Abstract

We report the gain factor, detection limit, and linearity of a femtosecond time-resolved spectrometer for ultraweak fluorescence based on a 400nm pumped femtosecond noncollinear optical parametric amplifier. By employing the parametric fluorescence amplifier, the time-resolved fluorescence spectra of Rhodamine 6G dye in ethanol was measured. It is proved that a good spectral fidelity has been achieved in the measurement of fluorescence spectra with this technique. The measured gain factor of this parametric fluorescence amplifier is found to be 1.2×106, and the detection limit is 5.1aJ per pulse, corresponding to 15 fluorescence photons at 580nm. With this technique, we have acquired the transient fluorescence spectra as well as the fluorescence decay profile of CdSxSe1x (x=0.78) nanobelts. Our results demonstrate the feasibility of this technique as an ultrasensitive time-resolved fluorescence spectrometer.

© 2007 Optical Society of America

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2006

X.-H. Chen, X.-F. Han, Y.-X. Weng, and J.-Y. Zhang, "Transient spectrometer for near-IR fluorescence based on parametric frequency upconversion," Appl. Phys. Lett. 89, 061127 (2006).
[CrossRef]

2005

S. Arzhantsev and M. Maroncelli, "Design and characterization of a femtosecond fluorescence spectrometer based on optical Kerr gating," Appl. Spectrosc. 59, 206-220 (2005).
[CrossRef] [PubMed]

C. Ma, W. M. Kwok, W. S. Chan, P. Zuo, J. T. W. Kan, P. H. Toy, and D. L. Phillips, "Ultrafast time-resolved study of photophysical processes involved in the photodeprotection of p-hydroxyphenacyl caged phototrigger compounds," J. Am. Chem. Soc. 127, 1463-1472 (2005).
[CrossRef] [PubMed]

L. J. Zhao, J. L. P. Lustres, V. Farztdinov, and N. P. Ernsting, "Femtosecond fluorescence spectroscopy by up-conversion with tilted gate pulses," Chem. Phys. 7, 1716-1725 (2005).
[CrossRef]

V. M. Martínez, F. L. Arbeloa, J. B. Prieto, and I. L. Arbeloa, "Characterization of Rhodamine 6G aggregates intercalated in solid thin films of laponite clay 2 fluorescence spectroscopy," J. Phys. Chem. B 109, 7443-7450 (2005).
[CrossRef]

A.-L. Pan, H. Yang, R.-B. Liu, R.-C. Yu, B.-S. Zou, and Z.-L. Wang, "Color-tunable photoluminescence of alloyed CdSxSe1−x nanobelts," J. Am. Chem. Soc. 127, 15692-15693 (2005).
[CrossRef] [PubMed]

P. Fita, Y. Stepanenko, and C. Radzewicz, "Femtosecond transient fluorescence spectrometer based on parametric amplification," Appl. Phys. Lett. 86, 021909 (2005).
[CrossRef]

2004

2003

2002

F. Treussart, R. Alleaume, V. Le Floc'h, L. T. Xiao, J.-M. Courty, and J.-F. Roch, "Direct measurement of the photon statistics of a triggered single photon source," Phys. Rev. Lett. 89, 093601 (2002).
[CrossRef] [PubMed]

2000

A. Shirakawa and T. Kobayashi, "Sub-10-fs tunable pulses in visible and NIR and visible sub-5-fs pulses generated by noncollinear OPA," J. Lumin. 87-89, 119-120 (2000).

J. Takeda, K. Nakajima, S. Kurita, S. Tomimoto, S. Saito, and T. Suemoto, "Time-resolved luminescence spectroscopy by the optical Kerr-gate method applicable to ultrafast relaxation processes," Phys. Rev. B 62, 10083-10087 (2000).
[CrossRef]

1999

S. Tomimoto, S. Saito, T. Suemoto, K. Sakata, J. Takeda, and S. Kurita, "Observation of the wave-packet oscillation during the exciton self-trapping process in a quasi-one-dimensional halogen-bridged Pt complex," Phys. Rev. B 60, 7961-7965 (1999).
[CrossRef]

1998

S. Iwai, S. Murata, and M. Tachiya, "Ultrafast fluorescence quenching by electron transfer and fluorescence from the second excited state of a charge transfer complex as studied by femtosecond up-conversion spectroscopy," J. Chem. Phys. 109, 5963-5970 (1998).
[CrossRef]

S. Tomimoto, H. Nansei, S. Saito, T. Suemoto, J. Takeda, and S. Kurita, "Femtosecond dynamics of the exciton self-trapping process in a quasi-one-dimensional halogen-bridged platinum complex," Phys. Rev. Lett. 81, 417-420 (1998).
[CrossRef]

A. Shirakawa and T. Kobayashi, "Noncollinearly phase-matched femtosecond optical parametric amplification with a 2000 cm−1 bandwidth," Appl. Phys. Lett. 72, 147-149 (1998).
[CrossRef]

1997

1990

1988

T. C. Damen and J. Shah, "Femtosecond luminescence spectroscopy with 60 fs compressed pulses," Appl. Phys. Lett. 52, 1291-1293 (1988).
[CrossRef]

J. Shah, "Ultrafast luminescence spectroscopy using sum frequency generation," IEEE J. Quantum Electron. 24, 276-288 (1988).
[CrossRef]

1987

J. Shah, T. C. Damen, B. Deveaud, and D. Block, "Subpicosecond luminescence spectroscopy using sum frequency generation," Appl. Phys. Lett. 50, 1307-1309 (1987).
[CrossRef]

1986

D. Block, J. Shah, and A. C. Gossard, "Femtosecond luminescence measurements in GaAs," Solid State Commun. 59, 527-531 (1986).
[CrossRef]

1975

H. Mahr and M. D. Hirsch, "An optical up-conversion light gate with picosecond resolution," Opt. Commun. 13, 96-99 (1975).
[CrossRef]

Alleaume, R.

F. Treussart, R. Alleaume, V. Le Floc'h, L. T. Xiao, J.-M. Courty, and J.-F. Roch, "Direct measurement of the photon statistics of a triggered single photon source," Phys. Rev. Lett. 89, 093601 (2002).
[CrossRef] [PubMed]

Arbeloa, F. L.

V. M. Martínez, F. L. Arbeloa, J. B. Prieto, and I. L. Arbeloa, "Characterization of Rhodamine 6G aggregates intercalated in solid thin films of laponite clay 2 fluorescence spectroscopy," J. Phys. Chem. B 109, 7443-7450 (2005).
[CrossRef]

Arbeloa, I. L.

V. M. Martínez, F. L. Arbeloa, J. B. Prieto, and I. L. Arbeloa, "Characterization of Rhodamine 6G aggregates intercalated in solid thin films of laponite clay 2 fluorescence spectroscopy," J. Phys. Chem. B 109, 7443-7450 (2005).
[CrossRef]

Arzhantsev, S.

Block, D.

J. Shah, T. C. Damen, B. Deveaud, and D. Block, "Subpicosecond luminescence spectroscopy using sum frequency generation," Appl. Phys. Lett. 50, 1307-1309 (1987).
[CrossRef]

D. Block, J. Shah, and A. C. Gossard, "Femtosecond luminescence measurements in GaAs," Solid State Commun. 59, 527-531 (1986).
[CrossRef]

Chan, W. S.

C. Ma, W. M. Kwok, W. S. Chan, P. Zuo, J. T. W. Kan, P. H. Toy, and D. L. Phillips, "Ultrafast time-resolved study of photophysical processes involved in the photodeprotection of p-hydroxyphenacyl caged phototrigger compounds," J. Am. Chem. Soc. 127, 1463-1472 (2005).
[CrossRef] [PubMed]

Chebira, A.

Chen, X.-H.

X.-H. Chen, X.-F. Han, Y.-X. Weng, and J.-Y. Zhang, "Transient spectrometer for near-IR fluorescence based on parametric frequency upconversion," Appl. Phys. Lett. 89, 061127 (2006).
[CrossRef]

Chesnoy, J.

Courty, J.-M.

F. Treussart, R. Alleaume, V. Le Floc'h, L. T. Xiao, J.-M. Courty, and J.-F. Roch, "Direct measurement of the photon statistics of a triggered single photon source," Phys. Rev. Lett. 89, 093601 (2002).
[CrossRef] [PubMed]

Coutaz, J.-L.

Damen, T. C.

T. C. Damen and J. Shah, "Femtosecond luminescence spectroscopy with 60 fs compressed pulses," Appl. Phys. Lett. 52, 1291-1293 (1988).
[CrossRef]

J. Shah, T. C. Damen, B. Deveaud, and D. Block, "Subpicosecond luminescence spectroscopy using sum frequency generation," Appl. Phys. Lett. 50, 1307-1309 (1987).
[CrossRef]

Deveaud, B.

J. Shah, T. C. Damen, B. Deveaud, and D. Block, "Subpicosecond luminescence spectroscopy using sum frequency generation," Appl. Phys. Lett. 50, 1307-1309 (1987).
[CrossRef]

Ernsting, N. P.

L. J. Zhao, J. L. P. Lustres, V. Farztdinov, and N. P. Ernsting, "Femtosecond fluorescence spectroscopy by up-conversion with tilted gate pulses," Chem. Phys. 7, 1716-1725 (2005).
[CrossRef]

Farztdinov, V.

L. J. Zhao, J. L. P. Lustres, V. Farztdinov, and N. P. Ernsting, "Femtosecond fluorescence spectroscopy by up-conversion with tilted gate pulses," Chem. Phys. 7, 1716-1725 (2005).
[CrossRef]

Fita, P.

P. Fita, Y. Stepanenko, and C. Radzewicz, "Femtosecond transient fluorescence spectrometer based on parametric amplification," Appl. Phys. Lett. 86, 021909 (2005).
[CrossRef]

Gossard, A. C.

D. Block, J. Shah, and A. C. Gossard, "Femtosecond luminescence measurements in GaAs," Solid State Commun. 59, 527-531 (1986).
[CrossRef]

Han, X.-F.

X.-H. Chen, X.-F. Han, Y.-X. Weng, and J.-Y. Zhang, "Transient spectrometer for near-IR fluorescence based on parametric frequency upconversion," Appl. Phys. Lett. 89, 061127 (2006).
[CrossRef]

Hirsch, M. D.

H. Mahr and M. D. Hirsch, "An optical up-conversion light gate with picosecond resolution," Opt. Commun. 13, 96-99 (1975).
[CrossRef]

Huang, J. Y.

Iwai, S.

S. Iwai, S. Murata, and M. Tachiya, "Ultrafast fluorescence quenching by electron transfer and fluorescence from the second excited state of a charge transfer complex as studied by femtosecond up-conversion spectroscopy," J. Chem. Phys. 109, 5963-5970 (1998).
[CrossRef]

Kan, J. T. W.

C. Ma, W. M. Kwok, W. S. Chan, P. Zuo, J. T. W. Kan, P. H. Toy, and D. L. Phillips, "Ultrafast time-resolved study of photophysical processes involved in the photodeprotection of p-hydroxyphenacyl caged phototrigger compounds," J. Am. Chem. Soc. 127, 1463-1472 (2005).
[CrossRef] [PubMed]

Kimmel, M.

Kobayashi, T.

A. Shirakawa and T. Kobayashi, "Sub-10-fs tunable pulses in visible and NIR and visible sub-5-fs pulses generated by noncollinear OPA," J. Lumin. 87-89, 119-120 (2000).

A. Shirakawa and T. Kobayashi, "Noncollinearly phase-matched femtosecond optical parametric amplification with a 2000 cm−1 bandwidth," Appl. Phys. Lett. 72, 147-149 (1998).
[CrossRef]

Kull, M.

Kurita, S.

J. Takeda, K. Nakajima, S. Kurita, S. Tomimoto, S. Saito, and T. Suemoto, "Time-resolved luminescence spectroscopy by the optical Kerr-gate method applicable to ultrafast relaxation processes," Phys. Rev. B 62, 10083-10087 (2000).
[CrossRef]

S. Tomimoto, S. Saito, T. Suemoto, K. Sakata, J. Takeda, and S. Kurita, "Observation of the wave-packet oscillation during the exciton self-trapping process in a quasi-one-dimensional halogen-bridged Pt complex," Phys. Rev. B 60, 7961-7965 (1999).
[CrossRef]

S. Tomimoto, H. Nansei, S. Saito, T. Suemoto, J. Takeda, and S. Kurita, "Femtosecond dynamics of the exciton self-trapping process in a quasi-one-dimensional halogen-bridged platinum complex," Phys. Rev. Lett. 81, 417-420 (1998).
[CrossRef]

Kwok, W. M.

C. Ma, W. M. Kwok, W. S. Chan, P. Zuo, J. T. W. Kan, P. H. Toy, and D. L. Phillips, "Ultrafast time-resolved study of photophysical processes involved in the photodeprotection of p-hydroxyphenacyl caged phototrigger compounds," J. Am. Chem. Soc. 127, 1463-1472 (2005).
[CrossRef] [PubMed]

Le Floc'h, V.

F. Treussart, R. Alleaume, V. Le Floc'h, L. T. Xiao, J.-M. Courty, and J.-F. Roch, "Direct measurement of the photon statistics of a triggered single photon source," Phys. Rev. Lett. 89, 093601 (2002).
[CrossRef] [PubMed]

Lee, C.-K.

Link, S.

Liu, R.-B.

A.-L. Pan, H. Yang, R.-B. Liu, R.-C. Yu, B.-S. Zou, and Z.-L. Wang, "Color-tunable photoluminescence of alloyed CdSxSe1−x nanobelts," J. Am. Chem. Soc. 127, 15692-15693 (2005).
[CrossRef] [PubMed]

Lustres, J. L. P.

L. J. Zhao, J. L. P. Lustres, V. Farztdinov, and N. P. Ernsting, "Femtosecond fluorescence spectroscopy by up-conversion with tilted gate pulses," Chem. Phys. 7, 1716-1725 (2005).
[CrossRef]

Ma, C.

C. Ma, W. M. Kwok, W. S. Chan, P. Zuo, J. T. W. Kan, P. H. Toy, and D. L. Phillips, "Ultrafast time-resolved study of photophysical processes involved in the photodeprotection of p-hydroxyphenacyl caged phototrigger compounds," J. Am. Chem. Soc. 127, 1463-1472 (2005).
[CrossRef] [PubMed]

Mahr, H.

H. Mahr and M. D. Hirsch, "An optical up-conversion light gate with picosecond resolution," Opt. Commun. 13, 96-99 (1975).
[CrossRef]

Maroncelli, M.

Martínez, V. M.

V. M. Martínez, F. L. Arbeloa, J. B. Prieto, and I. L. Arbeloa, "Characterization of Rhodamine 6G aggregates intercalated in solid thin films of laponite clay 2 fluorescence spectroscopy," J. Phys. Chem. B 109, 7443-7450 (2005).
[CrossRef]

Mokhtari, A.

Murata, S.

S. Iwai, S. Murata, and M. Tachiya, "Ultrafast fluorescence quenching by electron transfer and fluorescence from the second excited state of a charge transfer complex as studied by femtosecond up-conversion spectroscopy," J. Chem. Phys. 109, 5963-5970 (1998).
[CrossRef]

Nakajima, K.

J. Takeda, K. Nakajima, S. Kurita, S. Tomimoto, S. Saito, and T. Suemoto, "Time-resolved luminescence spectroscopy by the optical Kerr-gate method applicable to ultrafast relaxation processes," Phys. Rev. B 62, 10083-10087 (2000).
[CrossRef]

Nansei, H.

S. Tomimoto, H. Nansei, S. Saito, T. Suemoto, J. Takeda, and S. Kurita, "Femtosecond dynamics of the exciton self-trapping process in a quasi-one-dimensional halogen-bridged platinum complex," Phys. Rev. Lett. 81, 417-420 (1998).
[CrossRef]

Pan, A.-L.

A.-L. Pan, H. Yang, R.-B. Liu, R.-C. Yu, B.-S. Zou, and Z.-L. Wang, "Color-tunable photoluminescence of alloyed CdSxSe1−x nanobelts," J. Am. Chem. Soc. 127, 15692-15693 (2005).
[CrossRef] [PubMed]

Pan, C.-L.

Phillips, D. L.

C. Ma, W. M. Kwok, W. S. Chan, P. Zuo, J. T. W. Kan, P. H. Toy, and D. L. Phillips, "Ultrafast time-resolved study of photophysical processes involved in the photodeprotection of p-hydroxyphenacyl caged phototrigger compounds," J. Am. Chem. Soc. 127, 1463-1472 (2005).
[CrossRef] [PubMed]

Piel, J.

Prieto, J. B.

V. M. Martínez, F. L. Arbeloa, J. B. Prieto, and I. L. Arbeloa, "Characterization of Rhodamine 6G aggregates intercalated in solid thin films of laponite clay 2 fluorescence spectroscopy," J. Phys. Chem. B 109, 7443-7450 (2005).
[CrossRef]

Radzewicz, C.

P. Fita, Y. Stepanenko, and C. Radzewicz, "Femtosecond transient fluorescence spectrometer based on parametric amplification," Appl. Phys. Lett. 86, 021909 (2005).
[CrossRef]

Riedle, E.

Roch, J.-F.

F. Treussart, R. Alleaume, V. Le Floc'h, L. T. Xiao, J.-M. Courty, and J.-F. Roch, "Direct measurement of the photon statistics of a triggered single photon source," Phys. Rev. Lett. 89, 093601 (2002).
[CrossRef] [PubMed]

Saito, S.

J. Takeda, K. Nakajima, S. Kurita, S. Tomimoto, S. Saito, and T. Suemoto, "Time-resolved luminescence spectroscopy by the optical Kerr-gate method applicable to ultrafast relaxation processes," Phys. Rev. B 62, 10083-10087 (2000).
[CrossRef]

S. Tomimoto, S. Saito, T. Suemoto, K. Sakata, J. Takeda, and S. Kurita, "Observation of the wave-packet oscillation during the exciton self-trapping process in a quasi-one-dimensional halogen-bridged Pt complex," Phys. Rev. B 60, 7961-7965 (1999).
[CrossRef]

S. Tomimoto, H. Nansei, S. Saito, T. Suemoto, J. Takeda, and S. Kurita, "Femtosecond dynamics of the exciton self-trapping process in a quasi-one-dimensional halogen-bridged platinum complex," Phys. Rev. Lett. 81, 417-420 (1998).
[CrossRef]

Sakata, K.

S. Tomimoto, S. Saito, T. Suemoto, K. Sakata, J. Takeda, and S. Kurita, "Observation of the wave-packet oscillation during the exciton self-trapping process in a quasi-one-dimensional halogen-bridged Pt complex," Phys. Rev. B 60, 7961-7965 (1999).
[CrossRef]

Shah, J.

J. Shah, "Ultrafast luminescence spectroscopy using sum frequency generation," IEEE J. Quantum Electron. 24, 276-288 (1988).
[CrossRef]

T. C. Damen and J. Shah, "Femtosecond luminescence spectroscopy with 60 fs compressed pulses," Appl. Phys. Lett. 52, 1291-1293 (1988).
[CrossRef]

J. Shah, T. C. Damen, B. Deveaud, and D. Block, "Subpicosecond luminescence spectroscopy using sum frequency generation," Appl. Phys. Lett. 50, 1307-1309 (1987).
[CrossRef]

D. Block, J. Shah, and A. C. Gossard, "Femtosecond luminescence measurements in GaAs," Solid State Commun. 59, 527-531 (1986).
[CrossRef]

Shirakawa, A.

A. Shirakawa and T. Kobayashi, "Sub-10-fs tunable pulses in visible and NIR and visible sub-5-fs pulses generated by noncollinear OPA," J. Lumin. 87-89, 119-120 (2000).

A. Shirakawa and T. Kobayashi, "Noncollinearly phase-matched femtosecond optical parametric amplification with a 2000 cm−1 bandwidth," Appl. Phys. Lett. 72, 147-149 (1998).
[CrossRef]

Shreenath, A. P.

Stepanenko, Y.

P. Fita, Y. Stepanenko, and C. Radzewicz, "Femtosecond transient fluorescence spectrometer based on parametric amplification," Appl. Phys. Lett. 86, 021909 (2005).
[CrossRef]

Suemoto, T.

J. Takeda, K. Nakajima, S. Kurita, S. Tomimoto, S. Saito, and T. Suemoto, "Time-resolved luminescence spectroscopy by the optical Kerr-gate method applicable to ultrafast relaxation processes," Phys. Rev. B 62, 10083-10087 (2000).
[CrossRef]

S. Tomimoto, S. Saito, T. Suemoto, K. Sakata, J. Takeda, and S. Kurita, "Observation of the wave-packet oscillation during the exciton self-trapping process in a quasi-one-dimensional halogen-bridged Pt complex," Phys. Rev. B 60, 7961-7965 (1999).
[CrossRef]

S. Tomimoto, H. Nansei, S. Saito, T. Suemoto, J. Takeda, and S. Kurita, "Femtosecond dynamics of the exciton self-trapping process in a quasi-one-dimensional halogen-bridged platinum complex," Phys. Rev. Lett. 81, 417-420 (1998).
[CrossRef]

Tachiya, M.

S. Iwai, S. Murata, and M. Tachiya, "Ultrafast fluorescence quenching by electron transfer and fluorescence from the second excited state of a charge transfer complex as studied by femtosecond up-conversion spectroscopy," J. Chem. Phys. 109, 5963-5970 (1998).
[CrossRef]

Takeda, J.

J. Takeda, K. Nakajima, S. Kurita, S. Tomimoto, S. Saito, and T. Suemoto, "Time-resolved luminescence spectroscopy by the optical Kerr-gate method applicable to ultrafast relaxation processes," Phys. Rev. B 62, 10083-10087 (2000).
[CrossRef]

S. Tomimoto, S. Saito, T. Suemoto, K. Sakata, J. Takeda, and S. Kurita, "Observation of the wave-packet oscillation during the exciton self-trapping process in a quasi-one-dimensional halogen-bridged Pt complex," Phys. Rev. B 60, 7961-7965 (1999).
[CrossRef]

S. Tomimoto, H. Nansei, S. Saito, T. Suemoto, J. Takeda, and S. Kurita, "Femtosecond dynamics of the exciton self-trapping process in a quasi-one-dimensional halogen-bridged platinum complex," Phys. Rev. Lett. 81, 417-420 (1998).
[CrossRef]

Tomimoto, S.

J. Takeda, K. Nakajima, S. Kurita, S. Tomimoto, S. Saito, and T. Suemoto, "Time-resolved luminescence spectroscopy by the optical Kerr-gate method applicable to ultrafast relaxation processes," Phys. Rev. B 62, 10083-10087 (2000).
[CrossRef]

S. Tomimoto, S. Saito, T. Suemoto, K. Sakata, J. Takeda, and S. Kurita, "Observation of the wave-packet oscillation during the exciton self-trapping process in a quasi-one-dimensional halogen-bridged Pt complex," Phys. Rev. B 60, 7961-7965 (1999).
[CrossRef]

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[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Schematic of the transient fluorescence spectrometer. BS, 5:1 beam splitter; SH1, SH2, BBO crystals for the second-harmonic generation; S1, S2, mechanical shutter; SC, 1 mm thick sample cell; NF, notch filter centered at 800 nm ; CP, chopper; PA, 1 mm thick parametric amplification BBO crystal; FL, flat mirror.

Fig. 2
Fig. 2

Image of far-field pattern of optical parametric superfluorescence and the amplified seeding fluorescence spot.

Fig. 3
Fig. 3

Steady-state fluorescence spectrum of Rhodamine 6G (black curve) and transient fluorescence spectrum amplified by OPA recorded at a time delay of 2 ps (gray curve).

Fig. 4
Fig. 4

Kinetic traces of OPA amplified seeder at the peak wavelength signal ( 580 nm , 엯) and idler ( 1290 nm , ▵), respectively.

Fig. 5
Fig. 5

(a) Relation between the amplified fluorescence intensity at the signal branch and the corresponding seeder intensity at a fixed 400 nm pump power of 110 μ J per pulse. The intensity of the seeding fluorescence was attenuated from 100% to 0.1%. (b) Normalized kinetic traces with different attenuation level of the seeding fluorescence, i.e., with a transmission of 100%, 10%, and 1%, respectively.

Fig. 6
Fig. 6

NOPA amplified fluorescence decay kinetics with an attenuation factor of 0.05%.

Fig. 7
Fig. 7

(a) Steady-state fluorescence spectrum of Cd S x Se 1 x ( x = 0.78 ) nanobelts excited by 400 nm 150 fs pulsed laser (A), and the corresponding transient amplified fluorescence spectra recorded at different delay time of 1.5 (B) and 3.0 ps (C), respectively; the intensities were scaled to that of A. (b) Kinetic trace of the photoluminescence decay monitored at 587 nm after excitation at 400 nm . The rising and decay phases can be fitted by a monoexponential process with a time constant of 0.5 and 2.1 ps , respectively.

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