Abstract

The self-mixing (autodyne) effect in single-mode CO2 lasers with pulse-periodic (PP) pumping of the active medium is theoretically analyzed and experimentally investigated. A semiempirical model of the autodyne effect in CO2 lasers of this type is developed that allows the laser beat signal to be described from the known shape of the generated pulses. The self-mixing effect in PP CO2 lasers is shown to be identical with that in continuous-wave CO2 lasers, except that the autodyne amplification during the laser pulse proves time-dependent. It is demonstrated that the amplitude-frequency characteristic of the autodyne amplification for PP CO2 lasers is also of resonance nature, but its bandwidth is broadened, as compared with that in the case of continuous laser pumping. As in the case of continuous pumping, the self-mixing effect in PP CO2 lasers can be used to detect and analyze backscattered signals, specifically for measuring the rates of destruction of materials by the 10 μm radiation and for monitoring this process.

© 2012 Optical Society of America

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References

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  1. G. Liu, S. Zhang, J. Zhu, and Y. Li, “Theoretical and experimental study of intensity branch phenomena in self-mixing interference in a He–Ne laser,” Opt. Commun. 221, 387–393 (2003).
    [CrossRef]
  2. G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A: Pure Appl. Opt. 4, S283–S294 (2002).
    [CrossRef]
  3. G. A. Koganov, R. Shuker, and E. P. Gordov, “Multimirror autodyne lidar for local detection of hostile gases,” Appl. Opt. 44, 3105–3109 (2005).
    [CrossRef]
  4. V. M. Gordienko, A. N. Konovalov, and V. A. Ul’yanov, “Self-heterodyne detection of backscattered radiation in single-mode CO2 laser” Quantum Electron. 41, 433–440(2011).
    [CrossRef]
  5. J. Ko, T. Ohtomo, K. Abe, and K. Otsuka, “Nonlinear dynamics and application of laser-diode-pumped microchip solid-state lasers with optical feedback,” Int. J. Mod. Phys. B 15, 3369–3395 (2001).
    [CrossRef]
  6. M. Laroche, C. Bartolacci, G. Lesueur, H. Gilles, and S. Girard, “Serrodyne optical frequency shifting for heterodyne self-mixing in a distributed-feedback fiber laser” Opt. Lett. 33, 2746–2748 (2008).
    [CrossRef]
  7. S. L. Pogorelsky, V. F. Lazukin, V. F. Maiboroda, and A. M. Barmashov, “Single-mode waveguide gas laser,” Proc. SPIE 5137, 311–316 (2003).
    [CrossRef]
  8. O. Peng, A. Jusenieni, J. Chen, L. O. Svaasand, T. Warloe, K. E. Giercksky, and J. Moan, “Lasers in medicine,” Rep. Prog. Phys. 71, 056701 (2008).
    [CrossRef]
  9. A. K. Dmitriev, V. N. Kortunov, and V. A. Ul’yanov, “Doppler diagnostics of laser-ablated biotissues,” Proc. SPIE 4397, 425–430 (2001).
    [CrossRef]

2011 (1)

V. M. Gordienko, A. N. Konovalov, and V. A. Ul’yanov, “Self-heterodyne detection of backscattered radiation in single-mode CO2 laser” Quantum Electron. 41, 433–440(2011).
[CrossRef]

2008 (2)

M. Laroche, C. Bartolacci, G. Lesueur, H. Gilles, and S. Girard, “Serrodyne optical frequency shifting for heterodyne self-mixing in a distributed-feedback fiber laser” Opt. Lett. 33, 2746–2748 (2008).
[CrossRef]

O. Peng, A. Jusenieni, J. Chen, L. O. Svaasand, T. Warloe, K. E. Giercksky, and J. Moan, “Lasers in medicine,” Rep. Prog. Phys. 71, 056701 (2008).
[CrossRef]

2005 (1)

2003 (2)

S. L. Pogorelsky, V. F. Lazukin, V. F. Maiboroda, and A. M. Barmashov, “Single-mode waveguide gas laser,” Proc. SPIE 5137, 311–316 (2003).
[CrossRef]

G. Liu, S. Zhang, J. Zhu, and Y. Li, “Theoretical and experimental study of intensity branch phenomena in self-mixing interference in a He–Ne laser,” Opt. Commun. 221, 387–393 (2003).
[CrossRef]

2002 (1)

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A: Pure Appl. Opt. 4, S283–S294 (2002).
[CrossRef]

2001 (2)

J. Ko, T. Ohtomo, K. Abe, and K. Otsuka, “Nonlinear dynamics and application of laser-diode-pumped microchip solid-state lasers with optical feedback,” Int. J. Mod. Phys. B 15, 3369–3395 (2001).
[CrossRef]

A. K. Dmitriev, V. N. Kortunov, and V. A. Ul’yanov, “Doppler diagnostics of laser-ablated biotissues,” Proc. SPIE 4397, 425–430 (2001).
[CrossRef]

Abe, K.

J. Ko, T. Ohtomo, K. Abe, and K. Otsuka, “Nonlinear dynamics and application of laser-diode-pumped microchip solid-state lasers with optical feedback,” Int. J. Mod. Phys. B 15, 3369–3395 (2001).
[CrossRef]

Barmashov, A. M.

S. L. Pogorelsky, V. F. Lazukin, V. F. Maiboroda, and A. M. Barmashov, “Single-mode waveguide gas laser,” Proc. SPIE 5137, 311–316 (2003).
[CrossRef]

Bartolacci, C.

Bosch, T.

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A: Pure Appl. Opt. 4, S283–S294 (2002).
[CrossRef]

Chen, J.

O. Peng, A. Jusenieni, J. Chen, L. O. Svaasand, T. Warloe, K. E. Giercksky, and J. Moan, “Lasers in medicine,” Rep. Prog. Phys. 71, 056701 (2008).
[CrossRef]

Dmitriev, A. K.

A. K. Dmitriev, V. N. Kortunov, and V. A. Ul’yanov, “Doppler diagnostics of laser-ablated biotissues,” Proc. SPIE 4397, 425–430 (2001).
[CrossRef]

Donati, S.

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A: Pure Appl. Opt. 4, S283–S294 (2002).
[CrossRef]

Giercksky, K. E.

O. Peng, A. Jusenieni, J. Chen, L. O. Svaasand, T. Warloe, K. E. Giercksky, and J. Moan, “Lasers in medicine,” Rep. Prog. Phys. 71, 056701 (2008).
[CrossRef]

Gilles, H.

Girard, S.

Giuliani, G.

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A: Pure Appl. Opt. 4, S283–S294 (2002).
[CrossRef]

Gordienko, V. M.

V. M. Gordienko, A. N. Konovalov, and V. A. Ul’yanov, “Self-heterodyne detection of backscattered radiation in single-mode CO2 laser” Quantum Electron. 41, 433–440(2011).
[CrossRef]

Gordov, E. P.

Jusenieni, A.

O. Peng, A. Jusenieni, J. Chen, L. O. Svaasand, T. Warloe, K. E. Giercksky, and J. Moan, “Lasers in medicine,” Rep. Prog. Phys. 71, 056701 (2008).
[CrossRef]

Ko, J.

J. Ko, T. Ohtomo, K. Abe, and K. Otsuka, “Nonlinear dynamics and application of laser-diode-pumped microchip solid-state lasers with optical feedback,” Int. J. Mod. Phys. B 15, 3369–3395 (2001).
[CrossRef]

Koganov, G. A.

Konovalov, A. N.

V. M. Gordienko, A. N. Konovalov, and V. A. Ul’yanov, “Self-heterodyne detection of backscattered radiation in single-mode CO2 laser” Quantum Electron. 41, 433–440(2011).
[CrossRef]

Kortunov, V. N.

A. K. Dmitriev, V. N. Kortunov, and V. A. Ul’yanov, “Doppler diagnostics of laser-ablated biotissues,” Proc. SPIE 4397, 425–430 (2001).
[CrossRef]

Laroche, M.

Lazukin, V. F.

S. L. Pogorelsky, V. F. Lazukin, V. F. Maiboroda, and A. M. Barmashov, “Single-mode waveguide gas laser,” Proc. SPIE 5137, 311–316 (2003).
[CrossRef]

Lesueur, G.

Li, Y.

G. Liu, S. Zhang, J. Zhu, and Y. Li, “Theoretical and experimental study of intensity branch phenomena in self-mixing interference in a He–Ne laser,” Opt. Commun. 221, 387–393 (2003).
[CrossRef]

Liu, G.

G. Liu, S. Zhang, J. Zhu, and Y. Li, “Theoretical and experimental study of intensity branch phenomena in self-mixing interference in a He–Ne laser,” Opt. Commun. 221, 387–393 (2003).
[CrossRef]

Maiboroda, V. F.

S. L. Pogorelsky, V. F. Lazukin, V. F. Maiboroda, and A. M. Barmashov, “Single-mode waveguide gas laser,” Proc. SPIE 5137, 311–316 (2003).
[CrossRef]

Moan, J.

O. Peng, A. Jusenieni, J. Chen, L. O. Svaasand, T. Warloe, K. E. Giercksky, and J. Moan, “Lasers in medicine,” Rep. Prog. Phys. 71, 056701 (2008).
[CrossRef]

Norgia, M.

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A: Pure Appl. Opt. 4, S283–S294 (2002).
[CrossRef]

Ohtomo, T.

J. Ko, T. Ohtomo, K. Abe, and K. Otsuka, “Nonlinear dynamics and application of laser-diode-pumped microchip solid-state lasers with optical feedback,” Int. J. Mod. Phys. B 15, 3369–3395 (2001).
[CrossRef]

Otsuka, K.

J. Ko, T. Ohtomo, K. Abe, and K. Otsuka, “Nonlinear dynamics and application of laser-diode-pumped microchip solid-state lasers with optical feedback,” Int. J. Mod. Phys. B 15, 3369–3395 (2001).
[CrossRef]

Peng, O.

O. Peng, A. Jusenieni, J. Chen, L. O. Svaasand, T. Warloe, K. E. Giercksky, and J. Moan, “Lasers in medicine,” Rep. Prog. Phys. 71, 056701 (2008).
[CrossRef]

Pogorelsky, S. L.

S. L. Pogorelsky, V. F. Lazukin, V. F. Maiboroda, and A. M. Barmashov, “Single-mode waveguide gas laser,” Proc. SPIE 5137, 311–316 (2003).
[CrossRef]

Shuker, R.

Svaasand, L. O.

O. Peng, A. Jusenieni, J. Chen, L. O. Svaasand, T. Warloe, K. E. Giercksky, and J. Moan, “Lasers in medicine,” Rep. Prog. Phys. 71, 056701 (2008).
[CrossRef]

Ul’yanov, V. A.

V. M. Gordienko, A. N. Konovalov, and V. A. Ul’yanov, “Self-heterodyne detection of backscattered radiation in single-mode CO2 laser” Quantum Electron. 41, 433–440(2011).
[CrossRef]

A. K. Dmitriev, V. N. Kortunov, and V. A. Ul’yanov, “Doppler diagnostics of laser-ablated biotissues,” Proc. SPIE 4397, 425–430 (2001).
[CrossRef]

Warloe, T.

O. Peng, A. Jusenieni, J. Chen, L. O. Svaasand, T. Warloe, K. E. Giercksky, and J. Moan, “Lasers in medicine,” Rep. Prog. Phys. 71, 056701 (2008).
[CrossRef]

Zhang, S.

G. Liu, S. Zhang, J. Zhu, and Y. Li, “Theoretical and experimental study of intensity branch phenomena in self-mixing interference in a He–Ne laser,” Opt. Commun. 221, 387–393 (2003).
[CrossRef]

Zhu, J.

G. Liu, S. Zhang, J. Zhu, and Y. Li, “Theoretical and experimental study of intensity branch phenomena in self-mixing interference in a He–Ne laser,” Opt. Commun. 221, 387–393 (2003).
[CrossRef]

Appl. Opt. (1)

Int. J. Mod. Phys. B (1)

J. Ko, T. Ohtomo, K. Abe, and K. Otsuka, “Nonlinear dynamics and application of laser-diode-pumped microchip solid-state lasers with optical feedback,” Int. J. Mod. Phys. B 15, 3369–3395 (2001).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A: Pure Appl. Opt. 4, S283–S294 (2002).
[CrossRef]

Opt. Commun. (1)

G. Liu, S. Zhang, J. Zhu, and Y. Li, “Theoretical and experimental study of intensity branch phenomena in self-mixing interference in a He–Ne laser,” Opt. Commun. 221, 387–393 (2003).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (2)

S. L. Pogorelsky, V. F. Lazukin, V. F. Maiboroda, and A. M. Barmashov, “Single-mode waveguide gas laser,” Proc. SPIE 5137, 311–316 (2003).
[CrossRef]

A. K. Dmitriev, V. N. Kortunov, and V. A. Ul’yanov, “Doppler diagnostics of laser-ablated biotissues,” Proc. SPIE 4397, 425–430 (2001).
[CrossRef]

Quantum Electron. (1)

V. M. Gordienko, A. N. Konovalov, and V. A. Ul’yanov, “Self-heterodyne detection of backscattered radiation in single-mode CO2 laser” Quantum Electron. 41, 433–440(2011).
[CrossRef]

Rep. Prog. Phys. (1)

O. Peng, A. Jusenieni, J. Chen, L. O. Svaasand, T. Warloe, K. E. Giercksky, and J. Moan, “Lasers in medicine,” Rep. Prog. Phys. 71, 056701 (2008).
[CrossRef]

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Figures (11)

Fig. 1.
Fig. 1.

Scheme of the setup for investigating self-mixing effect in a CO2 laser: 1, single-mode CO2 laser; 2, beam-splitting plate; 3 and 6, attenuators; 4, lens; 5, rotating disk; 7, non-cooled HgCdTe photodetector; 8, amplifier; 9, analog-to-digital converter; and 10, computer.

Fig. 2.
Fig. 2.

Generation pulse, obtained by solving the system of equations in Eq. (2) for the rectangular shape of the time dependence of pumping parameter C(τ) with amplitude C0=10; (γc=107c1, τout2=0.1; L¯0=0.45, γ¯II=0.0075 и γ¯l=0.5).

Fig. 3.
Fig. 3.

Pulses of laser generation at different average output power. 1, P=5W; 2, P=10W; 3, P=15W; 4, P=20W.

Fig. 4.
Fig. 4.

Generation laser pulse at an average output power of 10 W. Thin curve, experimentally measured pulse; thick curve, approximation.

Fig. 5.
Fig. 5.

Generation laser pulse at an average output power of 10 W [thin curve, experimentally measured pulse; thick curve, the solution of the system of equations in Eq. (2) in the absence of feedback (σ=0) and for γc=107c1, τout2=0.1, γ¯II=0.0075, l0=9.225, и γ¯l=0.5, C0=20.5, I0=0.075].

Fig. 6.
Fig. 6.

Autodyne signal obtained by numerical simulation of system of equations in Eq. (2) for σ(t)=τoutβ0exp(iωdt), where ωd=400кΓц, β0=104, τout2=0.1.

Fig. 7.
Fig. 7.

Autodyne signal with Doppler frequency shift of 400 kHz obtained upon scattering of radiation from a rotating disk (experiment).

Fig. 8.
Fig. 8.

Autodyne signal (thin curve) with Doppler frequency shift of 400 kHz obtained upon subtracting the shape of the laser pulse and amplitude (thick curve) of the autodyne signal calculated by (3).

Fig. 9.
Fig. 9.

Amplitude-frequency characteristic of autodyne detection for a cw single-mode CO2 laser at different output powers.

Fig. 10.
Fig. 10.

Amplitude-frequency characteristic of autodyne detection averaged over the pumping pulse period for a CO2 laser in PP pumping regime at different output powers (1P=5W; 2P=10W; 3P=15W; 4P=20W).

Fig. 11.
Fig. 11.

Amplitude-frequency characteristic of autodyne amplification for a CO2 laser at 10 W output power (□, experimental data for PP pumping regime; 1, continuous-wave pumping; 2, averaged over the pumping pulse period amplitude-frequency characteristic; and 3, amplitude-frequency characteristic averaged over the time window on the trailing edge of the laser pulse).

Tables (1)

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Table 1. Approximated Coefficients for Different Output Radiation Powersa

Equations (9)

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

dIdτ=2I(1p(τ)α(UL)),dUdτ=γ¯II(U0(τ)U)(UL)I,dLdτ=γ¯I(L0L)+γ¯IIU+(UL)I,
dIdτ=2I(lκReσ(τ)(ul)),dudτ=γ¯II(C(τ)u)(ul)I,dldτ=γ¯I(l0l)+γ¯IIu+(ul)I.
|i0|=2I0G(Ω)β2.
G(Ω)PautPget=τout2κ2|jΩ2I01F(Ω)I0F(Ω)γ¯III0jΩ|2,
I0=γ¯II(C0(1l0)1),u0=1C0+l0,l0=γ¯IIγ¯l+l0C0.
C(τ)=γ¯lγ¯lγ¯II(I0γ¯II+l0+1).
P(t)=a+b*exp(t/t1),
Gp(ω)0T0G(ω,t)dtT0.
Gp1(ω)tp+δtT0δtG(ω,t)dtT0tp2δt.

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