Effect of implementation of a Bragg reflector in the photonic band structure of the Suzuki-phase photonic crystal lattice

We investigate the change of the photonic band structure of the Suzuki-phase photonic crystal lattice when the horizontal mirror symmetry is broken by an underlying Bragg reflector. The structure consists of an InP photonic crystal slab including four InAsP quantum wells, a SiO2 bonding layer, and a bottom high index contrast Si/SiO2 Bragg mirror deposited on a Si wafer. Angleand polarization-resolved photoluminescence spectroscopy has been used for measuring the photonic band structure and for investigating the coupling to a polarized plane wave in the far field. A drastic change in the k-space photonic dispersion between the structure with and without Bragg reflector is measured. An important enhancement on the photoluminescence emission up to seven times has been obtained for a nearly flat photonic band, which is characteristic of the Suzuki-phase lattice. 2008 Optical Society of America OCIS codes: (250.0250) Optoelectronics; (250.5300) Photonic integrated circuits; (250.5230) Photoluminescence References and links 1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987). 2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486-2489 (1987). 3. K. Inoue and K. Ohtaka, Photonic Crystals: Physics, Fabrication and Applications (SpringerVerlag, New York, 2004). 4. J.M. Lourtioz, H. Benisty, V. Berger, J. M. Gérad, D. Maystre, and A. Tchelnokov, Photonic Crystals (Springer, Berlin, 2005). 5. S. Noda, “Twoand three-dimensional photonic crystals in III-V semiconductors,” MRS Bull. 26, 618-621 (2001). #94270 $15.00 USD Received 25 Mar 2008; revised 28 Apr 2008; accepted 28 Apr 2008; published 27 May 2008 (C) 2008 OSA 9 June 2008 / Vol. 16, No. 12 / OPTICS EXPRESS 8509 6. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “TwoDimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819 (1999). 7. C. Monat, C. Seassal, X. Letartre, P. Regreny, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, J.P. Albert, E. Jalaguier, S. Pocas, and B. Aspar,“InP based 2-D photonic crystal on silicon: In-plane Bloch mode laser,” Appl. Phys. Lett. 81, 5102-5104 (2002). 8. Han-Youl Ryu, Soon-Hong Kwon, Yong-Jae Lee, Yong-Hee Lee, and Jeong-Soo Kim, “Very-lowthreshold photonic band-edge lasers from free-standing triangular photonic crystal slabs,” Appl. Phys. Lett. 80, 3476 (2002). 9. T. Baba, N. Fukaya and Yonekura, “Observation of light propagation in photonic crystal optical waveguides with bends,” Electron. Lett. 35, 654-656 (1999). 10. M. Loncar, D. Nedeljkovic, T. Doll, J. Vučković, A Scherer, and T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77, 1937-1939 (2000). 11. B. Ben Bakir, Ch. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. Di Cioccio, and J. M. Fedeli,“Surface-emitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror,” Appl. Phys. Lett. 88, 081113 (2006). 12. B. Ben Bakir, C. Seassal, X. Letartre, P. Regreny, M. Gendry, P. Viktorovitch, M. Zussy, L. Di Cioccio, and J.-M. Fedeli, “Room-temperature InAs/InP Quantum Dots laser operation based on heterogeneous “2.5 D” Photonic Crystal,” Opt. Express 14, 9269-9276 (2006). 13. D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vučković, “Controlling cavity reflectance with a single quantum dot,” Nature (London) 450 857-861 (2007). 14. Tien-Chang Lu, Shih-Wei Chen, Li-Fan Li, Tsung-Ting Kao, Chih-Chiang Kao, Peichen Yu, HaoChung Kuo, Shing-Chung Wang, and Shanhui Fan, “GaN-based two-dimensional surface-emitting photonic crystal lasers with AlN/GaN distributed Bragg reflector,” Appl. Phys. Lett. 92 011129 (2008). 15. A.R. Alija, L.J. Mart́ınez, P.A. Postigo, J. Sánchez-Dehesa, M. Galli, A. Politi, M. Patrini, L.C. Andreani, C. Seassal, and P. Viktorovitch, “Theoretical and experimental study of the Suzukiphase photonic crystal lattice by angle-resolved photoluminescence spectroscopy,” Opt. Express 15 704-713 (2007). 16. D. Cassagne, and C. Jouanin, and D. Bertho , “Photonic band gaps in a two-dimensional graphite structure,” Phys. Rev. B 52, R2217–R2220 (1995). 17. S. David, A. Chelnokov, and J.-M. Lourtioz, “Isotropic Photonic Structures: Archimedean-Like Tilings and Quasi-Crystals,” IEEE J. Quantum Electron. 37, 1427-1434 (2001). 18. H. Altug and J. Vučković, “Two-dimensional coupled photonic crystal resonator arrays,” Appl. Phys. Lett. 84, 161-163 (2004). 19. C. Monat, C. Seassal, X. Letartre, P. Regreny, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, J.P. Albert, E. Jalaguier, S. Pocas, and B. Aspar, “InP Bonded Membrane Photonics Components and Circuits: Toward 2.5 Dimensional Micro-Nano-Photonics,” IEEE J. Quantum Electron. 11, 395-407 (2005). 20. A. R. Alija, L. J. Mart́ınez, P. A. Postigo, C. Seassal, and P. Viktorovitch, “Coupled-cavity twodimensional photonic crystal waveguide ring laser,” Appl. Phys. Lett. 89, 101102 (2006). 21. S.G. Johnson, S. Fan, P.R. Villeneuve, J.D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751 (1999). 22. L. C. Andreani and M. Agio, “Photonic bands and gap maps in a photonic crystal slab,” IEEE J. Quantum Electron. 38, 891-898 (2002). 23. L. C. Andreani, and D. Gerace, “Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method,” Phys. Rev. B 73, 235114 (2006). 24. V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255 (1999). 25. M. Galli, M. Agio, L. C. Andreani, M. Belotti, G. Guizzetti, F. Marabelli, M. Patrini, P. Bettotti, L. Dal Negro, Z. Gaburro, L. Pavesi, A. Lui, and P. Bellutti, “Spectroscopy of photonic bands in macroporous silicon photonic crystals,” Phys. Rev. B 65, R113111 (2002). 26. A. David, C. Meier, R. Sharma, F.S. Diana, S.P. DenBaars, E. Hu, S. Nakamura, C. Weisbuch, and H. Benisty, “Photonic bands in two-dimensionally patterned multimode GaN waveguides for light extraction,” Appl. Phys. Lett. 87, 101107 (2005). 27. K. Sakai, E. Miyai, T. Sakaguchi, D. Ohnishi, T. Okano, and S. Noda, “Lasing band-edge identification for a surface-emitting photonic crystal laser,” IEEE J. Sel. Areas Commun. 23, 1335 (2005). 28. M. Galli, A. Politi, M. Belotti, D. Gerace, M. Liscidini, M. Patrini, L. C. Andreani, M. Miritello, A. Irrera, F. Priolo, and Y. Chen, “Strong enhancement of Er3+ emission at room temperature in silicon-on-insulator photonic crystal waveguides,” Appl. Phys. Lett. 88, 251114 (2006). #94270 $15.00 USD Received 25 Mar 2008; revised 28 Apr 2008; accepted 28 Apr 2008; published 27 May 2008 (C) 2008 OSA 9 June 2008 / Vol. 16, No. 12 / OPTICS EXPRESS 8510


Introduction
Since the discovery that certain periodic structures can confine the light, photonic crystals (PC) [1,2] have been deeply studied due to the possibility of accurate control of the light at the wavelength scale [3,4].Particular interest has been devoted to the use of two-dimensional photonic crystal slabs (2D-PCs) for the development of such building blocks of the future integrated photonic circuits [5] as photonic crystal lasers [6,7,8] and photonic crystal waveguides [9,10].A way for improving the properties of 2D-PCs is to combine them with one-dimensional Bragg reflectors.Some devices combining a 2D-PC and a one-dimensional Bragg reflector have been already done [11,12,13,14].The combination of a Bragg reflector with an active 2D-PC slab can enhance the quality factor of the resonant mode giving rise to a decreasing of the lasing threshold [11,12].In this way, we study the actual effect of the Bragg mirror on the photonic bands.For this purpose, we have fabricated the Suzuki-phase (SP) 2D-PC [15] in samples with and without bottom Bragg reflectors.The Suzuki lattice belongs to a set of 2D structures, like also the graphite and the Archimedean lattices [16,17], which possess a basis made of several rods per unit cell.All these lattices seem to support several lowdispersive photonic bands, similar to coupled cavity arrays [18].The SP lattice presents two features that are very useful for this study: On one side, it has a complex photonic band structure in two dimensions, which allows to probe several bands in the region of wavelengths of interest (around 1500 nm).On the other side, the SP pattern presents a flat band along the direction ΓX1, well isolated from other bands and which shape remains almost unchanged when we calculate the band structure in the "symmetric" and in the "nonsymmetric" or full band approach [15].The fabricated structures were characterized by polarization-resolved angle-resolved photoluminescense (PR-ARP) in order to obtain the photonic band structure and its polarization.A drastic difference in the photonic band structure was measured between the samples with and without Bragg mirror.Moreover, an important enhancement of the intensity of the photoluminescense (PL) emission between four and seven times for one particular photonic band was measured.A 90 nm-thick SiO 2 layer was deposited by plasma assisted sputtering on top of both samples as mask layer for the etching process.Electron-beam lithography and reactive ion-etching were used for the patterning [20].For the structure without Bragg mirror the lattice parameter a is 455 nm (d/a = 0.514) while for the structure with Bragg mirror a = 484 nm (d/a = 0.516).It is important to have the same d/a value for both samples because the photonic bands change with the thickness of the slab [21,22,23], which may prevent easy comparison of the emission properties between structures.The same value of the radius of the holes was r = 0.33a for both structures.The size of the fabricated structures was 25μm × 25μm for the sample without Bragg and 30μm × 30μm for the sample with Bragg.

Optical characterization
PR-ARP spectroscopy was used for optical characterization.The samples were optically pumped with a 635nm laser diode through a 10× (NA=0.angle of 45 • with respect to normal incidence.The angle-resolved PL emission was collected by a fiber coupled to a Fourier-transform spectrometer (Bruker IFS66/s).An InGaAs p-i-n photodiode was used as detector.The PL at room temperature can be collected with an angular resolution of ±1 • .The PL was collected at different angles from 0 • to 30 • at intervals of 5 • along the directions Γ − X1 and Γ − X2 with a linear polarizer in the collection arm.The measured PL spectra were used to determine the photonic band dispersion through conservation of the wavevector parallel to the sample surface [24,25,26,27,28], and their polarization.
The axes of polarization and the experimental geometry are defined according to Fig. 2. For incidence in a plane along the Γ-X1 direction, since the xz plane is a mirror plane of the Suzuki-phase lattice, the electromagnetic field can be even or odd under the mirror reflection operation σkz = σxz : the former states are denoted as σ kz = +1, while the latter are denoted as σ kz = −1.For incidence in a plane along the Γ-X2 direction, since the yz plane is again a mirror plane of the Suzuki lattice, the eigenstates of the electromagnetic field can be even (σ kz = +1) or odd (σ kz = −1) under the mirror reflection operation σkz = σyz .We notice that σ kz = +1 states are coupled to transverse-magnetic or p-polarized light with respect to the observation plane shown in Fig. 2(b), while σ kz = −1 states are coupled to transverse electric or s-polarized light: these denominations, however, relate only to vertical mirror symmetry σkz and have nothing to do with specular reflection σxy with respect to the xy plane, which is not a symmetry operation of the structure with Bragg. Figure 3 shows four typical normalized PL spectra along the Γ − X1 direction, for one particular angle (θ = 25 • ), for the samples with and without Bragg reflector.The PL spectra were normalized dividing the PL intensity from the patterned area over the PL intensity of a close unpatterned area.Similar spectra were obtained for the rest of the angles of measurement.A clear change in the intensity (Fig. 3(a,b)) and number of peaks (Fig. 3(c-d)) for each polarization (σ kz = +1, σ kz = −1 respectively) is observed between the samples with and without Bragg reflector.For each angle (θ ), the observed peaks were fitted to gaussian functions.The center of the fit function was extracted and plotted versus the parallel component of the wavevector.
Figure 4 shows the real part of the magnetic field component H z at the Γ point for the photonic modes corresponding to the resonant structures in Fig. 3(a) around ωa/(2πc) = 0.31 and in Fig. 3(c) around ωa/(2πc) = 0.337.These modes correspond to the fifth and the sixth band, respectively, of the sample without Bragg.Considering that the magnetic field H is a pseudo (or axial) vector, we notice that the fifth band is even along the Γ − X1 direction (σ xz = +1) and odd along the Γ − X2 direction (σ yz = −1).Thus, we expect the fifth band to couple to p-polarized light along the Γ − X1 direction and to s-polarized light along the Γ − X2 direction.The sixth band, instead, is odd along the Γ − X1 direction (σ xz = −1) and even along the Γ − X2 direction (σ yz = +1), thus it couples to s-polarized light along Γ − X1 and to p-polarized light along Γ − X2.These results are in agreement with those shown in Fig. 3(a,c) and show that polarization-resolved PL is a powerful tool to identify photonic bands through their symmetry properties.

Results
Figure 5 shows the photonic bands and their polarization measured for both samples with and without Bragg reflector.Figure 5(a) shows the photonic bands measured for the sample without Bragg and the calculated band structure in the "symmetric" approach [15,23] where mirror symmetry σxy with respect to a horizontal plane through the InP slab is enforced and only the even modes The sixth band shows the complementary behavior, i.e, it shows s-polarization along the Γ− X1 direction and p-polarization along Γ− X2.This is in good agreement with the expected field patterns calculated by guided-mode expansion for several k-vectors along both directions Γ − X1 and Γ − X2, as exemplified in Fig. 4 at the Γ point, and is also analogous to previous results found in reflectance spectra of macroporous Silicon [25].
The bands are dipole-active (i.e., coupled to polarized light in the far field) with the following orientation: For the fifth band the axis of the dipole is parallel to the Γ − X1 direction.For the sixth band, the axis of the dipole is parallel to the Γ − X2 direction.The same measurements were performed in samples with Bragg reflector.Figure 6 shows the normalized intensities measured for the Γ − X1 and Γ − X2 directions of the sample with the Bragg mirror.The data show that the photonic bands that should correspond to "TM-like" modes (electric field along z) can be measured, despite the emission of the quantum wells is mainly "TE-like" polarized (electric field in xy plane).This is naturally explained by the breaking of horizontal mirror symmetry σxy in the sample with Bragg.On the other hand, vertical mirror symmetry σkz along the Γ − X1 and Γ − X2 orientation is preserved even in the sample with Bragg and pure σ kz = +1 (p) or σ kz = −1 (s) modes are expected.However, mixing of p/s polarizations is also observed in some bands and for some k-vectors with different intensities for each polarization.In general the degree of polarization defined as ρ = (I x −I y ) (I x +I y ) corresponds to the mixing induced by any symmetry-breaking effect present in the sample.It is remarkable that the fifth band which has p-polarization along the direction Γ − X1 shows also s-component which was not observed in the sample without Bragg mirror.This band has a degree of polarization (ρ) between 86% and 91%.The polarization mixing effect is attributed to the presence of disorder (variation of hole size, position, microroughness of hole sidewalls, mainly) which breaks mirror symmetry and whose effect may be enhanced in the sample with Bragg.
Figure 7 shows the fifth band for both samples and the calculated photonic band structure.According to the calculations, the fifth band is nearly flat along the Γ − X1 direction, well isolated in frequency and remains almost unchanged in the "symmetric" and full band approach.This makes the fifth band very suitable for the comparison of the intensity of emission between both samples with and without Bragg mirror.For this band the quality factors (Qs) are slightly higher (below two times) for the sample with Bragg mirror.The intensity of the emission for p-polarization is between 4 and 7 times higher for the sample with Bragg mirror in the whole wavevector (corresponding to angular) range, except for the Γ point, where the enhancement is 1.9.The enhancement of PL signal towards the vertical direction arises from multiple reflections by the Bragg mirrors in the SiO 2 wafer bonding layer, as previously analyzed in Ref. [11].Notice that even at the X1 point, the internal angle in the SiO 2 layer is calculated to be around 20 degrees, which is well within the angular acceptance of a Si/SiO 2 Bragg reflector.This results in an almost k-independent enhancement, which is interesting for prospective applications of the Suzuki lattice to low-threshold lasing.

Summary
We have fabricated and measured the SP lattice on two kinds of InP semiconductor slabs with InAsP/InP quantum wells as active layer with and without underlying Bragg mirror.PR-ARP spectroscopy was used for the optical characterization.For the structure without Bragg reflector the experimental data are well fit by a "symmetric" calculation.For the sample with Bragg mirror are best fit by a full band calculation (i.e., TE-like and TM-like modes are coupled).A mixing of p/s polarizations defined with respect to a vertical mirror plane is observed for the structure with Bragg, whereas the polarization is well defined for the non-Bragg sample.An enhancement on the photoluminescence emission up to seven times has been obtained for a flat photonic band along the Γ − X1 direction, which is the main distinctive feature of the Suzuki-phase photonic lattice.

Fig. 1 . 2 .
Fig. 1.Layout of the transversal section of the fabricated structures.(a) InP/InAsP layer epitaxy bonded to a Si wafer.(b) InP/InAsP layer epitaxy bonded to a Bragg reflector on top of the Si wafer.(c) Scanning electron microscopy (SEM) image of the fabricated structure with Bragg mirror.

Fig. 2 .
Fig. 2. (a) Suzuki lattice with the axes in the XY plane.(b) Schematic drawing of the experimental geometry, for the specific case of Γ-X1 orientation, with the polarization directions of the electric field with respect to the plane of observation.Under specular reflection σkz with respect to a vertical mirror plane including the wavevector, transverse magnetic or p-modes are even (σ kz = +1) while transverse electric or s-modes are odd (σ kz = −1).

Fig. 3 .
Fig. 3. Normalized PL spectra along the direction Γ-X1, for the sample without Bragg (a,c) and for the sample with Bragg reflector (b,d) at angle θ = 25 • .Blue line for even (σ kz = +1) or p-polarization, red line for odd (σ kz = −1) or s-polarization with respect to a vertical mirror plane.

Fig. 5 .Fig. 6 .
Fig. 5. Photonic band structure of the Suzuki-phase lattice.Blue color for bands with σ kz = +1 polarization.Red color for bands mainly σ kz = −1 polarized.(a) Sample without Bragg: Solid lines show the bands calculated by guided-mode expansion in the "symmetric" approximation with the parameters d/a = 0.514 and r/a = 0.33.Only σ xy = +1 or TE-like modes are shown.Circles: measured points.(b) Sample with Bragg reflector: Solid lines show the full band structure calculated by guided-mode expansion with the parameters d/a = 0.514 and r/a = 0.33.Filled points for σ kz = −1 polarization.Blue open circles for σ kz = +1 polarization.
Figure5shows the photonic bands and their polarization measured for both samples with and without Bragg reflector.Figure5(a) shows the photonic bands measured for the sample without Bragg and the calculated band structure in the "symmetric" approach[15,23] where mirror symmetry σxy with respect to a horizontal plane through the InP slab is enforced and only the even modes σ xy = +1 (sometimes called TE-like) are shown.The parameters of the fitting are a = 455 nm, r = 0.33a and d/a = 0.514.It is remarkable that the fifth band (ω = 0.31 in Γ) and the sixth band (ω = 0.34 in Γ) have well defined polarization (p or s) for all k-vectors.The fifth band has σ kz = +1 or p-polarization along the direction Γ − X1 and σ kz = −1 or s-polarization along Γ − X2.The sixth band shows the complementary behavior, i.e, it shows s-polarization along the Γ− X1 direction and p-polarization along Γ− X2.This is in good agreement with the expected field patterns calculated by guided-mode expansion for several k-vectors along both directions Γ − X1 and Γ − X2, as exemplified in Fig.4at the Γ point, and is also analogous to previous results found in reflectance spectra of macroporous Silicon[25].

Figure 5 Fig. 7 .
Fig. 7. Fifth band along the direction Γ − X1.The numeric labels indicate the normalized intensity.(a) Sample without Bragg: Blue color for bands with σ kz = +1 or p-polarization.Red color for bands mainly σ kz = −1 or s-polarization.Blue dots for measured points detecting p-polarized light.(b) Sample with Bragg: σ kz = −1 or s-polarization.Red dots for experimental points detecting s-polarized light.(c) Sample with Bragg: σ kz = +1 or p-polarization.Blue dots for measured points detecting p-polarized light.