Abstract

We apply Fourier-transform spectral interferometry to complete phase and intensity characterization of a chirped filter engraved in a persistent spectral hole-burning (PSHB) material. The conjugated transfer function of a grating pair compressor is stored in a PSHB material as an accumulated spectral hologram that behaves as a pulse stretcher. By directing the diffracted pulse back through the compressor, we verified that the PSHB stretcher’s transfer function is indeed conjugated to that of the grating pair compressor. We have extended the spectral phase analysis to regions where the engraved structure is much narrower than the spectrometer’s resolution.

© 2003 Optical Society of America

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  1. M. Shapiro and P. Brumer, “Laser control of product quantum state populations in unimolecular reactions,” J. Chem. Phys. 84, 4103–4104 (1986).
    [CrossRef]
  2. P. Brumer and M. Shapiro, “Control of unimolecular reactions using coherent light,” Chem. Phys. Lett. 126, 541–546 (1986).
    [CrossRef]
  3. D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
    [CrossRef]
  4. C. Froehly, B. Colombeau, and M. Vampouille, “Shaping and analysis of picosecond light pulses,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1983), Vol. 20, pp. 65–153.
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  10. C. Froehly, A. Lacourt, and J. C. Vienot, “Notions de réponse impulsionnelle et de fonction de transfert temporelles des pupilles optiques, justifications expérimentales et applications,” Nouv. Rev. Opt. Appl. 4, 183–196 (1973).
    [CrossRef]
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    [CrossRef]
  13. F. H. Mok, M. C. Tackitt, and H.-M. Stoll, “Storage of 500 high-resolution holograms in a LiNbO 3 crystal,” Opt. Lett. 16, 605–607 (1991).
    [CrossRef] [PubMed]
  14. W. H. Hesselink and D. A. Wiersma, “Picosecond photon echoes stimulated from an accumulated grating,” Phys. Rev. Lett. 43, 1991–1994 (1979).
    [CrossRef]
  15. O. Ollikainen, C. Nilsson, J. Gallus, D. Erni, and A. Rebane, “Terahertz bit-rate parallel multiplication by photon echo in low-temperature dye-doped polymer film,” Opt. Commun. 147, 429–435 (1998).
    [CrossRef]

2000

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulator,” Rev. Sci. Instrum. 71, 1929–1960 (2000).
[CrossRef]

1998

O. Ollikainen, C. Nilsson, J. Gallus, D. Erni, and A. Rebane, “Terahertz bit-rate parallel multiplication by photon echo in low-temperature dye-doped polymer film,” Opt. Commun. 147, 429–435 (1998).
[CrossRef]

1995

1994

H. Schwoerer, D. Erni, A. Rebane, and U. P. Wild, “Subpicosecond pulse shaping via spectra hole burning,” Opt. Commun. 107, 123–128 (1994).
[CrossRef]

1991

1988

A. Rebane, “Compression and recovery of temporal profiles of picosecond light signals by persistent spectral hole-burning holograms,” Opt. Commun. 67, 301–304 (1988).
[CrossRef]

1986

M. Shapiro and P. Brumer, “Laser control of product quantum state populations in unimolecular reactions,” J. Chem. Phys. 84, 4103–4104 (1986).
[CrossRef]

P. Brumer and M. Shapiro, “Control of unimolecular reactions using coherent light,” Chem. Phys. Lett. 126, 541–546 (1986).
[CrossRef]

1985

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

1982

1979

W. H. Hesselink and D. A. Wiersma, “Picosecond photon echoes stimulated from an accumulated grating,” Phys. Rev. Lett. 43, 1991–1994 (1979).
[CrossRef]

1973

C. Froehly, A. Lacourt, and J. C. Vienot, “Notions de réponse impulsionnelle et de fonction de transfert temporelles des pupilles optiques, justifications expérimentales et applications,” Nouv. Rev. Opt. Appl. 4, 183–196 (1973).
[CrossRef]

Brumer, P.

M. Shapiro and P. Brumer, “Laser control of product quantum state populations in unimolecular reactions,” J. Chem. Phys. 84, 4103–4104 (1986).
[CrossRef]

P. Brumer and M. Shapiro, “Control of unimolecular reactions using coherent light,” Chem. Phys. Lett. 126, 541–546 (1986).
[CrossRef]

Chériaux, G.

Débarre, A.

Erni, D.

O. Ollikainen, C. Nilsson, J. Gallus, D. Erni, and A. Rebane, “Terahertz bit-rate parallel multiplication by photon echo in low-temperature dye-doped polymer film,” Opt. Commun. 147, 429–435 (1998).
[CrossRef]

H. Schwoerer, D. Erni, A. Rebane, and U. P. Wild, “Subpicosecond pulse shaping via spectra hole burning,” Opt. Commun. 107, 123–128 (1994).
[CrossRef]

Froehly, C.

C. Froehly, A. Lacourt, and J. C. Vienot, “Notions de réponse impulsionnelle et de fonction de transfert temporelles des pupilles optiques, justifications expérimentales et applications,” Nouv. Rev. Opt. Appl. 4, 183–196 (1973).
[CrossRef]

Gallus, J.

O. Ollikainen, C. Nilsson, J. Gallus, D. Erni, and A. Rebane, “Terahertz bit-rate parallel multiplication by photon echo in low-temperature dye-doped polymer film,” Opt. Commun. 147, 429–435 (1998).
[CrossRef]

Hesselink, W. H.

W. H. Hesselink and D. A. Wiersma, “Picosecond photon echoes stimulated from an accumulated grating,” Phys. Rev. Lett. 43, 1991–1994 (1979).
[CrossRef]

Joffre, M.

Keller, J.-C.

Lacourt, A.

C. Froehly, A. Lacourt, and J. C. Vienot, “Notions de réponse impulsionnelle et de fonction de transfert temporelles des pupilles optiques, justifications expérimentales et applications,” Nouv. Rev. Opt. Appl. 4, 183–196 (1973).
[CrossRef]

Le Gouët, J.-L.

Lepetit, L.

Mitsunaga, M.

Mok, F. H.

Mossberg, T. W.

Mourou, G.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

Nilsson, C.

O. Ollikainen, C. Nilsson, J. Gallus, D. Erni, and A. Rebane, “Terahertz bit-rate parallel multiplication by photon echo in low-temperature dye-doped polymer film,” Opt. Commun. 147, 429–435 (1998).
[CrossRef]

Ollikainen, O.

O. Ollikainen, C. Nilsson, J. Gallus, D. Erni, and A. Rebane, “Terahertz bit-rate parallel multiplication by photon echo in low-temperature dye-doped polymer film,” Opt. Commun. 147, 429–435 (1998).
[CrossRef]

Rebane, A.

O. Ollikainen, C. Nilsson, J. Gallus, D. Erni, and A. Rebane, “Terahertz bit-rate parallel multiplication by photon echo in low-temperature dye-doped polymer film,” Opt. Commun. 147, 429–435 (1998).
[CrossRef]

H. Schwoerer, D. Erni, A. Rebane, and U. P. Wild, “Subpicosecond pulse shaping via spectra hole burning,” Opt. Commun. 107, 123–128 (1994).
[CrossRef]

A. Rebane, “Compression and recovery of temporal profiles of picosecond light signals by persistent spectral hole-burning holograms,” Opt. Commun. 67, 301–304 (1988).
[CrossRef]

Schwoerer, H.

H. Schwoerer, D. Erni, A. Rebane, and U. P. Wild, “Subpicosecond pulse shaping via spectra hole burning,” Opt. Commun. 107, 123–128 (1994).
[CrossRef]

Shapiro, M.

P. Brumer and M. Shapiro, “Control of unimolecular reactions using coherent light,” Chem. Phys. Lett. 126, 541–546 (1986).
[CrossRef]

M. Shapiro and P. Brumer, “Laser control of product quantum state populations in unimolecular reactions,” J. Chem. Phys. 84, 4103–4104 (1986).
[CrossRef]

Stoll, H.-M.

Strickland, D.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

Tackitt, M. C.

Tchénio, P.

Uesugi, N.

Vienot, J. C.

C. Froehly, A. Lacourt, and J. C. Vienot, “Notions de réponse impulsionnelle et de fonction de transfert temporelles des pupilles optiques, justifications expérimentales et applications,” Nouv. Rev. Opt. Appl. 4, 183–196 (1973).
[CrossRef]

Weiner, A. M.

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulator,” Rev. Sci. Instrum. 71, 1929–1960 (2000).
[CrossRef]

Wiersma, D. A.

W. H. Hesselink and D. A. Wiersma, “Picosecond photon echoes stimulated from an accumulated grating,” Phys. Rev. Lett. 43, 1991–1994 (1979).
[CrossRef]

Wild, U. P.

H. Schwoerer, D. Erni, A. Rebane, and U. P. Wild, “Subpicosecond pulse shaping via spectra hole burning,” Opt. Commun. 107, 123–128 (1994).
[CrossRef]

Yano, R.

Chem. Phys. Lett.

P. Brumer and M. Shapiro, “Control of unimolecular reactions using coherent light,” Chem. Phys. Lett. 126, 541–546 (1986).
[CrossRef]

J. Chem. Phys.

M. Shapiro and P. Brumer, “Laser control of product quantum state populations in unimolecular reactions,” J. Chem. Phys. 84, 4103–4104 (1986).
[CrossRef]

J. Opt. Soc. Am. B

Nouv. Rev. Opt. Appl.

C. Froehly, A. Lacourt, and J. C. Vienot, “Notions de réponse impulsionnelle et de fonction de transfert temporelles des pupilles optiques, justifications expérimentales et applications,” Nouv. Rev. Opt. Appl. 4, 183–196 (1973).
[CrossRef]

Opt. Commun.

H. Schwoerer, D. Erni, A. Rebane, and U. P. Wild, “Subpicosecond pulse shaping via spectra hole burning,” Opt. Commun. 107, 123–128 (1994).
[CrossRef]

A. Rebane, “Compression and recovery of temporal profiles of picosecond light signals by persistent spectral hole-burning holograms,” Opt. Commun. 67, 301–304 (1988).
[CrossRef]

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

O. Ollikainen, C. Nilsson, J. Gallus, D. Erni, and A. Rebane, “Terahertz bit-rate parallel multiplication by photon echo in low-temperature dye-doped polymer film,” Opt. Commun. 147, 429–435 (1998).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

W. H. Hesselink and D. A. Wiersma, “Picosecond photon echoes stimulated from an accumulated grating,” Phys. Rev. Lett. 43, 1991–1994 (1979).
[CrossRef]

Rev. Sci. Instrum.

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulator,” Rev. Sci. Instrum. 71, 1929–1960 (2000).
[CrossRef]

Other

C. Froehly, B. Colombeau, and M. Vampouille, “Shaping and analysis of picosecond light pulses,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1983), Vol. 20, pp. 65–153.

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Figures (4)

Fig. 1
Fig. 1

Experimental setup: G’s, gratings; D1, D2, time-delay lines 1 and 2, respectively; other abbreviations defined in text.

Fig. 2
Fig. 2

Exposure of the OEP–PS sample to compound broadband chaotic pulses in a collinear configuration. (a) Recording of a compound engraving pulse spectrum. Note the uneven spacing of spectral fringes. Sample absorption profile (b) before and (c) after exposure to an ∼10-mJ dose on a 1 mm×1 mm area.

Fig. 3
Fig. 3

(a) Simulation of the spectral hologram engraved in the sample. Because of the finite resolution of the instrument, the spectrometer’s analysis of the interference pattern is affected by the reduction of fringe visibility to less than 0.5 in the hatched area. (b) Time development of the engraving pulses. The stretched pulse is followed by the short reference. The hatched area is the temporal counterpart of the spectral area in (a). (c), (d) Intensity and phase spectral profiles, respectively, of the stretched pulse. The quadratic phase is characteristic of linear chirp.

Fig. 4
Fig. 4

Experimental results. (a) Normalized interferogram of the recompressed pulse beating with the reference. (b), (c) Cosine and sine fast Fourier transforms (FFTs) of the interferogram. (d), (e) Spectral intensity and phase profiles of the recompressed echo, as derived from the inverse Fourier transform of the positive frequency component in (b) and (c). The phase is constant over the signal profile, which reflects the echo recompression. The dotted curves in (d) and (e), respectively, represent the average laser spectrum and the calculated phase shifts, as imparted by the dispersion line (lower curve) and the OEP–PS coherent filter (upper curve).

Equations (9)

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Eobj (ω)=Eref (ω)exp iΦ(ω, T0).
W(r, ω)=W0(ω){1+cos[Φ(ω, T0)+K  r]},
Eecho(ω)Eobj*(ω)Eref (ω)Eread(ω),
Eecho(ω)Eread(ω)W0(ω)exp[-iϕ(ω, T0)].
WS(ω)=|Eecho(ω)exp[iΦ(ω, T0)]
+Eread(ω)|2A(ω),
Is(ω)=Eread*(ω)Eread(ω)×Eobj*(ω)Eref(ω)exp[iΦ(ω, T0)]
Is(ω)=Eread*(ω)Eread(ω)Eobj*(ω)Eref(ω)×exp[iΦ(ω, T0)],
αL exp(-αL),

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