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Enhanced light extraction in Er3+ doped SiO2–TiO2 microcavity embedded in one-dimensional photonic crystal
Journal of Non-Crystalline Solids 352 (2006) 3823–3828 www.elsevier.com/locate/jnoncrysol
Enhanced light extraction in Er3+ doped SiO2–TiO2 microcavity embedded in one-dimensional photonic crystal D. Biallo *, A. D’Orazio, V. Petruzzelli Dipartimento di Elettrotecnica ed Elettronica, Politecnico di Bari, Via E. Orabona 4, 70125 Bari, Italy Received 20 January 2006; received in revised form 1 June 2006 Available online 28 August 2006
Abstract Erbium doped silica–titania one-dimensional photonic crystal microcavities have been analyzed by solving the erbium rate equations and the Maxwell equations by means of an auxiliary differential equation finite difference time domain technique. The interaction time between light and matter is enhanced by the presence of microcavity, used to localize the light inside the PC and allows to achieve a significant gain. The investigation treats the influence of the pump signal power, the device length and the dopant concentration, on the optical amplification in correspondence of the defect resonance. A comparison between the erbium doped photonic crystal microcavities and erbium doped photonic crystal band edge amplifiers is reported as well, which shows a higher compactness of the erbium doped photonic crystal microcavities respect with the erbium doped photonic crystals. 2006 Elsevier B.V. All rights reserved. PACS: 42.70.Qs; 42.55.Tv; 76.30.Kg Keyword: Photonic bandgap
1. Introduction In recent years photonic bandgap (PBG) structures have been attracting a lot of interest due to their unique optical properties such as the existence of photonic bandgaps, the appearance of localized states of light when a punctual or linear defect is introduced in the otherwise regular lattice, the modified density of states, the suppression or enhancement of non-linear effects [1–3]. PBG structures have opened up new features for the guidance of light in both passive and active devices, including waveguides and fibers with bandgap guidance, microcavities having improved Q-factors, straight bends. For active devices a lot of papers have been reported about the improvement on amplification properties and lasing with low threshold [4–9].
*
Corresponding author. E-mail address: [email protected] (D. Biallo).
0022-3093/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2006.06.031
Research in the field of rare-earth doped optical amplifier has demonstrated in recent years the extended range of their properties such as sharp absorption and emission bands and relatively long luminescence lifetimes. The erbium intra 4f-transition from the first excited state to the ground state around 1.53 lm (4I13/2–4I15/2) is attractive for the realization of Er-doped planar waveguide amplifiers, hosted in silica, Al2O3, phosphate glasses and LiNbO3 materials [10–15]. To date, most work has been performed on demonstrating or using these properties for a variety of rare-earth doped fibers [16–19] and rare-earth doped photonic crystal fibers [20–23]. Till now, only a few applications have considered the possibility to exploit the peculiar properties of planar photonic crystal to optimize the performance of EDWA [24]. In fact, the drawback of the erbium doped waveguide amplifiers (EDWAs) lies in the high requirement of Er3+ concentration values needed to obtain high gain figures and a compact length, thus making the concentration quenching effects become dominant; these effects reduce
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the population in the first excited state leading to a detriment of the optical gain. Erbium doped photonic crystal amplifier (EDPCA) offers the possibility to overcome this drawback. In fact, the small group velocity of electromagnetic eigenmodes brings about the enhancement of stimulated emission if the photonic crystals are doped by active media as the rare-earth ions Er3+ or Yb3+. This phenomenon originates from the long interaction time between radiation field and the matter caused by the small group velocity near the edge of the photonic bandgap [15,25,26], allowing to reduce the device length of about three order of magnitude with respect to the equivalent EDWA, as shown in a previous paper [27]. By introducing local defects inside PCs, an efficient confinement of light can be achieved in the frequency range lying within the bandgap. The density of electromagnetic states inside a cavity is significantly modified and the spontaneous emission of atoms in a cavity can be either enhanced or inhibited [28]. In this paper, we report the results of the analysis of the optical amplification in erbium doped photonic crystal microcavity amplifiers (EDPCMAs), pointing out the dependence of the transmittance on the energy-level radiative transitions for different distribution and concentration values of the rare-earth ions and the pumping conditions. The influence of the number of periods and of the length of the local defect, which constitutes the microcavity, on the optical properties of the PC-based amplifiers is also shown. 2. Theory The analysis of the erbium doped PC amplifier has been performed by means of a home made computer code which implements a model [29] based on the auxiliary differential equation finite-difference time domain (ADE-FDTD) scheme [30] which solves together the Maxwell equations, the electron oscillator (EO) equation and the erbium rate equations that give the energy states population time variation during the propagation of pump and input signals [31]. In particular the model considers the absorption and emission erbium cross-sections by solving the EO equation (the ADE) that takes into account the field effect on the medium during its propagation [32]. For self-consistency, we briefly describe the implemented model referring the interested readers to the paper
[29] for further details. Fig. 1 shows the four-level energy erbium laser system; the erbium rate equation model is described by the Eqs. (1)–(5): dN 4 N4 ¼ þ C up N 22 þ C3 N 23 C 14 N 1 N 4 ; dt s43 dN 3 N3 N4 ¼ W p N1 þ 2 C 3 N 23 ; dt s32 s43
ð1Þ ð2Þ
dN 2 N 3 eðtÞ dpðtÞ N 2 ¼ þ þ 2 C 14 N 1 N 4 2 C up N 22 ; dt s32 hms dt s21 ð3Þ dN 1 eðtÞ dpðtÞ N 2 þ ¼ W p N 1 C 14 N 1 N 4 hms dt dt s21 þ C up N 22 þ C 3 N 23 ;
ð4Þ
with the population densities on different energy levels Ni related to the total dopant concentration NT by the conservation equation: N T ¼ N 1 þ N 2 þ N 3 þ N 4:
ð5Þ
The model considers the following energy state transitions: the ground state absorption (GSA), that occurs at the pump wavelength kp = 980 nm, the stimulated emission (SE) that occurs at the input signal wavelength ka = 1532 nm, where the peak of stimulated emission (SE) takes place, and the radiative and non-radiative transitions that are governed by the fluorescence times s43 = s32 = 1 Æ 109 s and s21 = 7.1 Æ 103 s. Moreover, it includes the concentration quenching effects such as the up-conversion characterized by the coefficient rates C3 = Cup = 5 Æ 1023 m3/s, and the cross-relaxation, characterized by the coefficient rate C14 = 3.5 Æ 1023 m3/s [12]. The rate equations are linked to the propagating electric field e(t) and the macro-polarization vector p(t), by considering the EO equation: d2 pðtÞ dpðtÞ þ x2a pðtÞ ¼ kDN 12 ðtÞeðtÞ; þ Dxa 2 dt dt
ð6Þ
where the resonance frequency xa is the characteristic transition frequency related to the energy levels involved in the stimulated emission, Dxa is the full width at half maximum (FWHM) linewidth of the atomic transition, DN12 = N1 N2 is the electron population difference between the lower and upper energy levels involved in the transitions and the k factor depends on the oscillator strength.
Fig. 1. Energetic level transitions of a four-level erbium laser system.
D. Biallo et al. / Journal of Non-Crystalline Solids 352 (2006) 3823–3828
The experimentally measured erbium absorption and emission cross-sections have been recovered by a Lorentzian lineshape susceptibility. The transmittance has been evaluated by calculating the FFT of the input and output electromagnetic field components and evaluating the ratio between the Poynting vector along the propagation direction at the output of the structure and the Poynting vector at the input of the structure. For the FDTD simulations, a longitudinal step Dz = 5 Æ 109 m and a time step Dt = 1.5 Æ 1017 s, values which verify the Courant limit, have been considered. Each structure under analysis has been excited by a sinusoidal pump signal considering different power values and an input signal having a Gaussian lineshape, a power equal to 1 lW and centered around the erbium emission wavelength k = 1.532 lm.
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Np = 50, silica layer width ws = 0.2271 lm, titania layer width wt = 0.1432 lm. As we can see, the bandgap ranges between k = 1.2 lm and k = 1.532 lm where the upper band edge is located. Fig. 3 illustrates the transmittance of the active PC as a function of the period number for three different pump signal powers: Pp = 100 mW (dotted line), Pp = 200 mW (dashed line), Pp = 300 mW (solid line). The simulation is performed for a typical value of the erbium ion concentration equal to Nt = 2.2 Æ 1026 [ions/m3]. In the following, the perfect 1D-PC having Np = 100 has been considered. Fig. 4 shows the transmittance value at
3. Results We start our analysis by considering the one-dimensional erbium doped perfect photonic crystal. It is a quarter-wave Bragg reflector consisting of alternated layers of erbium doped amorphous SiO2 and TiO2; similar structures have been recently proposed in literature both for amplification phenomenon [33] non-linear effects [34] and omnidirectional reflector and microcavity resonator [35]. One-dimensional photonic crystals consisting of silica/titania bilayers have been fabricated by the sol–gel method [33–35], rf-sputtering [36] and vacuum deposition [37]. The refractive indices of the silica and titania layers are ns = 1.453 and nt = 2.304 at the wavelength k = 1.5 lm, respectively. The Bragg wavelength has been fixed to kB = 1.35 lm, thus setting the band edge in correspondence of k = 1.532 lm where the erbium emission cross-section is centered. Fig. 2 depicts the transmittance of the 18.51 lm long photonic crystal characterized by a period number
Fig. 2. Transmittance of a 1D-PC 18.51 lm long (period number Np = 50).
Fig. 3. Transmittance value at the band edge as a function of the period number for an EDPCA for an erbium ion concentration of Nt = 2.2 · 1026 and three different pump signal powers Pp = 100 mW (dotted line), Pp = 200 mW (dashed line), Pp = 300 mW (solid line).
Fig. 4. Transmittance value at the band edge as a function of erbium ion concentration for an EDPCA with Np = 100 for three different pump signal powers Pp = 100 mW (dotted line), Pp = 200 mW (dashed line), Pp = 300 mW (solid line).
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the upper band edge calculated by varying the erbium ion concentration inside the silica layers; the simulation has been performed for three different values of the pump signal power Pp = 100 mW (dotted line), Pp = 200 mW (dashed line), Pp = 300 mW (solid line). The considered defected photonic crystal is constituted by only 10 periods, 5 on the right and 5 on the left of the central SiO2 local defect in absence of pump signal. The width of the silica layer is ws = 0.2667 lm and that of the titania layer is wt = 0.1682 lm; the local defect is half-wave long (Lc = 0.5334 lm). The geometrical parameters of the defected photonic crystal have been optimized in order to have a resonant peak in correspondence of the signal wavelength k = 1.532 lm, which results to be around the center
Fig. 5. Transmittance of the 1D-PC microcavity 4.349 lm long (period number Np = 10).
Fig. 6. Transmittance value of the EDPCMA with only the silica defect erbium doped. The erbium ion concentration is Nt = 2.2 · 1026 and the period number is 10. The simulation has been performed by considering three different pump signal powers Pp = 100 mW (dotted line), Pp = 200 mW (dashed line), Pp = 300 mW (solid line).
of the bandgap ranging from k = 1.3 lm to k = 1.85 lm (see Fig. 5). The device has a total length of L = 4.349 lm which results to be lower than that of the 100 period EDPCA. Fig. 6 depicts the transmittance value in correspondence of the defect resonance for an EDPCMA, where only the local defect is doped with erbium, by considering three different value pump signal powers Pp = 100 mW (dotted line), Pp = 200 mW (dashed line), Pp = 300 mW (solid line), the erbium ion concentration being Nt = 2.2 Æ 1026 [ions/m3].
Fig. 7. Transmittance value of an EDPCMA at resonance wavelength and of a 100 period EDPCA at the band edge as a function of pump signal power.
Fig. 8. Transmittance value at resonance wavelength as a function of erbium ion concentration for an EDPCA with a local defect and Np = 10; the simulation has been performed by considering three different pump signal powers Pp = 100 mW (dotted line), Pp = 200 mW (dashed line), Pp = 300 mW (solid line).
D. Biallo et al. / Journal of Non-Crystalline Solids 352 (2006) 3823–3828
Fig. 7 shows the comparison between the transmittance of the EDPCMA, having all the silica layers doped with erbium, and the 100 period EDPCA to a parity of concentration Nt = 2.2 Æ 1026 [ions/m3]. Fig. 8 illustrates the transmittance value at the defect resonance of the EDPCMA with all the silica layers doped with erbium, as a function of the erbium ion concentration, for three different pump signal power values Pp = 100 mW (dotted line), Pp = 200 mW (dashed line), Pp = 300 mW (solid line). Fig. 9(a) and (b) depict the transmittance value at the defect resonance for three different pump signal power values Pp = 100 mW (dotted line), Pp = 200 mW (dashed line), Pp = 300 mW (solid line), considering, respectively, a k and a 3/2 k long defect and an erbium ion concentration of Nt = 2.2 Æ 1026 [ions/m3].
Fig. 9. Transmittance value of the EDPCMA having a microcavity (a) k long and (b) 3/2 k long. The erbium ion concentration is Nt = 2.2 · 1026 and the period number is 10. The simulation has been performed by considering three different pump signal powers Pp = 100 mW (dotted line), Pp = 200 mW (dashed line), Pp = 300 mW (solid line).
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4. Discussion The transmittance at the band edge depends mainly on the period number, i.e. the device length. As shown in Fig. 3, the transmittance increases by increasing the device length and reaches a value corresponding to 3 dB for a 37 lm long (Np = 150) EDPCA and for a pump signal power of 300 mW, showing a better compactness of these devices respect to the EDWA. For a period number smaller than 80, the transmittance does not reach values different from the unit and this period number can be considered as the inferior limit for the length of the EDPCA. Anyway, fixed the band edge transmittance value, if higher concentration values are considered, the device length can further decrease. It is interesting to note in Fig. 3 that the slope of three curves significantly changes in correspondence of a period number around 100. Since the device length is very short in all examined cases, if compared with the typical lengths (of the order of cm) of an EDWA, this fact suggests the possibility to consider smaller values of pump signal power. The curves reported in Fig. 4 show the concentration effect on the gain for different pump powers. The transmittance increases by increasing the active media concentration because the input signal sees more and more excited ions on the metastable level; moreover it can be noted that the gain detrimental concentration quenching effects are not yet evident, since the number of erbium ions is not sufficient to cause clustering phenomena. However the slope of the curves decreases by increasing the ion concentration and this saturation-like behavior indicates the rising of the quenching effects. The transmittance values become much higher as the pump signal power increases from 100 mW to 300 mW since the pump rate influences the inverted population density. The introduction of a local defect in the otherwise perfect 1D-PC strongly affects the amplification effect of the active structure. By erbium doping only the local defect in the periodic structure, the light at a certain frequency is localized inside the defect for a considerable long time allowing the interaction with the active media. For a pump power of 300 mW (see Fig. 6) the transmittance reaches a value corresponding to 1.76 dB, which is much higher than the 0.9 dB obtained for the 100 period EDPCA under the same pump and concentration condition. For this structure, the increase of the pump power value does not give significant transmittance improvement; this can be justified by the saturation effect that characterized all the erbium doped based devices. In this case, considering pump power values beyond the 200 mW does not give significant improvement in terms of gain. A further enhancement in the EDPCM performance is achieved if all the silica layers of the 1D-PC microcavity are erbium doped. As shown in Fig. 7 the transmittance is doubled; this is due to the fact that the light, before and after the localization in the microcavity, passes through the erbium doped activated layers and hence it is
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amplified during the propagation through the structure. It is possible to observe that the increasing of pump power value gives rise, in this structure, to a transmittance enhancement. Moreover the EDPCMA with all the silica layers doped with erbium reaches the transparency for a pump power of 10 mW, showing a lower threshold than that of the EDPCA which results to be 20 mW (see Fig. 8). The dependence of the transmittance at the resonance wavelength on the erbium ion concentration for the EDPCMA with all the silica layers doped with erbium has been calculated and reported in Fig. 8. The slope of the curves is much higher respect to the case of the perfect EDPCA; the transmittance reaches a value around nine corresponding to 9.5 dB for an erbium ion concentration of 4.5 Æ 1026 [ion/m3] and a pump signal power of 300 mW. The optical amplification is clearly affected by the microcavity length. In fact, as it can be noted in Fig. 9(a), (b), by increasing the length of the microcavity of an integer multiple of half-wave the transmittance peak increases until reaching a value of eight corresponding to 9 dB setting the pump power at 300 mW. For a 3/2 k long microcavity, under the same pump and concentration conditions the transmittance value raises to 11 dB, showing a strong improvement if compared to that of microcavity k/2 long, depicted in Fig. 7. 5. Conclusion In this paper the time domain analysis of the amplification phenomena in an erbium doped silica–titania 1D photonic crystal microcavity amplifier is reported. The presence of a microcavity in an erbium doped photonic crystal allows to optimize the performance of photonic crystal band edge amplifiers. In fact the erbium doped photonic crystal microcavity reaches transmittance values of about 5 dB in 5 lm, showing a threshold of 10 mW, while an erbium doped photonic crystal band edge amplifier need of a device length of 37 lm to get a transmittance value of 3 dB, having a threshold of 20 mW. Acknowledgement This work was partially sponsored by the MIUR research contract FIRB 2001, ‘Modelling and numerical methods of photonic devices for high capacity optical networks’. References [1] J.D. Joannopoulos, R.D. Meade, J.N. Winn, Princeton University, 1995. [2] S.G. Johnson, J.D. Joannopoulos, Kluwer Academic, 2002. [3] K. Sakoda, Springer, 2001. [4] K.H. Lee, J.H. Back, I.K. Hwang, Y.H. Lee, G.H. Lee, J.H. Ser, H.D. Kim, H.E. Shin, Opt. Express 12 (2004) 4136.
[5] C.L. Zhao, Z. Li, X. Yang, C. Lu, W. Jin, M.S. Demokan, IEEE Photonics Technol. Lett. 17 (2005) 561. [6] H.G. Park, S.K. Kim, S.H. Kwon, G.H. Kim, S.H. Kim, H.Y. Ryu, S.B. Kim, Y.H. Lee, IEEE Photonics Technol. Lett. 15 (2003) 1327. [7] A. Cucinotta, F. Poli, S. Selleri, IEEE Photonics Technol. Lett. 16 (2004) 2027. [8] H. Sherer, D. Gollup, M. Kamp, A. Forchel, IEEE Photonics Technol. Lett. 17 (2005) 2247. [9] S.H. Kwon, S.H. Kim, S.K. Kim, Y.H. Lee, S.B. Kim, Opt. Express 12 (2004) 5356. [10] A. Polman, J. Appl. Phys. 82 (1997) 1. [11] P.G. Kik, A. Polman, J. Appl. Phys. 93 (2003) 5008. [12] A. D’Orazio, M. De Sario, L. Mescia, V. Petruzzelli, F. Prudenzano, A. Chiasera, M. Montagna, C. Tosello, M. Ferrari, J. Non-Cryst. Solids 322 (2003) 278. [13] M. Federighi, I. Massarek, P.F. Trwoga, IEEE Photonics Technol. Lett. 5 (1993) 227. [14] D. Zhang, D. Wang, E.Y.B. Pun, IEEE J. Quantum Electron. 41 (2005) 958. [15] J.P. Dowling, M. Scalora, M. Bloemer, C.M. Bowden, J. Appl. Phys. 75 (1994) 1896. [16] J.B. Rosolem, A.A. Juriollo, R. Arradi, A.D. Coral, J.C.R.F. Oliveira, M.A. Romero, IEEE Photonics Technol. Lett. 17 (2005) 1399. [17] M. Bolshtyansky, I. Mandelbaum, F. Pan, J. Light. Technol. 23 (2005) 2796. [18] X. Yang, X. Dong, S. Zhang, F. Lu, X. Zhou, C. Lu, IEEE Photonics Technol. Lett. 17 (2005) 2538. [19] C. Berkdemir, S. Ozsoy, Opt. Quantum Electron. 37 (2005) 789. [20] K. Furosawa, T. Kogure, J.K. Sahu, J.H. Lee, T.M. Monro, D.J. Richardson, IEEE Photonics Technol. Lett. 17 (2005) 25. [21] F.C. McNeillie, E. Riis, J. Broeng, J.R. Folkenberg, A. Petersson, H. Simonsen, C. Jacobsen, Opt. Express 12 (2004) 3981. [22] A. D’Orazio, M. De Sario, L. Mescia, V. Petruzzelli, F. Prudenzano, Opt. Express 13 (2005) 9970. [23] F. Prudenzano, J. Light. Technol. 23 (2005) 330. [24] M.J.A. de Dood, A. Polman, J.G. Fleming, Phys. Rev. B 67 (2003) 1. [25] K. Sakoda, Opt. Express 14 (1999) 167. [26] M. Botey, M. Maymo`, D. Biallo, J. Martorell, Laser Phys. 14 (2004) 643. [27] D. Biallo, A. D’Orazio, M. De Sario, V. Petruzzelli, F. Prudenzano, ICTON 2005, in: Proc. of IEEE (2005) 149. [28] D.J. Ripin, K. Lim, G.S. Petrich, P.R. Villeneuve, S. Fan, E.R. Thoen, J.D. Joannopoulos, E.P. Ippen, A. Kolodziejski, J. Light. Technol. 17 (1999) 2152. [29] D. Biallo, A. D’Orazio, M. De Sario, V. Petruzzelli, F. Prudenzano, Opt. Express 13 (2005) 4683. [30] A. Taflove, S.C. Hagness, Artech House, Boston–London (2000). [31] A.S. Nagra, R.A. York, IEEE Trans. Antenn. Propag. 46 (1998) 334. [32] A.E. Siegman, University Science Book, 1986. [33] L. Zampedri, C. Tosello, H. Portales, M. Montagna, M. Mattarelli, A. Chiappini, G.C. Righini, S. Pelli, G. Nunzi Corti, M. Martino, S. Portal, Ana C. Marques, R.M. Almeida, Y. Jestin, M. Ferrari, A. Chiasera, Appl. Surf. Sci. 248 (2005) 3. [34] J. Hwang, M.J. Kim, J.W. Wu, S.M. Lee, B.K. Rhee, Opt. Lett. 31 (2006) 377. [35] K.M. Chen, A.W. Sparks, H.-C. Luan, D.R. Lim, K. Wada, L.C. Kimerling, Appl. Phys. Lett. 74 (1999) 3805. [36] C. Armellini, A. Chiasera, M. Ferrari, Y. Jestin, R. Belli, S.N.B. Baktha, A. Chiappini, M. Mattarelli, M. Montagna, C. Tosello, k.C. Vishunubhatla, L. Zampedri, D.N. Rao, R.M. Almeida, S. Portal, S. Berneschi, G. Nunzi Conti, S. Pelli, G.C. Righini, Proc. Fotonica (2005) 167. [37] T. Hattori, N. Tsurumachi, S. Kawato, H. Nakatsuka, Phys. Rev. B 50 (1994) 4220.
Enhanced light extraction in Er3+ doped SiO2–TiO2 microcavity embedded in one-dimensional photonic crystal D. Biallo *, A. D’Orazio, V. Petruzzelli Dipartimento di Elettrotecnica ed Elettronica, Politecnico di Bari, Via E. Orabona 4, 70125 Bari, Italy Received 20 January 2006; received in revised form 1 June 2006 Available online 28 August 2006
Abstract Erbium doped silica–titania one-dimensional photonic crystal microcavities have been analyzed by solving the erbium rate equations and the Maxwell equations by means of an auxiliary differential equation finite difference time domain technique. The interaction time between light and matter is enhanced by the presence of microcavity, used to localize the light inside the PC and allows to achieve a significant gain. The investigation treats the influence of the pump signal power, the device length and the dopant concentration, on the optical amplification in correspondence of the defect resonance. A comparison between the erbium doped photonic crystal microcavities and erbium doped photonic crystal band edge amplifiers is reported as well, which shows a higher compactness of the erbium doped photonic crystal microcavities respect with the erbium doped photonic crystals. 2006 Elsevier B.V. All rights reserved. PACS: 42.70.Qs; 42.55.Tv; 76.30.Kg Keyword: Photonic bandgap
1. Introduction In recent years photonic bandgap (PBG) structures have been attracting a lot of interest due to their unique optical properties such as the existence of photonic bandgaps, the appearance of localized states of light when a punctual or linear defect is introduced in the otherwise regular lattice, the modified density of states, the suppression or enhancement of non-linear effects [1–3]. PBG structures have opened up new features for the guidance of light in both passive and active devices, including waveguides and fibers with bandgap guidance, microcavities having improved Q-factors, straight bends. For active devices a lot of papers have been reported about the improvement on amplification properties and lasing with low threshold [4–9].
*
Corresponding author. E-mail address: [email protected] (D. Biallo).
0022-3093/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2006.06.031
Research in the field of rare-earth doped optical amplifier has demonstrated in recent years the extended range of their properties such as sharp absorption and emission bands and relatively long luminescence lifetimes. The erbium intra 4f-transition from the first excited state to the ground state around 1.53 lm (4I13/2–4I15/2) is attractive for the realization of Er-doped planar waveguide amplifiers, hosted in silica, Al2O3, phosphate glasses and LiNbO3 materials [10–15]. To date, most work has been performed on demonstrating or using these properties for a variety of rare-earth doped fibers [16–19] and rare-earth doped photonic crystal fibers [20–23]. Till now, only a few applications have considered the possibility to exploit the peculiar properties of planar photonic crystal to optimize the performance of EDWA [24]. In fact, the drawback of the erbium doped waveguide amplifiers (EDWAs) lies in the high requirement of Er3+ concentration values needed to obtain high gain figures and a compact length, thus making the concentration quenching effects become dominant; these effects reduce
3824
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the population in the first excited state leading to a detriment of the optical gain. Erbium doped photonic crystal amplifier (EDPCA) offers the possibility to overcome this drawback. In fact, the small group velocity of electromagnetic eigenmodes brings about the enhancement of stimulated emission if the photonic crystals are doped by active media as the rare-earth ions Er3+ or Yb3+. This phenomenon originates from the long interaction time between radiation field and the matter caused by the small group velocity near the edge of the photonic bandgap [15,25,26], allowing to reduce the device length of about three order of magnitude with respect to the equivalent EDWA, as shown in a previous paper [27]. By introducing local defects inside PCs, an efficient confinement of light can be achieved in the frequency range lying within the bandgap. The density of electromagnetic states inside a cavity is significantly modified and the spontaneous emission of atoms in a cavity can be either enhanced or inhibited [28]. In this paper, we report the results of the analysis of the optical amplification in erbium doped photonic crystal microcavity amplifiers (EDPCMAs), pointing out the dependence of the transmittance on the energy-level radiative transitions for different distribution and concentration values of the rare-earth ions and the pumping conditions. The influence of the number of periods and of the length of the local defect, which constitutes the microcavity, on the optical properties of the PC-based amplifiers is also shown. 2. Theory The analysis of the erbium doped PC amplifier has been performed by means of a home made computer code which implements a model [29] based on the auxiliary differential equation finite-difference time domain (ADE-FDTD) scheme [30] which solves together the Maxwell equations, the electron oscillator (EO) equation and the erbium rate equations that give the energy states population time variation during the propagation of pump and input signals [31]. In particular the model considers the absorption and emission erbium cross-sections by solving the EO equation (the ADE) that takes into account the field effect on the medium during its propagation [32]. For self-consistency, we briefly describe the implemented model referring the interested readers to the paper
[29] for further details. Fig. 1 shows the four-level energy erbium laser system; the erbium rate equation model is described by the Eqs. (1)–(5): dN 4 N4 ¼ þ C up N 22 þ C3 N 23 C 14 N 1 N 4 ; dt s43 dN 3 N3 N4 ¼ W p N1 þ 2 C 3 N 23 ; dt s32 s43
ð1Þ ð2Þ
dN 2 N 3 eðtÞ dpðtÞ N 2 ¼ þ þ 2 C 14 N 1 N 4 2 C up N 22 ; dt s32 hms dt s21 ð3Þ dN 1 eðtÞ dpðtÞ N 2 þ ¼ W p N 1 C 14 N 1 N 4 hms dt dt s21 þ C up N 22 þ C 3 N 23 ;
ð4Þ
with the population densities on different energy levels Ni related to the total dopant concentration NT by the conservation equation: N T ¼ N 1 þ N 2 þ N 3 þ N 4:
ð5Þ
The model considers the following energy state transitions: the ground state absorption (GSA), that occurs at the pump wavelength kp = 980 nm, the stimulated emission (SE) that occurs at the input signal wavelength ka = 1532 nm, where the peak of stimulated emission (SE) takes place, and the radiative and non-radiative transitions that are governed by the fluorescence times s43 = s32 = 1 Æ 109 s and s21 = 7.1 Æ 103 s. Moreover, it includes the concentration quenching effects such as the up-conversion characterized by the coefficient rates C3 = Cup = 5 Æ 1023 m3/s, and the cross-relaxation, characterized by the coefficient rate C14 = 3.5 Æ 1023 m3/s [12]. The rate equations are linked to the propagating electric field e(t) and the macro-polarization vector p(t), by considering the EO equation: d2 pðtÞ dpðtÞ þ x2a pðtÞ ¼ kDN 12 ðtÞeðtÞ; þ Dxa 2 dt dt
ð6Þ
where the resonance frequency xa is the characteristic transition frequency related to the energy levels involved in the stimulated emission, Dxa is the full width at half maximum (FWHM) linewidth of the atomic transition, DN12 = N1 N2 is the electron population difference between the lower and upper energy levels involved in the transitions and the k factor depends on the oscillator strength.
Fig. 1. Energetic level transitions of a four-level erbium laser system.
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The experimentally measured erbium absorption and emission cross-sections have been recovered by a Lorentzian lineshape susceptibility. The transmittance has been evaluated by calculating the FFT of the input and output electromagnetic field components and evaluating the ratio between the Poynting vector along the propagation direction at the output of the structure and the Poynting vector at the input of the structure. For the FDTD simulations, a longitudinal step Dz = 5 Æ 109 m and a time step Dt = 1.5 Æ 1017 s, values which verify the Courant limit, have been considered. Each structure under analysis has been excited by a sinusoidal pump signal considering different power values and an input signal having a Gaussian lineshape, a power equal to 1 lW and centered around the erbium emission wavelength k = 1.532 lm.
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Np = 50, silica layer width ws = 0.2271 lm, titania layer width wt = 0.1432 lm. As we can see, the bandgap ranges between k = 1.2 lm and k = 1.532 lm where the upper band edge is located. Fig. 3 illustrates the transmittance of the active PC as a function of the period number for three different pump signal powers: Pp = 100 mW (dotted line), Pp = 200 mW (dashed line), Pp = 300 mW (solid line). The simulation is performed for a typical value of the erbium ion concentration equal to Nt = 2.2 Æ 1026 [ions/m3]. In the following, the perfect 1D-PC having Np = 100 has been considered. Fig. 4 shows the transmittance value at
3. Results We start our analysis by considering the one-dimensional erbium doped perfect photonic crystal. It is a quarter-wave Bragg reflector consisting of alternated layers of erbium doped amorphous SiO2 and TiO2; similar structures have been recently proposed in literature both for amplification phenomenon [33] non-linear effects [34] and omnidirectional reflector and microcavity resonator [35]. One-dimensional photonic crystals consisting of silica/titania bilayers have been fabricated by the sol–gel method [33–35], rf-sputtering [36] and vacuum deposition [37]. The refractive indices of the silica and titania layers are ns = 1.453 and nt = 2.304 at the wavelength k = 1.5 lm, respectively. The Bragg wavelength has been fixed to kB = 1.35 lm, thus setting the band edge in correspondence of k = 1.532 lm where the erbium emission cross-section is centered. Fig. 2 depicts the transmittance of the 18.51 lm long photonic crystal characterized by a period number
Fig. 2. Transmittance of a 1D-PC 18.51 lm long (period number Np = 50).
Fig. 3. Transmittance value at the band edge as a function of the period number for an EDPCA for an erbium ion concentration of Nt = 2.2 · 1026 and three different pump signal powers Pp = 100 mW (dotted line), Pp = 200 mW (dashed line), Pp = 300 mW (solid line).
Fig. 4. Transmittance value at the band edge as a function of erbium ion concentration for an EDPCA with Np = 100 for three different pump signal powers Pp = 100 mW (dotted line), Pp = 200 mW (dashed line), Pp = 300 mW (solid line).
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the upper band edge calculated by varying the erbium ion concentration inside the silica layers; the simulation has been performed for three different values of the pump signal power Pp = 100 mW (dotted line), Pp = 200 mW (dashed line), Pp = 300 mW (solid line). The considered defected photonic crystal is constituted by only 10 periods, 5 on the right and 5 on the left of the central SiO2 local defect in absence of pump signal. The width of the silica layer is ws = 0.2667 lm and that of the titania layer is wt = 0.1682 lm; the local defect is half-wave long (Lc = 0.5334 lm). The geometrical parameters of the defected photonic crystal have been optimized in order to have a resonant peak in correspondence of the signal wavelength k = 1.532 lm, which results to be around the center
Fig. 5. Transmittance of the 1D-PC microcavity 4.349 lm long (period number Np = 10).
Fig. 6. Transmittance value of the EDPCMA with only the silica defect erbium doped. The erbium ion concentration is Nt = 2.2 · 1026 and the period number is 10. The simulation has been performed by considering three different pump signal powers Pp = 100 mW (dotted line), Pp = 200 mW (dashed line), Pp = 300 mW (solid line).
of the bandgap ranging from k = 1.3 lm to k = 1.85 lm (see Fig. 5). The device has a total length of L = 4.349 lm which results to be lower than that of the 100 period EDPCA. Fig. 6 depicts the transmittance value in correspondence of the defect resonance for an EDPCMA, where only the local defect is doped with erbium, by considering three different value pump signal powers Pp = 100 mW (dotted line), Pp = 200 mW (dashed line), Pp = 300 mW (solid line), the erbium ion concentration being Nt = 2.2 Æ 1026 [ions/m3].
Fig. 7. Transmittance value of an EDPCMA at resonance wavelength and of a 100 period EDPCA at the band edge as a function of pump signal power.
Fig. 8. Transmittance value at resonance wavelength as a function of erbium ion concentration for an EDPCA with a local defect and Np = 10; the simulation has been performed by considering three different pump signal powers Pp = 100 mW (dotted line), Pp = 200 mW (dashed line), Pp = 300 mW (solid line).
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Fig. 7 shows the comparison between the transmittance of the EDPCMA, having all the silica layers doped with erbium, and the 100 period EDPCA to a parity of concentration Nt = 2.2 Æ 1026 [ions/m3]. Fig. 8 illustrates the transmittance value at the defect resonance of the EDPCMA with all the silica layers doped with erbium, as a function of the erbium ion concentration, for three different pump signal power values Pp = 100 mW (dotted line), Pp = 200 mW (dashed line), Pp = 300 mW (solid line). Fig. 9(a) and (b) depict the transmittance value at the defect resonance for three different pump signal power values Pp = 100 mW (dotted line), Pp = 200 mW (dashed line), Pp = 300 mW (solid line), considering, respectively, a k and a 3/2 k long defect and an erbium ion concentration of Nt = 2.2 Æ 1026 [ions/m3].
Fig. 9. Transmittance value of the EDPCMA having a microcavity (a) k long and (b) 3/2 k long. The erbium ion concentration is Nt = 2.2 · 1026 and the period number is 10. The simulation has been performed by considering three different pump signal powers Pp = 100 mW (dotted line), Pp = 200 mW (dashed line), Pp = 300 mW (solid line).
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4. Discussion The transmittance at the band edge depends mainly on the period number, i.e. the device length. As shown in Fig. 3, the transmittance increases by increasing the device length and reaches a value corresponding to 3 dB for a 37 lm long (Np = 150) EDPCA and for a pump signal power of 300 mW, showing a better compactness of these devices respect to the EDWA. For a period number smaller than 80, the transmittance does not reach values different from the unit and this period number can be considered as the inferior limit for the length of the EDPCA. Anyway, fixed the band edge transmittance value, if higher concentration values are considered, the device length can further decrease. It is interesting to note in Fig. 3 that the slope of three curves significantly changes in correspondence of a period number around 100. Since the device length is very short in all examined cases, if compared with the typical lengths (of the order of cm) of an EDWA, this fact suggests the possibility to consider smaller values of pump signal power. The curves reported in Fig. 4 show the concentration effect on the gain for different pump powers. The transmittance increases by increasing the active media concentration because the input signal sees more and more excited ions on the metastable level; moreover it can be noted that the gain detrimental concentration quenching effects are not yet evident, since the number of erbium ions is not sufficient to cause clustering phenomena. However the slope of the curves decreases by increasing the ion concentration and this saturation-like behavior indicates the rising of the quenching effects. The transmittance values become much higher as the pump signal power increases from 100 mW to 300 mW since the pump rate influences the inverted population density. The introduction of a local defect in the otherwise perfect 1D-PC strongly affects the amplification effect of the active structure. By erbium doping only the local defect in the periodic structure, the light at a certain frequency is localized inside the defect for a considerable long time allowing the interaction with the active media. For a pump power of 300 mW (see Fig. 6) the transmittance reaches a value corresponding to 1.76 dB, which is much higher than the 0.9 dB obtained for the 100 period EDPCA under the same pump and concentration condition. For this structure, the increase of the pump power value does not give significant transmittance improvement; this can be justified by the saturation effect that characterized all the erbium doped based devices. In this case, considering pump power values beyond the 200 mW does not give significant improvement in terms of gain. A further enhancement in the EDPCM performance is achieved if all the silica layers of the 1D-PC microcavity are erbium doped. As shown in Fig. 7 the transmittance is doubled; this is due to the fact that the light, before and after the localization in the microcavity, passes through the erbium doped activated layers and hence it is
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amplified during the propagation through the structure. It is possible to observe that the increasing of pump power value gives rise, in this structure, to a transmittance enhancement. Moreover the EDPCMA with all the silica layers doped with erbium reaches the transparency for a pump power of 10 mW, showing a lower threshold than that of the EDPCA which results to be 20 mW (see Fig. 8). The dependence of the transmittance at the resonance wavelength on the erbium ion concentration for the EDPCMA with all the silica layers doped with erbium has been calculated and reported in Fig. 8. The slope of the curves is much higher respect to the case of the perfect EDPCA; the transmittance reaches a value around nine corresponding to 9.5 dB for an erbium ion concentration of 4.5 Æ 1026 [ion/m3] and a pump signal power of 300 mW. The optical amplification is clearly affected by the microcavity length. In fact, as it can be noted in Fig. 9(a), (b), by increasing the length of the microcavity of an integer multiple of half-wave the transmittance peak increases until reaching a value of eight corresponding to 9 dB setting the pump power at 300 mW. For a 3/2 k long microcavity, under the same pump and concentration conditions the transmittance value raises to 11 dB, showing a strong improvement if compared to that of microcavity k/2 long, depicted in Fig. 7. 5. Conclusion In this paper the time domain analysis of the amplification phenomena in an erbium doped silica–titania 1D photonic crystal microcavity amplifier is reported. The presence of a microcavity in an erbium doped photonic crystal allows to optimize the performance of photonic crystal band edge amplifiers. In fact the erbium doped photonic crystal microcavity reaches transmittance values of about 5 dB in 5 lm, showing a threshold of 10 mW, while an erbium doped photonic crystal band edge amplifier need of a device length of 37 lm to get a transmittance value of 3 dB, having a threshold of 20 mW. Acknowledgement This work was partially sponsored by the MIUR research contract FIRB 2001, ‘Modelling and numerical methods of photonic devices for high capacity optical networks’. References [1] J.D. Joannopoulos, R.D. Meade, J.N. Winn, Princeton University, 1995. [2] S.G. Johnson, J.D. Joannopoulos, Kluwer Academic, 2002. [3] K. Sakoda, Springer, 2001. [4] K.H. Lee, J.H. Back, I.K. Hwang, Y.H. Lee, G.H. Lee, J.H. Ser, H.D. Kim, H.E. Shin, Opt. Express 12 (2004) 4136.
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