Abstract

We report the design and testing of a novel linear scanning periodic optical delay line (ODL) by use of a helicoid reflective mirror based on a tilted parabolic generatrix that was driven by an electrical motor for a periodic change in the optical path length of the reflected light beam. The divergence and pulse front distortion of the optical beam reflected by the helicoid reflective mirror were simulated based on differential geometry. With a round-trip pass arrangement, a scanning range of delay time as large as 100ps was obtained by spinning the helicoid reflective mirror with a pitch distance of 7.5mm. This periodic ODL was used in an optical second-harmonic generation autocorrelator to test the linearity and temporal resolution in comparison with the autocorrelation signal obtained using an ODL structured with a motorized linear translation stage. Experiments demonstrate that our helicoid optical delay device may provide exceptional performance for optical interference, high-resolution terahertz time-domain spectroscopy, and general optical pump–probe experiments.

© 2009 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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2008

G.-J. Kim, S.-G. Jeon, J.-I. Kim, and Y.-S. Jin, “High speed scanning of terahertz pulse by a rotary optical delay line,” Rev. Sci. Instrum. 79, 106102 (2008).
[CrossRef] [PubMed]

2004

2003

2002

1996

1993

1991

D. C. Edelstein, R. B. Romney, and M. Scheuermann, “Rapid programmable 300 ps optical delay scanner and signal-averaging system for ultrafast measurements,” Rev. Sci. Instrum. 62, 579-583 (1991).
[CrossRef]

P. Haschberger, O. Mayer, V. Tank, and H. Dietl, “Ray tracing through an eccentrically rotating retroreflector used for path-length alteration in a new Michelson interferometer,” J. Opt. Soc. Am. A 8, 1991-2000 (1991).
[CrossRef]

1978

Beissoer, R. A.

Boppart, S. A.

Bouma, B. E.

Chen, N. G.

Chu, K. G.

Chudoba, C.

Cobb, M. J.

Dienes, A.

Dietl, H.

do Carmo, M. P.

M. P. do Carmo, Differential Geometry of Curves and Surfaces (Prentice Hall, 1976).

Edelstein, D. C.

D. C. Edelstein, R. B. Romney, and M. Scheuermann, “Rapid programmable 300 ps optical delay scanner and signal-averaging system for ultrafast measurements,” Rev. Sci. Instrum. 62, 579-583 (1991).
[CrossRef]

Fork, R. F.

Fujimoto, J. G.

Golubovic, B.

Hart, I.

Haschberger, P.

Heritage, J. P.

Hsiung, P.-L.

Jeon, S.-G.

G.-J. Kim, S.-G. Jeon, J.-I. Kim, and Y.-S. Jin, “High speed scanning of terahertz pulse by a rotary optical delay line,” Rev. Sci. Instrum. 79, 106102 (2008).
[CrossRef] [PubMed]

Jin, Y.-S.

G.-J. Kim, S.-G. Jeon, J.-I. Kim, and Y.-S. Jin, “High speed scanning of terahertz pulse by a rotary optical delay line,” Rev. Sci. Instrum. 79, 106102 (2008).
[CrossRef] [PubMed]

Kim, G.-J.

G.-J. Kim, S.-G. Jeon, J.-I. Kim, and Y.-S. Jin, “High speed scanning of terahertz pulse by a rotary optical delay line,” Rev. Sci. Instrum. 79, 106102 (2008).
[CrossRef] [PubMed]

Kim, J.-I.

G.-J. Kim, S.-G. Jeon, J.-I. Kim, and Y.-S. Jin, “High speed scanning of terahertz pulse by a rotary optical delay line,” Rev. Sci. Instrum. 79, 106102 (2008).
[CrossRef] [PubMed]

Ko, T. H.

Kwong, K. F.

Li, X.

Liu, X.

Marks, D. L.

Mayer, O.

Oldenburg, A. L.

Pan, C.-L.

C.-L. Wang and C.-L. Pan, “Scanning optical delay device having a helicoid reflecting mirror,” U.S. patent 5,784,186 (21 July 1998).

Pan, O.-L.

C.-L. Wang, S.-A. Wang, S. C. Wang, and O.-L. Pan, “Programmable wavelength tuning of an external-cavity diode laser,” Conference on Lasers and Electro-Optics (CLEO), Technical Digest Series (Optical Society of America, 1998), paper CWN5, Vol. 6.

Reynolds, J. J.

Romney, R. B.

D. C. Edelstein, R. B. Romney, and M. Scheuermann, “Rapid programmable 300 ps optical delay scanner and signal-averaging system for ultrafast measurements,” Rev. Sci. Instrum. 62, 579-583 (1991).
[CrossRef]

Scheuermann, M.

D. C. Edelstein, R. B. Romney, and M. Scheuermann, “Rapid programmable 300 ps optical delay scanner and signal-averaging system for ultrafast measurements,” Rev. Sci. Instrum. 62, 579-583 (1991).
[CrossRef]

Swanson, E. A.

Tank, V.

Tearney, G. J.

Wang, C.-L.

C.-L. Wang and C.-L. Pan, “Scanning optical delay device having a helicoid reflecting mirror,” U.S. patent 5,784,186 (21 July 1998).

C.-L. Wang, S.-A. Wang, S. C. Wang, and O.-L. Pan, “Programmable wavelength tuning of an external-cavity diode laser,” Conference on Lasers and Electro-Optics (CLEO), Technical Digest Series (Optical Society of America, 1998), paper CWN5, Vol. 6.

Wang, S. C.

C.-L. Wang, S.-A. Wang, S. C. Wang, and O.-L. Pan, “Programmable wavelength tuning of an external-cavity diode laser,” Conference on Lasers and Electro-Optics (CLEO), Technical Digest Series (Optical Society of America, 1998), paper CWN5, Vol. 6.

Wang, S.-A.

C.-L. Wang, S.-A. Wang, S. C. Wang, and O.-L. Pan, “Programmable wavelength tuning of an external-cavity diode laser,” Conference on Lasers and Electro-Optics (CLEO), Technical Digest Series (Optical Society of America, 1998), paper CWN5, Vol. 6.

Xu, J.

Yankelevich, D.

Zhang, X.-C.

Zhu, Q.

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Lett.

Rev. Sci. Instrum.

D. C. Edelstein, R. B. Romney, and M. Scheuermann, “Rapid programmable 300 ps optical delay scanner and signal-averaging system for ultrafast measurements,” Rev. Sci. Instrum. 62, 579-583 (1991).
[CrossRef]

G.-J. Kim, S.-G. Jeon, J.-I. Kim, and Y.-S. Jin, “High speed scanning of terahertz pulse by a rotary optical delay line,” Rev. Sci. Instrum. 79, 106102 (2008).
[CrossRef] [PubMed]

Other

C.-L. Wang, S.-A. Wang, S. C. Wang, and O.-L. Pan, “Programmable wavelength tuning of an external-cavity diode laser,” Conference on Lasers and Electro-Optics (CLEO), Technical Digest Series (Optical Society of America, 1998), paper CWN5, Vol. 6.

C.-L. Wang and C.-L. Pan, “Scanning optical delay device having a helicoid reflecting mirror,” U.S. patent 5,784,186 (21 July 1998).

M. P. do Carmo, Differential Geometry of Curves and Surfaces (Prentice Hall, 1976).

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Figures (13)

Fig. 1
Fig. 1

Schematic illustration of a helicoid in Cartesian coordinates.

Fig. 2
Fig. 2

Separation angle between incident beam and beam reflected by helicoid reflective mirror versus pitch of the helicoid reflective mirror for different tilted angles.

Fig. 3
Fig. 3

Divergence angle of reflected laser beam versus radius of straight helicoid mirror for different pitches: (a) radial divergence angle and (b) angular divergence angle.

Fig. 4
Fig. 4

Simulated results about maximum divergence angle versus tilted angle of helicoid reflective mirror. Solid line is the angular divergence angle and dashed line is radial divergence angle.

Fig. 5
Fig. 5

Maximum divergence angle versus the spot radius of incident beam impinging on the helicoid reflective mirror.

Fig. 6
Fig. 6

(a) Laser beam pulse front of reflected beam by straight helicoid reflective mirror, and interference pattern between laser beam reflected by straight helicoid reflective mirror and incident laser beam: (b) theoretical simulation and (c) experimental result. The photo was enlarged relative to the calculated one to show the experimental result more clearly.

Fig. 7
Fig. 7

(a) Laser beam pulse front of reflected beam by modified helicoid reflective mirror, and interference pattern between laser beam reflected by modified helicoid reflective mirror and incident laser beam: (b) theoretical simulation and (c) experimental result. The photo was enlarged relative to the calculated one to show the experimental result more clearly.

Fig. 8
Fig. 8

Maximum deformability of pulse front of reflected laser beam versus incident beam size.

Fig. 9
Fig. 9

Photo of the modified helicoid reflective mirror used in our experiment and its schematic diagram.

Fig. 10
Fig. 10

Experimental setup of an autocorrelator without background with linear ODL and periodically scanning modified HODL. M 1 M 8 , mirrors; BS, beam splitter; D1 D2, detectors; H, modified helicoid reflective mirror; L, lens; A, aperture.

Fig. 11
Fig. 11

Optical autocorrelation [based on a second harmonic generation (SHG)] signal measured by the HODL and a linear stage.

Fig. 12
Fig. 12

Repetitive autocorrelation (based on SHG) traces by periodically scanning HODL driven by an AC motor of 7.5 Hz .

Fig. 13
Fig. 13

Optical time delay versus rotation angle of second-order modified HODL. The curve is the result calculated from Δ L = 4 d ϕ / 360 .

Equations (16)

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r ( ρ , ϕ ) = ( ρ cos ϕ , ρ sin ϕ , d 2 π ϕ ) ,
r ( ρ , ϕ ) = ( ρ cos ϕ , ρ sin ϕ , d 2 π ϕ ρ tan θ ) .
n = r ρ × r ϕ | r ρ × r ϕ | = ( d 2 π sin ϕ + ρ cos ϕ tan θ [ ρ 2 sec 2 θ + ( d / 2 π ) 2 ] 1 / 2 , d 2 π cos ϕ + ρ sin ϕ tan θ [ ρ 2 sec 2 θ + ( d / 2 π ) 2 ] 1 / 2 , ρ [ ρ 2 sec 2 θ + ( d / 2 π ) 2 ] 1 / 2 ) ,
r ρ = r ρ = ( cos ϕ , sin ϕ , tan θ ) , r ϕ = r ϕ = ( ρ sin ϕ , ρ cos ϕ , d 2 π ) .
K = k 1 k 2 ,
k 2 L G 2 M F + N E E G F 2 k + L N M 2 E G F 2 = 0.
{ E = r ρ · r ρ F = r ρ · r ϕ G = r ϕ · r ϕ { L = r ρ ρ · n = 2 r ρ 2 · n M = r ρ ϕ · n = ϕ ( r ρ ) · n N = r ϕ ϕ · n = 2 r ϕ 2 · n .
K = ( d / 2 π ) 2 ( ρ 2 sec 2 θ + ( d / 2 π ) 2 ) 2 < 0 ,
Δ L = d 2 π · ϕ .
Δ θ = 2 arccos ( n · l ) = 2 arccos ( ρ [ ρ 2 sec 2 θ + ( d / 2 π ) 2 ] 1 / 2 ) ,
θ ρ ^ = arcsin ( | n × n ' | ) = arcsin ( ( d / 2 π ) Δ ρ | sec θ | [ ρ 2 sec 2 θ + ( d / 2 π ) 2 ] 1 / 2 · [ ( ρ + Δ ρ ) 2 sec 2 θ + ( d / 2 π ) 2 ] 1 / 2 ) .
θ ϕ ^ = arcsin ( | n × n ' ' | ) = arcsin ( { 2 [ ( d / 2 π ) 2 ρ 2 + ρ 4 tan 2 θ ] ( 1 cos Δ ϕ ) + [ ( d / 2 π ) 2 + ρ 2 tan 2 θ ] 2 sin 2 θ } 1 / 2 ρ 2 sec 2 θ + ( d / 2 π ) 2 ) .
A ( x ρ 0 cos ϕ 0 ) + B ( y ρ 0 sin ϕ 0 ) + C ( z d 2 π ϕ 0 + ρ 0 tan θ ) = 0 ,
Δ l = | A ρ cos ϕ + B ρ sin ϕ + C ( d 2 π ϕ ρ tan θ ) ( A 2 + B 2 + C 2 ) 1 / 2 ( A ρ 0 cos ϕ 0 + B ρ 0 sin ϕ 0 + C ( d 2 π ϕ 0 ρ 0 tan θ ) ) ( A 2 + B 2 + C 2 ) 1 / 2 | .
{ ρ sin ( θ ) + z cos ( θ ) = ( ρ cos ( θ ) z sin ( θ ) R ) 2 M + R 2 M z = b + b 2 4 a c 2 a ,
r ( ρ , ϕ ) = ( ρ cos ϕ , ρ sin ϕ , d 2 π ϕ + z ) ,

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