Abstract

We propose a new tunable linear laser oscillator–amplifier system that incorporates a Fizeau wedge with unequal mirrors as the coupler. Because of asymmetry in reflection and wedge focusing in unequal mirrors, our system acts as a highly efficient selector in the oscillator and practically eliminates reinjection of spontaneous emission in the amplifier. We studied the wedge action by developing a procedure for the calculation of reflected interference patterns at a distance from the wedge. Using this procedure we found the feedback factors for both the oscillator and the amplifier. Background emission levels of less than 1% of the peak intensity in the emitted line were experimentally obtained.

© 2001 Optical Society of America

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References

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  1. E. Stoykova, M. Nenchev, “Strong optical asymmetry of an interference wedge with unequal reflectivity mirrors and its use in unidirectional ring laser designs,” Opt. Lett. 19, 1925–1927 (1994).
    [CrossRef] [PubMed]
  2. E. Stoykova, M. Nenchev, “Reflection and transmission of unequal mirrors interference wedge,” Opt. Quantum Electron. 27, 155–167 (1996).
  3. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).
  4. Y. Meyer, “Fringe shape with an interferential wedge,” J. Opt. Soc. Am. 71, 1255–1261 (1981).
    [CrossRef]
  5. Y. Meyer, M. Nenchev, “Tuning of dye lasers with a reflecting Fizeau wedge,” Opt. Commun. 35, 115–119 (1980).
    [CrossRef]
  6. M. Gorris-Neveux, M. Nenchev, R. Barbe, J.-C. Keller, “A two-wavelength, passively self-injection locked, cw Ti3+:Al2O3 laser,” IEEE J. Quantum Electron. 31, 1263–1260 (1995).
    [CrossRef]
  7. M. Deneva, E. Stoykova, M. Nenchev, “A novel technique for a narrow-line selection and wideband tuning of Ti3+:Al2O3 and dye lasers,” Rev. Sci. Instrum. 67, 1705–1714 (1996).
    [CrossRef]
  8. M. Nenchev, E. Stoykova, “Interference wedge properties relevant to laser applications: transmission and reflection of the restricted light beams,” Opt. Quantum Electron. 25, 789–799 (1993).
    [CrossRef]
  9. C. Reiser, R. Lopert, “Laser wavemeter with solid Fizeau wedge interferometer,” Appl. Opt. 27, 3656–3660 (1988).
    [CrossRef] [PubMed]
  10. L. Nair, K. Dasgupta, “Amplified spontaneous emission in narrow-band pulsed dye laser oscillators: theory and experiment,” IEEE J. Quantum Electron. QE-21, 1782–1790 (1985).
    [CrossRef]
  11. O. Svelto, S. Taccheo, C. Svelto, “Analysis of amplified spontaneous emission: some corrections to the Linford formula,” Opt. Commun. 149, 277–282 (1998).
    [CrossRef]
  12. C. Ni, A. Kung, “Amplified spontaneous emission reduction by use of stimulated Brillouin scattering: 2-ns pulses from a Ti:Al2O3 amplifier chain,” Appl. Opt. 37, 530–535 (1998).
    [CrossRef]
  13. M. Nenchev, “Cavity configuration in a dye laser for dispersion on the two output beams,” Opt. Commun. 50, 36–40 (1980).
    [CrossRef]
  14. M. Schitz, U. Heitmann, A. Hese, “Development of a dual-wavelength dye-laser system for the UV and its application to simultaneous multi-element detector,” Appl. Phys. B 61, 339–343 (1995).
    [CrossRef]
  15. I. McIntyre, M. Dunn, “Dual wavelength dye laser incorporating distributed feedback,” Opt. Commun. 55, 28–32 (1985).
    [CrossRef]
  16. Z. Lei, Q. Liejian, Z. Guiyan, L. Fucheng, “High repetition tunable picosecond dye laser pumped by a copper bromide laser,” IEEE J. Quantum Electron. 27, 283–287 (1991).
    [CrossRef]

1998 (2)

O. Svelto, S. Taccheo, C. Svelto, “Analysis of amplified spontaneous emission: some corrections to the Linford formula,” Opt. Commun. 149, 277–282 (1998).
[CrossRef]

C. Ni, A. Kung, “Amplified spontaneous emission reduction by use of stimulated Brillouin scattering: 2-ns pulses from a Ti:Al2O3 amplifier chain,” Appl. Opt. 37, 530–535 (1998).
[CrossRef]

1996 (2)

E. Stoykova, M. Nenchev, “Reflection and transmission of unequal mirrors interference wedge,” Opt. Quantum Electron. 27, 155–167 (1996).

M. Deneva, E. Stoykova, M. Nenchev, “A novel technique for a narrow-line selection and wideband tuning of Ti3+:Al2O3 and dye lasers,” Rev. Sci. Instrum. 67, 1705–1714 (1996).
[CrossRef]

1995 (2)

M. Gorris-Neveux, M. Nenchev, R. Barbe, J.-C. Keller, “A two-wavelength, passively self-injection locked, cw Ti3+:Al2O3 laser,” IEEE J. Quantum Electron. 31, 1263–1260 (1995).
[CrossRef]

M. Schitz, U. Heitmann, A. Hese, “Development of a dual-wavelength dye-laser system for the UV and its application to simultaneous multi-element detector,” Appl. Phys. B 61, 339–343 (1995).
[CrossRef]

1994 (1)

1993 (1)

M. Nenchev, E. Stoykova, “Interference wedge properties relevant to laser applications: transmission and reflection of the restricted light beams,” Opt. Quantum Electron. 25, 789–799 (1993).
[CrossRef]

1991 (1)

Z. Lei, Q. Liejian, Z. Guiyan, L. Fucheng, “High repetition tunable picosecond dye laser pumped by a copper bromide laser,” IEEE J. Quantum Electron. 27, 283–287 (1991).
[CrossRef]

1988 (1)

1985 (2)

L. Nair, K. Dasgupta, “Amplified spontaneous emission in narrow-band pulsed dye laser oscillators: theory and experiment,” IEEE J. Quantum Electron. QE-21, 1782–1790 (1985).
[CrossRef]

I. McIntyre, M. Dunn, “Dual wavelength dye laser incorporating distributed feedback,” Opt. Commun. 55, 28–32 (1985).
[CrossRef]

1981 (1)

1980 (2)

Y. Meyer, M. Nenchev, “Tuning of dye lasers with a reflecting Fizeau wedge,” Opt. Commun. 35, 115–119 (1980).
[CrossRef]

M. Nenchev, “Cavity configuration in a dye laser for dispersion on the two output beams,” Opt. Commun. 50, 36–40 (1980).
[CrossRef]

Barbe, R.

M. Gorris-Neveux, M. Nenchev, R. Barbe, J.-C. Keller, “A two-wavelength, passively self-injection locked, cw Ti3+:Al2O3 laser,” IEEE J. Quantum Electron. 31, 1263–1260 (1995).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

Dasgupta, K.

L. Nair, K. Dasgupta, “Amplified spontaneous emission in narrow-band pulsed dye laser oscillators: theory and experiment,” IEEE J. Quantum Electron. QE-21, 1782–1790 (1985).
[CrossRef]

Deneva, M.

M. Deneva, E. Stoykova, M. Nenchev, “A novel technique for a narrow-line selection and wideband tuning of Ti3+:Al2O3 and dye lasers,” Rev. Sci. Instrum. 67, 1705–1714 (1996).
[CrossRef]

Dunn, M.

I. McIntyre, M. Dunn, “Dual wavelength dye laser incorporating distributed feedback,” Opt. Commun. 55, 28–32 (1985).
[CrossRef]

Fucheng, L.

Z. Lei, Q. Liejian, Z. Guiyan, L. Fucheng, “High repetition tunable picosecond dye laser pumped by a copper bromide laser,” IEEE J. Quantum Electron. 27, 283–287 (1991).
[CrossRef]

Gorris-Neveux, M.

M. Gorris-Neveux, M. Nenchev, R. Barbe, J.-C. Keller, “A two-wavelength, passively self-injection locked, cw Ti3+:Al2O3 laser,” IEEE J. Quantum Electron. 31, 1263–1260 (1995).
[CrossRef]

Guiyan, Z.

Z. Lei, Q. Liejian, Z. Guiyan, L. Fucheng, “High repetition tunable picosecond dye laser pumped by a copper bromide laser,” IEEE J. Quantum Electron. 27, 283–287 (1991).
[CrossRef]

Heitmann, U.

M. Schitz, U. Heitmann, A. Hese, “Development of a dual-wavelength dye-laser system for the UV and its application to simultaneous multi-element detector,” Appl. Phys. B 61, 339–343 (1995).
[CrossRef]

Hese, A.

M. Schitz, U. Heitmann, A. Hese, “Development of a dual-wavelength dye-laser system for the UV and its application to simultaneous multi-element detector,” Appl. Phys. B 61, 339–343 (1995).
[CrossRef]

Keller, J.-C.

M. Gorris-Neveux, M. Nenchev, R. Barbe, J.-C. Keller, “A two-wavelength, passively self-injection locked, cw Ti3+:Al2O3 laser,” IEEE J. Quantum Electron. 31, 1263–1260 (1995).
[CrossRef]

Kung, A.

Lei, Z.

Z. Lei, Q. Liejian, Z. Guiyan, L. Fucheng, “High repetition tunable picosecond dye laser pumped by a copper bromide laser,” IEEE J. Quantum Electron. 27, 283–287 (1991).
[CrossRef]

Liejian, Q.

Z. Lei, Q. Liejian, Z. Guiyan, L. Fucheng, “High repetition tunable picosecond dye laser pumped by a copper bromide laser,” IEEE J. Quantum Electron. 27, 283–287 (1991).
[CrossRef]

Lopert, R.

McIntyre, I.

I. McIntyre, M. Dunn, “Dual wavelength dye laser incorporating distributed feedback,” Opt. Commun. 55, 28–32 (1985).
[CrossRef]

Meyer, Y.

Y. Meyer, “Fringe shape with an interferential wedge,” J. Opt. Soc. Am. 71, 1255–1261 (1981).
[CrossRef]

Y. Meyer, M. Nenchev, “Tuning of dye lasers with a reflecting Fizeau wedge,” Opt. Commun. 35, 115–119 (1980).
[CrossRef]

Nair, L.

L. Nair, K. Dasgupta, “Amplified spontaneous emission in narrow-band pulsed dye laser oscillators: theory and experiment,” IEEE J. Quantum Electron. QE-21, 1782–1790 (1985).
[CrossRef]

Nenchev, M.

E. Stoykova, M. Nenchev, “Reflection and transmission of unequal mirrors interference wedge,” Opt. Quantum Electron. 27, 155–167 (1996).

M. Deneva, E. Stoykova, M. Nenchev, “A novel technique for a narrow-line selection and wideband tuning of Ti3+:Al2O3 and dye lasers,” Rev. Sci. Instrum. 67, 1705–1714 (1996).
[CrossRef]

M. Gorris-Neveux, M. Nenchev, R. Barbe, J.-C. Keller, “A two-wavelength, passively self-injection locked, cw Ti3+:Al2O3 laser,” IEEE J. Quantum Electron. 31, 1263–1260 (1995).
[CrossRef]

E. Stoykova, M. Nenchev, “Strong optical asymmetry of an interference wedge with unequal reflectivity mirrors and its use in unidirectional ring laser designs,” Opt. Lett. 19, 1925–1927 (1994).
[CrossRef] [PubMed]

M. Nenchev, E. Stoykova, “Interference wedge properties relevant to laser applications: transmission and reflection of the restricted light beams,” Opt. Quantum Electron. 25, 789–799 (1993).
[CrossRef]

Y. Meyer, M. Nenchev, “Tuning of dye lasers with a reflecting Fizeau wedge,” Opt. Commun. 35, 115–119 (1980).
[CrossRef]

M. Nenchev, “Cavity configuration in a dye laser for dispersion on the two output beams,” Opt. Commun. 50, 36–40 (1980).
[CrossRef]

Ni, C.

Reiser, C.

Schitz, M.

M. Schitz, U. Heitmann, A. Hese, “Development of a dual-wavelength dye-laser system for the UV and its application to simultaneous multi-element detector,” Appl. Phys. B 61, 339–343 (1995).
[CrossRef]

Stoykova, E.

E. Stoykova, M. Nenchev, “Reflection and transmission of unequal mirrors interference wedge,” Opt. Quantum Electron. 27, 155–167 (1996).

M. Deneva, E. Stoykova, M. Nenchev, “A novel technique for a narrow-line selection and wideband tuning of Ti3+:Al2O3 and dye lasers,” Rev. Sci. Instrum. 67, 1705–1714 (1996).
[CrossRef]

E. Stoykova, M. Nenchev, “Strong optical asymmetry of an interference wedge with unequal reflectivity mirrors and its use in unidirectional ring laser designs,” Opt. Lett. 19, 1925–1927 (1994).
[CrossRef] [PubMed]

M. Nenchev, E. Stoykova, “Interference wedge properties relevant to laser applications: transmission and reflection of the restricted light beams,” Opt. Quantum Electron. 25, 789–799 (1993).
[CrossRef]

Svelto, C.

O. Svelto, S. Taccheo, C. Svelto, “Analysis of amplified spontaneous emission: some corrections to the Linford formula,” Opt. Commun. 149, 277–282 (1998).
[CrossRef]

Svelto, O.

O. Svelto, S. Taccheo, C. Svelto, “Analysis of amplified spontaneous emission: some corrections to the Linford formula,” Opt. Commun. 149, 277–282 (1998).
[CrossRef]

Taccheo, S.

O. Svelto, S. Taccheo, C. Svelto, “Analysis of amplified spontaneous emission: some corrections to the Linford formula,” Opt. Commun. 149, 277–282 (1998).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

Appl. Opt. (2)

Appl. Phys. B (1)

M. Schitz, U. Heitmann, A. Hese, “Development of a dual-wavelength dye-laser system for the UV and its application to simultaneous multi-element detector,” Appl. Phys. B 61, 339–343 (1995).
[CrossRef]

IEEE J. Quantum Electron. (3)

Z. Lei, Q. Liejian, Z. Guiyan, L. Fucheng, “High repetition tunable picosecond dye laser pumped by a copper bromide laser,” IEEE J. Quantum Electron. 27, 283–287 (1991).
[CrossRef]

L. Nair, K. Dasgupta, “Amplified spontaneous emission in narrow-band pulsed dye laser oscillators: theory and experiment,” IEEE J. Quantum Electron. QE-21, 1782–1790 (1985).
[CrossRef]

M. Gorris-Neveux, M. Nenchev, R. Barbe, J.-C. Keller, “A two-wavelength, passively self-injection locked, cw Ti3+:Al2O3 laser,” IEEE J. Quantum Electron. 31, 1263–1260 (1995).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (4)

Y. Meyer, M. Nenchev, “Tuning of dye lasers with a reflecting Fizeau wedge,” Opt. Commun. 35, 115–119 (1980).
[CrossRef]

O. Svelto, S. Taccheo, C. Svelto, “Analysis of amplified spontaneous emission: some corrections to the Linford formula,” Opt. Commun. 149, 277–282 (1998).
[CrossRef]

I. McIntyre, M. Dunn, “Dual wavelength dye laser incorporating distributed feedback,” Opt. Commun. 55, 28–32 (1985).
[CrossRef]

M. Nenchev, “Cavity configuration in a dye laser for dispersion on the two output beams,” Opt. Commun. 50, 36–40 (1980).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (2)

E. Stoykova, M. Nenchev, “Reflection and transmission of unequal mirrors interference wedge,” Opt. Quantum Electron. 27, 155–167 (1996).

M. Nenchev, E. Stoykova, “Interference wedge properties relevant to laser applications: transmission and reflection of the restricted light beams,” Opt. Quantum Electron. 25, 789–799 (1993).
[CrossRef]

Rev. Sci. Instrum. (1)

M. Deneva, E. Stoykova, M. Nenchev, “A novel technique for a narrow-line selection and wideband tuning of Ti3+:Al2O3 and dye lasers,” Rev. Sci. Instrum. 67, 1705–1714 (1996).
[CrossRef]

Other (1)

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

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Figures (19)

Fig. 1
Fig. 1

Ray tracing for reflection from an interference wedge at negative incidence.

Fig. 2
Fig. 2

Distance between the focal plane and the UMIW versus the refractive index n w at α W = 5 × 10-5 rad (solid curves) and α W = 3 × 10-5 rad (dashed curves). The numbers at right give the ratio between the angle of inclination β of the focal plane and the angle of incidence θ0 (thick solid curve). Note that in practice the ratio β/θ0 does not depend on the wedge thickness and apex angle.

Fig. 3
Fig. 3

Calculation of phase differences of rays that interfere at point P(x′, z) for the negative incidence of a beam with arbitrary amplitude distribution f(x) and uniform phase distribution.

Fig. 4
Fig. 4

Resonant reflection at the lower-reflectivity side of a 200-µm air-gap UMIW with R 1 = 0.9, R 2 = 0.99, α W = 3 × 10-5 rad and a Gaussian beam falling at θ0 = 30 arc min.

Fig. 5
Fig. 5

Normalized intensity distribution and phase distribution in a plane parallel to the wedge surface: (a), (b) on the wedge (z = 0 cm), (c), (d) in the focal plane (z = 8.67 cm), (e), (f) behind the focal plane (z = 12 cm) for a 50-µm air-gap UMIW with R 1 = 0.86, R 2= 0.99, α W = 5 × 10-5 rad, and a Gaussian beam with FWHM of 200 µm falling at θ0 = -5°. Thick curve, resonant reflection; thin curve, off-resonant reflection.

Fig. 6
Fig. 6

Computed spatial displacement between the peak intensities in the off-resonant and resonant reflected beams as a function of distance z for a 20-µm UMIW (△, ○, □) and a 50-µm UMIW (▲, ⛏, ■) for a Gaussian beam with a different FWHM falling at θ0 = -5°.

Fig. 7
Fig. 7

Computed angular displacement θ0- θ R between the angle of incidence θ0 = -5° and angle of reflection θ R for resonant and off-resonant Gaussian beams with a FWHM of 200 µm reflected from a 50-µm air-gap UMIW with R 1 = 0.86, R 2= 0.99, and α W = 5 × 10-5 rad. Solid curve, z = 0 cm; dashed curve, z = 12 cm.

Fig. 8
Fig. 8

Setup of a tunable linear oscillator–amplifier system with an UMIW tilted by a few milliradians to the resonator axis.

Fig. 9
Fig. 9

Schematic of the resonant reflection.

Fig. 10
Fig. 10

Computed spectral dependence of the feedback factor η(θ0) for a 20-µm air-gap wedge with α W = 3 × 10-5 rad, R 1 = 0.92 and R 2 = 0.99, a 500-µm diaphragm positioned at z = 4 cm from the UMIW and a Gaussian incident beam with a FWHM of 200 µm: top, θ0 = 0 mrad; middle, θ0 = 1.5 mrad; bottom, θ0 = 3 mrad.

Fig. 11
Fig. 11

Peak value of the feedback factor η(θ0) and FWHM of the wedge transmission curve: ⛏, a function of wedge thickness at θ0 = 3 mrad for R 1 = 0.92 and R 2 = 0.99 with 1% background emission at off-resonant wavelengths: ■, z = 6 cm, D 1 = 550 µm; □, z = 5 cm, D 1 = 500 µm; □, z = 3 cm, D 1 = 400 µm.

Fig. 12
Fig. 12

Wedge transmission curves at different thicknesses for θ0 = 3 mrad, R 1 = 0.92, R 2 = 0.99, and α W = 3 × 10-5 rad.

Fig. 13
Fig. 13

Feedback factor for spontaneous emission in the amplifier as a function of distance between diaphragm D 2 and the UMIW: ▲, θ0 = 0 mrad, z 1 = z 2; ◆, θ0 = 3 mrad, z 1 = z 2.

Fig. 14
Fig. 14

Focal distance as a function of angle of incidence for a 20-µm air-gap wedge with α W = 2 × 10-5 rad. (b) Focal distance as a function of wedge thickness at α W = 4 × 10-5 rad, θ0 = 5°, and n w = 1.

Fig. 15
Fig. 15

Emission spectra of the oscillator in Fig. 8 at different angles of rotation of the UMIW with respect to the resonator axis: top, θ0 = 3 mrad; middle, θ0 = 1.5 mrad; bottom, θ0 = 0 mrad. The two Hg lines (577 and 579 nm) in the bottom spectrogram are given as reference lines. The output of the oscillator is taken from mirror M.

Fig. 16
Fig. 16

Spectrogram of the output emission of the oscillator–amplifier system with grazing incidence grating as a selector obtained at a magnification of 10 of the registration system (the full scale of the spectrogram corresponds to 10% of the peak intensity of the line given in the inset).

Fig. 17
Fig. 17

Emission spectrogram of the oscillator in Fig. 8 at a factor of 100 increased sensitivity of the OMA. The output of the oscillator was taken from the UMIW.

Fig. 18
Fig. 18

Spectrograms of the output emission of the oscillator–amplifier system with a 20-µm UMIW as the coupler. The bottom spectrogram is obtained at a magnification of 100 compared with the top spectrogram (the full scale of the bottom spectrogram corresponds to 1% of the peak intensity in the selected line).

Fig. 19
Fig. 19

Spectrogram of the output emission of the oscillator–amplifier system with a 200-µm UMIW as the coupler obtained at a magnification of 100 (the full scale of the spectrogram corresponds to 1% of the peak intensity in the selected line). The regular sequence of spikes on the spectrogram is due to transmission resonances of the 200-µm wedge.

Equations (18)

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

F0p=e1-ep+1tan αWtan θ0-tan θp,  p=1, 2, 3
ep=ep-11-tan αW tan δp1+tan αW tan δp-1=ep-1Lp, p=1, 2, 3.
Fpqx=ep+1x-eq+1xαWtan θp-tan θq=ep+1x-eq+1xΩpq,
F0px=e1x-ep+1xΩ0p=e1x1-i=2p LiΩ0p=e1-x tan αW1-i=2p LiΩ0p.
F0pxF0p=1-x tan αwe1,  p=1, 2, 3.
z tan θ0xz tan θ0+e1-h1tan αw.
z tan θp+e1-eptan αwxz tan θp+e1-hptan αw.
x02=e1tan αw1-ex2e2
s0=x1 sin θ0+zcos θ0.
s1=x02 sin θ0+e1-x2 tan αw1-tan αw tanδ1-2αw×1cos δ1+1cosδ1-2αw+zcosθ0-2αw.
s2=x03 sin θ0+ex31-tan αW tan δ31cos δ2+1cos δ3+ex3/L31-tan αw tan δ21cos δ1+1cos δ2+zcosθ0-4αw,
sp=x0p sin θ0+zcos θp+expk=1p-1ek+1ep×1cos δk+1cos δk+111-tan αw tan δk+1=x0p sin θ0+zcos θp+expFp,
x0p=e1αw1-e1ep+e1ep xp,exp=e1-xp tan αw, xp=x-z tan θp.
φp=2πλx0p sin θ0+zcos θp+nWexpFp+2p-3π.
Ax, z=R1 fx1expiφ1-1-R1R1×p=mn fx0pρp-1 expiφp,
Ix, z=R1f2x1-21-R1fx1Vmn+1-R12R1Vmn2+Umn2,
Vmn=p=mn fx0pρp-1 cosφp-φ1,Umn=p=mn fx0pρp-1 sinφp-φ1.
ηθ=-D/2D/2 IRx, z, θ0dx-D/2D/2 I0x, 0, θ0dx

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