Abstract

The interference effects caused by the Fresnel reflections of a Gaussian beam on the boundaries of a dielectric plate, which can be considered as a Fabry-Perot etalon, were theoretically and experimentally investigated. In addition to the incident angle and the polarization of the incident light, two additional parameters—the plate’s parallelism and the temperature—which are often neglected, were analyzed. Based on the theoretical predictions and the measured behavior of the transmittance of the dielectric plate a new, temperature-controlled variable high-power-laser attenuator is proposed. Unwanted changes in the plate’s transmittance caused by the absorption of laser pulses within the plate are also presented. These phenomena are important in many applications where dielectric plates are used for a variety of purposes.

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References

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  1. R. O. Rice and J. D. Macomber, “Attenuation of giant laser pulses by absorbing filters,” Appl. Opt. 14(9), 2203–2206 (1975).
    [CrossRef] [PubMed]
  2. R. M. A. Azzam, “Tilted parallel dielectric slab as a multilevel attenuator for incident p- or s-polarized light,” Appl. Opt. 48(2), 425–428 (2009).
    [CrossRef] [PubMed]
  3. Y. H. Wu, Y. H. Lin, Y. Q. Lu, H. W. Ren, Y. H. Fan, J. R. Wu, and S. T. Wu, “Submillisecond response variable optical attenuator based on sheared polymer network liquid crystal,” Opt. Express 12(25), 6382–6389 (2004).
    [CrossRef] [PubMed]
  4. H. Lotem, A. Eyal, and A. R. Shuker, “Variable attenuator for intense unpolarized laser beams,” Opt. Lett. 16(9), 690–692 (1991).
    [CrossRef] [PubMed]
  5. D. Gauden, D. Mechin, C. Vaudry, P. Yvernault, and D. Pureur, “Variable optical attenuator based on thermally tuned Mach-Zehnder interferometer within a twin core fiber,” Opt. Commun. 231(1-6), 213–216 (2004).
    [CrossRef]
  6. K. Bennett and R. L. Byer, “Computer-controllable wedged-plate optical-variable attenuator,” Appl. Opt. 19(14), 2408–2412 (1980).
    [CrossRef] [PubMed]
  7. J. Staromlynska, R. A. Clay, and K. F. Dexter, “Variable optical attenuator for use in the visible spectrum,” Appl. Opt. 26(18), 3827–3830 (1987).
    [CrossRef] [PubMed]
  8. J. H. Lehman, D. Livigni, X. Y. Li, C. L. Cromer, and M. L. Dowell, “Reflective attenuator for high-energy laser measurements,” Appl. Opt. 47(18), 3360–3363 (2008).
    [CrossRef] [PubMed]
  9. M. J. Mughal and N. A. Riza, “Compact acoustooptic high-speed variable attenuator for high-power applications,” IEEE Photon. Technol. Lett. 14(4), 510–512 (2002).
    [CrossRef]
  10. H. B. Yu, G. Y. Zhou, C. F. Siong, and L. Feiwen, “A variable optical attenuator based on optofluidic technology,” J. Micromech. Microeng. 18(11), 115016 (2008).
    [CrossRef]
  11. J. C. Cotteverte, F. Bretenaker, and A. Lefloch, “Jones matrices of a tilted plate for Gaussian beams,” Appl. Opt. 30(3), 305–311 (1991).
    [CrossRef] [PubMed]
  12. H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt. 5(10), 1550–1567 (1966).
    [CrossRef] [PubMed]
  13. S. Nemoto, “Waist shift of a Gaussian-beam by a dielectric plate,” Appl. Opt. 28(9), 1643–1647 (1989).
    [CrossRef] [PubMed]
  14. E. Hecht, Optics (2nd Edition, Addison Wesley, 1987), pp. 100.
    [PubMed]
  15. H. Abu-Safia, R. Al-Tahtamouni, I. Abu-Aljarayesh, and N. A. Yusuf, “Transmission of a Gaussian-beam through a Fabry-Perot interferometer,” Appl. Opt. 33(18), 3805–3811 (1994).
    [CrossRef] [PubMed]
  16. P. Gregorčič, T. Požar, and J. Možina, “Quadrature phase-shift error analysis using a homodyne laser interferometer,” Opt. Express 17(18), 16322–16331 (2009).
    [CrossRef] [PubMed]
  17. T. Požar, P. Gregorčič, and J. Možina, “Optical measurements of the laser-inducedultrasonic waves on moving objects,” Opt. Express 17(25), 22906–22911 (2009).
    [CrossRef]
  18. P. Gregorčič, R. Petkovšek, J. Možina, and G. Močnik, “Measurements of cavitation bubble dynamics based on a beam-deflection probe,” Appl. Phys., A Mater. Sci. Process. 93(4), 901–905 (2008).
    [CrossRef]

2009 (3)

2008 (3)

J. H. Lehman, D. Livigni, X. Y. Li, C. L. Cromer, and M. L. Dowell, “Reflective attenuator for high-energy laser measurements,” Appl. Opt. 47(18), 3360–3363 (2008).
[CrossRef] [PubMed]

H. B. Yu, G. Y. Zhou, C. F. Siong, and L. Feiwen, “A variable optical attenuator based on optofluidic technology,” J. Micromech. Microeng. 18(11), 115016 (2008).
[CrossRef]

P. Gregorčič, R. Petkovšek, J. Možina, and G. Močnik, “Measurements of cavitation bubble dynamics based on a beam-deflection probe,” Appl. Phys., A Mater. Sci. Process. 93(4), 901–905 (2008).
[CrossRef]

2004 (2)

D. Gauden, D. Mechin, C. Vaudry, P. Yvernault, and D. Pureur, “Variable optical attenuator based on thermally tuned Mach-Zehnder interferometer within a twin core fiber,” Opt. Commun. 231(1-6), 213–216 (2004).
[CrossRef]

Y. H. Wu, Y. H. Lin, Y. Q. Lu, H. W. Ren, Y. H. Fan, J. R. Wu, and S. T. Wu, “Submillisecond response variable optical attenuator based on sheared polymer network liquid crystal,” Opt. Express 12(25), 6382–6389 (2004).
[CrossRef] [PubMed]

2002 (1)

M. J. Mughal and N. A. Riza, “Compact acoustooptic high-speed variable attenuator for high-power applications,” IEEE Photon. Technol. Lett. 14(4), 510–512 (2002).
[CrossRef]

1994 (1)

1991 (2)

1989 (1)

1987 (1)

1980 (1)

1975 (1)

1966 (1)

Abu-Aljarayesh, I.

Abu-Safia, H.

Al-Tahtamouni, R.

Azzam, R. M. A.

Bennett, K.

Bretenaker, F.

Byer, R. L.

Clay, R. A.

Cotteverte, J. C.

Cromer, C. L.

Dexter, K. F.

Dowell, M. L.

Eyal, A.

Fan, Y. H.

Feiwen, L.

H. B. Yu, G. Y. Zhou, C. F. Siong, and L. Feiwen, “A variable optical attenuator based on optofluidic technology,” J. Micromech. Microeng. 18(11), 115016 (2008).
[CrossRef]

Gauden, D.

D. Gauden, D. Mechin, C. Vaudry, P. Yvernault, and D. Pureur, “Variable optical attenuator based on thermally tuned Mach-Zehnder interferometer within a twin core fiber,” Opt. Commun. 231(1-6), 213–216 (2004).
[CrossRef]

Gregorcic, P.

Kogelnik, H.

Lefloch, A.

Lehman, J. H.

Li, T.

Li, X. Y.

Lin, Y. H.

Livigni, D.

Lotem, H.

Lu, Y. Q.

Macomber, J. D.

Mechin, D.

D. Gauden, D. Mechin, C. Vaudry, P. Yvernault, and D. Pureur, “Variable optical attenuator based on thermally tuned Mach-Zehnder interferometer within a twin core fiber,” Opt. Commun. 231(1-6), 213–216 (2004).
[CrossRef]

Mocnik, G.

P. Gregorčič, R. Petkovšek, J. Možina, and G. Močnik, “Measurements of cavitation bubble dynamics based on a beam-deflection probe,” Appl. Phys., A Mater. Sci. Process. 93(4), 901–905 (2008).
[CrossRef]

Možina, J.

Mughal, M. J.

M. J. Mughal and N. A. Riza, “Compact acoustooptic high-speed variable attenuator for high-power applications,” IEEE Photon. Technol. Lett. 14(4), 510–512 (2002).
[CrossRef]

Nemoto, S.

Petkovšek, R.

P. Gregorčič, R. Petkovšek, J. Možina, and G. Močnik, “Measurements of cavitation bubble dynamics based on a beam-deflection probe,” Appl. Phys., A Mater. Sci. Process. 93(4), 901–905 (2008).
[CrossRef]

Požar, T.

Pureur, D.

D. Gauden, D. Mechin, C. Vaudry, P. Yvernault, and D. Pureur, “Variable optical attenuator based on thermally tuned Mach-Zehnder interferometer within a twin core fiber,” Opt. Commun. 231(1-6), 213–216 (2004).
[CrossRef]

Ren, H. W.

Rice, R. O.

Riza, N. A.

M. J. Mughal and N. A. Riza, “Compact acoustooptic high-speed variable attenuator for high-power applications,” IEEE Photon. Technol. Lett. 14(4), 510–512 (2002).
[CrossRef]

Shuker, A. R.

Siong, C. F.

H. B. Yu, G. Y. Zhou, C. F. Siong, and L. Feiwen, “A variable optical attenuator based on optofluidic technology,” J. Micromech. Microeng. 18(11), 115016 (2008).
[CrossRef]

Staromlynska, J.

Vaudry, C.

D. Gauden, D. Mechin, C. Vaudry, P. Yvernault, and D. Pureur, “Variable optical attenuator based on thermally tuned Mach-Zehnder interferometer within a twin core fiber,” Opt. Commun. 231(1-6), 213–216 (2004).
[CrossRef]

Wu, J. R.

Wu, S. T.

Wu, Y. H.

Yu, H. B.

H. B. Yu, G. Y. Zhou, C. F. Siong, and L. Feiwen, “A variable optical attenuator based on optofluidic technology,” J. Micromech. Microeng. 18(11), 115016 (2008).
[CrossRef]

Yusuf, N. A.

Yvernault, P.

D. Gauden, D. Mechin, C. Vaudry, P. Yvernault, and D. Pureur, “Variable optical attenuator based on thermally tuned Mach-Zehnder interferometer within a twin core fiber,” Opt. Commun. 231(1-6), 213–216 (2004).
[CrossRef]

Zhou, G. Y.

H. B. Yu, G. Y. Zhou, C. F. Siong, and L. Feiwen, “A variable optical attenuator based on optofluidic technology,” J. Micromech. Microeng. 18(11), 115016 (2008).
[CrossRef]

Appl. Opt. (9)

Appl. Phys., A Mater. Sci. Process. (1)

P. Gregorčič, R. Petkovšek, J. Možina, and G. Močnik, “Measurements of cavitation bubble dynamics based on a beam-deflection probe,” Appl. Phys., A Mater. Sci. Process. 93(4), 901–905 (2008).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M. J. Mughal and N. A. Riza, “Compact acoustooptic high-speed variable attenuator for high-power applications,” IEEE Photon. Technol. Lett. 14(4), 510–512 (2002).
[CrossRef]

J. Micromech. Microeng. (1)

H. B. Yu, G. Y. Zhou, C. F. Siong, and L. Feiwen, “A variable optical attenuator based on optofluidic technology,” J. Micromech. Microeng. 18(11), 115016 (2008).
[CrossRef]

Opt. Commun. (1)

D. Gauden, D. Mechin, C. Vaudry, P. Yvernault, and D. Pureur, “Variable optical attenuator based on thermally tuned Mach-Zehnder interferometer within a twin core fiber,” Opt. Commun. 231(1-6), 213–216 (2004).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Other (1)

E. Hecht, Optics (2nd Edition, Addison Wesley, 1987), pp. 100.
[PubMed]

Supplementary Material (1)

» Media 1: MOV (2609 KB)     

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Figures (4)

Fig. 1
Fig. 1

a) The propagation of a Gaussian beam through the dielectric plate of thickness d and refractive index n. The probe-beam-waist radius is denoted by w0 , D is the distance between the laser output and the lens L, which collects the transmitted light into the photodiode PD. When the beam incidences the dielectric plate with an angle θi , the transverse displacement Δx between two adjacent reflected beams needs to be taken into account. b) The experimental setup for measurements of the angle and the temperature-dependent interference effects. A He-Ne laser was used as the probe beam. The dielectric plate was rotated with a constant angular velocity ω. c) Measurements of the plate’s transmittance during the absorption of high-power-laser pulses. A fourth-harmonic-generation Nd-YAG laser (λ = 266 nm) was used as an excitation laser. A band-pass filter BPF for the probe beam was placed in front of the PD.

Fig. 2
Fig. 2

The transmittance of a dielectric plate as a function of the incident angle. The black curve shows the theoretical results (Eq. (10)) for incoherent light. a) Theoretical transmittance of the plan-parallel plate for an s-polarized Gaussian beam. b) Theoretical transmittance of the plan-parallel plate for the p-polarized plane wave. c) The measured transmittance for the s-polarized probe beam. The parallelism of the plate was 15 μrad. d) The measured transmittance of the plates with different parallelisms for the s-polarized probe beam. The plate’s parallelisms were 45 μrad (the gray curve) and 200 μrad (the red curve).

Fig. 3
Fig. 3

a) The transmittance as a function of the incident angle at different plate temperatures (Media 1). b) Measured transmittance as a function of the temperature change for normal incidence of the probe beam. c) Measured transmittance as a function of temperature change at θi = 70°. The black curve shows the theoretical fit.

Fig. 4
Fig. 4

The measurement of the plate’s transmittance for the probe beam during the absorption of the excitation laser pulses. a) The entire measurement in the time period of 40 s. In the first 25 s a total of 500 pulses were absorbed in the plate, increasing its temperature from room temperature to 490 K. After that the excitation laser was switched off and the transmittance was measured during the plate’s cooling. b) The magnification of the transmittance shows discontinuous changes of the transmittance for each laser pulse. c) When the temperature losses during two pulses equal the temperature rise caused by a single pulse, steady-state conditions are achieved (the red curve). The blue curve shows the plate’s transmittance during spontaneous cooling.

Equations (14)

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r ( θ i ) = [ r s ( θ i ) 0 0 r p ( θ i ) ] ,     t ( θ i ) = [ t s ( θ i ) 0 0 t p ( θ i ) ] .
E = [ E s E p ] ,      I r ( r E ) ( r E ) = E s 2 R s ( θ i ) + E p 2 R p ( θ i ) ,
R ( θ i ) = I s I R s ( θ i ) + I p I R p ( θ i ) , R s = ( sin ( θ t θ i ) sin ( θ t + θ i ) ) 2 ,     R p = ( tan ( θ t θ i ) tan ( θ t + θ i ) ) 2 ,
E ( x , y , z ) = [ E 0 s E 0 p ] w 0 w ( z ) exp ( x 2 + y 2 w 2 ( z ) ) exp ( i k x 2 + y 2 2 ρ ( z ) ) exp ( i [ k z η ( z ) ] ) , w 2 ( z ) = w 0 2 [ 1 + z 2 z 0 2 ] ,    z 0 = π w 0 2 λ ,    ρ ( z ) = z + z 0 2 z ,    k = 2 π λ ,   η ( z ) = arctan ( z z 0 ) .
E m = A w 0 w ( z m ) exp ( [ x m Δ x ] 2 + y 2 w 2 ( z m ) i k [ x m Δ x ] 2 + y 2 2 ρ ( z m ) ) exp ( i [ δ 0 + m δ η ( z m ) ] ) , A = [ t s 2 r s 2 m E 0 s t p 2 r p 2 m E 0 p ] ,     Δ x = 2 d tan θ t cos θ i ,    δ = 2 k d n cos θ t + 2 δ r , z m = D + d n cos θ t ( 1 n cos [ θ i θ t ] ) + 2 m d n cos θ t ( 1 n sin θ t sin θ i ) ,
δ r = { 0   ; (p-polarization)           π   ;  θ t θ B  (s-polarization) 0   ;  θ t θ B  (s-polarization) ,
E t ( x , y , z ) = m = 0 E m ( x m , y , z m ) ,       I t ( x , y , z ) l = 0 m = 0 E l ( x l , y , z l ) E m ( x m , y , z m ) .
P t = I 0 w 0 2 w 2 ( 1 R ( θ i ) ) 2 l = 0 m = 0 R ( θ i ) m + l exp ( 2 y 2 w 2 ) d y × exp ( ( x m Δ x ) 2 + ( x l Δ x ) 2 w 2 ) cos ( k ( x l Δ x ) 2 ( x m Δ x ) 2 2 ρ + ( l m ) δ ) d x .
exp ( a x 2 ) cos ( b x ) d x = π a exp ( b 2 4 a ) ,
T P ( G ) = ( 1 R ( θ i ) ) 2 l = 0 m = 0 R ( θ i ) m + l exp { Δ x 2 ( m l ) 2 2 ( k 2 w 2 4 ρ 2 + 1 w 2 ) } cos ( ( m l ) δ ) .
T P ( G ) = ( 1 R ( θ i ) ) 2 l = 0 m = 0 R ( θ i ) m + l exp { Δ x 2 2 w 0 2 ( m l ) 2 } cos ( ( m l ) δ ) .
T P ( P W ) = 1 1 + 4 R ( θ i ) ( 1 R ( θ i ) ) 2 sin 2 ( δ / 2 ) ,
T P ( N C ) = ( 1 R ) 2 l = 0 R 2 l = ( 1 R ( θ i ) ) 2 1 R ( θ i ) 2 ,
δ ( Δ T ) 2 k n 0 d 0 ( 1 + ( α + n T α d , n ) Δ T ) cos ( θ t ) .

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