Tuning 2-D Photonic Crystals

Transcription

1 Invited Paper Tuning 2-D Photonic Crystals Henry M. van Driel* a, S.W. Leonard a, H.W. Tan a, A. Birner c, J. Schilling c, S. L Schweizer b, R. B. Wehrspohn b, U. Gösele c a Department of Physics, University of Toronto, Toronto, Canada, M5S-1A7 b Nanophotonics Materials Group, Department of Physics, University of Paderborn, Paderborn, Germany c Max Planck Institute for Microstructure Physics, Weinberg 2, D Halle, Germany ABSTRACT We demonstrate three ways in which the optical band-gap of 2-D macroporous silicon photonic crystals can be tuned. In the first method the temperature dependence of the refractive index of an infiltrated nematic liquid crystal is used to tune the high frequency edge of the photonic band gap by up to 70 nm for H-polarized radiation as the temperature is increased from 35 to 59 C. In a second technique we have optically pumped the silicon backbone using 150 fs, 800 nm pulses, injecting high density electron hole pairs. Through the induced changes to the dielectric constant via the Drude contribution we have observed shifts upt to 30 nm of the high frequency edge of the E-polarized band-gap. Finally, we show that below-band-gap radiation at 2.0 and 1.7 µm can induce changes to the optical properties of silicon via the Kerr effect and tune the band edges of the 2-D macroporous silicon photonic crystal. Keywords: photonic crystal, tuning, liquid crystal, electron hole plasma, Kerr effect 1. INTRODUCTION Photonic crystals are regarded as materials that have the potential to mold or inhibit the flow of light by virtue of a spatial periodicity of the dielectric constant. 1-3 Many applications for these novel materials have been or are being considered including high efficiency, directional light sources, optical microcircuits and high-q nanoresonators. However, one could considerably enlarge the range of applications of photonic crystals, particularly for active devices, by providing methods to tune their optical properties. Because photonic crystals are normally composites of two different materials, one can tune the optical properties of the crystal by altering the dielectric constant of one or both the constituent materials or by changing some aspect of the geometrical configuration. In this paper we review three techniques that we have recently employed to tune 2-D macroporous silicon photonic crystals consisting of air cylinders embedded in a silicon host or backbone. Such crystals have a complete band gap for optical radiation propagating in the plane of periodicity, although light can escape in the 3 rd dimension. In the first method we have infiltrated the air cylinders with a nematic liquid crystal. By varying the temperature we are able to tune the refractive index of the liquid crystal and induce a shift in the photonic band-gap. 4 In the second method we have optically injected electron-hole pairs into the silicon backbone. By taking advantage of the Drude contribution the carriers make to the dielectric constant 5-7 we are able to shift the band-edge of the photonic crystal by as much 5 as 30 nm. The rise time for this effect is related to the pulse width although the turn-off time can be much longer and related to the carrier recombination time. The third technique involves using the optical Kerr effect to alter the refractive index of the silicon backbone. 8 The changes in the optical properties are limited only by the pulsewidth of the optical excitation. Techniques such as the three discussed here may find application for switching not only the optical band gaps, but also other aspects of photonic crystals (e.g., dispersion curves, group velocity characteristics, waveguide modes, nanoresonator transmission, etc.) on time scales ranging from millisecond to femtoseconds. Two-dimensional photonic crystals, possessing a triangular lattice of air pores were fabricated in silicon samples using a pre-patterned electrochemical etching process as described by Grüning et al.. 9 This process allows one to achieve high geometrical accuracy in photonic crystal fabrication with large ordered arrays of pores with high aspect Tuning the Optical Response of Photonic Bandgap Structures, edited by Philippe M. Fauchet, Paul V. Braun, Proceedings of SPIE Vol (SPIE, Bellingham, WA, 2004) X/04/$15 doi: /

2 ratio. Fig. 1 shows an example of a typical structure, engineered in such a way so as to allow crystals with variable thickness to be fabricated. For the experiments involving liquid crystals described below, a thin bar of a micro-structured silicon photonic crystal with a width of 127 crystal rows (200 µm) was fixed on a silicon substrate; the pitch of the structure is 1.58 µm. Samples oriented in the photonic crystal Γ Κ direction with a height of 100 µm and a length of 5 mm were used. The samples had a complete stop gap between 3.5 and 5.5 µm for H-polarized light and a slightly smaller gap for E- polarized light. The crystals were infiltrated with the liquid crystal E7, which is nematic at room temperature but undergoes a phase transition to the isotropic phase at 59 C. The liquid crystal was chosen for its high degree of optical anisotropy (n=1.49 and 1.69 for ordinary and extraordinary rays, respectively, at ~ 10 µm) and the low temperature of the phase transition. The infiltration of this nonvolatile material into the cylinders was carried out at room temperature and the temperature of the infiltrated crystal was varied using a kapton heater. 4 Fig. 1. Scanning electron microscope images of macroporous silicon photonic crytals, the width of which is periodically altered. The separation between pore centers for this structure is ~ 1.5 µm. For the experiments involving optically injected carriers, the sample used had a pitch of 500 nm with a pore radius of 206 nm. The optically thick samples were cleaved perpendicular to the Γ Μ direction for which an H-polarization stop-gap exists between 1.9 and 2.3 µm. For the samples used in the Kerr switching experiments the sample pitch is 700 nm and a stop-gap exists between 1.3 and 1.6 µm for E-polarized light propagating along the Γ Μ direction. 2. LIQUID CRYSTAL TUNING The optical characteristics of the photonic crystal, with and without infiltration, were determined using an infrared Fourier Transform infrared spectrometer, with the beam focused onto the wall of the cleaved samples. Figure 2 shows the transmission spectrum of the photonic crystal before and after infiltration for H-polarized radiation (electric field of the beam perpendicular to the cylinder axis). Before infiltration the sample shows the characteristic transmission stop gap in the expected spectral region. After infiltration the transmission spectrum shifts dramatically to the red and the stop gap for E-polarized radiation vanishes (not shown). The high frequency edge ( air band edge ) of the band gap shifts by about 60 nm to the long wavelength side as the temperature is varied between 35 and 62 C. Note however that there is negligible shift of the dielectric band edge on the long wavelength side. A measure of the air band edge shift as a function of temperature was taken by monitoring the transmission of the 3dB point of the transmission edge relative to the peak transmission. It was observed that this edge is red shifted continuously until the nematic/isotropic liquid crystal phase transition occurs. Figure 3 summarizes the observed shift as a function of temperature. 2 Proc. of SPIE Vol. 5511

3 Fig. 2. H-polarized transmission spectrum of photonic crystal oriented in the Γ Κ direction (upper figure) prior to and (lower figure) after infiltration with liquid crystal E7. Solid curves: nematic phase (35 C); dotted curve: isotropic phase (62 C). The additional sharp features and troughs in the lower figure are due to liquid crystal absorption peaks. Proc. of SPIE Vol

4 120 Band Edge Shift (nm) Experimental data Double exp. fit to data Theory based on axial alignment Temperature ( 0 C) Fig. 3. Wavelength shift of the air band edge with temperature of the infiltrated photonic crystal. The upper curve is based on theoretical complete axial alignment of the director field throughout the pore. In order to explain the observed temperature dependence of the edge we have employed a simple model 4 in which account is taken of the distribution of the liquid crystal director field within the pores. Ideally the director field might be fully axially aligned throughout the pore. If this were the case, and taking into account the temperature dependence of the refractive index associated with the extraordinary rays, we could anticipate that the shift of the air band edge would follow the solid curve indicated in figure 3 with a maximum shift of 113 nm being observable. The fact that the measured shift is smaller than the theoretical value is indicative of partial alignment of the director field. Indeed, using a simple model based on reasonable thermo-elastic properties of the liquid crystal, we are able to deduce that the liquid crystal in the nematic phase follows an escaped radial alignment in which the director field at the pore edge makes a non-zero angle with the pore wall and increasingly tilts to be parallel to the cylinder axis at the center. The solid curve passing through the data points shows the predicted temperature dependence of the shift based on this escaped radial configuration. Details are given in reference 4. Finally, the fact that the shift of the band-gap with temperature is only noted on the air band edge can be related to the electromagnetic energy distribution for the photonic crystal modes. For the air-band the energy is concentrated within the pores and is therefore very sensitive to alteration of the optical properties of the pores. For the dielectric band the 4 Proc. of SPIE Vol. 5511

5 energy is concentrated mainly in the silicon and the low frequency band-edge is therefore not nearly as sensitive to what is happening in the pores. The above experiments have illustrated how liquid crystals have potential for tuning the optical properties of photonic crystals. The shifts are sufficiently large that a number of device applications can be contemplated, including tunable filters and switches. Although we did not carry out experiments to monitor possible switching times of optical properties, it is anticipated that the times would be of the order of milliseconds if molecular reorientation times are the determining factor. While the experiments here were conducted using temperature tuning, it might be preferable in actual devices to use DC electric or magnetic field tuning. This was not possible in our initial set of experiments since the electrochemical etching process requires that the samples be intentionally doped. An applied electric field is therefore screened by the free carriers. However, even for our samples one can contemplate a number of compensation techniques which could be used to reduce the free carrier density. 3. TUNING VIA ELECTRON-HOLE PLASMA To explore a less invasive method to tune photonic crystals, and one that might lead to ultrafast switching behavior, we have optically injected carriers in a native macroporous silicon sample using optical techniques and monitored the shift of a stopgap edge. 5 The pump beam was derived from a 250 KHz repetition rate source producing 300 fs wide pulses at a center wavelength of 800 nm. The (indirect band-gap) absorption edge of silicon is at 1.1 µm for room temperature and therefore electron-hole pairs can be efficiently produced at shorter wavelengths. The pulses were focused onto the silicon photonic crystal with fluence per pulse up to ~2mJcm -2. Simple estimates based on anticipated absorption properties of the photonic crystal at this wavelength indicate that the peak density of electron hole pairs is > cm -3. The presence of the high density (N) carriers is expected to alter the real part of the dielectric constant (ε ) at probe frequency ω through the expression ε = ε Si Ne2 ε 0 ω 2 m * (1) where ε Si (11.9) is the quiescent dielectric constant of silicon, ε 0 is the permittivity of free space and m* is the optical effective mass of the electrons and holes. The carrier relaxation rate (~6 THz) has been neglected in comparison with the probing frequencies of interest to us. In the infrared region of the spectrum for wavelengths between 1and 5 µm this is a reasonable approximation. Similarly, we have neglected the influence of the imaginary part of the dielectric constant that would contribute to loss. From the frequency dependence in Eq. 1 one observes that for probing wavelengths in the near infrared region changes in the dielectric constant of the order of 10% can be obtained for our peak carrier densities. These substantial changes are expected to modify the location of the band gaps. For the experiments we have focused our attention on the lowest stop band between 1.9 and 2.3 µm in the crystal described above and which occurs for E-polarized light propagating along the Γ Μ direction. In particular we have concentrated on the shift of the shorter wavelength band-edge. Similar shifts are expected for the longer wavelength band-edge. The experimental results were obtained with a parametric generator pumped by a 250 khz repetition rate Ti-sapphire oscillator/regenerative amplifier which produces 130 fs pulses at 800 nm at an average power of 1.1 W. The signal pulse from the parametric generator is tunable from 1.2 to 1.6 µm and the idler pulse is tunable from 2.1 to 1.6 µm. Reflection measurements were made using 150 fs pulses with center wavelength of 1.9 µm and of sufficient bandwidth to probe the dynamical behavior of this edge. The focal spot diameter of the probe beam was 30 µm, reasonably small compared to the ~ 100 µm spot diameter of the H-polarized pump beam. Figure 4 shows how the probe reflection characteristics change with the fluence of the pump beam. Proc. of SPIE Vol

6 Fig. 4. Variation of the air band edge of the silicon photon crystal following optical pumping by a 300 fs, 800 nm pulse of variable fluence. The major effect of the optical pumping is to shift the band edge to shorter wavelengths as expected since the Drude contribution decreases the dielectric constant of the silicon. Detailed calculations based on absorption characteristics of the photonic crystal at the pump wavelength and the variation of the photonic crystal dispersion curves with injected carrier density are in agreement with the maximum shift of about 30 nm (at the 3 db point) that is observed here. Indeed we note that the shift of the edge scales linearly with the pump fluence, or injected carrier density, as expected theoretically. It should be noted however that the shift of the edge is not rigid. The shift is less for higher values of the reflectivity. We believe this is due to the fact that the 800 nm pump radiation is inhomogeneously absorbed, with an absorption depth of a few microns. When probing near the peak value of the reflectivity associated with a stop gap, one is more sensitive to the distributed reflectivity which occurs from lattice planes over a considerable depth within the crystal, rather than when one is probing in the higher transmission region where Fresnel reflectivity of the near surface region dictates the reflectivity characteristics. In future other pumping schemes will be used to overcome this. We have also been able to time resolve the reflectivity behavior by monitoring the probe reflectivity of the band edge as a function of delay between the probe and pump beams. Not surprisingly the probe reflectivity change is virtually complete within the duration of the pump beam as charge carrier accumulate in the silicon. However the recovery of the induced change occurs on a much longer time scale (at least nanoseconds) in our photonic crystal reflecting the electron-hole carrier recombination characteristics. 4. TUNING VIA KERR EFFECT As a final illustration of a tuning mechanism we consider all optical tuning of a 2-D silicon photonic crystal. 8 Above, using carrier injection into the silicon backbone, we showed that pulse-width limited turn-on times were observed, but that the recovery time was limited by carrier lifetime (>> 100 ps). In general, overall pulse-width limited response can 6 Proc. of SPIE Vol. 5511

7 only be achieved using non-resonant, nonlinear induced changes to material optical properties such as the optical Kerr effect (a third order nonlinearity). In this case the change in refractive index for a probe beam is given by n = n 2 I (2) where I is the intensity of the pump beam and n 2 frequencies. is the Kerr coefficient associated with the pump and probe Note that, because of the link between the signal and idler wavelengths, different pump wavelengths (2.0 µm for a 1.3 µm probe; 1.76 µm for a 1.6 µm probe) must be used when the probe wavelength is changed. However, as will be shown in what follows, small changes in the pump wavelength can lead to significant changes in the induced optical processes. For the time-resolved reflectivity experiments pump pulses polarized along the Γ M direction are focused to a spot size of 25 µm on the top surface of the PC near a crystal face and propagate along the direction (z) of the pore axis. An E-polarized probe beam focused to a spot size of 13 µm is incident normal to the face of the PC approximately 60 µm below the entry point of the pump beam. The reflected probe beam is passed through a 0.25 m monochromator and detected by a cooled germanium detector. The pump-probe beam geometry ensures that a reasonably uniform excitation region is probed and is also necessary to avoid the high reflectivity stop gaps which would be encountered by the pump beam if it were also incident along the Γ M direction. The region of pump-probe interaction is defined by the spot size and effective penetration depth of the probe beam, which is only a few photonic crystal unit cells. Fig. 5 shows the time dependent change in reflectivity at 1.3 µm for a 2.0 µm pump pulse and the cross-correlation trace of both pulses. The pump and probe intensities are 17.6 and 0.5 GW/cm 2 respectively. The decrease in reflectivity is consistent with a red-shift of the band-edge due to a positive non-degenerate Kerr index. The FWHM of the Reflectivity Change (10-3 ) Probe Delay (fs) Cross Correlation Amplitude (arb. unit) Fig. 5. Temporal response of reflectivity change at the 1.3 µm band-edge when the PC is pumped with a 2.0 µm pulse at 17.6 GW/cm 2. Also shown is the cross correlation trace of the pump and probe pulses. reflectivity trace is 365 ± 10 fs which is 1.8x larger than the pump-probe cross-correlation width as measured by sum frequency generation in a BBO crystal. This difference can be explained in terms of pump and probe beam transit time effects in the PC. Indeed, from the pump group velocity and probe spot size, one can deduce from Fig. 2 that the Proc. of SPIE Vol

8 reflected probe pulse is delayed by 110 fs within the PC sample. After these effects are taken into account, the intrinsic interaction times are essentially pulse width-limited, consistent with the Kerr effect. Results from experiments used to probe the 1.6 µm band-edge when the sample is pumped with 1.76 µm pulses are illustrated in Fig. 6 which shows the temporal response of the change in probe reflectivity at different pump intensities for a probe intensity of 0.13 GW/cm 2. 2 Reflectivity Change (10-3 ) Intensity (GW /cm 2 ) 20 GW/cm 2 39 GW/cm 2 59 GW/cm 2 78 GW/cm Probe Delay (ps) Fig. 6. Temporal response of the reflectivity change at the 1.6µm band-edge for different pump intensities at 1.76 µm. The inset shows the dependence of the carrier-induced reflectivity change on pump intensity for low pump powers. There is an initial increase and decrease in probe reflectivity on a sub-picosecond time scale followed by a response that decays on a time scale of 900 ps and partially masks the Kerr effect near zero delay. At this band-edge, the subpicosecond behavior is consistent with a Kerr effect similar to the previous experiments. The long time response could possibly be due to thermal or Drude contributions to the dielectric constant due to the generation of free carriers. Using a peak pump intensity of 120 GW/cm 2 and a 0.8 cm/gw 2PA coefficient for 1.55 µm as an upper limit, one can estimate the surface peak carrier density to be < cm -3 and the maximum change in temperature to be < 0.15 K. Simple analyses show that thermally induced changes to the refractive index are negligible as are changes to the imaginary part of the dielectric constant. Hence we assume all free carrier related changes are due to the real part of the dilectric constant. At low pump powers the change in probe reflectivity scales quadratically with pump intensity, consistent with free carrier generation by 2PA. However, at higher pump intensities there is an apparent deviation from this quadratic dependence due to attenuation of the pump beam by 2PA in the near surface region. 8 With increasing intensity in a 2PA process, an increasing fraction of the carriers are created closer to the surface where the pump pulse enters and the probe region develops a reduced and increasingly non-uniform carrier density. We estimate that at a depth of 60 µm, the expected saturation pump intensity is about an order of magnitude larger than the maximum pump intensity used here. The carrier lifetime of 900 ps is most likely associated with surface recombination within the PC sample with its large internal surface area. From the low intensity behavior in the inset to Fig. 6, the 2PA coefficient is estimated to be 0.02 cm/gw which is within an order of magnitude but smaller than that reported for wavelengths near 1.55 µm; this is not an unexpected result given our longer pump wavelength. 8 Proc. of SPIE Vol. 5511

9 5. SUMMARY We have been able to show how liquid crystals and injected electron-hole pairs can be used to modify the band gap characteristics of 2D silicon photonic crystals. Infiltrated liquid crystals can be used to induce large changes in the air band edge but do not modify the dielectric band edge. It is anticipated that active devices based on liquid crystal tuning would have time constants of the order of milliseconds. In order to induce faster changes to the optical properties one must make use of electronic effects and we have done so by injecting electron hole pairs into the silicon photonic crystal backbone using 300 femtosecond optical pulses, and making use of the Drude contribution to the dielectric constant. Shifts of the air band edge of ~30 nm have been measured; similar shifts are anticipated for the dielectric band edge. The rise time of the shift is related to the width of the pump optical pulse while the fall time is related to the carrier recombination kinetics. This latter time may be reduced into the picosecond range by appropriately doping the silicon or by the introduction of defects. The fastest tuning effects are observed using the Kerr effect in silicon. ACKNOWLEDGEMENTS We gratefully acknowledge financial support from the Natural Science and Engineering Research Council of Canada, Photonics Research Ontario and the Deutsche Forschungsgemeinschaft. We have also benefited extensively from helpful discussions with J. Mondia, and F. Müller. REFERENCES 1. E. Yablonovitch, Inhibited spontaneous emission in solid-physics and electronics. Rev. Lett. 58, 2059, 1987; S.John, Strong localization of light in certain disordered dielectric superlattices, Phys. Rev. Lett. 58, 2486, A. Blanco et al., Large scale synthesis of a silicon photonic crystal with a complete three-dimensional band-gap near 1.5 µm, Nature 405, 437, C.M. Soukoulis, Photonics Crystals and Light Localization in the 21 st Century, NATO Science Series C: Mathematical and Physical Sciences, vol 563, Kluwer Academic Publ., Dordrect, Netherlands, S.W. Leonard, J.P. Mondia, H.M. van Driel, O. Toader, S.John, K. Busch, A. Birner, U. Gösele and V.Lehman, Tunable Two-dimensional Photonic Crystals Via Liquid Crystal Infiltration, Phys. Rev. B (Rapid Comm.) 61, R , S.W. Leonard, H.M. van Driel, J. Schilling and R.B. Wehrspohn, Ultrafast Tuning of a Two-dimensional silicon photonic crystal via free-carrier injection, Phys. Rev. B, (Rap. Com.) 66, , M.I. Gallant and H.M. van Driel, Infrared reflectivity probing of thermal and spatial properties of laser-generated plasmas in germanium, Phys. Rev. B 61, R2389, P. Halevi and F. Ramos-Mendieta, Tunable photonic crystals with semiconductor constituents,phys. Rev. Lett. 85, 1875, H.W. Tan, H.M. van Driel, S.L. Schweizer, R.B. Wehrspohn, U. Gösele, Tuning a 2-D silicon photonic crystal using nonlinear optics, Phys Phys. Rev. B (in press), U. Grüning, V. Lehman, S. Ottow, and K. Busch, Macroporous silicon with a two-dimensional photonic bandgap centered at 5µm Appl.Phys. Lett. 68, 747, * vandriel@physics.utoronto.ca ; tel: , FAX: Proc. of SPIE Vol