Abstract

In an investigation of extraordinary- (E-) ray behavior and the index of refraction for E waves in a uniaxial crystal, a precise and versatile formula for birefringent filters, based on the exact construction of the optical path difference, is set up with neither the approximation Δn = n on en o (or n e), nor the ambiguity sin(θ)/sin(r w) = n e. The exact construction gives the correct variation of the position and the dimension in each path, yielding the path difference while the filter is tuning. The formula is applicable not only to a filter with its optical axis parallel to the entrance surface (FAPS) but also to a filter with its axis inclined to the surface (FAIS). Also, the formula indicates that a FAIS allows laser wavelengths to be tuned over a wider range than does a FAPS. The origin of the wider range is interpreted to be the greater variation in the index for the FAIS while the filter is tuning. With the help of the formula we design a FAIS for tuning a cw Ti:sapphire laser.

© 1996 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. Holtom, O. Teschke, “Design of a birefringent filter for high power dye laser,” IEEE J. Quantum Electron. QE-10, 577–579 (1974).
    [Crossref]
  2. J. Hodgkinson, J. I. Vukosic, “Birefringent filters for tuning flashlamp-pumped dye lasers: simplified theory and design,” Appl. Opt. 17, 1944–1948 (1978).
    [Crossref] [PubMed]
  3. D. R. Preuss, J. L. Gole, “Three-stage birefringent filter tuning smoothly over the visible region: theoretical treatment and experiment design,” Appl. Opt. 19, 702–710 (1980).
    [Crossref] [PubMed]
  4. M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1975), Chap. 14.4.3, p. 694, Chap. 14.2.1, p. 668.
  5. Z. Shao, C. Yi, “Extraordinary rays’ behavior in uniaxial crystals,” Appl. Opt. 33, 1209–1212 (1994).
    [Crossref] [PubMed]
  6. Z. Shao, “Refractive index for extraordinary waves in uniaxial crystals,” Phy. Rev. E 52, 1043–1046 (1995).
    [Crossref]
  7. S. D. Zhu, “Birefringent filter with tilt optic axis for tuning dye laser: theory and design,” Appl. Opt. 29, 410–415 (1990).
    [Crossref] [PubMed]
  8. A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), Chap. 5.4, p. 88.
  9. T. Izawa, M. Maeda, N. Yamamura, R. Uchimura, R. Ikeda, S. Kimura, T. Yakuoh, N. Sarukura, Z. Kiu, Y. Segawa, H. Tashira, “Full-range tunable operation of a cw Ti:sapphire laser with a single set of extreme broad-band, low-loss mirrors,” in Digest of Advanced Solid-State Lasers (Optical Society of America, Washington D.C., 1995) paper ThB7.

1995 (1)

Z. Shao, “Refractive index for extraordinary waves in uniaxial crystals,” Phy. Rev. E 52, 1043–1046 (1995).
[Crossref]

1994 (1)

1990 (1)

1980 (1)

1978 (1)

1974 (1)

G. Holtom, O. Teschke, “Design of a birefringent filter for high power dye laser,” IEEE J. Quantum Electron. QE-10, 577–579 (1974).
[Crossref]

Born, M.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1975), Chap. 14.4.3, p. 694, Chap. 14.2.1, p. 668.

Gole, J. L.

Hodgkinson, J.

Holtom, G.

G. Holtom, O. Teschke, “Design of a birefringent filter for high power dye laser,” IEEE J. Quantum Electron. QE-10, 577–579 (1974).
[Crossref]

Ikeda, R.

T. Izawa, M. Maeda, N. Yamamura, R. Uchimura, R. Ikeda, S. Kimura, T. Yakuoh, N. Sarukura, Z. Kiu, Y. Segawa, H. Tashira, “Full-range tunable operation of a cw Ti:sapphire laser with a single set of extreme broad-band, low-loss mirrors,” in Digest of Advanced Solid-State Lasers (Optical Society of America, Washington D.C., 1995) paper ThB7.

Izawa, T.

T. Izawa, M. Maeda, N. Yamamura, R. Uchimura, R. Ikeda, S. Kimura, T. Yakuoh, N. Sarukura, Z. Kiu, Y. Segawa, H. Tashira, “Full-range tunable operation of a cw Ti:sapphire laser with a single set of extreme broad-band, low-loss mirrors,” in Digest of Advanced Solid-State Lasers (Optical Society of America, Washington D.C., 1995) paper ThB7.

Kimura, S.

T. Izawa, M. Maeda, N. Yamamura, R. Uchimura, R. Ikeda, S. Kimura, T. Yakuoh, N. Sarukura, Z. Kiu, Y. Segawa, H. Tashira, “Full-range tunable operation of a cw Ti:sapphire laser with a single set of extreme broad-band, low-loss mirrors,” in Digest of Advanced Solid-State Lasers (Optical Society of America, Washington D.C., 1995) paper ThB7.

Kiu, Z.

T. Izawa, M. Maeda, N. Yamamura, R. Uchimura, R. Ikeda, S. Kimura, T. Yakuoh, N. Sarukura, Z. Kiu, Y. Segawa, H. Tashira, “Full-range tunable operation of a cw Ti:sapphire laser with a single set of extreme broad-band, low-loss mirrors,” in Digest of Advanced Solid-State Lasers (Optical Society of America, Washington D.C., 1995) paper ThB7.

Maeda, M.

T. Izawa, M. Maeda, N. Yamamura, R. Uchimura, R. Ikeda, S. Kimura, T. Yakuoh, N. Sarukura, Z. Kiu, Y. Segawa, H. Tashira, “Full-range tunable operation of a cw Ti:sapphire laser with a single set of extreme broad-band, low-loss mirrors,” in Digest of Advanced Solid-State Lasers (Optical Society of America, Washington D.C., 1995) paper ThB7.

Preuss, D. R.

Sarukura, N.

T. Izawa, M. Maeda, N. Yamamura, R. Uchimura, R. Ikeda, S. Kimura, T. Yakuoh, N. Sarukura, Z. Kiu, Y. Segawa, H. Tashira, “Full-range tunable operation of a cw Ti:sapphire laser with a single set of extreme broad-band, low-loss mirrors,” in Digest of Advanced Solid-State Lasers (Optical Society of America, Washington D.C., 1995) paper ThB7.

Segawa, Y.

T. Izawa, M. Maeda, N. Yamamura, R. Uchimura, R. Ikeda, S. Kimura, T. Yakuoh, N. Sarukura, Z. Kiu, Y. Segawa, H. Tashira, “Full-range tunable operation of a cw Ti:sapphire laser with a single set of extreme broad-band, low-loss mirrors,” in Digest of Advanced Solid-State Lasers (Optical Society of America, Washington D.C., 1995) paper ThB7.

Shao, Z.

Z. Shao, “Refractive index for extraordinary waves in uniaxial crystals,” Phy. Rev. E 52, 1043–1046 (1995).
[Crossref]

Z. Shao, C. Yi, “Extraordinary rays’ behavior in uniaxial crystals,” Appl. Opt. 33, 1209–1212 (1994).
[Crossref] [PubMed]

Tashira, H.

T. Izawa, M. Maeda, N. Yamamura, R. Uchimura, R. Ikeda, S. Kimura, T. Yakuoh, N. Sarukura, Z. Kiu, Y. Segawa, H. Tashira, “Full-range tunable operation of a cw Ti:sapphire laser with a single set of extreme broad-band, low-loss mirrors,” in Digest of Advanced Solid-State Lasers (Optical Society of America, Washington D.C., 1995) paper ThB7.

Teschke, O.

G. Holtom, O. Teschke, “Design of a birefringent filter for high power dye laser,” IEEE J. Quantum Electron. QE-10, 577–579 (1974).
[Crossref]

Uchimura, R.

T. Izawa, M. Maeda, N. Yamamura, R. Uchimura, R. Ikeda, S. Kimura, T. Yakuoh, N. Sarukura, Z. Kiu, Y. Segawa, H. Tashira, “Full-range tunable operation of a cw Ti:sapphire laser with a single set of extreme broad-band, low-loss mirrors,” in Digest of Advanced Solid-State Lasers (Optical Society of America, Washington D.C., 1995) paper ThB7.

Vukosic, J. I.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1975), Chap. 14.4.3, p. 694, Chap. 14.2.1, p. 668.

Yakuoh, T.

T. Izawa, M. Maeda, N. Yamamura, R. Uchimura, R. Ikeda, S. Kimura, T. Yakuoh, N. Sarukura, Z. Kiu, Y. Segawa, H. Tashira, “Full-range tunable operation of a cw Ti:sapphire laser with a single set of extreme broad-band, low-loss mirrors,” in Digest of Advanced Solid-State Lasers (Optical Society of America, Washington D.C., 1995) paper ThB7.

Yamamura, N.

T. Izawa, M. Maeda, N. Yamamura, R. Uchimura, R. Ikeda, S. Kimura, T. Yakuoh, N. Sarukura, Z. Kiu, Y. Segawa, H. Tashira, “Full-range tunable operation of a cw Ti:sapphire laser with a single set of extreme broad-band, low-loss mirrors,” in Digest of Advanced Solid-State Lasers (Optical Society of America, Washington D.C., 1995) paper ThB7.

Yariv, A.

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), Chap. 5.4, p. 88.

Yi, C.

Zhu, S. D.

Appl. Opt. (4)

IEEE J. Quantum Electron. (1)

G. Holtom, O. Teschke, “Design of a birefringent filter for high power dye laser,” IEEE J. Quantum Electron. QE-10, 577–579 (1974).
[Crossref]

Phy. Rev. E (1)

Z. Shao, “Refractive index for extraordinary waves in uniaxial crystals,” Phy. Rev. E 52, 1043–1046 (1995).
[Crossref]

Other (3)

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1975), Chap. 14.4.3, p. 694, Chap. 14.2.1, p. 668.

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), Chap. 5.4, p. 88.

T. Izawa, M. Maeda, N. Yamamura, R. Uchimura, R. Ikeda, S. Kimura, T. Yakuoh, N. Sarukura, Z. Kiu, Y. Segawa, H. Tashira, “Full-range tunable operation of a cw Ti:sapphire laser with a single set of extreme broad-band, low-loss mirrors,” in Digest of Advanced Solid-State Lasers (Optical Society of America, Washington D.C., 1995) paper ThB7.

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 (2)

Fig. 1
Fig. 1

Diagram showing the exact construction of the optical path difference in a FAIS. OA′ is the optical axis inclined at an angle η to the entrance surface. OO′ and OW are the O- and the E-wave normals respectively. Φ denotes the tuning angle (for Φ = 0, the axis, the rays, and the wave normals are in the incidence plane). β w denotes the angle between the E-wave normal and the axis. Note that plane WDD′ is parallel to the incidence (YZ) plane.

Fig. 2
Fig. 2

Tuning characteristics of a FAIS with η = 10° and a FAPS. The center of the tuning wavelengths is assigned to 850 nm at Φ = 45°. The other parameters are the same as in Table 2. The curves with open symbols are for a FAIS: The curve with open circles corresponds to the ratio T/m = constant; that with squares is for m = 4 and T equal to the thickness of the third period; that with triangles is for m = 5 and T equal to the thickness of the fourth period. The curve with solid circles is for a FAPS with T/m = constant.

Tables (2)

Tables Icon

Table 1 Tuning Angle Φ at the 0.7–1-mm Wavelength and Tuning Sector ΔΦ for a 1-Period-Thick Quartz Filter, Eq. (6) a

Tables Icon

Table 2 E Wave Index n e w ) in Quartz versus the Axis Angle η and the Tuning Angle Φ, Eqs. (4) and (5) a

Equations (8)

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

δ = 2 π T [ n e n o ] sin 2 ( β w ) / [ λ sin ( θ ) ]
cos ( β w ) = cos ( Φ ) cos ( θ ) ,
Δ = n o O O [ n e ( β w ) O W + W D ] .
1 / n e 2 ( β w ) = cos 2 ( β w ) / n o 2 + sin 2 ( β w ) / n e 2 .
cos ( β w ) = sin ( r w ) cos ( Φ γ w ) cos ( η ) + cos ( r w ) sin ( η ) ,
δ = 2 π T F ( θ , Φ , η ) / λ ,
n o cos ( r o ) { n e ( β w ) cos ( r w ) + [ tan ( r o ) y w / z w ] sin ( θ ) } .
λ = ( T / m ) F ( θ , Φ , η ) ( m = 1 , 2 , 3 ) .

Metrics