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Spectral modulation of ultra-broadband femtosecond laser pulses based on surface plasmon resonance
Optics Communications 283 (2010) 2373–2377
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
Spectral modulation of ultra-broadband femtosecond laser pulses based on surface plasmon resonance Xiaoan Huang a, Pengfei Zhu a,*, Xiangmin Liu b, Yuxin Leng c, Xiaoming Lu c, Helin Wang c a
Department of Physics, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China Department of Mathematics and Physics, Shijiazhuang Railway Institute, Shijiazhuang 050043, China c State Key Laboratory of High Field Laser Physics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China b
a r t i c l e
i n f o
Article history: Received 14 September 2009 Received in revised form 25 November 2009 Accepted 30 January 2010
Keywords: Spectral modulation Surface plasmon resonance Femtosecond pulses
a b s t r a c t The surface plasmon resonance (SPR) for spectral modulation of the femtosecond laser pulses with 110 nm ultra-broad bandwidth is demonstrated on the basis of the development of ultrashort pulse laser sources which supports good spatial resolution and high peak intensity. Employing the femtosecond surface plasmon polariton pulses launched by a Kretschmann configuration, whose reflectivity curve has the characteristic of the ultra-broad bandwidth, we observe a frequency-dependent loss with greater attenuation at the peak of the spectrum profile than in the wings, which is very useful for adequate spectral modulation. The SPR for the spectral modulation is investigated in theoretical and experimental aspects. The arbitrary spectral modulation of the femtosecond laser pulses can be fulfilled by controlling and optimizing the SPR of the gold film. The experimental result agrees well with the calculation. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Over the past decades, considerable efforts have been made in ultrashort pulse laser sources. Pulse durations has decreased from several picoseconds, by employing a passively modelocked Nd:glass laser, to single-digit femtoseconds with the help of Kerr-lens mode-locking (KLM) technique [1,2], which have opened up new applications of the spectral modulation ranging from optical wireless communications [3], optical parametric chirped pulse amplification (OPCPA) system [4], quantum control [5–7], and twophoton laser scanning microscopy [8] to the [2-methoxy-5-(20 ethyl-hexyloxy)-1,4-phenylenevinylene] photobleaching control [9]. However, successful amplification of the ultra-broadband laser pulses is limited primarily by the gain narrowing effect which has resulted in rapid progress in spectral modulation techniques [10– 22]. Spectral modulation components such as etalon [10], birefringent crystal [10], Gaussian spectral filter [13], electro-optic modulation [14], spatial light modulator [15], dynamic holograms [17], acousto-optic modulation [18], and prism-waveguide coupler [19] have broadened the bandwidth of the amplified laser pulses effectively. More recently, spectral modulation of femtosecond laser pulses induced by molecular alignment revivals is demonstrated, which leads to a spectral red- or blue-shift of the probe pulses [21]. For an etalon as a spectral modulation device, it is difficult to adjust the position of the modulation conveniently [22]. As a spectral modulation device, the full width at half maximum * Corresponding author. E-mail addresses: [email protected] (X. Huang), [email protected] (P. Zhu). 0030-4018/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2010.01.070
(FWHM) of the prism-waveguide coupler [19] is not broad enough to meet the requirements for the ultra-broadband femtosecond laser pulses, and it is subjected to the effect of the partial coherence property of the ultrashort laser pulses at high-order modes [23,24]. Fortunately, the bandwidth of the femtosecond surface plasmon polariton (SPP) pulses [25–32] which have attracted much attention due to high packing densities and strong nonlinearities, is broad enough to fulfill the spectral modulation of the ultra-broadband femtosecond laser pulses. The femtosecond surface plasmon resonance (SPR) was used to monitor the evolution of acoustic phonons in impulsively heated metal films [28] and to resolve the dynamics of an electron gas weakly excited by the femtosecond laser pulses [29]. Very recently, the significant distortion of the femtosecond laser pulses at the SPR excitation in a plasmonic crystal is observed [31], and the spectral phase shift and the narrowing of the SPP pulse spectrum caused by the femtosecond laser pulses are reported [32]. But to our knowledge, the femtosecond SPR has not yet been applied to the spectral modulation of the ultra-broadband femtosecond pulses. In this letter we employ the SPR to fulfill the spectral modulation of 110 nm ultra-broadband femtosecond pulses, which has the advantages of the exceedingly broad bandwidth and being free from the effect of partial coherence property of the ultrashort laser pulses.
2. The principle of the SPR Let us consider the attenuated total reflection (ATR) of a TMpolarized laser in the Kretschmann configuration [33,34] which is
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X. Huang et al. / Optics Communications 283 (2010) 2373–2377
here,
c12 ¼ ðer1 a2 er2 a1 Þ=ðer1 a2 þ er2 a1 Þ; c23 ¼ ðer2 a3 er3 a2 Þ=ðer2 a3 þ er3 a2 Þ;
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffi 2 where aj ¼ ðb2 k0 erj Þ (j = 1,2,3), b ¼ k0 er3 sin h, k0 = 2p/k, k is the wavelength of the incident laser in air and d is the thickness of the gold film. Since Kx(h) is real and K is complex, only an approximate match can be reached at
pffiffiffiffiffiffi h ¼ hATR ¼arcsin½ReðKÞk=ð2 _ p er3 Þ:
Fig. 1. The Kretschmann configuration: 1, air; 2, a thin gold film; 3, a ZF7 prism; er1 = 1, er2 (the Drude model), er3 (Eq. (3)).
composed of a prism and a gold film, as shown in Fig. 1. When the laser arrives at the base of the prism at the incident angle h larger than the critical angle, it can couple directly with the SPP pulses at the metal–air interface and the coupling only takes place when the parallel wave vector Kx(h) of the incident laser matches with the complex wave vector K of the SPP pulses. The reflectance R of the Kretschmann configuration [35] is given by
Rðk; hÞ ¼ jðc23 þ c12 e2a2 d Þ=ð1 þ c23 c12 e2a2 d Þj2 ;
ð1Þ
Fig. 2. The reflectance of the SPR excited by the Kretschmann configuration with respect to the laser wavelength.
ð2Þ
At the resonant angle hATR, the SPR is excited and the incident light is attenuated during the reflection. The relative dielectric permittivity er2 of the gold film which depends on the wavelength strongly is calculated from the Drude model [36]. Also, the relative dielectric permittivity er3 of the ZF7 glass prism depending on the wavelength is given by
er3 ¼ A0 þ A1 k2 þ A2 k2 þ A3 k4 þ A4 k6 þ A5 k8 ;
ð3Þ
where, k is the wavelength of the incident light in vacuum (unit: lm), and A0 to A5 are the constants with A0 = 3.12192, A2 = 0.0419, A3 = 0.00314, A4 = 0.000221, A1 = 0.0101, A5 = 0.0000274, respectively. 3. Numerical simulation According to Eq. (1), the reflectance of the SPR excited by the Kretschmann configuration with respect to the wavelength of laser is shown in Fig. 2. The corresponding parameters used for calculation are er1 = 1, er2 (the Drude model), er3 (Eq. (3)), d = 50 nm, h = 37.79°, respectively. We can see that the reflectance curve exhibits an absorption dip at the resonant wavelength and the bandwidth of the ATR curve obtained by the SPR is very broad owing to the great energy dissipation caused by the imaginary part of the dielectric constant of the gold film. The wavelength-dependent ATR curve can be characterized by three main parameters: central wavelength, attenuation depth and attenuation bandwidth. Numerical simulation for the ATR curves with respect to the angle of incidence h and the thickness of the thin gold film d are displayed in Fig. 3a and b, respectively. For the Kretschmann configuration, we can observe that the central wavelength of the ATR curves can be arbitrarily shifted by changing the angle of incidence h, and the attenuation depth and bandwidth are determined by the thickness of thin gold film d, as shown in Fig. 3b. Surface plasmon wave (SPW) has similar ATR curve with the existing spectral modulation devices, such as etalon [10], birefringent crystal [10], Gaussian spectral filter [13], prism-waveguide coupler [19] and so on. Furthermore, the SPW has ultra-broad
Fig. 3. The wavelength-dependent ATR curves with respect to the angle of incidence h and the thickness of the gold film d: (a) the changing central wavelengths of the ATR curves at different angles of incidence h; (b) the changing attenuation depths and bandwidths of the ATR curves with different thicknesses of the gold film d.
X. Huang et al. / Optics Communications 283 (2010) 2373–2377
Fig. 4. Simulated modulated spectrum (solid line), the original spectrum (dashdotted line) and the ATR of the SPW (dashed line) for the perfect Gaussian femtosecond laser pulses.
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bandwidth of 110 nm, and can be tuned to match the much broader bandwidth of 200 nm which corresponds to the pulse duration of 5 fs [37], as is shown in Fig. 3. Therefore, we propose the SPW may be applied to the spectral modulation of the ultra-broadband femtosecond laser pulses. Through the above simulations we can draw the conclusion that the required ATR curves can be obtained by designing the appropriate thickness of the gold film d which determines the bandwidth and the attenuation depth of the SPW. Furthermore, the central wavelength of the ATR curves can be arbitrarily shifted by adjusting the angle of incidence h, as shown in Fig. 3. Consequently, it can be applied in the arbitrary spectral modulation of the ultra-broadband femtosecond laser pulses. For preparing the experiments, we make a simulation as follows: the Gaussian shape femtosecond laser pulse with the central wavelength of 800 nm and the FWHM of 110 nm (the dash-dotted line in Fig. 4) arrives at the base of the prism at the incident angle h of 35.79°, exciting the SPW (the dashed line in Fig. 4) in the gold film of 63 nm and the reflected femtosecond laser pulse (the solid curve in Fig. 4) is spectral modulated. The intensity at the center of the original spectrum is attenuated about 73%, which is very encouraging for the expected spectral modulation.
4. Experiment of spectral modulation of the ultra-broadband femtosecond laser pulses based on the SPR
1.0 (a) 0.9 0.8 0.7 0.6 broaden 0.5 0.4 deeper 0.3 0.2 0.1 0.0 600 650 700 750 800 850 900 950 1000 Wavelength (nm)
Intensity (a. u.)
Intensity (a. u.)
Fig. 5. Experimental setup for spectral modulation of the femtosecond laser pulses employing the SPR. M1, M2: spherical mirror; P9 and P10: intra-cavity chirped mirror; P11 and P12: extra-cavity chirped mirror; P1–P8: plane mirror.
The experiment setup is shown in Fig. 5. The self-mode-locked (SML) Ti:sapphire laser produces 10 fs pulses with 800 nm central wavelength, 110 nm bandwidth (FWHM) and 600 mw output power at a repetition rate of 76 MHz. The adjustment of the angle of incidence h is carried out by a goniometer. Since the femtosecond laser is TE-polarized, a half-wave plate is used to convert the TE-polarized to be the TM-polarized only that can excite the SPR. The femtosecond laser pulses arrive at the base of the ZF7 glass prism with the incident angle h = 35.79°, corresponding to the central wavelength of 800 nm. A gold film was vacuum sputtered onto the base of a ZF7 glass prism to fabricate a Kretschmann configuration. Based on the simulation of Fig. 4, we design the thickness of the gold film to be 63 nm that ensures a deep enough dip at the central wavelength and an appropriate bandwidth for the femtosecond laser pulse. The thickness of the gold film was measured by Chen’s method [35]. The spectrum of the reflected femtosecond laser pulses is detected by a USB 2000 Miniature Fiber Optic Spectrometer (Ocean Optics Corporation). As shown in Fig. 6a, the reflected spectrum is broadened by 6 nm and the intensity at the central wavelength is attenuated by 24%. Compared with the theoretical result of Fig. 6b where
1.0 0.9 (b) 0.8 0.7 broaden 0.6 0.5 0.4 0.3 deeper 0.2 0.1 0.0 600 650 700 750 800 850 900 950 1000 Wavelength (nm)
Fig. 6. (a) Measured and (b) calculated modulated result for the femtosecond laser pulses with the FWHM of 110 nm, the original spectrum (dashed line) and the modulated spectrum (solid line).
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X. Huang et al. / Optics Communications 283 (2010) 2373–2377
1.0
1.0
(a)
0.8
0.8
0.7
0.7
0.6 0.5 0.4
0.6 0.5 0.4
0.3
0.3
0.2
0.2
0.1 0.0 600 650 700 750 800 850 900 950 1000 Wavelength (nm)
(b)
0.9
Reflectance
Reflectance
0.9
0.1 0.0 35.0
35.5 36.0 36.5 Angle of incidence (deg)
37.0
Fig. 7. (a) ATR curves of the SPW excited by the femtosecond laser pulses with the FWHM of 110 nm with respect to the wavelength and (b) ATR curves of the SPW excited by the 650 nm semiconductor monochromatic laser with respect to the angle of incidence, measured (solid line) and calculated result (dashed line).
the FWHM is broadened by 15 nm and the intensity at the centre is attenuated by 34%, experimental result agrees approximately with the theoretical expectation. However, it should be noted that the experimental result has little discrepancy with the simulative result. After the first refraction in the ZF7 prism, the obliquely incident femtosecond laser pulses with the very broad FWHM of 110 nm will undergo the spatial dispersion which results in the deviation of the angle of incidence at the base of the prism, and the discrepancy of the reflectivity between the experimental results and the calculation occurs according to Eq. (1), as is shown in Fig. 7a. Furthermore, after the second refraction, the angular dispersion causes the spectral shift of the output laser pulses from another surface of the ZF7 prism inevitably. The issue mentioned above can be avoided if the femtosecond laser pulses are vertically incident onto the surface of the ZF7 prism. The dependence of the ATR curves with respect to the incident angle h is shown in Fig. 7b, where we employ the 650 nm semiconductor monochromatic laser. We can observe that the measured ATR curve in Fig. 7a is narrower than the calculated with respect to the bandwith and the measured ATR curve in Fig. 7b is broader than the calculated with respect to the incident angle, which are both essentially attributed to the angular dispersion. Also, it should be mentioned that the measured ATR curve in Fig. 7a is shallower than that in Fig. 7b, because the ultra-broadband femtosecond laser pulses undergo the great wavelength dispersion of the ZF7 prism besides the angular dispersion only which the 650 nm semiconductor monochromatic laser undergo.
technique is not adapted to the spectral modulation of the femtosecond laser pulses with the spectrum ranging in the long-wavelength near-infrared region (1100–2500 nm), because the absorption is exceedingly large for the noble metal in that range, which causes a much shallower dip for the ATR curve of the SPR. Fortunately, our technology can be used to most of the Ti:sapphire femtosecond laser systems working at the central wavelength of 800 nm. Moreover, the new technology demonstrated in this letter is based on the reflective structure, which has the advantages of the lower insertion loss and the smaller phase distortion, compared with the existing transmission spectral modulation devices (etalon, birefringent crystal and so on). Acknowledgments This work is supported by National Nature Science Foundation of China under Grant Nos. 60408010, 60908008 and 10804076, the National Basic Research Program of China under Grant No. 2006CB806001, the Knowledge Innovation Program of the Chinese Academy of Sciences under Grant No. KGCX-YW-417, and Shanghai Commission of Science and Technology under Grants Nos. 07JC14055 and 09QA1406500. References [1] [2] [3] [4]
5. Discussion and conclusion In this letter, we report that the SPR shows good potential to implement the arbitrary spectral modulation of the ultra-broadband femtosecond laser pulses, which has advantages of the ultra-broad bandwidth and modulating central wavelengths ranging from 700 nm to 900 nm. Considering the dispersion of the ZF7 prism, the femtosecond laser pulses will be stretched a little in time domain generally. Group-velocity dispersion (GVD) and the third-order dispersion (TOD) caused by the ZF7 material at the central wavelength of 800 nm, which can be compensated with the broadband double-chirped mirrors and so on, are 2.00 fs2/mm and 1.29 fs3/mm, respectively, and the spectral phase error is about 0.083. Mainly due to the dip at the central wavelength of the femtosecond laser pulses, the peak is reduced and the spectrum is broadened after the intensity normalization, which can overcome the gain narrowing effect in the chirped pulse amplification (CPA) system and the OPCPA system. It should be noted that this
[5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]
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[28] M. van Exter, A. Lagendijk, Phys. Rev. Lett. 60 (1988) 49. [29] Rogier H.M. Groeneveld, Rudolf Sprik, Ad Lagendijk, Phys. Rev. Lett. 64 (1990) 784. [30] Vasily V. Temnov, Keith Nelson, Gaspar Armelles, Alfonso Cebollada, Tim Thomay, Alfred Leitenstorfer, Rudolf Bratschitsch, Opt. Express 17 (2009) 10. [31] A.S. Vengurlekarar, A. Venu Gopal, Appl. Phys. Lett. 89 (2006) 181927. [32] S.E. Yalcin, Y. Wang, M. Achermann, Appl. Phys. Lett. 93 (2008) 101103. [33] E. Kretschmann, Z. Phys. 241 (1971) 313. [34] E. Burstein et al., J. Vac. Sci. Technol. 11 (1974) 1004. [35] W.P. Chen, J.M. Chen, J. Opt. Soc. Am. 71 (1981) 2. [36] N.W. Ashcroft, N.D. Mermin, Solid State Physics, Saunders College Publishing, New York, 1976, pp. 1–28. [37] X. Chen, X. Li, J. Liu, P. Wei, X. Ge, R. Li, Z. Xu, Opt. Lett. 32 (2007) 2402.
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Spectral modulation of ultra-broadband femtosecond laser pulses based on surface plasmon resonance Xiaoan Huang a, Pengfei Zhu a,*, Xiangmin Liu b, Yuxin Leng c, Xiaoming Lu c, Helin Wang c a
Department of Physics, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China Department of Mathematics and Physics, Shijiazhuang Railway Institute, Shijiazhuang 050043, China c State Key Laboratory of High Field Laser Physics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China b
a r t i c l e
i n f o
Article history: Received 14 September 2009 Received in revised form 25 November 2009 Accepted 30 January 2010
Keywords: Spectral modulation Surface plasmon resonance Femtosecond pulses
a b s t r a c t The surface plasmon resonance (SPR) for spectral modulation of the femtosecond laser pulses with 110 nm ultra-broad bandwidth is demonstrated on the basis of the development of ultrashort pulse laser sources which supports good spatial resolution and high peak intensity. Employing the femtosecond surface plasmon polariton pulses launched by a Kretschmann configuration, whose reflectivity curve has the characteristic of the ultra-broad bandwidth, we observe a frequency-dependent loss with greater attenuation at the peak of the spectrum profile than in the wings, which is very useful for adequate spectral modulation. The SPR for the spectral modulation is investigated in theoretical and experimental aspects. The arbitrary spectral modulation of the femtosecond laser pulses can be fulfilled by controlling and optimizing the SPR of the gold film. The experimental result agrees well with the calculation. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Over the past decades, considerable efforts have been made in ultrashort pulse laser sources. Pulse durations has decreased from several picoseconds, by employing a passively modelocked Nd:glass laser, to single-digit femtoseconds with the help of Kerr-lens mode-locking (KLM) technique [1,2], which have opened up new applications of the spectral modulation ranging from optical wireless communications [3], optical parametric chirped pulse amplification (OPCPA) system [4], quantum control [5–7], and twophoton laser scanning microscopy [8] to the [2-methoxy-5-(20 ethyl-hexyloxy)-1,4-phenylenevinylene] photobleaching control [9]. However, successful amplification of the ultra-broadband laser pulses is limited primarily by the gain narrowing effect which has resulted in rapid progress in spectral modulation techniques [10– 22]. Spectral modulation components such as etalon [10], birefringent crystal [10], Gaussian spectral filter [13], electro-optic modulation [14], spatial light modulator [15], dynamic holograms [17], acousto-optic modulation [18], and prism-waveguide coupler [19] have broadened the bandwidth of the amplified laser pulses effectively. More recently, spectral modulation of femtosecond laser pulses induced by molecular alignment revivals is demonstrated, which leads to a spectral red- or blue-shift of the probe pulses [21]. For an etalon as a spectral modulation device, it is difficult to adjust the position of the modulation conveniently [22]. As a spectral modulation device, the full width at half maximum * Corresponding author. E-mail addresses: [email protected] (X. Huang), [email protected] (P. Zhu). 0030-4018/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2010.01.070
(FWHM) of the prism-waveguide coupler [19] is not broad enough to meet the requirements for the ultra-broadband femtosecond laser pulses, and it is subjected to the effect of the partial coherence property of the ultrashort laser pulses at high-order modes [23,24]. Fortunately, the bandwidth of the femtosecond surface plasmon polariton (SPP) pulses [25–32] which have attracted much attention due to high packing densities and strong nonlinearities, is broad enough to fulfill the spectral modulation of the ultra-broadband femtosecond laser pulses. The femtosecond surface plasmon resonance (SPR) was used to monitor the evolution of acoustic phonons in impulsively heated metal films [28] and to resolve the dynamics of an electron gas weakly excited by the femtosecond laser pulses [29]. Very recently, the significant distortion of the femtosecond laser pulses at the SPR excitation in a plasmonic crystal is observed [31], and the spectral phase shift and the narrowing of the SPP pulse spectrum caused by the femtosecond laser pulses are reported [32]. But to our knowledge, the femtosecond SPR has not yet been applied to the spectral modulation of the ultra-broadband femtosecond pulses. In this letter we employ the SPR to fulfill the spectral modulation of 110 nm ultra-broadband femtosecond pulses, which has the advantages of the exceedingly broad bandwidth and being free from the effect of partial coherence property of the ultrashort laser pulses.
2. The principle of the SPR Let us consider the attenuated total reflection (ATR) of a TMpolarized laser in the Kretschmann configuration [33,34] which is
2374
X. Huang et al. / Optics Communications 283 (2010) 2373–2377
here,
c12 ¼ ðer1 a2 er2 a1 Þ=ðer1 a2 þ er2 a1 Þ; c23 ¼ ðer2 a3 er3 a2 Þ=ðer2 a3 þ er3 a2 Þ;
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffi 2 where aj ¼ ðb2 k0 erj Þ (j = 1,2,3), b ¼ k0 er3 sin h, k0 = 2p/k, k is the wavelength of the incident laser in air and d is the thickness of the gold film. Since Kx(h) is real and K is complex, only an approximate match can be reached at
pffiffiffiffiffiffi h ¼ hATR ¼arcsin½ReðKÞk=ð2 _ p er3 Þ:
Fig. 1. The Kretschmann configuration: 1, air; 2, a thin gold film; 3, a ZF7 prism; er1 = 1, er2 (the Drude model), er3 (Eq. (3)).
composed of a prism and a gold film, as shown in Fig. 1. When the laser arrives at the base of the prism at the incident angle h larger than the critical angle, it can couple directly with the SPP pulses at the metal–air interface and the coupling only takes place when the parallel wave vector Kx(h) of the incident laser matches with the complex wave vector K of the SPP pulses. The reflectance R of the Kretschmann configuration [35] is given by
Rðk; hÞ ¼ jðc23 þ c12 e2a2 d Þ=ð1 þ c23 c12 e2a2 d Þj2 ;
ð1Þ
Fig. 2. The reflectance of the SPR excited by the Kretschmann configuration with respect to the laser wavelength.
ð2Þ
At the resonant angle hATR, the SPR is excited and the incident light is attenuated during the reflection. The relative dielectric permittivity er2 of the gold film which depends on the wavelength strongly is calculated from the Drude model [36]. Also, the relative dielectric permittivity er3 of the ZF7 glass prism depending on the wavelength is given by
er3 ¼ A0 þ A1 k2 þ A2 k2 þ A3 k4 þ A4 k6 þ A5 k8 ;
ð3Þ
where, k is the wavelength of the incident light in vacuum (unit: lm), and A0 to A5 are the constants with A0 = 3.12192, A2 = 0.0419, A3 = 0.00314, A4 = 0.000221, A1 = 0.0101, A5 = 0.0000274, respectively. 3. Numerical simulation According to Eq. (1), the reflectance of the SPR excited by the Kretschmann configuration with respect to the wavelength of laser is shown in Fig. 2. The corresponding parameters used for calculation are er1 = 1, er2 (the Drude model), er3 (Eq. (3)), d = 50 nm, h = 37.79°, respectively. We can see that the reflectance curve exhibits an absorption dip at the resonant wavelength and the bandwidth of the ATR curve obtained by the SPR is very broad owing to the great energy dissipation caused by the imaginary part of the dielectric constant of the gold film. The wavelength-dependent ATR curve can be characterized by three main parameters: central wavelength, attenuation depth and attenuation bandwidth. Numerical simulation for the ATR curves with respect to the angle of incidence h and the thickness of the thin gold film d are displayed in Fig. 3a and b, respectively. For the Kretschmann configuration, we can observe that the central wavelength of the ATR curves can be arbitrarily shifted by changing the angle of incidence h, and the attenuation depth and bandwidth are determined by the thickness of thin gold film d, as shown in Fig. 3b. Surface plasmon wave (SPW) has similar ATR curve with the existing spectral modulation devices, such as etalon [10], birefringent crystal [10], Gaussian spectral filter [13], prism-waveguide coupler [19] and so on. Furthermore, the SPW has ultra-broad
Fig. 3. The wavelength-dependent ATR curves with respect to the angle of incidence h and the thickness of the gold film d: (a) the changing central wavelengths of the ATR curves at different angles of incidence h; (b) the changing attenuation depths and bandwidths of the ATR curves with different thicknesses of the gold film d.
X. Huang et al. / Optics Communications 283 (2010) 2373–2377
Fig. 4. Simulated modulated spectrum (solid line), the original spectrum (dashdotted line) and the ATR of the SPW (dashed line) for the perfect Gaussian femtosecond laser pulses.
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bandwidth of 110 nm, and can be tuned to match the much broader bandwidth of 200 nm which corresponds to the pulse duration of 5 fs [37], as is shown in Fig. 3. Therefore, we propose the SPW may be applied to the spectral modulation of the ultra-broadband femtosecond laser pulses. Through the above simulations we can draw the conclusion that the required ATR curves can be obtained by designing the appropriate thickness of the gold film d which determines the bandwidth and the attenuation depth of the SPW. Furthermore, the central wavelength of the ATR curves can be arbitrarily shifted by adjusting the angle of incidence h, as shown in Fig. 3. Consequently, it can be applied in the arbitrary spectral modulation of the ultra-broadband femtosecond laser pulses. For preparing the experiments, we make a simulation as follows: the Gaussian shape femtosecond laser pulse with the central wavelength of 800 nm and the FWHM of 110 nm (the dash-dotted line in Fig. 4) arrives at the base of the prism at the incident angle h of 35.79°, exciting the SPW (the dashed line in Fig. 4) in the gold film of 63 nm and the reflected femtosecond laser pulse (the solid curve in Fig. 4) is spectral modulated. The intensity at the center of the original spectrum is attenuated about 73%, which is very encouraging for the expected spectral modulation.
4. Experiment of spectral modulation of the ultra-broadband femtosecond laser pulses based on the SPR
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Intensity (a. u.)
Intensity (a. u.)
Fig. 5. Experimental setup for spectral modulation of the femtosecond laser pulses employing the SPR. M1, M2: spherical mirror; P9 and P10: intra-cavity chirped mirror; P11 and P12: extra-cavity chirped mirror; P1–P8: plane mirror.
The experiment setup is shown in Fig. 5. The self-mode-locked (SML) Ti:sapphire laser produces 10 fs pulses with 800 nm central wavelength, 110 nm bandwidth (FWHM) and 600 mw output power at a repetition rate of 76 MHz. The adjustment of the angle of incidence h is carried out by a goniometer. Since the femtosecond laser is TE-polarized, a half-wave plate is used to convert the TE-polarized to be the TM-polarized only that can excite the SPR. The femtosecond laser pulses arrive at the base of the ZF7 glass prism with the incident angle h = 35.79°, corresponding to the central wavelength of 800 nm. A gold film was vacuum sputtered onto the base of a ZF7 glass prism to fabricate a Kretschmann configuration. Based on the simulation of Fig. 4, we design the thickness of the gold film to be 63 nm that ensures a deep enough dip at the central wavelength and an appropriate bandwidth for the femtosecond laser pulse. The thickness of the gold film was measured by Chen’s method [35]. The spectrum of the reflected femtosecond laser pulses is detected by a USB 2000 Miniature Fiber Optic Spectrometer (Ocean Optics Corporation). As shown in Fig. 6a, the reflected spectrum is broadened by 6 nm and the intensity at the central wavelength is attenuated by 24%. Compared with the theoretical result of Fig. 6b where
1.0 0.9 (b) 0.8 0.7 broaden 0.6 0.5 0.4 0.3 deeper 0.2 0.1 0.0 600 650 700 750 800 850 900 950 1000 Wavelength (nm)
Fig. 6. (a) Measured and (b) calculated modulated result for the femtosecond laser pulses with the FWHM of 110 nm, the original spectrum (dashed line) and the modulated spectrum (solid line).
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Fig. 7. (a) ATR curves of the SPW excited by the femtosecond laser pulses with the FWHM of 110 nm with respect to the wavelength and (b) ATR curves of the SPW excited by the 650 nm semiconductor monochromatic laser with respect to the angle of incidence, measured (solid line) and calculated result (dashed line).
the FWHM is broadened by 15 nm and the intensity at the centre is attenuated by 34%, experimental result agrees approximately with the theoretical expectation. However, it should be noted that the experimental result has little discrepancy with the simulative result. After the first refraction in the ZF7 prism, the obliquely incident femtosecond laser pulses with the very broad FWHM of 110 nm will undergo the spatial dispersion which results in the deviation of the angle of incidence at the base of the prism, and the discrepancy of the reflectivity between the experimental results and the calculation occurs according to Eq. (1), as is shown in Fig. 7a. Furthermore, after the second refraction, the angular dispersion causes the spectral shift of the output laser pulses from another surface of the ZF7 prism inevitably. The issue mentioned above can be avoided if the femtosecond laser pulses are vertically incident onto the surface of the ZF7 prism. The dependence of the ATR curves with respect to the incident angle h is shown in Fig. 7b, where we employ the 650 nm semiconductor monochromatic laser. We can observe that the measured ATR curve in Fig. 7a is narrower than the calculated with respect to the bandwith and the measured ATR curve in Fig. 7b is broader than the calculated with respect to the incident angle, which are both essentially attributed to the angular dispersion. Also, it should be mentioned that the measured ATR curve in Fig. 7a is shallower than that in Fig. 7b, because the ultra-broadband femtosecond laser pulses undergo the great wavelength dispersion of the ZF7 prism besides the angular dispersion only which the 650 nm semiconductor monochromatic laser undergo.
technique is not adapted to the spectral modulation of the femtosecond laser pulses with the spectrum ranging in the long-wavelength near-infrared region (1100–2500 nm), because the absorption is exceedingly large for the noble metal in that range, which causes a much shallower dip for the ATR curve of the SPR. Fortunately, our technology can be used to most of the Ti:sapphire femtosecond laser systems working at the central wavelength of 800 nm. Moreover, the new technology demonstrated in this letter is based on the reflective structure, which has the advantages of the lower insertion loss and the smaller phase distortion, compared with the existing transmission spectral modulation devices (etalon, birefringent crystal and so on). Acknowledgments This work is supported by National Nature Science Foundation of China under Grant Nos. 60408010, 60908008 and 10804076, the National Basic Research Program of China under Grant No. 2006CB806001, the Knowledge Innovation Program of the Chinese Academy of Sciences under Grant No. KGCX-YW-417, and Shanghai Commission of Science and Technology under Grants Nos. 07JC14055 and 09QA1406500. References [1] [2] [3] [4]
5. Discussion and conclusion In this letter, we report that the SPR shows good potential to implement the arbitrary spectral modulation of the ultra-broadband femtosecond laser pulses, which has advantages of the ultra-broad bandwidth and modulating central wavelengths ranging from 700 nm to 900 nm. Considering the dispersion of the ZF7 prism, the femtosecond laser pulses will be stretched a little in time domain generally. Group-velocity dispersion (GVD) and the third-order dispersion (TOD) caused by the ZF7 material at the central wavelength of 800 nm, which can be compensated with the broadband double-chirped mirrors and so on, are 2.00 fs2/mm and 1.29 fs3/mm, respectively, and the spectral phase error is about 0.083. Mainly due to the dip at the central wavelength of the femtosecond laser pulses, the peak is reduced and the spectrum is broadened after the intensity normalization, which can overcome the gain narrowing effect in the chirped pulse amplification (CPA) system and the OPCPA system. It should be noted that this
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