Abstract

The present article addresses itself to the prime power requirements of a coupling-modulated gas laser transmitter. The latter consists of a gas discharge tube and electrooptic modulator inside a laser resonator. In performing the calculations, the laser discharge length and the modulator voltage are simultaneously varied so that the transmitted power remains constant. In this way, tradeoffs can be made between the prime power supplied individually to the discharge tube and to the modulator driver to obtain a transmitter configuration that minimizes the total prime power consumption. An analytical expression is derived that describes the effects of information bandwidth and transmitter output power on the prime power requirements. Specific numerical results are obtained for a CO2 laser transmitter based on presently available experimental data.

© 1974 Optical Society of America

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References

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  1. A. Yariv, Quantum Electronics (Wiley, New York, 1967), Chaps. 18 and 19.
  2. F. R. Nash, P. W. Smith, IEEE J. Quantum Electron. QE-4, 26 (1968).
    [CrossRef]
  3. N. McAvoy, J. Osmundson, G. Schiffner, Appl. Opt. 11, 473 (1972).
    [CrossRef] [PubMed]
  4. J. E. Kiefer, T. A. Nussmeier, F. E. Goodwin, IEEE Quantum Electron. QE-8, 173 (1972).
    [CrossRef]
  5. I. P. Kaminow, Appl. Opt. 4, 123 (1965).
    [CrossRef]
  6. M. DiDomenico, J. Appl. Phys., 35, 2870 (1964).
    [CrossRef]
  7. A. Yariv, T. A. Nussmeier, J. E. Kiefer, IEEE J. Quantum Electron., QE-9, 594 (1973).
    [CrossRef]
  8. F. E. Goodwin, J. E. Kiefer, A. Braunstein, j. H. Lange, NASA Contract Report NAS 1-10894, (1973), p. 19.
  9. W. W. Rigrod, J. Appl. Phys., 36, 2487 (1965).
    [CrossRef]
  10. Some of the values reported here have only been verified for modulator bandwidths of less than 300 MHz.

1973 (1)

A. Yariv, T. A. Nussmeier, J. E. Kiefer, IEEE J. Quantum Electron., QE-9, 594 (1973).
[CrossRef]

1972 (2)

J. E. Kiefer, T. A. Nussmeier, F. E. Goodwin, IEEE Quantum Electron. QE-8, 173 (1972).
[CrossRef]

N. McAvoy, J. Osmundson, G. Schiffner, Appl. Opt. 11, 473 (1972).
[CrossRef] [PubMed]

1968 (1)

F. R. Nash, P. W. Smith, IEEE J. Quantum Electron. QE-4, 26 (1968).
[CrossRef]

1965 (2)

W. W. Rigrod, J. Appl. Phys., 36, 2487 (1965).
[CrossRef]

I. P. Kaminow, Appl. Opt. 4, 123 (1965).
[CrossRef]

1964 (1)

M. DiDomenico, J. Appl. Phys., 35, 2870 (1964).
[CrossRef]

Braunstein, A.

F. E. Goodwin, J. E. Kiefer, A. Braunstein, j. H. Lange, NASA Contract Report NAS 1-10894, (1973), p. 19.

DiDomenico, M.

M. DiDomenico, J. Appl. Phys., 35, 2870 (1964).
[CrossRef]

Goodwin, F. E.

J. E. Kiefer, T. A. Nussmeier, F. E. Goodwin, IEEE Quantum Electron. QE-8, 173 (1972).
[CrossRef]

F. E. Goodwin, J. E. Kiefer, A. Braunstein, j. H. Lange, NASA Contract Report NAS 1-10894, (1973), p. 19.

Kaminow, I. P.

Kiefer, J. E.

A. Yariv, T. A. Nussmeier, J. E. Kiefer, IEEE J. Quantum Electron., QE-9, 594 (1973).
[CrossRef]

J. E. Kiefer, T. A. Nussmeier, F. E. Goodwin, IEEE Quantum Electron. QE-8, 173 (1972).
[CrossRef]

F. E. Goodwin, J. E. Kiefer, A. Braunstein, j. H. Lange, NASA Contract Report NAS 1-10894, (1973), p. 19.

Lange, j. H.

F. E. Goodwin, J. E. Kiefer, A. Braunstein, j. H. Lange, NASA Contract Report NAS 1-10894, (1973), p. 19.

McAvoy, N.

Nash, F. R.

F. R. Nash, P. W. Smith, IEEE J. Quantum Electron. QE-4, 26 (1968).
[CrossRef]

Nussmeier, T. A.

A. Yariv, T. A. Nussmeier, J. E. Kiefer, IEEE J. Quantum Electron., QE-9, 594 (1973).
[CrossRef]

J. E. Kiefer, T. A. Nussmeier, F. E. Goodwin, IEEE Quantum Electron. QE-8, 173 (1972).
[CrossRef]

Osmundson, J.

Rigrod, W. W.

W. W. Rigrod, J. Appl. Phys., 36, 2487 (1965).
[CrossRef]

Schiffner, G.

Smith, P. W.

F. R. Nash, P. W. Smith, IEEE J. Quantum Electron. QE-4, 26 (1968).
[CrossRef]

Yariv, A.

A. Yariv, T. A. Nussmeier, J. E. Kiefer, IEEE J. Quantum Electron., QE-9, 594 (1973).
[CrossRef]

A. Yariv, Quantum Electronics (Wiley, New York, 1967), Chaps. 18 and 19.

Appl. Opt. (2)

IEEE J. Quantum Electron. (2)

F. R. Nash, P. W. Smith, IEEE J. Quantum Electron. QE-4, 26 (1968).
[CrossRef]

A. Yariv, T. A. Nussmeier, J. E. Kiefer, IEEE J. Quantum Electron., QE-9, 594 (1973).
[CrossRef]

IEEE Quantum Electron. (1)

J. E. Kiefer, T. A. Nussmeier, F. E. Goodwin, IEEE Quantum Electron. QE-8, 173 (1972).
[CrossRef]

J. Appl. Phys. (2)

M. DiDomenico, J. Appl. Phys., 35, 2870 (1964).
[CrossRef]

W. W. Rigrod, J. Appl. Phys., 36, 2487 (1965).
[CrossRef]

Other (3)

Some of the values reported here have only been verified for modulator bandwidths of less than 300 MHz.

F. E. Goodwin, J. E. Kiefer, A. Braunstein, j. H. Lange, NASA Contract Report NAS 1-10894, (1973), p. 19.

A. Yariv, Quantum Electronics (Wiley, New York, 1967), Chaps. 18 and 19.

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Figures (6)

Fig. 1
Fig. 1

Coupling modulation.

Fig. 2
Fig. 2

Fractional power contained in distortion harmonics as a function of the dc and ac phase shifts, Γ0 and Γm.

Fig. 3
Fig. 3

Effective reflectivity of the modulator as a function of the dc and ac phase shifts, Γ0 and Γm.

Fig. 4
Fig. 4

Equivalent circuit of an electrooptic modulator.

Fig. 5
Fig. 5

The dependence of (a) the total prime power consumption PP, (b) the modulator driver consumption PD, (c) the laser high voltage supply consumption PHV, (d) the circulating power PC, and (e) the discharge length L on the peak ac phase shift Γm when the transmitter output power is held to a constant value of 1 W, the ratio of sideband to carrier powers is equal to 10, and the maximum modulated frequency is 400 MHz.

Fig. 6
Fig. 6

The dependence of (a) the minimum prime power consumption Pmin, (b) the modulator driver consumption PD, (c) the laser high voltage supply consumption PHV, (d) the circulating power PC, and (e) the optimum discharge length L on the value of the transmitted power PT and the maximum modulation frequency fmax.

Tables (1)

Tables Icon

Table I Numerical Values for the Parameters

Equations (56)

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E in = E c 2 ( e ˆ x + e ˆ y ) cos ω c t = E c 2 ( e ˆ x + e ˆ y ) Re [ exp ( j ω c t ) ] ,
E = E c sin Γ ( t ) sin ω c t ,
E = E c cos Γ ( t ) cos ω c t ,
Γ ( t ) = [ 2 Δ n ( t ) ω c l ] / c .
Γ ( t ) = Γ 0 + Γ m cos ω m t ,
E = E c [ sin Γ 0 J 0 ( Γ m ) sin ω c t + sin Γ 0 k = 1 ( 1 ) k J 2 k ( Γ m ) { sin [ ( ω c + 2 k ω m ) t ] + sin [ ( ω c 2 k ω m ) t ] } + cos Γ 0 k = 0 ( 1 ) k J 2 k + 1 ( Γ m ) × ( sin { [ ω c + ( 2 k + 1 ) ω m ] t } + sin { [ ω c ( 2 k + 1 ) ω m ] t } ) ] .
P ( ω c + k ω m ) = { η C P C sin 2 Γ 0 J k 2 ( Γ m ) k = .. 4 , 2,0 , + 2 , + 4 , η C P C cos 2 Γ 0 J k 2 ( Γ m ) k = .. 3 , 1 , + 1 , + 3 ,
P carrier = η C P C sin 2 Γ 0 J 0 2 ( Γ m ) ,
P s b = 2 η C P C cos 2 Γ 0 J 1 2 ( Γ m ) .
P total = k = P ( ω c + k ω m ) = η C P C 2 [ 1 J 0 ( 2 Γ m ) cos 2 Γ 0 ] .
F = 1 2 sin 2 Γ 0 J 0 2 ( Γ m ) + 4 cos 2 Γ 0 J 1 2 ( Γ m ) 1 J 0 ( 2 Γ m ) cos 2 Γ 0
E = E c [ cos Γ 0 J 0 ( Γ m ) cos ω c t + cos Γ 0 k = 1 ( 1 ) k J 2 k ( Γ m ) { cos [ ( ω c + 2 k ω m ) t ] + cos [ ( ω c 2 k ω m ) t ] } sin Γ 0 k = 0 ( 1 ) k J 2 k + 1 ( Γ m ) ( cos { [ ω c + ( 2 k + 1 ) ω m ] t } + cos { [ ω c ( 2 k + 1 ) ω m ] t } ) ] .
P R ( ω c + k ω m ) = { ( 1 a 2 ) P C cos 2 Γ 0 J k 2 ( Γ m ) k = 2,0 , + 2 , ( 1 a 2 ) P C sin 2 Γ 0 J k 2 ( Γ m ) k 3 , 1 , + 1 , + 3 ,
r 2 = ( 1 a 2 ) cos 2 Γ 0 J 0 2 ( Γ m )
f max = 1 / ( 2 π R C ) ,
V ( t ) = V 0 + V m cos ω m t
P M = 2 π f max C ( V 0 2 + 1 2 V m 2 ) .
Γ 0 = ( 2 π / λ 0 ) n 0 3 r 41 V 0 ( 2 l / d )
Γ m = ( 2 π / λ 0 ) n 0 3 r 41 V m ( 2 l / d ) ,
P D = P M η D = f max C 2 π η D ( V π l / d ) 2 ( Γ 0 2 + 1 2 Γ m 2 ) ( l / d ) 2 ,
V π ( l / d ) = λ 0 / ( 2 n 0 3 r 41 )
P HV = ( 1 / η HV ) [ P B + ( d P / d L ) L ] ,
P C = P S ( r 1 ) 1 / 2 [ g 0 L + ln ( r 1 r 2 ) 1 / 2 ] [ ( r 1 ) 1 / 2 + ( r 2 ) 1 / 2 ] [ 1 ( r 1 r 2 ) 1 / 2 ]
R = P s b P carrier = 2 cot 2 Γ 0 J 1 2 ( Γ m ) J 0 2 ( Γ m ) .
tan Γ 0 = ( 2 / R ) 1 / 2 [ J 1 ( Γ m ) / J 0 ( Γ m ) ] .
P T = P carrier + P s b = η C P C [ sin 2 Γ 0 J 0 2 ( Γ m ) + 2 cos 2 Γ 0 J 1 2 ( Γ m ) ] ,
P C = P T η C [ sin 2 Γ 0 J 0 2 ( Γ m ) + 2 cos 2 Γ 0 J 1 2 ( Γ m ) ] 1 .
L = 1 g 0 { P C P S [ ( r 1 ) 1 / 2 + ( r 2 ) 1 / 2 ] [ 1 ( r 1 r 2 ) 1 / 2 ] ( r 1 ) 1 / 2 ln ( r 1 r 2 ) 1 / 2 } ,
P P = f max C 2 π η D ( V π l / d ) 2 ( l / d ) 2 ( Γ 0 2 + 1 2 Γ m 2 ) + 1 η HV [ P B + ( d P d L ) L ] .
r 2 1 ( a 2 + Γ 0 2 + 1 2 Γ m 2 ) ,
P C P T / [ η C ( Γ 0 2 + 1 2 Γ m 2 ) ] .
L = 1 g 0 [ P T η C P S ( Γ 0 2 + 1 2 Γ m 2 ) + 1 2 ] × ( a 1 + a 2 + Γ 0 2 + 1 2 Γ m 2 ) ,
P P = α 1 + β 1 x 1 + ( γ 1 / x 1 ) ,
α 1 P B η HV + ( d P / d L ) η HV g 0 ( P T η C P S + a 1 + a 2 2 ) ,
β 1 ( d P / d L ) 2 η HV g 0 + f max C 2 π η D ( V π l / d ) 2 ( l / d ) 2 ,
γ 1 ( d P / d L ) η HV g 0 P T ( a 1 + a 2 ) η C P S ,
x 1 Γ 0 2 + 1 2 Γ m 2 .
x 1 = ( γ 1 / β 1 ) 1 / 2
P min = α 1 + 2 ( β 1 γ 1 ) 1 / 2 .
r 2 = 1 a 2 ( γ 1 / β 1 ) 1 / 2 ,
P C = ( P T / η C ) ( β 1 / γ 1 ) 1 / 2 ,
L = 1 g 0 [ P T η C P S ( β 1 γ 1 ) 1 / 2 + 1 2 ] [ a 1 + a 2 + ( γ 1 β 1 ) 1 / 2 ] .
P P = α 2 + β 2 x 2 + ( γ 2 / x 2 ) ,
α 2 = α 1 P B η HV + ( d P / d L ) η HV g 0 ( P T η C P S + a 1 + a 2 2 ) ,
β 2 ( d P / d L ) 2 η HV g 0 [ 1 + ( 1 / R ) ] + f max C 2 π η D ( V π l / d ) 2 ( l / d ) 2 ,
γ 2 ( d P / d L ) η HV g 0 P T η C P S [ 1 + ( 1 / R ) ] = γ 1 [ 1 + ( 1 / R ) ] ,
x 2 = ( Γ m 2 ) / 2 .
x 2 = ( γ 2 / β 2 ) 1 / 2 ,
P min = α 2 + 2 ( β 2 γ 2 ) 1 / 2 .
P total = k = P ( ω c + k ω m ) = η c P c [ sin 2 Γ 0 k even J k 2 ( Γ m ) + cos 2 Γ 0 k odd J k 2 ( Γ m ) ] .
k even J k 2 ( Γ m ) = 1 2 [ k = J k 2 ( Γ m ) + k = ( 1 ) k J k 2 ( Γ m ) ] = 1 2 { [ J 0 2 ( Γ m ) + 2 k = 1 J k 2 ( Γ m ) ] + [ J 0 2 ( Γ m ) + 2 k = 1 ( 1 ) k J k 2 ( Γ m ) ] } .
1 = J 0 2 ( z ) + 2 k = 1 J k 2 ( z )
J 0 ( 2 z ) = J 0 2 ( z ) + 2 k = 1 ( 1 ) k J k 2 ( z ) .
k even J k 2 ( Γ m ) = 1 2 [ 1 + J 0 ( 2 Γ m ) ] .
k odd J k 2 ( Γ m ) = 1 2 [ k = J k 2 ( Γ m ) k = ( 1 ) k J k 2 ( Γ m ) ] = 1 2 [ 1 J 0 ( 2 Γ m ) ] .
P total = η C P C 2 { sin 2 Γ 0 [ 1 + J 0 ( 2 Γ m ) ] + cos 2 Γ 0 [ 1 J 0 ( 2 Γ m ) ] } = η C P C 2 [ 1 J 0 ( 2 Γ m ) cos 2 Γ 0 ] .

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