Abstract

Two alternative methods for determining phase distortions of radiation in the heated active element of a high-power Nd:glass laser are compared: direct phase measurement with the Mach–Zehnder interferometer and phase front reconstruction from measured distributions of depolarization factor. It is shown that the latter method can quite quickly and accurately determine the wavefront distortions of laser radiation with minimal interference to the optical scheme of the laser.

© 2012 Optical Society of America

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References

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  1. A. A. Kuzmin, A. G. Luchinin, A. K. Poteomkin, A. A. Soloviev, E. A. Khazanov, and A. A. Shaikin, “Thermally induced distortions in neodymium glass rod amplifiers,” Quantum Electron. 39, 895–900 (2009).
    [CrossRef]
  2. A. A. Kuzmin, E. A. Khazanov, and A. A. Shaykin, “Large-aperture Nd:glass laser amplifiers with high pulse repetition rate,” Opt. Express 19, 14223–14232 (2011).
    [CrossRef]
  3. A. A. Kuzmin, E. A. Khazanov, and A. A. Shaykin, “Repetitively pulsed regimes of Nd:glass large-aperture laser amplifiers,” Quantum Electron. 42, 283–291 (2012).
  4. L. I. Avakyants, I. M. Buzhinskiĭ, E. I. Koryagina, and V. F. Surkova, “Characteristics of laser glasses (review),” Quantum Electron. 8, 423–434 (1978).
    [CrossRef]
  5. G. S. Gorelik, “On application of the modulation method to optical interferometry,” Dokl. Akad. Nauk SSSR 83, 549–552 (1952).
  6. K. Creath, “Phase-measurement interferometry techniques,” Prog. Opt. 26, 349–393 (1989).
    [CrossRef]
  7. O. Sasaki and H. Okazaki, “Sinusoidal phase modulating interferometry for surface profile measurements,” Appl. Opt. 25, 3137–3140 (1986).
    [CrossRef]
  8. I. E. Kozhevatov, E. Kh. Kulikova, and N. P. Cheragin, “Phase modulation methods for control and stabilization of Fabry–Perot interferometers,” Opt. Spectrosc. 80, 914–919 (1996).
  9. A. V. Mezenov, L. N. Soms, and A. I. Stepanov, Termooptika Tverdotelnykh Laserov [Thermooptics of Solid-State Lasers] (Mashinostroenie, 1986).
  10. V. V. Blazhko, M. M. Bubnov, E. M. Dianov, and A. V. Chikolini, “Determination of the temperature dependence of the linear expansion coefficient and of the temperature coefficient of the refractive index of laser glasses,” Quantum Electron. 6, 624–625 (1976).
    [CrossRef]

2012 (1)

A. A. Kuzmin, E. A. Khazanov, and A. A. Shaykin, “Repetitively pulsed regimes of Nd:glass large-aperture laser amplifiers,” Quantum Electron. 42, 283–291 (2012).

2011 (1)

2009 (1)

A. A. Kuzmin, A. G. Luchinin, A. K. Poteomkin, A. A. Soloviev, E. A. Khazanov, and A. A. Shaikin, “Thermally induced distortions in neodymium glass rod amplifiers,” Quantum Electron. 39, 895–900 (2009).
[CrossRef]

1996 (1)

I. E. Kozhevatov, E. Kh. Kulikova, and N. P. Cheragin, “Phase modulation methods for control and stabilization of Fabry–Perot interferometers,” Opt. Spectrosc. 80, 914–919 (1996).

1989 (1)

K. Creath, “Phase-measurement interferometry techniques,” Prog. Opt. 26, 349–393 (1989).
[CrossRef]

1986 (1)

1978 (1)

L. I. Avakyants, I. M. Buzhinskiĭ, E. I. Koryagina, and V. F. Surkova, “Characteristics of laser glasses (review),” Quantum Electron. 8, 423–434 (1978).
[CrossRef]

1976 (1)

V. V. Blazhko, M. M. Bubnov, E. M. Dianov, and A. V. Chikolini, “Determination of the temperature dependence of the linear expansion coefficient and of the temperature coefficient of the refractive index of laser glasses,” Quantum Electron. 6, 624–625 (1976).
[CrossRef]

1952 (1)

G. S. Gorelik, “On application of the modulation method to optical interferometry,” Dokl. Akad. Nauk SSSR 83, 549–552 (1952).

Avakyants, L. I.

L. I. Avakyants, I. M. Buzhinskiĭ, E. I. Koryagina, and V. F. Surkova, “Characteristics of laser glasses (review),” Quantum Electron. 8, 423–434 (1978).
[CrossRef]

Blazhko, V. V.

V. V. Blazhko, M. M. Bubnov, E. M. Dianov, and A. V. Chikolini, “Determination of the temperature dependence of the linear expansion coefficient and of the temperature coefficient of the refractive index of laser glasses,” Quantum Electron. 6, 624–625 (1976).
[CrossRef]

Bubnov, M. M.

V. V. Blazhko, M. M. Bubnov, E. M. Dianov, and A. V. Chikolini, “Determination of the temperature dependence of the linear expansion coefficient and of the temperature coefficient of the refractive index of laser glasses,” Quantum Electron. 6, 624–625 (1976).
[CrossRef]

Buzhinskii, I. M.

L. I. Avakyants, I. M. Buzhinskiĭ, E. I. Koryagina, and V. F. Surkova, “Characteristics of laser glasses (review),” Quantum Electron. 8, 423–434 (1978).
[CrossRef]

Cheragin, N. P.

I. E. Kozhevatov, E. Kh. Kulikova, and N. P. Cheragin, “Phase modulation methods for control and stabilization of Fabry–Perot interferometers,” Opt. Spectrosc. 80, 914–919 (1996).

Chikolini, A. V.

V. V. Blazhko, M. M. Bubnov, E. M. Dianov, and A. V. Chikolini, “Determination of the temperature dependence of the linear expansion coefficient and of the temperature coefficient of the refractive index of laser glasses,” Quantum Electron. 6, 624–625 (1976).
[CrossRef]

Creath, K.

K. Creath, “Phase-measurement interferometry techniques,” Prog. Opt. 26, 349–393 (1989).
[CrossRef]

Dianov, E. M.

V. V. Blazhko, M. M. Bubnov, E. M. Dianov, and A. V. Chikolini, “Determination of the temperature dependence of the linear expansion coefficient and of the temperature coefficient of the refractive index of laser glasses,” Quantum Electron. 6, 624–625 (1976).
[CrossRef]

Gorelik, G. S.

G. S. Gorelik, “On application of the modulation method to optical interferometry,” Dokl. Akad. Nauk SSSR 83, 549–552 (1952).

Khazanov, E. A.

A. A. Kuzmin, E. A. Khazanov, and A. A. Shaykin, “Repetitively pulsed regimes of Nd:glass large-aperture laser amplifiers,” Quantum Electron. 42, 283–291 (2012).

A. A. Kuzmin, E. A. Khazanov, and A. A. Shaykin, “Large-aperture Nd:glass laser amplifiers with high pulse repetition rate,” Opt. Express 19, 14223–14232 (2011).
[CrossRef]

A. A. Kuzmin, A. G. Luchinin, A. K. Poteomkin, A. A. Soloviev, E. A. Khazanov, and A. A. Shaikin, “Thermally induced distortions in neodymium glass rod amplifiers,” Quantum Electron. 39, 895–900 (2009).
[CrossRef]

Koryagina, E. I.

L. I. Avakyants, I. M. Buzhinskiĭ, E. I. Koryagina, and V. F. Surkova, “Characteristics of laser glasses (review),” Quantum Electron. 8, 423–434 (1978).
[CrossRef]

Kozhevatov, I. E.

I. E. Kozhevatov, E. Kh. Kulikova, and N. P. Cheragin, “Phase modulation methods for control and stabilization of Fabry–Perot interferometers,” Opt. Spectrosc. 80, 914–919 (1996).

Kulikova, E. Kh.

I. E. Kozhevatov, E. Kh. Kulikova, and N. P. Cheragin, “Phase modulation methods for control and stabilization of Fabry–Perot interferometers,” Opt. Spectrosc. 80, 914–919 (1996).

Kuzmin, A. A.

A. A. Kuzmin, E. A. Khazanov, and A. A. Shaykin, “Repetitively pulsed regimes of Nd:glass large-aperture laser amplifiers,” Quantum Electron. 42, 283–291 (2012).

A. A. Kuzmin, E. A. Khazanov, and A. A. Shaykin, “Large-aperture Nd:glass laser amplifiers with high pulse repetition rate,” Opt. Express 19, 14223–14232 (2011).
[CrossRef]

A. A. Kuzmin, A. G. Luchinin, A. K. Poteomkin, A. A. Soloviev, E. A. Khazanov, and A. A. Shaikin, “Thermally induced distortions in neodymium glass rod amplifiers,” Quantum Electron. 39, 895–900 (2009).
[CrossRef]

Luchinin, A. G.

A. A. Kuzmin, A. G. Luchinin, A. K. Poteomkin, A. A. Soloviev, E. A. Khazanov, and A. A. Shaikin, “Thermally induced distortions in neodymium glass rod amplifiers,” Quantum Electron. 39, 895–900 (2009).
[CrossRef]

Mezenov, A. V.

A. V. Mezenov, L. N. Soms, and A. I. Stepanov, Termooptika Tverdotelnykh Laserov [Thermooptics of Solid-State Lasers] (Mashinostroenie, 1986).

Okazaki, H.

Poteomkin, A. K.

A. A. Kuzmin, A. G. Luchinin, A. K. Poteomkin, A. A. Soloviev, E. A. Khazanov, and A. A. Shaikin, “Thermally induced distortions in neodymium glass rod amplifiers,” Quantum Electron. 39, 895–900 (2009).
[CrossRef]

Sasaki, O.

Shaikin, A. A.

A. A. Kuzmin, A. G. Luchinin, A. K. Poteomkin, A. A. Soloviev, E. A. Khazanov, and A. A. Shaikin, “Thermally induced distortions in neodymium glass rod amplifiers,” Quantum Electron. 39, 895–900 (2009).
[CrossRef]

Shaykin, A. A.

A. A. Kuzmin, E. A. Khazanov, and A. A. Shaykin, “Repetitively pulsed regimes of Nd:glass large-aperture laser amplifiers,” Quantum Electron. 42, 283–291 (2012).

A. A. Kuzmin, E. A. Khazanov, and A. A. Shaykin, “Large-aperture Nd:glass laser amplifiers with high pulse repetition rate,” Opt. Express 19, 14223–14232 (2011).
[CrossRef]

Soloviev, A. A.

A. A. Kuzmin, A. G. Luchinin, A. K. Poteomkin, A. A. Soloviev, E. A. Khazanov, and A. A. Shaikin, “Thermally induced distortions in neodymium glass rod amplifiers,” Quantum Electron. 39, 895–900 (2009).
[CrossRef]

Soms, L. N.

A. V. Mezenov, L. N. Soms, and A. I. Stepanov, Termooptika Tverdotelnykh Laserov [Thermooptics of Solid-State Lasers] (Mashinostroenie, 1986).

Stepanov, A. I.

A. V. Mezenov, L. N. Soms, and A. I. Stepanov, Termooptika Tverdotelnykh Laserov [Thermooptics of Solid-State Lasers] (Mashinostroenie, 1986).

Surkova, V. F.

L. I. Avakyants, I. M. Buzhinskiĭ, E. I. Koryagina, and V. F. Surkova, “Characteristics of laser glasses (review),” Quantum Electron. 8, 423–434 (1978).
[CrossRef]

Appl. Opt. (1)

Dokl. Akad. Nauk SSSR (1)

G. S. Gorelik, “On application of the modulation method to optical interferometry,” Dokl. Akad. Nauk SSSR 83, 549–552 (1952).

Opt. Express (1)

Opt. Spectrosc. (1)

I. E. Kozhevatov, E. Kh. Kulikova, and N. P. Cheragin, “Phase modulation methods for control and stabilization of Fabry–Perot interferometers,” Opt. Spectrosc. 80, 914–919 (1996).

Prog. Opt. (1)

K. Creath, “Phase-measurement interferometry techniques,” Prog. Opt. 26, 349–393 (1989).
[CrossRef]

Quantum Electron. (4)

A. A. Kuzmin, E. A. Khazanov, and A. A. Shaykin, “Repetitively pulsed regimes of Nd:glass large-aperture laser amplifiers,” Quantum Electron. 42, 283–291 (2012).

L. I. Avakyants, I. M. Buzhinskiĭ, E. I. Koryagina, and V. F. Surkova, “Characteristics of laser glasses (review),” Quantum Electron. 8, 423–434 (1978).
[CrossRef]

A. A. Kuzmin, A. G. Luchinin, A. K. Poteomkin, A. A. Soloviev, E. A. Khazanov, and A. A. Shaikin, “Thermally induced distortions in neodymium glass rod amplifiers,” Quantum Electron. 39, 895–900 (2009).
[CrossRef]

V. V. Blazhko, M. M. Bubnov, E. M. Dianov, and A. V. Chikolini, “Determination of the temperature dependence of the linear expansion coefficient and of the temperature coefficient of the refractive index of laser glasses,” Quantum Electron. 6, 624–625 (1976).
[CrossRef]

Other (1)

A. V. Mezenov, L. N. Soms, and A. I. Stepanov, Termooptika Tverdotelnykh Laserov [Thermooptics of Solid-State Lasers] (Mashinostroenie, 1986).

Supplementary Material (4)

» Media 1: AVI (3975 KB)     
» Media 2: AVI (3500 KB)     
» Media 3: AVI (3501 KB)     
» Media 4: AVI (3337 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of the setup for measurement of depolarization in a laser amplifier. A, amplifier; L, objective.

Fig. 2.
Fig. 2.

Schematic of the setup for measurement of thermally induced lens in a laser amplifier.

Fig. 3.
Fig. 3.

Theoretical and experimental distributions of depolarization in an active element 4.5 cm in diameter (a) after the first pump pulse and (b) in the steady-state mode. (Media 1)

Fig. 4.
Fig. 4.

Dynamics of the integral depolarization in an active element 4.5 cm in diameter in a sequence of pump pulses with a repetition rate of one shot per 3 min. The star designates the last pump pulse in the pulse sequence.

Fig. 5.
Fig. 5.

Distributions of thermally induced phase incursions of (a) radially (Media 2) and (b) tangentially (Media 3) polarized eigenwaves over the aperture of the active element and (c) corresponding radial distributions averaged over azimuthal angle (Media 4); t is the time passed from the moment of the corresponding pump pulse (hours:minutes:seconds).

Tables (1)

Tables Icon

Table 1. Characteristics of the Studied Active Element

Equations (7)

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Ij(r,ϕ)=Aj(r,ϕ)cosϑj(r,ϕ)+Cj(r,ϕ),j=x,y,
Δψr(r,ϕ)=λ0λargAxhot(r,ϕ)cosϕexp[iϑxhot(r,ϕ)]+Axhot(r,ϕ)sinϕexp[iϑxhot(r,ϕ)]Axcold(r,ϕ)cosϕexp[iϑxcold(r,ϕ)]+Axcold(r,ϕ)sinϕexp[iϑxcold(r,ϕ)],
Δψϕ(r,ϕ)=λ0λargAyhot(r,ϕ)cosϕexp[iϑyhot(r,ϕ)]Axhot(r,ϕ)sinϕexp[iϑxhot(r,ϕ)]Aycold(r,ϕ)cosϕexp[iϑycold(r,ϕ)]Axcold(r,ϕ)sinϕexp[iϑxcold(r,ϕ)],
|ϑj|<πN/R,j=x,y,
|Δψr,ϕ|<πλ0N/(λR).
Γ=sin2(2ϕ)sin2(δ(r)/2),
|Δψr,ϕ|<πN/(2R).

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