser with controlled coupling,” Sov. J. Quantum Electron. 20, 48–49 (1990).

Kumar, S. R.

S. R. Kumar, R. J. Tansy, J. Waldman, “Optically pumped submillimeter wave laser with Michelson interferometric output coupling,” IEEE J. Quantum Electron. QE-13, 30–33 (1977).

Lebertre, T.

J. L. Bruneau, P. Belland, T. Lebertre, D. Veron, “CW HCN laser gain in a hollow dielectric rectangular cross-section discharge tube,” Appl. Phys. 19, 359–361 (1979).

Matarrese, L. M.

K. M. Evenson, J. S. Wells, L. M. Matarrese, D. A. Jennings, “Variable output-coupling far-infrared Michelson laser,” J. Appl. Phys. 42, 1233–1234 (1971).

McAvoy, N.

J. J. Degnan, H. E. Walker, J. H. McElroy, N. McAvoy, “Gain and saturation intensity measurements in a waveguide CO2 laser,” IEEE J. Quantum Electron. QE-9, 489–491 (1973).

McElroy, J. H.

J. J. Degnan, H. E. Walker, J. H. McElroy, N. McAvoy, “Gain and saturation intensity measurements in a waveguide CO2 laser,” IEEE J. Quantum Electron. QE-9, 489–491 (1973).

Patel, B. S.

B. S. Patel, “Determination of gain, saturation intensity, and internal losses of a laser using an intracavity rotatable reflector,” IEEE J. Quantum Electron. QE-9, 1150–1151 (1973).

Pollack, M. A.

Stimson, P. A.

P. A. Stimson, L. B. Whitbourn, “GLAYERS: A program for the IBM PC which calculates the properties of metal grids in dielectric stacks,” Tech. Memo. no. 61 (Commonwealth Scientific and Industrial Research Organization Divisionof Applied Physics, Lindfield, Australia, 1989). Built into the program are optical constants for materials commonly used at far-infrared wavelengths.

Tansy, R. J.

S. R. Kumar, R. J. Tansy, J. Waldman, “Optically pumped submillimeter wave laser with Michelson interferometric output coupling,” IEEE J. Quantum Electron. QE-13, 30–33 (1977).

Ulrich, R.

Veron, D.

J. L. Bruneau, P. Belland, T. Lebertre, D. Veron, “CW HCN laser gain in a hollow dielectric rectangular cross-section discharge tube,” Appl. Phys. 19, 359–361 (1979).

Waldman, J.

S. R. Kumar, R. J. Tansy, J. Waldman, “Optically pumped submillimeter wave laser with Michelson interferometric output coupling,” IEEE J. Quantum Electron. QE-13, 30–33 (1977).

Walker, H. E.

J. J. Degnan, H. E. Walker, J. H. McElroy, N. McAvoy, “Gain and saturation intensity measurements in a waveguide CO2 laser,” IEEE J. Quantum Electron. QE-9, 489–491 (1973).

Weiss, C. O.

C. O. Weiss, “Optically pumped FIR-laser with variable Fabry–Perot output coupler,” Appl. Phys. 13, 383–385 (1977).

Wells, J. S.

K. M. Evenson, J. S. Wells, L. M. Matarrese, D. A. Jennings, “Variable output-coupling far-infrared Michelson laser,” J. Appl. Phys. 42, 1233–1234 (1971).

Whitbourn, L. B.

P. A. Stimson, L. B. Whitbourn, “GLAYERS: A program for the IBM PC which calculates the properties of metal grids in dielectric stacks,” Tech. Memo. no. 61 (Commonwealth Scientific and Industrial Research Organization Divisionof Applied Physics, Lindfield, Australia, 1989). Built into the program are optical constants for materials commonly used at far-infrared wavelengths.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1965).

Woskoboinikow, P.

P. Woskoboinikow, W. C. Jennings, “The measurement of far-infrared laser gain and loss using a Michelson coupler,” IEEE J. Quantum Electron. QE-12, 613–615 (1976).

Appl. Opt. (2)

Appl. Phys. (2)

J. L. Bruneau, P. Belland, T. Lebertre, D. Veron, “CW HCN laser gain in a hollow dielectric rectangular cross-section discharge tube,” Appl. Phys. 19, 359–361 (1979).

C. O. Weiss, “Optically pumped FIR-laser with variable Fabry–Perot output coupler,” Appl. Phys. 13, 383–385 (1977).

IEEE J. Quantum Electron. (1)

S. R. Kumar, R. J. Tansy, J. Waldman, “Optically pumped submillimeter wave laser with Michelson interferometric output coupling,” IEEE J. Quantum Electron. QE-13, 30–33 (1977).

IEEE J. Quantum Electron. (2)

P. Woskoboinikow, W. C. Jennings, “The measurement of far-infrared laser gain and loss using a Michelson coupler,” IEEE J. Quantum Electron. QE-12, 613–615 (1976).

J. J. Degnan, H. E. Walker, J. H. McElroy, N. McAvoy, “Gain and saturation intensity measurements in a waveguide CO2 laser,” IEEE J. Quantum Electron. QE-9, 489–491 (1973).

IEEE J. Quantum Electron. (1)

B. S. Patel, “Determination of gain, saturation intensity, and internal losses of a laser using an intracavity rotatable reflector,” IEEE J. Quantum Electron. QE-9, 1150–1151 (1973).

J. Appl. Phys. (1)

K. M. Evenson, J. S. Wells, L. M. Matarrese, D. A. Jennings, “Variable output-coupling far-infrared Michelson laser,” J. Appl. Phys. 42, 1233–1234 (1971).

J. Phys. E (1)

G. Duxbury, H. Herman, “CW optically pumped far-infrared waveguide laser with variable-output Michelson coupler,” J. Phys. E 11, 419–420 (1978).

Sov. J. Quantum Electron. (1)

Yu. E. Kamenev, E. M. Kuleshov, “Waveguide HCN laser with controlled coupling,” Sov. J. Quantum Electron. 20, 48–49 (1990).

Other (2)

P. A. Stimson, L. B. Whitbourn, “GLAYERS: A program for the IBM PC which calculates the properties of metal grids in dielectric stacks,” Tech. Memo. no. 61 (Commonwealth Scientific and Industrial Research Organization Divisionof Applied Physics, Lindfield, Australia, 1989). Built into the program are optical constants for materials commonly used at far-infrared wavelengths.

M. Born, E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1965).

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Figures (2)

Fig. 1
Fig. 1

Essential elements of the physical setup of the Michelson coupler. A dielectric slab beam splitter is shown, but the theory applies to any symmetrical beam splitter.

Fig. 2
Fig. 2

Solid curve labeled T shows the theoretical transmittance of the variable Michelson coupler used in this study as a function of coupler setting Δz, and the curve labeled A shows the corresponding absorbtance. The discrete points (open circles) are experimental values of output power as a function of coupler setting, and the dashed curve is a theoretical best-fit plot.

Equations (10)

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

ρ c = ρ s 2 ρ a γ a 2 + τ s 2 ρ b γ b 2 ,
τ c = ρ s τ s ( ρ a γ a 2 + ρ b γ b 2 ) ,
R c = T s 2 R a + R s 2 R b + 2 R s T s R a R b    × cos [ 2 ( ν s μ s ) + δ ] ,
T c = R s T s ( R a + R b ) + 2 R s T s R a R b cos δ ,
δ = π 4 π ( Δ z Δ z 0 ) / λ 0 ,
R c = T s 2 R a + R s 2 R b 2 R s T s R a R b cos ( δ ) .
R c = T s 2 R a + R s 2 R b 2 R s T s R a R b ( cos δ + sin δ ) .
A c = 1 T s 2 R a R s 2 R b R s T s ( R a + R b )    + 2 R s T s R a R b sin δ .
ρ s = ρ 12 + τ 12 τ 21 ρ 21 γ 2 1 ρ 21 2 γ 2 ,
τ s = τ 12 τ 21 γ 1 ρ 21 2 γ 2 ,

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