Abstract

We study the factors that ultimately limit the performance of an external enhancement resonator for optical second-harmonic generation (SHG). To describe the resonant SHG process we introduce a theoretical model that accounts for the intensity-dependent cavity loss that is due to harmonic generation and that also includes a realistic assumption about the shape and the frequency width of the laser mode. With the help of this model we optimized the performance of a doubling cavity based on a lithium triborate (LBO) crystal. This cavity was used for frequency doubling the output of a single-frequency titanium-doped sapphire laser at 850 nm. We were able to push the total second-harmonic conversion efficiency to 53% (a 1.54-W pump resulted in 820 mW of second-harmonic light), which to our knowledge is the best result ever reported for a LBO-based doubling cavity.

© 2002 Optical Society of America

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References

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  1. P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
    [CrossRef]
  2. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
    [CrossRef]
  3. A. Ashkin, G. D. Boyd, and J. M. Dziendzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. QE-2, 109–124 (1966).
    [CrossRef]
  4. C. S. Adams and A. I. Ferguson, “Tunable narrow linewidth ultra-violet light generation by frequency doubling of a ring Ti:sapphire laser using lithium tri-borate in an external enhancement cavity,” Opt. Commun. 90, 89–94 (1992).
    [CrossRef]
  5. S. Bourzeix, M. D. Plimmer, F. Nez, L. Julien, and F. Biraben, “Efficient frequency doubling of a continuous wave titanium:sapphire laser in an external enhancement cavity,” Opt. Commun. 99, 89–94 (1993).
    [CrossRef]
  6. H. Tsuchida, “Frequency doubling of tunable Ti:sapphire laser with KNbO3 in external cavity,” Jpn. J. Appl. Phys., Part 1 33, 6190–6194 (1994).
    [CrossRef]
  7. S. Bourzeix, B. de Beauvoir, F. Nez, F. de Tomasi, L. Julien, and F. Biraben, “Ultraviolet light generation at 205 nm by two frequency doubling steps of a cw titanium-sapphire laser,” Opt. Commun. 133, 239–244 (1997).
    [CrossRef]
  8. T. Fujii, H. Kumagai, K. Midorikawa, and M. Obara, “Development of a high-power deep-ultraviolet continuous-wave coherent light source for laser cooling of silicon atoms,” Opt. Lett. 25, 1457–1459 (2000).
    [CrossRef]
  9. G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
    [CrossRef]
  10. Throughout this paper we follow the usual convention that both the reflectivity and the transmissivity are related to the optical intensity (power).
  11. M. J. Lawrence, B. Willke, M. E. Husman, E. K. Gustafson, and R. L. Byer, “Dynamic response of a Fabry–Perot interferometer,” J. Opt. Soc. Am. B 16, 523–532 (1999).
    [CrossRef]
  12. T. W. Hänsch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
    [CrossRef]
  13. To get a continuous scan range larger than ±3 GHz, one could mount a Brewster plate into the cavity. It could then take care of slow variations while the PZT-driven mirror would correct for higher frequencies.
  14. The Hänsch–Couillaud stabilization method is not suitable for spectroscopic applications, especially when a broad wavelength range is required. In carrying out the wavelength tuning measurements we applied the Pound–Drewer–Hall stabilization scheme [see R. W. P. Drewer, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983)]. The power stability with both of these two techniques remained the same (at least within the limit that we could detect).
    [CrossRef]
  15. Absolute power values are uncertain to ±2.5% of the stated value because of uncertainty in detector calibration.

2000 (1)

1999 (1)

1997 (1)

S. Bourzeix, B. de Beauvoir, F. Nez, F. de Tomasi, L. Julien, and F. Biraben, “Ultraviolet light generation at 205 nm by two frequency doubling steps of a cw titanium-sapphire laser,” Opt. Commun. 133, 239–244 (1997).
[CrossRef]

1994 (1)

H. Tsuchida, “Frequency doubling of tunable Ti:sapphire laser with KNbO3 in external cavity,” Jpn. J. Appl. Phys., Part 1 33, 6190–6194 (1994).
[CrossRef]

1993 (1)

S. Bourzeix, M. D. Plimmer, F. Nez, L. Julien, and F. Biraben, “Efficient frequency doubling of a continuous wave titanium:sapphire laser in an external enhancement cavity,” Opt. Commun. 99, 89–94 (1993).
[CrossRef]

1992 (1)

C. S. Adams and A. I. Ferguson, “Tunable narrow linewidth ultra-violet light generation by frequency doubling of a ring Ti:sapphire laser using lithium tri-borate in an external enhancement cavity,” Opt. Commun. 90, 89–94 (1992).
[CrossRef]

1983 (1)

The Hänsch–Couillaud stabilization method is not suitable for spectroscopic applications, especially when a broad wavelength range is required. In carrying out the wavelength tuning measurements we applied the Pound–Drewer–Hall stabilization scheme [see R. W. P. Drewer, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983)]. The power stability with both of these two techniques remained the same (at least within the limit that we could detect).
[CrossRef]

1980 (1)

T. W. Hänsch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
[CrossRef]

1968 (1)

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[CrossRef]

1966 (1)

A. Ashkin, G. D. Boyd, and J. M. Dziendzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. QE-2, 109–124 (1966).
[CrossRef]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

1961 (1)

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[CrossRef]

Adams, C. S.

C. S. Adams and A. I. Ferguson, “Tunable narrow linewidth ultra-violet light generation by frequency doubling of a ring Ti:sapphire laser using lithium tri-borate in an external enhancement cavity,” Opt. Commun. 90, 89–94 (1992).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Ashkin, A.

A. Ashkin, G. D. Boyd, and J. M. Dziendzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. QE-2, 109–124 (1966).
[CrossRef]

Biraben, F.

S. Bourzeix, B. de Beauvoir, F. Nez, F. de Tomasi, L. Julien, and F. Biraben, “Ultraviolet light generation at 205 nm by two frequency doubling steps of a cw titanium-sapphire laser,” Opt. Commun. 133, 239–244 (1997).
[CrossRef]

S. Bourzeix, M. D. Plimmer, F. Nez, L. Julien, and F. Biraben, “Efficient frequency doubling of a continuous wave titanium:sapphire laser in an external enhancement cavity,” Opt. Commun. 99, 89–94 (1993).
[CrossRef]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Bourzeix, S.

S. Bourzeix, B. de Beauvoir, F. Nez, F. de Tomasi, L. Julien, and F. Biraben, “Ultraviolet light generation at 205 nm by two frequency doubling steps of a cw titanium-sapphire laser,” Opt. Commun. 133, 239–244 (1997).
[CrossRef]

S. Bourzeix, M. D. Plimmer, F. Nez, L. Julien, and F. Biraben, “Efficient frequency doubling of a continuous wave titanium:sapphire laser in an external enhancement cavity,” Opt. Commun. 99, 89–94 (1993).
[CrossRef]

Boyd, G. D.

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[CrossRef]

A. Ashkin, G. D. Boyd, and J. M. Dziendzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. QE-2, 109–124 (1966).
[CrossRef]

Byer, R. L.

Couillaud, B.

T. W. Hänsch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
[CrossRef]

de Beauvoir, B.

S. Bourzeix, B. de Beauvoir, F. Nez, F. de Tomasi, L. Julien, and F. Biraben, “Ultraviolet light generation at 205 nm by two frequency doubling steps of a cw titanium-sapphire laser,” Opt. Commun. 133, 239–244 (1997).
[CrossRef]

de Tomasi, F.

S. Bourzeix, B. de Beauvoir, F. Nez, F. de Tomasi, L. Julien, and F. Biraben, “Ultraviolet light generation at 205 nm by two frequency doubling steps of a cw titanium-sapphire laser,” Opt. Commun. 133, 239–244 (1997).
[CrossRef]

Drewer, R. W. P.

The Hänsch–Couillaud stabilization method is not suitable for spectroscopic applications, especially when a broad wavelength range is required. In carrying out the wavelength tuning measurements we applied the Pound–Drewer–Hall stabilization scheme [see R. W. P. Drewer, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983)]. The power stability with both of these two techniques remained the same (at least within the limit that we could detect).
[CrossRef]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Dziendzic, J. M.

A. Ashkin, G. D. Boyd, and J. M. Dziendzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. QE-2, 109–124 (1966).
[CrossRef]

Ferguson, A. I.

C. S. Adams and A. I. Ferguson, “Tunable narrow linewidth ultra-violet light generation by frequency doubling of a ring Ti:sapphire laser using lithium tri-borate in an external enhancement cavity,” Opt. Commun. 90, 89–94 (1992).
[CrossRef]

Ford, G. M.

The Hänsch–Couillaud stabilization method is not suitable for spectroscopic applications, especially when a broad wavelength range is required. In carrying out the wavelength tuning measurements we applied the Pound–Drewer–Hall stabilization scheme [see R. W. P. Drewer, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983)]. The power stability with both of these two techniques remained the same (at least within the limit that we could detect).
[CrossRef]

Franken, P. A.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[CrossRef]

Fujii, T.

Gustafson, E. K.

Hall, J. L.

The Hänsch–Couillaud stabilization method is not suitable for spectroscopic applications, especially when a broad wavelength range is required. In carrying out the wavelength tuning measurements we applied the Pound–Drewer–Hall stabilization scheme [see R. W. P. Drewer, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983)]. The power stability with both of these two techniques remained the same (at least within the limit that we could detect).
[CrossRef]

Hänsch, T. W.

T. W. Hänsch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
[CrossRef]

Hill, A. E.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[CrossRef]

Hough, J.

The Hänsch–Couillaud stabilization method is not suitable for spectroscopic applications, especially when a broad wavelength range is required. In carrying out the wavelength tuning measurements we applied the Pound–Drewer–Hall stabilization scheme [see R. W. P. Drewer, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983)]. The power stability with both of these two techniques remained the same (at least within the limit that we could detect).
[CrossRef]

Husman, M. E.

Julien, L.

S. Bourzeix, B. de Beauvoir, F. Nez, F. de Tomasi, L. Julien, and F. Biraben, “Ultraviolet light generation at 205 nm by two frequency doubling steps of a cw titanium-sapphire laser,” Opt. Commun. 133, 239–244 (1997).
[CrossRef]

S. Bourzeix, M. D. Plimmer, F. Nez, L. Julien, and F. Biraben, “Efficient frequency doubling of a continuous wave titanium:sapphire laser in an external enhancement cavity,” Opt. Commun. 99, 89–94 (1993).
[CrossRef]

Kleinman, D. A.

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[CrossRef]

Kowalski, F. V.

The Hänsch–Couillaud stabilization method is not suitable for spectroscopic applications, especially when a broad wavelength range is required. In carrying out the wavelength tuning measurements we applied the Pound–Drewer–Hall stabilization scheme [see R. W. P. Drewer, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983)]. The power stability with both of these two techniques remained the same (at least within the limit that we could detect).
[CrossRef]

Kumagai, H.

Lawrence, M. J.

Midorikawa, K.

Munley, A. J.

The Hänsch–Couillaud stabilization method is not suitable for spectroscopic applications, especially when a broad wavelength range is required. In carrying out the wavelength tuning measurements we applied the Pound–Drewer–Hall stabilization scheme [see R. W. P. Drewer, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983)]. The power stability with both of these two techniques remained the same (at least within the limit that we could detect).
[CrossRef]

Nez, F.

S. Bourzeix, B. de Beauvoir, F. Nez, F. de Tomasi, L. Julien, and F. Biraben, “Ultraviolet light generation at 205 nm by two frequency doubling steps of a cw titanium-sapphire laser,” Opt. Commun. 133, 239–244 (1997).
[CrossRef]

S. Bourzeix, M. D. Plimmer, F. Nez, L. Julien, and F. Biraben, “Efficient frequency doubling of a continuous wave titanium:sapphire laser in an external enhancement cavity,” Opt. Commun. 99, 89–94 (1993).
[CrossRef]

Obara, M.

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Peters, C. W.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[CrossRef]

Plimmer, M. D.

S. Bourzeix, M. D. Plimmer, F. Nez, L. Julien, and F. Biraben, “Efficient frequency doubling of a continuous wave titanium:sapphire laser in an external enhancement cavity,” Opt. Commun. 99, 89–94 (1993).
[CrossRef]

Tsuchida, H.

H. Tsuchida, “Frequency doubling of tunable Ti:sapphire laser with KNbO3 in external cavity,” Jpn. J. Appl. Phys., Part 1 33, 6190–6194 (1994).
[CrossRef]

Ward, H.

The Hänsch–Couillaud stabilization method is not suitable for spectroscopic applications, especially when a broad wavelength range is required. In carrying out the wavelength tuning measurements we applied the Pound–Drewer–Hall stabilization scheme [see R. W. P. Drewer, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983)]. The power stability with both of these two techniques remained the same (at least within the limit that we could detect).
[CrossRef]

Weinreich, G.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[CrossRef]

Willke, B.

Appl. Phys. B (1)

The Hänsch–Couillaud stabilization method is not suitable for spectroscopic applications, especially when a broad wavelength range is required. In carrying out the wavelength tuning measurements we applied the Pound–Drewer–Hall stabilization scheme [see R. W. P. Drewer, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983)]. The power stability with both of these two techniques remained the same (at least within the limit that we could detect).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. Ashkin, G. D. Boyd, and J. M. Dziendzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. QE-2, 109–124 (1966).
[CrossRef]

J. Appl. Phys. (1)

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[CrossRef]

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

Jpn. J. Appl. Phys., Part 1 (1)

H. Tsuchida, “Frequency doubling of tunable Ti:sapphire laser with KNbO3 in external cavity,” Jpn. J. Appl. Phys., Part 1 33, 6190–6194 (1994).
[CrossRef]

Opt. Commun. (4)

S. Bourzeix, B. de Beauvoir, F. Nez, F. de Tomasi, L. Julien, and F. Biraben, “Ultraviolet light generation at 205 nm by two frequency doubling steps of a cw titanium-sapphire laser,” Opt. Commun. 133, 239–244 (1997).
[CrossRef]

C. S. Adams and A. I. Ferguson, “Tunable narrow linewidth ultra-violet light generation by frequency doubling of a ring Ti:sapphire laser using lithium tri-borate in an external enhancement cavity,” Opt. Commun. 90, 89–94 (1992).
[CrossRef]

S. Bourzeix, M. D. Plimmer, F. Nez, L. Julien, and F. Biraben, “Efficient frequency doubling of a continuous wave titanium:sapphire laser in an external enhancement cavity,” Opt. Commun. 99, 89–94 (1993).
[CrossRef]

T. W. Hänsch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Phys. Rev. Lett. (1)

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[CrossRef]

Other (3)

Throughout this paper we follow the usual convention that both the reflectivity and the transmissivity are related to the optical intensity (power).

To get a continuous scan range larger than ±3 GHz, one could mount a Brewster plate into the cavity. It could then take care of slow variations while the PZT-driven mirror would correct for higher frequencies.

Absolute power values are uncertain to ±2.5% of the stated value because of uncertainty in detector calibration.

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Figures (6)

Fig. 1
Fig. 1

Four-mirror ring cavity for SHG: M1, input coupler; M2–M4, cavity mirrors; C, nonlinear crystal.

Fig. 2
Fig. 2

Calculated (a) steady-state enhancement factor, (b) reflectivity, and (c) SH conversion efficiency as functions of fundamental power. Calculation parameters: R0=99.8%, α=2.8×10-5 W-1; R1=95.5%, 99.3%, 99.8%.

Fig. 3
Fig. 3

Schematic design of the doubling cavity: L1, L2, mode-matching lenses; M, folding mirror; HWP, half-wave plate; M1, input coupler; M2, PZT-driven mirror; M3, M4, concave mirrors; C, LBO crystal; GP, glass plate; M5, folding mirror; F, neutral-density filter (10%); QWP, quarter-wave plate; PBS, polarization beam splitter; D1, D2, photodiodes. Data plot, measured Hänsch–Couillaud signal as a function of the detuning of a 1-W, 850-nm fundamental beam from the cavity resonance.

Fig. 4
Fig. 4

Steady-state dependence of (a) the reflected fundamental power and (b) the total SH power on the incident pump power for R1=95.5%, 97.3%, 98.5%, 98.7%, and 99.7%. Solid curves, modeled dependencies.

Fig. 5
Fig. 5

Best achieved performance: (a) SH power and (b) conversion efficiency as functions of incident fundamental power. Squares, measured data; solid curves, modeled dependence; dashed curve, dependence modeled with the assumption that δω=0 and R1=99.3% [see also the dashed curve in Fig. 2(c)].

Fig. 6
Fig. 6

Comparison of measured and calculated transients of the cavity for a 1.25-W, 850-nm pump: (a) reflected fundamental power and (b) SH power. R1=95.5%, 98.5%, 99.7%. Lighter solid curves, modeled time dependencies.

Equations (12)

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

ISH(n)=αIc2(n).
TSH(n)=1-αIc(n).
Ec(n)=iT1Ei+R(n-1) exp(-iϕ)Ec(n-1),
R(n)=R0TSH(n)R1.
Er(n)=-R1Ei-i[T1R(n)/R1]1/2 exp(-iϕ)Ec(n).
Ic,r(n)=½0c|Ec,r(n)|2
Ic=T1 11+r-2r cos(ϕ)Ii,
Ir=R1+T1 T1R0+2r-2r cos(ϕ)1+r-2r cos(ϕ)Ii,
η=αβ2Ii.
ISH(Ω, n)=½0cα-+ Ec(Ω-ω, n)Ec(ω, n)dω2.
TSH(n)=1-½0cα -+|Ec(ω, n)|2dω.
Ii(ω)1-ω-ω0δω/22,

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