One-dimensional (1D) photonic crystals (PC) containing two-layer CdS defects are proposed and fabricated by using electron beam evaporation. Ultrafast nonlinear optical responses were characterized with the ultrafast pump-probe method in both time and spectral domains. Two-photon absorption coefficient enhancement and pump-beam-induced defect mode shift were reported. Both effects are attributed to the light localization in the defect layer of the multilayer structures. Our results demonstrated that defective photonic crystals are good candidates for fabrication of ultrafast all-optical switching devices.
© 2006 Optical Society of America
Ever since the pioneering research by Yablonovitch , photonic crystals (PCs) have attracted a fair amount of attention because the new class of materials offers a novel method to control electromagnetic wave propagation [2–5]. Recently, although PCs have been studied extensively from both fundamental and application points of view, some technical challenges still remain [1, 3–6]; one such challenge is the design of the controllable defect mode in the bandgap structure of two- and three-dimensional PCs with a periodicity equivalent to the visible wavelength . Normally, a 1D PC consists of alternating dielectric stacks of two materials with high and low refractive indices nH and nL, respectively. A defective 1D PC can be constructed by inserting a defect layer into the center of such a multilayer structure . With the introduction of a defect layer into a PC structure, a resonant mode appears in the frequency region of the bandgap [8–10]. The frequency of the resonant mode strongly depends on the optical thickness of the defect layer . Because of the high localization of the electrical field at the defect mode, strong enhancement of optical nonlinearity by several orders of magnitude can be expected in the defect layer [11–13]. If the defect layer includes nonlinear optical materials, it is envisaged that the optical nonlinearity may be substantially intensified by the presence of such a strong electric field [2, 8, 12, 13]. In particular, defect modes that lie in the vicinity of the mid-gap of the photonic bandgap (PBG) structure will have stronger effects on light localization and its associated optical nonlinearity . As the incident field is intricately coupled to the local defect modes, such a structure has emerged as a promising candidate for many optical applications requiring ultrafast all-optical switching and modulation [5, 14]. In fact, ever since the first theoretical predictions, intensive efforts on optical switching and limiting in nonlinear periodic structure have been carried out since the late 1970s [15–22].
In this paper we present our computational and experimental studies on a 1D PC structure with multiple defect modes, focusing especially on the two-defect mode structure. Similar to a single-mode defective PC, a multimode defective 1D PC is constructed by inserting multiple defect layers into a 1D PC structure. It is shown that the separation of neighboring defect modes can be monitored by modifying the structure parameters of the 1D PC. An ultrafast nonlinear optical response was characterized with the femtosecond pump-probe method. An intense pump beam induced resonant defect mode shift was observed resulting from the enhanced nonlinearity in the defect layer. The results agree qualitatively with the expectations of the matrix transfer formulation . Our results show that defective 1D PC structures are good candidates for constructing ultrafast all-optical switching devices.
2. Simulations and experiments
For the sake of simplicity, our pure 1D PC (with no defects) structure consists of 8 units of alternating high (H) and low (L) refractive index layers, and is denoted as (HL)8. A defective PC can be constructed by inserting a multidefect layer (D) in the center of the pure PC structure; for instance, (HL)4D(LD)m(LH)4. Here, m=0, 1, 2, 3… corresponds to single, two, three, … defect modes in the PC structure, respectively. On the other hand, with a fixed value for m, the separation of the two defect states is dependent on the distance between the two defect layers. In the present work, we focus on two-defect mode PCs where n=0, 1, 2… in the structure defined by (HL)4D(LH)nLD(LH)4. By adjusting the parameter n, the position as well as the separation of the two defect modes can be modified correspondingly. In order to simulate the transmission spectra of the defective 1D PC, the transfer matrix method was employed . Without loss of generality, we assumed that the light falls at a normal incidence and propagates in the PC structure as a plane wave, and that the dielectrics are nondispersive and lossless. TiO2 and SiO2 were chosen as the high and low refractive index media and CdS was chosen as defect layer.
The refractive indices are nH=2.21 for TiO2, nL=1.45 for SiO2, and nD=2.26 for CdS around the wavelength of 760 nm. The respective thicknesses of the dielectric layers dH (TiO2) and dL(SiO2) are 86 and 131 nm, and the corresponding midgap position of the 1D PC is approximately 760 nm. The thickness of each defect layer dD (CdS) was set to 352 nm. Figure 1 shows the simulated transmission spectra of 1D PC structures of (HL)4D(LD)m(LH)4 with m = 1 and 7. It is seen that the number of the defect modes in the photonic bandgap is equal to the number of defect layers. The split defect modes have approximately the same frequency intervals as the property of a comb filter . It should be emphasized that there is no one-to-one correspondence of split modes to the defect layers in a PC. Each split mode, in fact, consists of contributions from all of the defect layers. Figure 2 shows the transmission spectra of the PC structures of (HL)4D(LH)nLD(LH)4, with n=0, 1, 2, 3, and 7. This is the case with a 1D PC structure with two-defect modes. It is seen that the mode separation can be modulated by changing the distance of the two defect layers. The frequency difference between two split modes diminishes with the increasing separation between the two defect layers. This is because the coupling coefficients of the two localized states are weaker when their separation becomes larger. When the separation of the two defect layers is sufficiently large, mode degeneracy is observed where the defect states merge into a single state as shown in Fig. 2 .
In our experiment, two types of 1D PC samples with two defects were fabricated, where one sample was designed with n=2 and the other n=3. The detailed fabrication process is described in Ref. . Characterization of an ultrafast nonlinear optical response was performed using a pump-probe setup consisting of a Ti: Sapphire laser (Tsunami, Spectra-Physics) with a pulse duration of 200 fs, repetition rate of 82 MHz, and a center wavelength of 800 nm. The laser output was split into pump and probe beams by a beam splitter. The pump beam was chopped at 1620 Hz, after which it passed through an optical delay line controlled by a computer. The two beams with a separation of 12 mm were focused on the same spot of the sample with a spot size of about 50 μm by two identical lenses, each with a focus length of 5 cm. The transmitted probe beam was detected by a photodiode connected with a lock-in amplifier, and the data were stored in a computer. The peak intensity of the pump beam was kept below 2 GW/cm2 at the sample position, and the probe beam intensity was less than 10% of the pump beam.
3. Results and discussions
Figure 3 shows the measured transmission spectra of two-defect structure (HL)4D(LH)nLD(LH)4 with n=2 and 3, respectively. The two resonant modes are located at 765 and 805 nm for n=2, and at 772 and 800 nm for n=3, respectively. In the simulated results the resonant modes are respectively located at 761 and 798 nm for n=2 (Fig. 2, green line) and 767 and 792 nm for n=3 (Fig. 2, blue line). The difference between the measured and simulated results may have originated from a deviation of the thickness of defect layers in the sample from the value 352 nm used in simulation. Because the defect layer was deposited with thermal evaporation, it is difficult to control the deposition rate precisely with this technique. The optical spectroscopy analysis indicates that the two defect layers have different thicknesses; one has a thickness of about 352 nm, and the other has a thickness of 362 nm.
Ultrafast nonlinear optical response characterization was carried out on the sample with n=3, where the defect mode localized at 800 nm is in resonance with the wavelength of the laser output. Figure 4 shows the transient time evolution of the PC sample with the pump intensity of 1.1 GW/cm2 at wavelength of 800 nm. A pump-probe signal of 0.5-mm-thick bulk ZnSe crystal is also plotted in Fig. 4 with a red line, where the signal of the bulk ZnSe was multiplied by a factor of 0.1 for comparison. The ultrafast negative transmission change of the probe beam is seen to have arisen from the two-photon absorption (TPA) in the CdS layer. In order to rule out any contributions from the TiO2 and SiO2 films, the pump-probe measurement was repeated for homogeneous films of TiO2 and SiO2 as well as multilayer films of alternating TiO2/SiO2 with 8 periods. No TPA signal was observed in all these films. As a reference, the two-photon absorption (TPA) coefficient β of bulk ZnSe is reported to be 3.5 cm/GW at wavelength of 780 nm . The β value of CdS layers in the 1D PC structure was calibrated as 307 cm/GW. Thus the enhancement relative to the bulk CdS is about 48 times (β=6.4 cm/GW is reported at wavelength of 780 nm  for bulk CdS). It is well known that such enhancement of optical nonlinearity in 1D PC structure with defects originates from the high electric field localized within the defect layers.
As reported in our previous papers [8, 13], the total magnitude of the electric field in the defect layer is determined mainly by two factors: the resonant transmittance and the position in the rejection band. Under an intense pump beam, the refractive index at the CdS layers can be expressed as n=n0+n2I0, where n0 is the linear refractive index under weak light (I0~0), n2 is the nonlinear refractive index, and I0 is for the incoming pump beam intensity in the air, 1.1GW/cm2. Owing to the TPA process, as well as electric field localization at the defect layer, the total refractive index n, and hence the resonant mode, can be substantially modified. Under an intense pump beam, the resonant mode will show either a red shift or a blue shift for positive or negative n2, respectively. For CdS film with a polycrystal structure, n2 is positive at a wavelength of approximately 800 nm. It is expected that the resonant mode will show a red shift under an intense pump beam. The experimental results are shown in Fig. 5. The ultrashort probe pulse at 800 nm has sa pectra bandwidth (FWHM) of 8 nm before the sample due to the spatio-temporal correlation (green line). When the pump beam is blocked, the transmitted probe after the sample has a relative narrow spectrum of 4 nm (black line) due to the filtering property of the narrowing defect mode centered at 800 nm. The red line in the figure represents the transmitted spectrum of a probe beam when the pump pulse overlapped completely with the probe pulse (the delay time between pump and probe pulses reaches zero). As expected, the transmitted spectrum of the probe beam shows a red shift with a magnitude of 3 nm. In addition, it should be mentioned that the laser pulse has a center wavelength at 800 nm (green line), which is in accordance with one in the defect mode (black line). A pump-induced transmitted spectrum of the probe is contributed by an overlapping of the probe spectrum centered at 800 nm and the defect mode centered at 803 nm. Therefore, the red line shows a slightly narrower band width and lower transmitted intensity than that of the black line. It is also seen that the red line shows an asymmetric property, while the black line is almost symmetric.
Taking the linear refractive index n0 = 2.26 and the thickness of CdS layers in the PC structure to be 704 nm (352×2 nm), n2 can be calculated from n2=Δn/I0=(n-n0)/I0. Here, I0 denotes the light intensity of the incident pump beam, which has a value of about 1.1 GW/cm2. The value of n2 of the CdS layers is calculated to be 3.9×10-3 cm2/GW. Compared with the reported value of n2 in bulk CdS of 7.9×10-5 cm2/GW , n2 of CdS layers inside the PC have achieved an enhancement greater than 48 times. This enhancement factor is almost the same as that in the TPA measurement mentioned previously. Again, such a large nonlinear refractive coefficient inside the defect layers is seen to have originated from light localization in the defect modes. It should be pointed out that the large value of n2 of the CdS layer is obtained from the formulation n2=Δn/I0=(n-n0)/I0, where I0 denotes the light intensity of incident pump beam instead of light intensity I inside the CdS layer. Due to the local field enhancement, the light intensity inside the CdS layer, I, is much stronger than that of incident light, I0. In fact, if we define an effective nonlinear refractive index as (n2)eff=(n-n0)/I, we can find that (n2)eff remains exactly the same value as in bulk status, i.e., 9×10-5 cm2/GW. The same conclusion can also be applied to the discussion on the enhancement of the TPA process mentioned above. Additionally, the optical response is as fast as the pulse duration, which in our case is 200 fs as seen from the time evolution shown in Fig. 4. By combining Fig. 4 and Fig. 5, ultrafast optical switching can be designed in both time and spectrum domains using the 1D PC structure containing appropriate defect modes.
Finally, we would mention material requirements for the fabrication of all-optical switching devices based on waveguide structures with the exploration of nonlinear phase changes. To evaluate the material requirement for all-optical switching devices, one often introduces one-photon and two-photon figures of merit, W and T, respectively. The two figures of merit are defined as W=n2I0/(αλ) and T=βλ/n2 , where I0 is the light intensity outside the material, α is the one-photon absorption coefficient due to absorption and scattering, and λ is the working wavelength. For realization of all-optical switching devices, materials with W>1 and T<1 have to be met. In our case, considering 50% transmittance at defect mode of 800 nm and the total thickness of 3232 nm for PC films, the value of α was calculated to be 2.14×103 cm-1. With other data, n2=3.9×10-3 cm2/GW, β=307 cm/GW, I0=1.1 GW/cm2, and λ=800 nm, T and W were calculated to be 6.3 and 0.025, respectively. Although our data show that our samples are not yet up to the requirements of all-optical switching devices, it is expected that this target can be achieved by choosing proper materials. The condition of W>1 can be met by reducing light scattering in the PC structure. In a high quality PC structure, the transmittance at a defect mode can be as high as 99%, and then the W>1 can be achieved. The condition T<1 can be met by choosing a Kerr material in which the value of β is as small as possible at the working wavelength; for example, some polymers or wide gap semiconductors such as ZnO nad ZnS etc.
Structures of 1D PC containing multilayer defect modes were proposed and fabricated. An ultrafast nonlinear optical response was characterized in both time and spectrum domains with the femtosecond pump-probe method. A two-photon absorption coefficient enhancement and an ultrafast resonant defect mode shift were observed, which is attributed to the light localization in the defect layers of the 1D PC structure. Our results show that 1D PC with appropriate defect modes is a good candidate for fabricating ultrafast all-optical switching.
This work was supported in part by the Shanghai Leading Academic Discipline Program (T0104); grant 60377025 from the National Natural Science Foundation of China; and grants 03QMH1405 and 04JC14036 from the Science and Technology Commission of Shanghai Municipal.
References and links
2. I. R. Matias, I. D. Villar, F. J. Arregui, and R. O. Claus, “Development of an optical refractometer by analysis of one-dimensional photonic bandgap structures with defects,” Opt. Lett. 28, 1099–1101 (2003). [CrossRef] [PubMed]
3. G. J. Schneider and G. H. Wastson, “Nonlinear optical spectroscopy in one-dimensional photonic crystals,” Appl. Phys. Lett. 83, 5350–5352 (2003). [CrossRef]
4. M. C. Larciprete, C. Sibilia, S. Paoloni, M. Bertolotti, F. Sarto, and M. Scalora, “Accessing the optical limiting properties of metallo-dielectric photonic bandgap structures,” J. Appl. Phys. 93, 5013–5017 (2003). [CrossRef]
5. Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, “Resonance transmission modes in dual-periodical dielectric multilayer films,” Appl. Phys. Lett. 82, 4654–4656 (2003). [CrossRef]
6. H. Nemec, L. Duvillaret, F. Quemeneur, and P. Kuzel, “Defect modes caused by twinning in oned-imensional photonic crystals,” J. Opt. Soc. Am. B 21, 548–553 (2004). [CrossRef]
7. B. I. Senyuk, I. I. Smalyukh, and O. D. Lavrentovich, “Switchable two-dimensional gratings based on field-induced layer undulations in cholesteric liquid crystals,” Opt. Lett. 30, 349–351 (2005). [CrossRef] [PubMed]
8. G. H. Ma, S. H. Tang, J. Shen, Z. J. Zhang, and Z. Y. Hua, “Defect-mode dependence of two-photon-absorption enhancement in a one-dimensional photonic bandgap structure,” Opt. Lett. 29, 1769–1771(2004). [CrossRef] [PubMed]
9. R. Ozaki, Y. Matsuhisa, M. Ozaki, and K. Yoshino, “Nonlinear optical spectroscopy in one-dimensional photonic crystals,” Appl. Phys. Lett. 84, 1844–1846 (2004). [CrossRef]
11. Ryotaro Ozaki, Yuko Matsuhisa, Masanori Ozaki, and Katsumi Yoshino, “Electrically tunable lasing based on defect mode in one-dimensional photonic crystal with conducting polymer and liquid crystal defect layer,” Appl. Phys. Lett. 84, 1844–1846 (2004). [CrossRef]
12. T. Hattori, N. Tsurumachi, and H. Nakatsuka, “Analysis of optical nonlinearity by defect states in one-dimensional photonic crystals,” J. Opt. Soc. Am. B 14, 348–355 (1997). [CrossRef]
13. G. H. Ma, J. Shen, K. Rajiv, S. H. Tang, Z. J. Zhang, and Z. Y. Hua, “Optimization of two-photon absorption enhancement in one-dimensional photonic crystals with defect states,” Appl. Phys. B 80, 359–363 (2005). [CrossRef]
14. N. Tsurumaehi, S. Yamashita, N. Muroi, T. Fuji, T. Hattoti, and H. Nakatsuka, “Enhancement of nonlinear optical effect in one-dimensional photonic crystal structures,” Jpn. J. Appl. Phys. 38, 6302–6308 (1999). [CrossRef]
15. B. Wild, R. Ferrini, R. Houdre, M. Mulot, S. Anand, and C. J. M. Smith, “Temperature tuning of the optical properties of planar photonic crystal microcavities,” Appl. Phys. Lett. 84, 846–848 (2004). [CrossRef]
16. M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic bandgap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994). [CrossRef] [PubMed]
18. A. E. Bieber, A. F. Prelewitz, T. G. Brown, and R. C. Tiberio, “Optical switching in a metal-semiconductor-metal waveguide structure,” Appl. Phys. Lett. 66, 3401–3403 (1995). [CrossRef]
19. H. G. Winful, J. H. Morburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381 (1979). [CrossRef]
21. T. G. Brown and B. J. Eggleton, “Bragg solitons and optical switching in nonlinear periodic structures: an historical perspective,” Opt. Express 3, 385–388 (1998), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-3-11-385. [CrossRef] [PubMed]
22. N. D. Sankey, D. F. Prelewitz, and T. G. Brown, “All-optical switching in a nonlinear periodical-waveguide structure,” Appl. Phys. Lett. 60, 1427–1429 (1992). [CrossRef]
23. J. Danlaert, K. Fobelets, I. Veretennicoff, G. Vitran, and R. Reinisch, “Dispersive optical bistability in stratified structures,” Phys. Rev. B 44, 8214–8225 (1991). [CrossRef]
24. X.-Q. Huang and Y. -P. Cui, “Degeneracy and split of defect states in photonic crystals ,” Chin Phys.Lett. 20, 1721–1723 (2003). [CrossRef]
25. T. D. Krauss and F. W. Wise, “Femtosecond measurement of nonlinear absorption and refraction in CdS, ZnSe, and ZnS,” Appl. Phys. Lett. 65, 1739–1741 (1994). [CrossRef]
26. A. Miller, K. R. Welford, and B. Baino, Nonlinear Optical Materials for Applications in Information Technology (Kluwer, Dordrecht, 1995).