This work demonstrates that arbitrary types of spatially modulated second-order susceptibility (χ(2)) structures such as 1D and 2D, periodic and quasi-periodic structures can be obtained by using the combination of corona poling and direct laser writing (DLW) techniques. The fabrication technique is based on the photodepoling of azo-dye molecules caused by one-photon or two-photon absorption during the DLW process. Polarization and second harmonic generation (SHG) images of the fabricated structures were measured by electrostatic force microscope and SHG mapping techniques, respectively. Furthermore, quasi-phase-matched (QPM) enhanced SHG from a 1D periodically poled azo-copolymer planar waveguide is demonstrated using an optical parametric oscillator laser by scanning wavelength from 1500 to 1600 nm. The resonant wavelength of the QPM enhanced SHG is peaked at 1537 nm with FWHM≅2.5nm.
©2008 Optical Society of America
Nonlinear optical (NLO) polymer materials have attracted considerable attention due to their large NLO responses and ease of processing for devices such as electro-optic modulators, and frequency converters [1-4]. In particular, quasi-phase-matched (QPM) second harmonic generation (SHG) in periodically poled materials can result in efficient frequency conversion . Previous studies have shown NLO polymer materials offer many advantages for realizing QPM SHG, for example: low cost, fast response, large nonlinearity, and flexible processing options [6-11]. Various techniques have been employed to fabricate periodically poled structures (i.e., second-order susceptibility (χ(2)) grating) in polymer thin films such as serial grafting [7,9], periodic poling , photodepoling with photolithographic masks , ultraviolet (UV) photobleaching , direct electron-beam (EB) irradiation , two-beam interference , and direct laser writing (DLW) .
In the DLW technique, the non-zero χ(2) induced by uniformly corona-poling a polymer thin film is locally erased by locally irradiating the film with a laser beam to that randomizes the molecular orientation alignment. By scanning the focused laser across the polymer thin film, a spatially modulated χ(2) structure can be obtained. Compared with other techniques, the DLW approach is easier and more flexible for controlling the structural design and period, because no mask or etching is required. Okamoto et al. used the DLW technique to fabricate χ(2) grating structures in a poled polymer thin film based on an one-photon absorption induced depoling mechanism . One-photon absorption-based depoling can be done with relatively low power lasers, but two-photon absorption-based depoling [16, 17] using pulsed lasers can provide higher lateral (2D) spatial resolution for a fixed laser wavelength, and it also allows 3D control over the depoling structure, if there is a limited depth of focus over which absorption occurs. Previous work on two-photon absorption-based DLW demonstrated it is feasible for optical data storage applications [18-20].
In this work we demonstrate that complex 2D χ(2) patterned structures, with no measurable surface topography, and minor modulation of the linear refractive index (Δn<0.01), can be easily fabricated by DLW techniques using both one-photon and two-photon absorption induced photodepoling in azo-copolymer thin films. Azo-copolymer thin films have photoisomerization effect, which can easily induce molecular orientation randomization at low exposure dosage. In this work, we show they are suitable for generating pure photo depoling effect by employing DLW technique. Furthermore, as an example of the possible device applications of this technique, the QPM SHG properties of a periodically poled azo-copolymer planar waveguide obtained by DLW technique are investigated. To our knowledge this is the first measurement of QPM enhanced SHG in a χ(2) periodic structure obtained by the DLW technique.
This paper is organized as follows. Section 2 presents the DLW fabrication techniques used to produce a variety of periodic and quasi-periodic χ(2) structures. Section 3 shows the spatial modulation of molecular-orientation in 1D and 2D structures characterized by SHG and electrostatic force microscopy (EFM) mapping techniques. Section 4 shows the measured QPM SHG signal obtained from a periodically poled azo-copolymer planar waveguide obtained by the one photon DLW technique. Conclusions are drawn in Section 5.
2. Fabrication of periodic and quasi-periodic nonlinear structures
The polymer thin films were formed from a DR1-PMMA copolymer with 15% molar azo-dye concentration. The copolymer was dissolved in chloroform, and spin coated on the backside of an indium-tin-oxide (ITO) glass substrate after the copolymer solution had been filtered with a 250 nm filter. The copolymer thin films were then baked for 12 hours at 70 °C in an oven before use. Figure 1(a) shows the absorption spectrum and molecular structure of the DR1-PMMA copolymer. The film thickness was about 2 µm and its absorption band ranged from 400 to 600 nm, with an absorption peak at 470 nm. A corona poling technique was used to align the NLO molecules at 4.5 kV and T~100°C for 45 minutes. The distance between the needle electrode and the copolymer thin film was about 1cm. The uniform poling area is about 1 cm2.
After corona poling, the DLW technique was first applied to fabricate χ(2) periodic structures on poled copolymer thin films based on one-photon absorption induced photodepoling. Figure 1(b) shows the experimental setup. A CW Argon laser with wavelength at 514 nm was used as the light source. An objective lens (OL) with numerical aperture (NA)=0.4 mounted on a z-directional translation stage was used to focus the circularly polarized laser beam on the sample and the focusing spot size obtained was about 6 µm. The sample was mounted onto a 2D motor-controlled stage. The lateral travel range and the resolution of the motor stage are 2.5 cm and 1 µm, respectively. The motor stage and shutter were controlled by a computer. The exposure dosage can be controlled by changing laser power, exposure time or the scanning speed of the motor stage. The typical average power used in this work was about 0.3 mW. A similar DLW setup was also used to fabricate χ(2) periodic and quasi-periodic structures based on two-photon absorption induced photodepoling effect. The modifications in the setup are as follows: a Ti: Sapphire laser with central wavelength at 830 nm, 100 fs pulse width, and 80 MHz repetition rate was used as the light source; a high NA (=0.85) OL was used to focus the incident laser beam and the focusing spot size obtained was about 1 µm; a 3D piezoelectric translation (PZT) stage with a resolution of 1 nm was used to translate the samples in 3D. The average power used in two-photon DLW experiment was about 35 mW.
During the DLW process, the second order nonlinearity of the corona-poled azo-copolymer thin film can be erased by the photodepoling effect [1, 10, 14-15, 21-22]. This photodepoling effect is initiated by the absorption of laser irradiation (by either one photon or two photon processes) in the azo-copolymer thin film, which leads azo-dye molecules to undergo many trans→cis→trans reversible photoisomerization cycles, and thus results in molecular orientation randomization at laser exposure sites [10, 21-22]. It is important to note that other photo-induced effects such as: bleaching [12, 23], mass transport [1, 24], and micro explosions  can also be generated during the DLW process, but these occur at much higher laser exposure dosages. These higher dosage effects result in significant linear-refractive index and surface morphology modulations that can induce large propagation loss and are unfavorable for most optical waveguide device applications . Although a pure-photodepoling effect can also induce refractive index variation, it is shown below that the associated change of refractive index is much smaller than those induced at higher dosages.
3. Characterization of nonlinear χ(2) structures
A SHG mapping technique was applied to map images of the χ(2) structures. Its setup was the same as that of the two-photon absorption DLW technique except a photomultiplier tube covered with an interference filter (center wavelength=415 nm) was added to detect the SHG signal. The details of the laser scanning SHG mapping technique can be found in elsewhere . The transverse resolution of this mapping technique was approximately 1 µm corresponding to the diffraction limit of the OL used (NA=0.85) at 830 nm. This laser scanning SHG mapping technique provides a direct measure of the χ(2) spatial distribution in photo-depoled azo-copolymer samples. In Fig. 2(a) a high contrast 1D SHG modulation is clearly observed; and almost no SHG signal can be found from the exposure regions. In the one-photon absorption CW DLW experiment, we found when the laser writing average intensity and scan speed were chosen to be 0.01 mW/µm2 and 2 mm/s, respectively, about 80% of the SHG response was removed at the laser exposed region in the corona poled azo copolymer thin film.
The contrast of the electric polarization (P⃗) between the poled and depoled regions can be a significant evidence for the χ(2) modulation. Therefore, a scanning probe microscope (SPM) was employed to measure the topography and electric polarization modulation based on atomic force microscope (AFM) and electrostatic force microscope (EFM) schemes  respectively. During EFM imaging, a metallic-coated probe, oscillating at the resonant frequency and biased by -8 V, was scanned across the sample surface at a fixed height to sense the force between the probe and the film. The surface bound charges with the charge density σ b(=P⃗·n̂, where n̂ is the surface normal unit vector) exert a Coulomb force (-σ b E⃗) to the biased probe and results in a phase shift of the oscillating probe. By mapping the phase shift at different positions, the electric polarization distribution of the sample can be obtained. An additional attractive/repulsive force causes a minus/plus phase shift, corresponding to a lower/higher (darker/brighter) EFM signal level, so EFM is sensitive to both the amplitude and direction of P⃗, while the SHG measurement can determine the former only. Consequently, the EFM measurement result is also included in this work.
Figures 2(b) and 2(c) show the AFM and EFM images of the same 1D χ(2) grating imaged in Fig. 2(a). The AFM image in Fig. 2(b) reveals that the sample after patterning with a 1D χ(2) grating still possessed a very smooth surface; there are no signs of a periodic modulation of the sample texture. The result is different to a previous observation obtained by the same experimental irradiation scheme, in which a nanoscale surface deformation induced by a tightly focused laser beam was found . The difference is due to our exposure dosage is below the threshold of inducing surface deformation. On the other hand, Fig. 2(c) clearly shows that the EFM image has 1D periodic modulation on electric polarization. In the bright regions exposed to laser, the NLO molecules are randomly oriented so that the electric polarizations in those regions are zero or rather small. On the other hand, in the dark regions not exposed to laser, the force is attractive, indicating most NLO molecules are still aligned in the upward direction, which cannot be determined from the SHG image. In addition, EFM is a more favorable approach to investigate the polarization in NLO copolymers than SHG mapping, because EFM is based on the electric interaction between probe and polymer film, hardly disturb the molecular orientation from our experiences. Note that when the sample was exposed by high dosage of laser, mass transport and micro explosion of polymer material were induced and large modulations of surface topographic (> 100 nm) and refractive index (Δn>0.01) were observed.
The variation of refractive index between poling and depoling regions also possibly contribute the contrast of EFM image. However, the modulation of refractive index is very shallow (Δn<0.01), compared with its background index, so it is difficult to detect by EFM. In addition, the contrast of EFM image associated with the variation of refractive index is independent with the polarity of the imaging bias, but that associated with polarization modulation is reverse as the polarity of the bias changes. We observed such a reverse of contrast when we changed the polarity of the bias (because the sign of the force changed accordingly). Therefore, we assure the contrast of EFM is due to the variation of electric polarization, instead of the modulation of refractive index, inferring 1D χ(2) modulation generated by DLW.
The χ(2) response can be erased not only by one-photon absorption induced photodepoling effect but also by two-photon absorption induced photodepoling. Fig. 3(a) and (b) demonstrate SHG mapping images of a 2D hexagonal χ(2) structure and a 2D circular χ(2) structure fabricated using the two-photon DLW technique, respectively. The lattice constant in the 2D hexagonal χ(2) structure and the radial distance between circles in the 2D circular χ(2) structure are 4 µm. As illustrated in these two SHG mapping images, a high contrast ratio of 2D SHG spatial modulation and a near-zero SHG response at the laser exposure regions can be clearly observed in both structures. From additional optical microcopy and AFM measurements, we confirmed again that refractive index variation and surface modulation are small in both of these structures. For this two-photon absorption DLW experiment, pure photodepoling effect occurred when exposing copolymer thin films with 11.15 mW/µm2 average intensity of the femtosecond laser pulse train for 50 ms, which corresponds to the exposure dosage about 490 mJ/cm2. Under this exposure condition, more than 90% of the SHG response was erased in the exposed regions. To make sure the samples only experienced a pure photodepoling effect, we have reapplied corona poling to the previously exposed samples and performed an SHG mapping experiment again; we found the samples could generate a uniform SHG response just like that of obtained from a sample without exposing by laser irradiation.
By scanning the focused femtosecond pulses beneath the surface of the sample, the two-photon absorption DLW technique can result in photodepoling throughout a thick film, whereas in the one-photon absorption DLW technique, strong absorption limits the penetration depth of the depoling irradiation . Together with the above results, this suggests that the two-photon absorption DLW technique can be used to fabricate 3D polymer χ(2) photonic crystals and photonic quasi-crystals. Those kinds of structures provide the possibility of multi phase matching and multi color parametric conversion and are potentially useful for spatial and temporal shaping of input beams through appropriately designed structures, [30-34].
4. Quasi-phase-matched SHG measurement
After characterizing the χ(2) responses of structures obtained by the DLW technique, in this section QPM SHG of a 1D periodically poled azo-copolymer planar waveguide obtained by the one-photon absorption DLW technique is presented. To design an appropriate QPM SHG sample, the bulk TM mode refractive indices of a corona poled azo-copolymer thin film at four different wavelengths was measured using a prism coupler technique. The measured refractive indices at 632.8 nm, 845 nm, 1300 nm, and 1550 nm were fitted to a Sellmeier equation 
where n(λ) is the refractive index at the wavelength λ, and A, B and C are the fitting constants. The fitting result is shown in Fig. 4(a). The period for 1D QPM χ(2) grating for collinear TM-in TM-out SHG conversion can be determined from 
where Λ is the grating period; q is the QPM order; λF is the fundamental wavelength; nω and n 2ω are refractive indices at fundamental and second harmonic wavelengths, respectively.
The period of a +/0 1D χ(2) grating (q=1) for different fundamental wavelengths were determined from Eqs. (1) and (2), and the result is shown in Fig. 4(b). Accordingly, a period of 12 µm was chosen for the χ(2) grating period to observe QPM for a fundamental wavelength near 1510 nm.
A 1D χ(2) grating with pitch 12 µm and an area of 10 mm×2 mm was thus formed using one-photon DLW. The surface morphology, electric polarization and SHG mapping images of the 1D χ(2) grating are the same as those shown in Fig. 2. Fig. 5(a) shows the experimental set up for measuring QPM SHG from the 1D periodic poled azo-copolymer planar waveguide. The signal output from an optical parametric oscillator (OPO), with wavelength tuning range from 1.3 to 1.6 µm, 100 fs pulse width, and 80 MHz repetition rate, was used as the fundamental beam . The fundamental beam with average power of 20 mW was focused into the polymer planar waveguide (butt-coupling geometry) by a lens with focus length 1 cm and the SHG output was collected by a lens (f=3 cm). The SHG output was analyzed using a grating spectrometer. It was found that both TE mode and TM mode fundamental beams were able to generate TM polarized QPM SHG. The TMω →TM2ω conversion is related to χ (2) zzz (z is the electric filed poling direction) and the TEω→TM2ω conversion is related to χ (2) zxx. Since χ (2) zzz is much larger than χ (2) zxx for an electric poled thin film, the TM mode fundamental generated much stronger SHG compared to TE mode fundamental . Consequently, only the TM mode fundamental results are presented here.
Figure 5(b) shows the normal incidence SHG output spectra of the 1D periodically poled azo-copolymer planar waveguide obtained by scanning the fundamental wavelength from 1500 nm to 1565 nm. The SHG spectra exhibit two QPM enhanced SHG peaks located at 768.5 nm (fundamental wavelength at 1537 nm) and 759 nm (fundamental wavelength 1518 nm). The former corresponds to converting fundamental waveguide mode TMω o to second harmonic waveguide mode TM2ω o and the latter corresponds to the conversion from TMω o to TM2ω 1. The fundamental wavelengths of these two QPM SHG resonant modes are close to our theoretically predicted value (1510 nm) shown in Fig. 4(b). When the fundamental wavelength is out of the resonance regions, for example at 1500nm, the SHG spectra are much weaker (about 20 times less than resonance case) and wider due to the existence of non-compensated phase mismatch between fundamental and second harmonic waves. The inset in Fig. 5 (b) shows a close-up of the QPM SHG resonance mode peak at 768.5 nm. The FWHM of the QMP SHG resonance mode is 2.5 nm.
A simple and efficient way to fabricate χ(2) spatial modulated structures in azo-copolymer thin films is demonstrated. Various types of χ(2) structures, including 1D gratings and 2D periodic and quasi-periodic patterns were fabricated by the combination of corona poling and either one-photon or two-photon absorption DLW. SHG, AFM and EFM mapping techniques were employed to show that SHG modulation depths as large as 90% could be obtained with no measurable surface topography and minor modulation of the linear refractive index (Δn<0.01). This low power DLW technique, applied to DR1-PMMA, thus offers a flexible means of realizing “pure χ(2)” texture with feature sizes on the order of microns. This kind of structure has smaller propagation loss and it is more favorable for QPM SHG than those structures obtained by photobleaching, mass transport, and micro explosion.
To demonstrate a potential device application, QPM enhanced SHG from a 1D periodically poled azo-copolymer planar waveguide was measured. A QPM SHG resonant mode was identified at 1537 nm with 2.5 nm FWHM and with more than 20 times enhancement for TMω o to TM2ω o conversion. Since the DLW technique is versatile for fabricating arbitrary χ(2) patterned structures such as periodic and quasi-periodic, 1D, 2D and even 3D (by the two photon absorption DLW technique), it should be further explored for the fabrication of polymer based EO devices.
The authors gratefully acknowledge financial support from the National Science Council (NSC), Taiwan, under grant Nos. NSC 95-2120-M194-006 and NSC 95-2112-M194-014. N. D. Lai acknowledges the support of postdoctoral fellowship from NSC Taiwan. The support of the Natural Science and Engineering Research Council of Canada, and the Canadian Institute for Advanced Research is also gratefully acknowledged.
References and links
1. Z. Sekkat and W. Knoll, Photoreactive Organic Thin Films (Academic Press, USA, 2002).
2. P. Prasad and D. J. Williams, Introduction to Nonlinear Optical Effects in Molecules and Polymers (John Wiley & Sons, USA, 1991).
3. D. S. Chemla and J. Zyss, Nonlinear Optical Properties of Organic Molecules and Crystals (Academic Press, USA, 1987).
4. J. Zyss, Molecular Nonlinear Optics Materials, Physics, and Devices (Academic Press, USA, 1994).
5. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962). [CrossRef]
6. G. Kanarian, R. A. Norwood, D. Haas, B. Feuer, and D. Karim, “Phase-matched second-harmonic generation in a polymer waveguides,” Appl. Phys. Lett. 57, 977–979 (1990). [CrossRef]
7. Y. Shuto, T. Watanabe, S. Tomaru, I. Yokohama, M. Hikita, and M. Amano, “Quasi-phase-matched second-harmonic generation in diazo-dye-substituted polymer channel waveguides,” IEEE J. Quantum Electron. 33, 349–357 (1997). [CrossRef]
8. M. Jager, G. I. Stegeman, W. Brinker, S. Yilmaz, S. Bauer, W. H. G. Horsthuis, and G. R. Mohlmann, “Comparison of quasi-phase-matching geometries for second-harmonic generation in poled polymer channel waveguides at 1.5 µm,” Appl. Phys. Lett. 68, 1183–1185 (1996). [CrossRef]
9. S. Tomaru, T. Watanabe, M. Hikita, M. Amano, Y. Shuto, I. Yokohoma, T. Kaino, and M. Asobe, “Quasi-phase-mateched second harmonic generation in a polymer waveguide with a periodic poled structure,” Appl. Phys. Lett. 68, 1760–1762 (1996). [CrossRef]
10. G. Martin, S. Ducci, R. Hierle, D. Josse, and J. Zyss, “Quasiphase matched second-harmonic generation from periodic optical randomization of poled polymer channel waveguides,” Appl. Phys. Lett. 83, 1086–1088 (2003). [CrossRef]
11. J. J. Ju, J. Kim, J. Y. Do, M.-S. Kim, S. K. Park, S. Park, and M.-H. Lee, “Second-harmonic generation in periodically poled nonlinear polymer waveguides,” Opt. Lett. 29, 89–91 (2004). [CrossRef] [PubMed]
12. G. L. J. A. Rikken, C. J. E. Seppen, S. Nijhuis, and E. W. Meijer, “Poled polymers for frequency doubling of diode lasers,” Appl. Phys. Lett. 58, 435–437 (1991). [CrossRef]
13. O. Sugihara, Y. Che, N. Okamoto, H. Fujimura, C. Egami, and S. Umegaki, “High-resolution periodically poled structure in diazo-dye-substituted polymer film based on direct electron-beam writing technique,” Appl. Phys. Lett. 73, 3028–3030 (1998). [CrossRef]
14. O. Sugihara, M. Nakanishi, Y. Che, C. Egami, Y. Kawata, and N. Okamoto, “Single-pulse ultraviolet laser recording of periodically poled structures in polymer thin films,” Appl. Opt. 39, 5632–5637 (2000). [CrossRef]
15. X. Ni, M. Nakanishi, O. Sugihara, and N. Okamato, “Fabrication of χ(2) grating in poled polymer waveguide based on direct laser beam writing,” Opt. Rev. 5, 9–11 (1998). [CrossRef]
16. H. Ishitobi, Z. Sekkat, and S. Kawata, “Photo-orientation by multiphoton photonselection,” J. Opt. Soc. Am. B 23, 868–872 (2006). [CrossRef]
19. M. Maeda, H. Ishitobi, Z. Sekkat, and S. Kawata, “Polarization storage by nonlinear orientational hole burning in azo dye-containing polymer films,” Appl. Phys. Lett. 85, 351–353 (2004). [CrossRef]
20. X. Li, J. W. M. Chon, R. A. Evans, and M. Gu, “Two photon energy transfer enhanced three-dimensional optical memory in quantum-dot and azo-dye doped polymers,” Appl. Phys. Lett. 92, 063309–063309-3 (2008). [CrossRef]
21. Z. Sekkat, J. Wood, E. F. Aust, W. Knoll, W. Volksen, and R. D. Miller, “Light induced orientation in a high glass transition temperature polyimide with polar azo dyes in the side chain,” J. Opt. Soc. Am. B 13, 1713–1724 (1996).. [CrossRef]
22. R. Loucif-Saibi, K. Nakatani, J. A. Delaire, M. Dumont, and Z. Sekkat, “Photoisomerization and second harmonic generation in disperse one-doped and functionalized poly(methyl methacrylate) films,” Chem. Mater. 5, 229–236 (1993). [CrossRef]
23. V. M. Churikov and C. C. Hsu, “Optical control of third-harmonic generation in azo-doped polymethylmethacrylate thin films,” Appl. Phys. Lett. 77, 2095–2097 (2000). [CrossRef]
24. S. Bian, L. Li, J. Kumar, D. Y. Kim, J. Williams, and S. K. Tripathy , “Single laser beam-induced surface deformation on azobenzene polymer films,” Appl. Phys. Lett. 73, 1817–1819 (1998). [CrossRef]
25. M. J. Ventura, M. Straub, and M. Gu, “Void channel microstructures in resin solids as an efficient way to infrared photonic crystals,” Appl. Phys. Lett. 82, 1649 (2003). [CrossRef]
26. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: Tuning and Tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992). [CrossRef]
27. N. D. Lai, J. H. Lin, W. P. Liang, and C. C. Hsu, “Precisely introducing defects into periodic structures by using a double-step laser scanning technique,” Appl. Opt. 45, 5777–5782 (2006). [CrossRef] [PubMed]
28. R. Dianoux, F. Martins, F. Marchi, C. Alandi, F. Comin, and J. Chevrier, “Detection of electrostatic forces with an atomic force microscope: Analytical and experimental dynamic force curves in the nonlinear regime,” Phys. Rev. B 68, 045403 (2003). [CrossRef]
30. V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81, 4136–4139 (1998). [CrossRef]
31. N.G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonal poled lithium niobate: a two dimensional nonlinear photonic crystal,” Phys. Rev. Lett. 84, 4345–4347 (2000). [CrossRef] [PubMed]
32. S. Saltiel and Y. Kivshar, “Phase matching in nonlinear χ(2) photonic crystals,” Opt. Lett. 25, 1204–1206 (2000). [CrossRef]
34. R. J. Bratfalean, A. C. Peacock, N. G. R. Broderick, K. G allon, and R. Lewen, “Harmonic generation in a two-dimensional nonlinear quasi-crystal,” Opt. Lett. 30, 424–426 (2005). [CrossRef] [PubMed]
35. E. Kim, Y.-K. Choi, and M.-H. Lee, “Photoinduced refractive index change of a photochromic diarylethene polymer,” Macromolecules , 32, 4855–4860 (1999). [CrossRef]
36. M. W. McCutcheon, G. W. Rieger, I. W. Cheung, J. F. Young, D. Dalacu, S. Frederick, P. J. Poole, G. C. Aers, and R. L. Williams, “Resonant scattering and second-harmonic spectroscopy of planar photonic crystal microcavities,” Appl. Phys. Lett. 87, 221110(1–3) (2005). [CrossRef]