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Femtosecond Bragg switching in opal-a-nc-Si photonic crystals
Journal of Non-Crystalline Solids 338–340 (2004) 215–217 www.elsevier.com/locate/jnoncrysol
Femtosecond Bragg switching in opal-a-nc-Si photonic crystals Dmitry A. Mazurenko a,*, Robert Kerst a, Andrey V. Akimov b, Alexander B. Pevtsov b, Dmitry A. Kurdyukov b, Valery G. Golubev b, Alexander V. Sel’kin b, Jaap I. Dijkhuis a a
b
Department of Physics and Astronomy, Atom Optics and Ultrafast Dynamics, Debye Institute, University of Utrecht, P.O. Box 80000, 3508 TA Utrecht, The Netherlands Ioffe Physico-Technical Institute, Russian Academy of Sciences, Politechnicheskaya 26, St. Petersburg 194021, Russia Available online 24 March 2004
Abstract We demonstrate ultrafast all-optical switching in a three-dimensional photonic crystal made of an opal-silicon composite. We show that the switching-on time is faster than 30 fs and determined by the pump pulse duration. The switching-off time is in the order of several picoseconds. The maximum transient change in reflectivity reaches values as high as 46% at the highest excitation power. Ó 2004 Elsevier B.V. All rights reserved. PACS: 42.70.Qs; 42.65.Pc; 78.66.Jg; 78.66.Sq
1. Introduction A photonic crystal [1] is an ordered array of submicron objects creating a periodically modulated index of refraction. In case of sufficient dielectric contrast, this structure possesses a photonic band gap – a range of wavelengths within which electromagnetic fields cannot propagate [2]. Although a large number of nanofabrication methods have been developed during the last decade, e.g. holographic lithography [3,4], layer by layer fabrication [5], self-assembly, etc., the production of highly-ordered and defect-free three-dimensional (3D) photonic crystals remains a challenge. Self-assembly of colloidal spheres seems nowadays the most promising way to create 3D photonic crystals with thicknesses of up to hundreds of microns and higher. Recently, fabrication of ice [6], titania [7], zinc sulfide [8], and other 3D photonic crystals were reported. One of the most interesting potential applications of photonic crystals is all-optical switching. The optical properties can be modified by an external light source when the photonic crystal is made of weakly absorbing material with high non-linear optical coefficients. A light *
Corresponding author. Tel.: +31-30-253 2206; fax: +31-30-253 7469. E-mail address: [email protected] (D.A. Mazurenko). 0022-3093/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2004.02.056
pulse can change the dielectric constant and shift the photonic stop band (PSB) position, thus, realizing alloptical switching. This idea was recently analyzed by Johnson and co-workers [9], and here we demonstrate it experimentally in the ultrafast domain, using amorphous-nanocrystalline silicon (a-nc-Si) as the non-linear optical material. In this paper, we examine the transient change in reflectivity of an a-nc-Si-based three-dimensional photonic crystal induced by strong irradiation of a femtosecond light pulse. We choose a synthetic opal, because it is known as a model object to study PSB effects [10]. The voids of the opal were filled with a-nc-Si to control the PSB properties of our photonic crystal by optical excitation of free carriers. A sketch of our structure is shown in the inset to Fig. 1. As a filling substance a-ncSi is further advantageous because of its high index of refraction and its suitability to be integrated into microelectronic technology [11].
2. Sample and experimental setup Our sample was prepared from a commercially available fcc opal with an a-SiO2 ball diameter of 230 nm [12]. This ordered matrix has a polydomain structure. The voids of this opal were filled with mixed amorphous-nanocrystalline silicon up to a filling factor
D.A. Mazurenko et al. / Journal of Non-Crystalline Solids 338–340 (2004) 215–217
close to 100% by thermal decomposition of a 5%-SiH4 – Ar gas mixture. The sample was cut in a 0.5-mm thick plate almost parallel to the (1 1 1) surface. Further details of the sample fabrication can be found in Ref. [13]. The stationary Bragg reflectance spectra were measured with a halogen lamp and detected by a spectrometer equipped with a CCD. All time-resolved reflectivity measurements were performed by a conventional pump-probe technique. High-power excitation (5 mJ/cm2 ) was supplied by a Ti-sapphire laser with a pulse length of 120 fs operated at a repetition rate of 500 Hz. The wavelength of the laser was 800 nm, which is in the tail of the absorption edge of a-nc-Si. The reflectance spectrum was probed by a weak pulse of white light continuum generated in a sapphire plate, which was excited by the same pulse of the Ti-sapphire laser. The time interval between the arrival of the pump and probe pulses at the sample was adjusted by a computer-controlled optical delay line. Low-power (70 lJ/cm2 ) high-temporal resolution Bragg reflectivity traces were measured with a 30 fs Tisapphire laser again with a wavelength of 800 nm. Here, the measuring sensitivity was increased up to 104 using a double-modulation technique and a lock-in amplifier. All pump and probe beams were incident in the [1 1 1] direction. The deviation of the (1 1 1) plane of the opal lattice from the plane of the sample surface allowed us to separate the Bragg diffracted light from the trivial specular surface reflection.
0 -3 ∆R/R (x10 )
Fig. 1. Measured () and calculated (––) spectra of Bragg diffraction efficiency of an a-nc-Si-based photonic crystal. Solid line is shown in absolute units. Insert shows a sketch of the fcc opal-Si structure.
width of the line is about 70 nm. Both the spectral position and the width of the reflectance maximum are in agreement with earlier studies of a similar sample [13] and can be attributed to the PSB in the [1 1 1] direction. The solid line in Fig. 1 shows the calculated spectrum of the Bragg reflectivity according to a theoretical model (developed by A.V. Sel’kin) based on the so-called twoband mixing formalizm [14], which is described in detail elsewhere [15]. We note the excellent agreement between the measured and calculated spectra. The temporal evolution of the relative transient change in the Bragg reflection DRðtÞ=R induced by a strong (5 mJ/cm2 ) optical pump pulse is shown for three probe wavelengths in Fig. 2, the solid curve at 780 nm (PSB region), and the dashed at 760 nm and dotted curves at 850 nm (wings of the PSB). The reflection signal shows an abrupt decrease directly after the arrival of the pump pulse (t ¼ 0) and partly recovers on a picosecond timescale. The changes in the Bragg reflection are maximum at the PSB where they reach DRðtÞ=R ¼ 46%. The inset to Fig. 2 displays the time trace of DRðtÞ=R measured at k ¼ 800 nm at a lower pump power density (70 lJ/cm2 ) and higher temporal resolution. Here, the amplitude of the relative changes in reflectivity is DR=R ¼ 1:2 102 . The initial peak in DRðtÞ=R occurs when pump and probe overlap in time and can be explained by the instantaneous Kerr effect [16]. The decay at longer delays appears to have a multi-exponential shape with the time constants s1 0:5 ps and s2 5 ps. The fact that the ultrafast switching takes place within 30 fs suggests that induced changes are caused by photoexcited carriers in a-nc-Si [17,18]. Photoinduced changes in the real and imaginary parts of the refractive index suppress the Bragg interference of the light inside the photonic crystal and diminish the Bragg reflection. This results in a rapid switching of the reflectivity of the
0.0 -0.1
-4 -8 -12
∆R/R
216
-0.2
0.0
0.5
1.0
1.5
Time, ps
-0.3 -0.4
3. Experimental result and discussion
-0.5 0
In Fig. 1 the symbols show the measured stationary Bragg reflectance spectrum of the opal-Si structure. The peak in the reflectivity is centered around k ¼ 790 nm and corresponds to the first order PSB. We note that the exact position of the reflectivity maximum varies between 780 and 820 nm over the sample surface. The
2
4 6 Time, ps
8
10
Fig. 2. Time-resolved transient differential reflection DRðtÞ=R at 760 nm (- - -), 780 nm (––), and 850 nm ( ) in case of high-power (5 mJ/cm2 ) optical pulse excitation. Insert shows DRðtÞ=R at 800 nm in case of moderate (70 lJ/cm2 ) optical pulse excitation, measured with a higher temporal resolution (30 fs).
D.A. Mazurenko et al. / Journal of Non-Crystalline Solids 338–340 (2004) 215–217
opal on the detected wavelength. The exact value of the recovery time of DRðtÞ=R depends on the selected points of the sample due to variation in volume fractions of aSi and nc-Si compounds. Generally, the shape of the transient reflectivity decay is reminiscent of the one obtained earlier in a layer comprised of nanocrystallites of silicon embedded in an amorphous silicon matrix [18]. We note, that defects and inhomogeneity of nanocrystalline silicon decrease the relaxation time of carriers and, consequently, increase the recovery speed of the transient reflectivity. This is promising for applications and demonstrates the suitability of using a-nc-Si as a filling material for ultrafast switching in photonic crystals. Photoinduced changes in the reflectivity DR can be calculated given the photoinduced changes DeSi in the dielectric constant of silicon. The dominant effect of DeSi is caused by photoexcited carriers and can be described by the Drude relationship [17] Ne2 1 1 i DeSi ¼ ; ð1Þ xsd m e0 ðx2 þ s2 d Þ where m ¼ 0:15m0 [19] is the optical reduced mass, sd ¼ 0:5 fs [17] the Drude damping time, x ¼ 2:4 1015 rad/s the center frequency of the probe light, and N the density of photoinduced carriers equal to Ppump a: ð2Þ hx For our experimental conditions Ppump ¼ 70 lJ/cm2 and a ¼ 104 cm1 [20,21], we obtain for Eq. (1) DeSi ¼ ð6:2 þ i5:3Þ 103 . Within the framework of the more sophisticated two-band mixing formalizm, a calculation of the amplitude of the relative changes in reflectivity for excitation at 800 nm with a spectral width of 39 nm gives DR=R ¼ 5 103 . The calculated value for DR=R is in the same order of magnitude as the experimentally measured one (see inset of Fig. 2). In conclusion, we have demonstrated a strong ultrafast response in the reflectivity of a-nc-Si-based threedimensional photonic crystal. We show that the switching time is less than 30 fs and determined by the pump pulse duration. The recovery time is in the order of several picoseconds. The observed transient changes in the Bragg reflectivity at high excitation power density can be as high as 46%. Our results are relevant for realizing an all-optical switching device based on a-nc-Si and operated at the sub-picosecond timescale. N¼
217
Acknowledgements The authors thank C.R. de Kok and P. Jurrius for technical assistance. This work was partially supported by the RFBR under Grants No. 02-02-16502, No. 0202-17601 and the RAS Program ‘Low-dimensional quantum structures’. A.V.A. acknowledges financial support from the Netherlands Foundation ‘Fundamenteel Onderzoek der Materie’ (FOM) and ‘Nederlandse Organisatie voor Wetenschappelijk Onderzoek’.
References [1] T.F. Krauss, R.M. De La Rue, Prog. Quantum Electron. 23 (1999) 51. [2] E. Yablonovitch, Phys. Rev. Lett. 58 (1987) 2059. [3] M. Campbell, D.N. Sharp, M.T. Harrison, R.G. Denning, A.J. Turberfield, Nature (London) 404 (2000) 53. [4] S. Yang, M. Megens, J. Aizenberg, P. Wiltzius, P.M. Chaikin, W.B. Russel, Chem. Mater. 14 (2002) 2831. [5] K.-M. Ho, C.T. Chan, C.M. Soukoulis, R. Biswas, M. Sigalas, Solid State Commun. 89 (1994) 413. [6] S.H. Im, O.O. Park, Appl. Phys. Lett. 80 (2002) 4133. [7] J.E.G.J. Wijnhoven, L. Bechger, W.L. Vos, Chem. Mater. 13 (2001) 4486. [8] K.P. Velikov, A. Moroz, A. van Blaaderen, Appl. Phys. Lett. 80 (2002) 49. [9] P.M. Johnson, A.F. Koenderink, W.L. Vos, Phys. Rev. B 66 (2002) 081102(R). [10] Yu.A. Vlasov, V.N. Astratov, O.Z. Karimov, A.A. Kaplyanskii, V.N. Bogomolov, A.V. Prokofiev, Phys. Rev. B 55 (1997) 13357. [11] Yu.A. Vlasov, X.-Zh. Bo, J.C. Sturm, D.J. Norris, Nature (London) 414 (2001) 289. [12] V.G. Golubev, J.L. Hutchison, V.A. Kosobukin, D.A. Kurdyukov, A.V. Medvedev, A.B. Pevtsov et al., J. Non-Cryst. Solids 299–302 (2002) 1062. [13] V.G. Golubev, V.A. Kosobukin, D.A. Kurdyukov, A.V. Medvedev, A.B. Pevtsov, Semiconductors 35 (2001) 680. [14] W.K. Shung, Y.C. Tsai, Phys. Rev. B 48 (1993) 11265. [15] D.A. Mazurenko, R. Kerst, J.I. Dijkhuis, A.V. Akimov, V.G. Golubev, D.A. Kurdyukov, A.B. Pevtsov, A.V. Sel’kin, Phys. Rev. Lett. 91 (2003) 213903. [16] D.H. Reitze, T.R. Zhang, Wm.M. Wood, M.C. Downer, J. Opt. Soc. Am. B 7 (1990) 84. [17] A. Esser, K. Seibert, H. Kurz, G.N. Parsons, C. Wang, B.N. Davidson, et al., Phys. Rev. B 41 (1990) 2879. [18] K.E. Myers, Q. Wang, S.L. Dexheimer, Phys. Rev. B 64 (2001) 161309. [19] A. Esser, H. Heesel, H. Kurz, C. Wang, G.N. Parsons, G. Lucovsky, J. Appl. Phys. 73 (1993) 1235. [20] H. Richter, L. Ley, J. Appl. Phys. 52 (1981) 7281. [21] Y. He, C. Yin, L. Wang, X. Liu, G.Y. Hu, J. Appl. Phys. 75 (1994) 797.
Femtosecond Bragg switching in opal-a-nc-Si photonic crystals Dmitry A. Mazurenko a,*, Robert Kerst a, Andrey V. Akimov b, Alexander B. Pevtsov b, Dmitry A. Kurdyukov b, Valery G. Golubev b, Alexander V. Sel’kin b, Jaap I. Dijkhuis a a
b
Department of Physics and Astronomy, Atom Optics and Ultrafast Dynamics, Debye Institute, University of Utrecht, P.O. Box 80000, 3508 TA Utrecht, The Netherlands Ioffe Physico-Technical Institute, Russian Academy of Sciences, Politechnicheskaya 26, St. Petersburg 194021, Russia Available online 24 March 2004
Abstract We demonstrate ultrafast all-optical switching in a three-dimensional photonic crystal made of an opal-silicon composite. We show that the switching-on time is faster than 30 fs and determined by the pump pulse duration. The switching-off time is in the order of several picoseconds. The maximum transient change in reflectivity reaches values as high as 46% at the highest excitation power. Ó 2004 Elsevier B.V. All rights reserved. PACS: 42.70.Qs; 42.65.Pc; 78.66.Jg; 78.66.Sq
1. Introduction A photonic crystal [1] is an ordered array of submicron objects creating a periodically modulated index of refraction. In case of sufficient dielectric contrast, this structure possesses a photonic band gap – a range of wavelengths within which electromagnetic fields cannot propagate [2]. Although a large number of nanofabrication methods have been developed during the last decade, e.g. holographic lithography [3,4], layer by layer fabrication [5], self-assembly, etc., the production of highly-ordered and defect-free three-dimensional (3D) photonic crystals remains a challenge. Self-assembly of colloidal spheres seems nowadays the most promising way to create 3D photonic crystals with thicknesses of up to hundreds of microns and higher. Recently, fabrication of ice [6], titania [7], zinc sulfide [8], and other 3D photonic crystals were reported. One of the most interesting potential applications of photonic crystals is all-optical switching. The optical properties can be modified by an external light source when the photonic crystal is made of weakly absorbing material with high non-linear optical coefficients. A light *
Corresponding author. Tel.: +31-30-253 2206; fax: +31-30-253 7469. E-mail address: [email protected] (D.A. Mazurenko). 0022-3093/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2004.02.056
pulse can change the dielectric constant and shift the photonic stop band (PSB) position, thus, realizing alloptical switching. This idea was recently analyzed by Johnson and co-workers [9], and here we demonstrate it experimentally in the ultrafast domain, using amorphous-nanocrystalline silicon (a-nc-Si) as the non-linear optical material. In this paper, we examine the transient change in reflectivity of an a-nc-Si-based three-dimensional photonic crystal induced by strong irradiation of a femtosecond light pulse. We choose a synthetic opal, because it is known as a model object to study PSB effects [10]. The voids of the opal were filled with a-nc-Si to control the PSB properties of our photonic crystal by optical excitation of free carriers. A sketch of our structure is shown in the inset to Fig. 1. As a filling substance a-ncSi is further advantageous because of its high index of refraction and its suitability to be integrated into microelectronic technology [11].
2. Sample and experimental setup Our sample was prepared from a commercially available fcc opal with an a-SiO2 ball diameter of 230 nm [12]. This ordered matrix has a polydomain structure. The voids of this opal were filled with mixed amorphous-nanocrystalline silicon up to a filling factor
D.A. Mazurenko et al. / Journal of Non-Crystalline Solids 338–340 (2004) 215–217
close to 100% by thermal decomposition of a 5%-SiH4 – Ar gas mixture. The sample was cut in a 0.5-mm thick plate almost parallel to the (1 1 1) surface. Further details of the sample fabrication can be found in Ref. [13]. The stationary Bragg reflectance spectra were measured with a halogen lamp and detected by a spectrometer equipped with a CCD. All time-resolved reflectivity measurements were performed by a conventional pump-probe technique. High-power excitation (5 mJ/cm2 ) was supplied by a Ti-sapphire laser with a pulse length of 120 fs operated at a repetition rate of 500 Hz. The wavelength of the laser was 800 nm, which is in the tail of the absorption edge of a-nc-Si. The reflectance spectrum was probed by a weak pulse of white light continuum generated in a sapphire plate, which was excited by the same pulse of the Ti-sapphire laser. The time interval between the arrival of the pump and probe pulses at the sample was adjusted by a computer-controlled optical delay line. Low-power (70 lJ/cm2 ) high-temporal resolution Bragg reflectivity traces were measured with a 30 fs Tisapphire laser again with a wavelength of 800 nm. Here, the measuring sensitivity was increased up to 104 using a double-modulation technique and a lock-in amplifier. All pump and probe beams were incident in the [1 1 1] direction. The deviation of the (1 1 1) plane of the opal lattice from the plane of the sample surface allowed us to separate the Bragg diffracted light from the trivial specular surface reflection.
0 -3 ∆R/R (x10 )
Fig. 1. Measured () and calculated (––) spectra of Bragg diffraction efficiency of an a-nc-Si-based photonic crystal. Solid line is shown in absolute units. Insert shows a sketch of the fcc opal-Si structure.
width of the line is about 70 nm. Both the spectral position and the width of the reflectance maximum are in agreement with earlier studies of a similar sample [13] and can be attributed to the PSB in the [1 1 1] direction. The solid line in Fig. 1 shows the calculated spectrum of the Bragg reflectivity according to a theoretical model (developed by A.V. Sel’kin) based on the so-called twoband mixing formalizm [14], which is described in detail elsewhere [15]. We note the excellent agreement between the measured and calculated spectra. The temporal evolution of the relative transient change in the Bragg reflection DRðtÞ=R induced by a strong (5 mJ/cm2 ) optical pump pulse is shown for three probe wavelengths in Fig. 2, the solid curve at 780 nm (PSB region), and the dashed at 760 nm and dotted curves at 850 nm (wings of the PSB). The reflection signal shows an abrupt decrease directly after the arrival of the pump pulse (t ¼ 0) and partly recovers on a picosecond timescale. The changes in the Bragg reflection are maximum at the PSB where they reach DRðtÞ=R ¼ 46%. The inset to Fig. 2 displays the time trace of DRðtÞ=R measured at k ¼ 800 nm at a lower pump power density (70 lJ/cm2 ) and higher temporal resolution. Here, the amplitude of the relative changes in reflectivity is DR=R ¼ 1:2 102 . The initial peak in DRðtÞ=R occurs when pump and probe overlap in time and can be explained by the instantaneous Kerr effect [16]. The decay at longer delays appears to have a multi-exponential shape with the time constants s1 0:5 ps and s2 5 ps. The fact that the ultrafast switching takes place within 30 fs suggests that induced changes are caused by photoexcited carriers in a-nc-Si [17,18]. Photoinduced changes in the real and imaginary parts of the refractive index suppress the Bragg interference of the light inside the photonic crystal and diminish the Bragg reflection. This results in a rapid switching of the reflectivity of the
0.0 -0.1
-4 -8 -12
∆R/R
216
-0.2
0.0
0.5
1.0
1.5
Time, ps
-0.3 -0.4
3. Experimental result and discussion
-0.5 0
In Fig. 1 the symbols show the measured stationary Bragg reflectance spectrum of the opal-Si structure. The peak in the reflectivity is centered around k ¼ 790 nm and corresponds to the first order PSB. We note that the exact position of the reflectivity maximum varies between 780 and 820 nm over the sample surface. The
2
4 6 Time, ps
8
10
Fig. 2. Time-resolved transient differential reflection DRðtÞ=R at 760 nm (- - -), 780 nm (––), and 850 nm ( ) in case of high-power (5 mJ/cm2 ) optical pulse excitation. Insert shows DRðtÞ=R at 800 nm in case of moderate (70 lJ/cm2 ) optical pulse excitation, measured with a higher temporal resolution (30 fs).
D.A. Mazurenko et al. / Journal of Non-Crystalline Solids 338–340 (2004) 215–217
opal on the detected wavelength. The exact value of the recovery time of DRðtÞ=R depends on the selected points of the sample due to variation in volume fractions of aSi and nc-Si compounds. Generally, the shape of the transient reflectivity decay is reminiscent of the one obtained earlier in a layer comprised of nanocrystallites of silicon embedded in an amorphous silicon matrix [18]. We note, that defects and inhomogeneity of nanocrystalline silicon decrease the relaxation time of carriers and, consequently, increase the recovery speed of the transient reflectivity. This is promising for applications and demonstrates the suitability of using a-nc-Si as a filling material for ultrafast switching in photonic crystals. Photoinduced changes in the reflectivity DR can be calculated given the photoinduced changes DeSi in the dielectric constant of silicon. The dominant effect of DeSi is caused by photoexcited carriers and can be described by the Drude relationship [17] Ne2 1 1 i DeSi ¼ ; ð1Þ xsd m e0 ðx2 þ s2 d Þ where m ¼ 0:15m0 [19] is the optical reduced mass, sd ¼ 0:5 fs [17] the Drude damping time, x ¼ 2:4 1015 rad/s the center frequency of the probe light, and N the density of photoinduced carriers equal to Ppump a: ð2Þ hx For our experimental conditions Ppump ¼ 70 lJ/cm2 and a ¼ 104 cm1 [20,21], we obtain for Eq. (1) DeSi ¼ ð6:2 þ i5:3Þ 103 . Within the framework of the more sophisticated two-band mixing formalizm, a calculation of the amplitude of the relative changes in reflectivity for excitation at 800 nm with a spectral width of 39 nm gives DR=R ¼ 5 103 . The calculated value for DR=R is in the same order of magnitude as the experimentally measured one (see inset of Fig. 2). In conclusion, we have demonstrated a strong ultrafast response in the reflectivity of a-nc-Si-based threedimensional photonic crystal. We show that the switching time is less than 30 fs and determined by the pump pulse duration. The recovery time is in the order of several picoseconds. The observed transient changes in the Bragg reflectivity at high excitation power density can be as high as 46%. Our results are relevant for realizing an all-optical switching device based on a-nc-Si and operated at the sub-picosecond timescale. N¼
217
Acknowledgements The authors thank C.R. de Kok and P. Jurrius for technical assistance. This work was partially supported by the RFBR under Grants No. 02-02-16502, No. 0202-17601 and the RAS Program ‘Low-dimensional quantum structures’. A.V.A. acknowledges financial support from the Netherlands Foundation ‘Fundamenteel Onderzoek der Materie’ (FOM) and ‘Nederlandse Organisatie voor Wetenschappelijk Onderzoek’.
References [1] T.F. Krauss, R.M. De La Rue, Prog. Quantum Electron. 23 (1999) 51. [2] E. Yablonovitch, Phys. Rev. Lett. 58 (1987) 2059. [3] M. Campbell, D.N. Sharp, M.T. Harrison, R.G. Denning, A.J. Turberfield, Nature (London) 404 (2000) 53. [4] S. Yang, M. Megens, J. Aizenberg, P. Wiltzius, P.M. Chaikin, W.B. Russel, Chem. Mater. 14 (2002) 2831. [5] K.-M. Ho, C.T. Chan, C.M. Soukoulis, R. Biswas, M. Sigalas, Solid State Commun. 89 (1994) 413. [6] S.H. Im, O.O. Park, Appl. Phys. Lett. 80 (2002) 4133. [7] J.E.G.J. Wijnhoven, L. Bechger, W.L. Vos, Chem. Mater. 13 (2001) 4486. [8] K.P. Velikov, A. Moroz, A. van Blaaderen, Appl. Phys. Lett. 80 (2002) 49. [9] P.M. Johnson, A.F. Koenderink, W.L. Vos, Phys. Rev. B 66 (2002) 081102(R). [10] Yu.A. Vlasov, V.N. Astratov, O.Z. Karimov, A.A. Kaplyanskii, V.N. Bogomolov, A.V. Prokofiev, Phys. Rev. B 55 (1997) 13357. [11] Yu.A. Vlasov, X.-Zh. Bo, J.C. Sturm, D.J. Norris, Nature (London) 414 (2001) 289. [12] V.G. Golubev, J.L. Hutchison, V.A. Kosobukin, D.A. Kurdyukov, A.V. Medvedev, A.B. Pevtsov et al., J. Non-Cryst. Solids 299–302 (2002) 1062. [13] V.G. Golubev, V.A. Kosobukin, D.A. Kurdyukov, A.V. Medvedev, A.B. Pevtsov, Semiconductors 35 (2001) 680. [14] W.K. Shung, Y.C. Tsai, Phys. Rev. B 48 (1993) 11265. [15] D.A. Mazurenko, R. Kerst, J.I. Dijkhuis, A.V. Akimov, V.G. Golubev, D.A. Kurdyukov, A.B. Pevtsov, A.V. Sel’kin, Phys. Rev. Lett. 91 (2003) 213903. [16] D.H. Reitze, T.R. Zhang, Wm.M. Wood, M.C. Downer, J. Opt. Soc. Am. B 7 (1990) 84. [17] A. Esser, K. Seibert, H. Kurz, G.N. Parsons, C. Wang, B.N. Davidson, et al., Phys. Rev. B 41 (1990) 2879. [18] K.E. Myers, Q. Wang, S.L. Dexheimer, Phys. Rev. B 64 (2001) 161309. [19] A. Esser, H. Heesel, H. Kurz, C. Wang, G.N. Parsons, G. Lucovsky, J. Appl. Phys. 73 (1993) 1235. [20] H. Richter, L. Ley, J. Appl. Phys. 52 (1981) 7281. [21] Y. He, C. Yin, L. Wang, X. Liu, G.Y. Hu, J. Appl. Phys. 75 (1994) 797.