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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 20 — Sep. 26, 2011
  • pp: 19532–19541
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Transfer of photonic crystal membranes to a transparent gel substrate

Lj. Babić, R. Leijssen, E.F.C. Driessen, and M.J.A. de Dood  »View Author Affiliations


Optics Express, Vol. 19, Issue 20, pp. 19532-19541 (2011)
http://dx.doi.org/10.1364/OE.19.019532


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Abstract

We report a method of transferring 150 nm thick Al0.35Ga0.65As photonic crystal slabs to a transparent gel, without compromising their optical properties. We demonstrate successful transfer for membranes as large as ∼ 425 × 425 μm2. The transfer results in a 2.5% frequency red shift and increases the visibility of the resonances in reflection spectra. The avoided crossings between the modes show a subradiant mode with quality factors up to ∼300. This suggests that the quality factor is only limited by the finite size of the crystal.

© 2011 OSA

1. Introduction

Photonic crystals, in particular photonic crystal cavities, have been very succesful in creating strong interactions between light and matter [1

1. M. Notomi, “Manipulating light with strongly modulated photonic crystals,” Rep. Prog. Phys. 73, 096501 (2010). [CrossRef]

]. The strong confinement provided by the large refractive index difference between GaAs and air in a two-dimensional photonic crystal slab enables a single quantum dot emitter to reach the strong-coupling regime [2

2. T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 9–12 (2004). [CrossRef]

, 3

3. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system.” Nature 445, 896–899 (2007). [CrossRef] [PubMed]

]. Many other applications, such as small mode volume lasers, light-emitting diodes [4

4. J. J. Wierer, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency with high extraction efficiency,” Nat. Photonics 3, 163–169 (2009). [CrossRef]

], nonlinear interactions [5

5. J. P. Mondia, H. M. van Driel, W. Jiang, A. R. Cowan, and J. F. Young, “Enhanced second-harmonic generation from planar photonic crystals,” Opt. Lett. 28, 2500–2502 (2003). [CrossRef] [PubMed]

7

7. A. D. Bristow, J. P. Mondia, and H. M. van Driel, “Sum and difference frequency generation as diagnostics for leaky eigenmodes in two-dimensional photonic crystal waveguides,” J. Appl. Phys. 99, 023105 (2006). [CrossRef]

], and nanoscale sensors all benefit from the strong confinement of light, and use intrinsic emission of III–V semiconductors as an internal light source. Although well established fabrication protocols exist to create nanophotonic devices in layers of III-V semiconductors grown on an epitaxial support wafer, it is not obvious how to transfer these devices to other substrate materials. Wafer bonding techniques exist to transfer (Al)GaAs layers to silicon [8

8. P. Kopperschmidt, S. Senz, G. Kästner, D. Hesse, and U. M. Gösele, “Materials integration of gallium arsenide and silicon by wafer bonding,” Appl. Phys. Lett. 72, 3181–3183 (1998). [CrossRef]

, 9

9. Z. Hatzopoulos, D. Cenghera, G. Deligeorgisa, M. Androulidakia, E. Aperathitisa, and G. H. A. Georgakilas, “Molecular beam epitaxy of GaAs/AlGaAs epitaxial structures for integrated optoelectronic devices on Si using GaAs-Si wafer bonding,” J. Cryst. Growth 227–228, 193–196 (2001). [CrossRef]

] or optically transparent sapphire [10

10. P. Kopperschmidt, G. Kästner, S. Senz, D. Hesse, and U. Gösele, “Wafer bonding of gallium arsenide on sapphire,” Appl. Phys. A 64, 533–537 (1997). [CrossRef]

] substrates. These wafer bonding methods are done at high temperatures with flat, unpatterned substrates and cannot be applied to transfer an existing nanostructure. Therefore, an alternative method that allows to transfer existing devices to other substrates at room temperature are highly desirable. Such a method would greatly facilitate the use of photonic crystal devices in a wide range of applications and environments, for instance in biochemical sensors in liquid phase [11

11. E. Chow, A. Grot, L. W. Mirkarimi, M. Sigalas, and G. Girolami, “Ultracompact biochemical sensor built with two-dimensional photoniccrystal microcavity,” Opt. Lett. 29, 1093–1095 (2004). [CrossRef] [PubMed]

] or to couple single nitrogen-vacany centers in diamond [12

12. T. van der Sar, E. C. Heeres, G. M. Dmochowski, G. de Lange, L. Robledo, T. H. Oosterkamp, and R. Hanson, “Nanopositioning of a diamond nanocrystal containing a single nitrogen-vacancy defect center,” Appl. Phys. Lett. 94, 173104 (2009). [CrossRef]

, 13

13. D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vučkovič, H. Park, and M. D. Lukin, “Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity,” Nano Lett. 10, 3922–3926 (2010). [CrossRef] [PubMed]

] to a cavity for quantum information purposes.

In this letter we show that it is possible to transfer a 150 nm thick Al0.35Ga0.65As photonic crystal membranes with a square lattice of holes, to a gel substrate that can be combined with any other material of choice. The gel substrate is optically transparent and has a relatively low refractive index which allows for a large refractive index contrast with the Al0.35Ga0.65As material of the photonic crystal. This large contrast is necessary in order to create structures with a band gap of guided modes that can support photonic crystal cavities [14

14. K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990). [CrossRef] [PubMed]

16

16. C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, “A7 structure: a family of photonic crystals,” Phys. Rev. B 50, 1988–1991 (1994). [CrossRef]

]. We study the transferred structures in detail using reflection and transmission measurements, and compare these results to similar measurements on the same membrane before transfer. From this comparison, we infer that the optical properties of a photonic crystal membrane on gel are similar or even improved compared to the optical properties of the freestanding structure before transfer.

2. Sample fabrication and transfer to a gel

The square lattice photonic crystal structures in this study are fabricated in a 150 nm thick Al0.35Ga0.65As layer on top of a 1 μm thick Al0.7Ga0.3As sacrificial layer. Regular arrays of holes are defined using standard e-beam lithography and reactive ion etching techniques in a chlorine based plasma [17

17. T. Maeda, J. Lee, R. Shul, J. Han, J. Hong, E. Lambers, S. Pearton, C. Abernathy, and W. Hobson, “Inductively coupled plasma etching of III–V semiconductors in BCl3-based chemistries. I. GaAs, GaN, GaP, GaSb and AlGaAs,” Appl. Surf. Sci. 143, 174–182 (1999). [CrossRef]

]. Freestanding membranes with an area up to ∼ 425 × 425 μm2 are created by removal of the sacrificial layer in hydrofluoric acid followed by critical point drying. Details of the fabrication process are published elsewhere [18

18. E. F. C. Driessen, D. Stolwijk, and M. J. A. de Dood, “Asymmetry reversal in the reflection from a two-dimensional photonic crystal,” Opt. Lett. 32, 3137–3139 (2007). [CrossRef] [PubMed]

, 19

19. L. Babić and M. J. A. de Dood, “Interpretation of the fano lineshape reversal in the reflectivity spectra of photonic crystal slabs,” Opt. Express 18, 26569–26582 (2011). [CrossRef]

].

Figure 1 shows a schematic of the transfer process (a) and optical microscope images before (b) and after (c) the transfer process. The transfer of the membranes is accomplished by attaching a commercial gel layer of highly cross-linked polymer (gel-pak gel-film PF, retention level X4, 0.15 mm thickness [20

20. Detailed information and technical datasheets are available via the manufacturers website: http://www.gelpak.com

]) to a glass microscope slide. The sample is then carefully pushed into the gel layer and the substrate is gently peeled off in the last step. The small lattice mismatch between the Al0.35Ga0.65As (l = 0.565603 nm) top layer and the GaAs (l = 0.565325 nm) substrate [21] together with a thin oxide film on the membrane generates compressive strain in the membrane and causes the membrane to buckle. The buckling of the membrane before the transfer is best illustrated by the atomic force microscopy (AFM) image (d), since this gives absolute height information. Based on AFM and optical microcopy images made with a double beam interference objective (Nikon, M plan 20 DI), we find height variations up to 10 μm before the transfer. Images with the interference objective show that height variations are reduced to well below 1 μm after the transfer process.

Fig. 1 Transfer of a photonic crystal membrane to a gel. (a) Schematic drawing of the process. (b) Optical microscope images of 300×300 μm2 large photonic crystal membrane before (b) and after (c) the transfer. The membrane is 150 nm thick, and contains a square lattice of 300 nm diameter holes with a lattice constant a = 820 nm. (d) Atomic force microscope image of a 12 × 12 μm2 section of a similar membrane (300 nm diameter holes, a = 640 nm) before the transfer, showing typical height variations.

We have tested the transfer technique for 150 nm thick membranes with different membrane sizes (∼ 10 × 10 μm2 up to ∼ 425 × 425 μm2), photonic crystal lattice constants (350 nm ≤ a ≤ 960 nm), and hole radii (100 nm ≤ r ≤ 270 nm). The transfer process is successful for membranes larger than ∼ 30 × 30 μm2. The important parameter for the transfer is the ratio between the force that connects the membrane to the gel and the force needed to break the membrane free from the substrate. In both cases the minimum force needed is given by a peeling process where bonds are broken line-by-line instead of all the bonds at once. The total energy required to break all gel-to-membrane bonds scales with the area L 2, while the energy required to break all atomic bonds along the edges of the membranes scales with L × d, with L and d the membrane dimensions and thickness respectively. Since the forces both act over a distance L the ratio of the two forces is proportional to Ld [22

22. The force Fs to peel off the membrane breaking all gel-membrane bonds on the surface is proportional to L × (1 – π(r/a)2)). The force needed to break the membrane free Fb is given by the work needed to peel free the membranes along the sides and gives Fbd × (a – 2r). The ratio between the two forces Fs/Fb is then proportional to Ld×1π(r/a)2a2r, where the second term is a geometrical factor that accounts for the square lattice of air holes in the membrane.

]. Out of a total of ∼50 transferred membranes, only the first 5 membranes sustained significant damage in the transfer process. We estimate that a device yield > 90% is possible. Membranes that break or stick to the substrate either during or after the wet-chemical underetching step in the fabrication can still be successfully transferred to the gel. This opens a route to creating large photonic crystal membranes without the use of critical point drying.

3. Optical properties

To test the quality of the optical structures, both before and after the transfer, we perform reflection and transmission measurements for wavelengths between 650 and 1700 nm using a fiber coupled halogen lamp in combination with fiber coupled spectrometers. The spectral resolution varies from 1.5 nm to 3.0 nm over the wavelength range. Apertures placed in the beam limit the numerical aperture of the incident beam to NA < 0.025. The polarization of the incident beam is controlled by a Glan-Thompson polarizing beamsplitter cube. In this way, the reflection and transmission for both s- and p-polarized light are measured as a function of wavelength and angle of incidence.

Figure 2 compares the reflectance spectra before (triangles) and after (circles) the transfer to the gel. Data are shown for p-polarized light at an angle of incidence of 35° along the ΓX symmetry direction of the square lattice. The spectra consist of a slowly varying background with two sharp resonant features superimposed. These features are due to the excitation of leaky modes above the light-line of the photonic crystal structure [23

23. M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70, 1438–1440 (1997). [CrossRef]

, 24

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–R16258 (1999). [CrossRef]

]. A clear 2.5% frequency red shift of the resonant peaks is observed, and the peaks are more pronounced in the reflection spectrum after the transfer to the gel. From the figure we estimate that the difference between the minimum and the maximum of the peak is increased by a factor ∼4 for both resonances.

Fig. 2 Comparison of the measured reflection spectra for p-polarized light before (triangles) and after (circles) transfer to the gel. Resonances due to the (0,±1) and (−1,±1) leaky modes are clearly visible and show that the transfer process leads to a red shift of the leaky modes. The solid lines through the data are fits of a Fano model with two resonances to the experimental data (see text).

A Fano model [18

18. E. F. C. Driessen, D. Stolwijk, and M. J. A. de Dood, “Asymmetry reversal in the reflection from a two-dimensional photonic crystal,” Opt. Lett. 32, 3137–3139 (2007). [CrossRef] [PubMed]

, 25

25. S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the fano resonance in optical resonators,” J. Opt. Soc. Am. A 20, 569–572 (2003). [CrossRef]

] can be applied to explain the lineshape of the resonance as the result of interference between a constant background and the resonant contribution. The reflectivity as a function of frequency, R(ν), is given by
R(ν)=|rd(ν)+jAji(ννj)+(γj+Γj)|2,
(1)
where rd (ν) is the field amplitude of the background or direct reflection. The sum expresses the coupling to multiple resonances. Each resonance is characterized by a complex valued amplitude Aj, center frequency νj, escape rate Γj, loss rate γj [18

18. E. F. C. Driessen, D. Stolwijk, and M. J. A. de Dood, “Asymmetry reversal in the reflection from a two-dimensional photonic crystal,” Opt. Lett. 32, 3137–3139 (2007). [CrossRef] [PubMed]

], and has a corresponding quality factor defined by Qjνj/(2(Γj + γj)).

The solid lines in Fig. 2 show the fit of the Fano model with two resonances to the measured data using a linear frequency dependence of the background rd over the limited frequency range of Fig. 2. In the fitting procedure we deliberately kept the quality factors of the resonances before and after the transfer equal in order to limit the number of fit parameters. The fitted dimensionless frequencies are 0.561 c/a and 0.633 c/a before the transfer, and 0.547 c/a and 0.615 c/a after the transfer, corresponding to red shifts of 2.5% and 2.8% respectively. Additional measurements at six different angles (not shown) reveal that the entire measured dispersion relation is red shifted by ∼2.5% in frequency. This is explained by the increase in the effective refractive index of the slab by ∼2.5% due to the introduction of the gel substrate [26

26. T. Ochiai and K. Sakoda, “Nearly free-photon approximation for two-dimensional photonic crystal slabs,” Phys. Rev. B 64, 045108 (2001). [CrossRef]

, 27

27. K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006). [CrossRef]

].

The increased visibility of the resonances in Fig. 2 after the transfer corresponds to larger amplitudes |A 1,2|. From the fit we find that both of these amplitudes are increased by a factor of 3. For a lossless, symmetric, case the amplitude |A| of the resonance of the photonic crystal is equal to Γ and is independent of the value of rd [25

25. S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the fano resonance in optical resonators,” J. Opt. Soc. Am. A 20, 569–572 (2003). [CrossRef]

]. We explain the increase in the amplitude by an incoherent contribution to rd(ν) in Fig. 1, which directly affects the amplitude |A|. Due to the buckling of the freestanding membrane variations in the incident angle and in the distance between the substrate and the membrane are introduced. Angle variations lead to variations in the exact resonance frequency and consequently to a lower quality factor, which is not observed in the experimental data. Variations in distance between the membrane and the substrate that are much larger than λ/4 leads to variations in the phase and amplitude of rd(ν) over the illumination spot which lowers the visibility of the Fano interference.

4. Quality factors and dispersion relation of the resonances.

Fig. 3 Measured transmission for s-polarized incident light of a photonic crystal slab after the transfer to the gel. Data are shown as grayscale as a function of frequency (vertical axis) and in-plane wavevector k|| along the ΓM and ΓX symmetry directions of the square lattice. The leaky modes are visible in the figure as the darker lines in the grayscale plot. The lattice constant of the square lattice is a = 820 nm.

The resonances and their dispersion are due to a coupling of the incoming light to a mode of the photonic crystal slab via diffraction from the periodic lattice and are well understood [24

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–R16258 (1999). [CrossRef]

, 25

25. S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the fano resonance in optical resonators,” J. Opt. Soc. Am. A 20, 569–572 (2003). [CrossRef]

]. Each of these modes can be labeled by the reciprocal lattice vector (Gx, Gy) responsible for the coupling that transforms a waveguide mode of the slab to a guided resonance or leaky mode. The corresponding dispersion relation of these leaky modes can be approximated by folding the calculated dispersion relation of a slab waveguide to the first Brillouin zone of the periodic structure [26

26. T. Ochiai and K. Sakoda, “Nearly free-photon approximation for two-dimensional photonic crystal slabs,” Phys. Rev. B 64, 045108 (2001). [CrossRef]

].

A large number of avoided crossings are visible in Fig. 3. Typically, the lower frequency mode in the avoided crossing becomes subradiant and disappears from the transmission spectra, while the higher frequency mode becomes a shorter living superradiant mode [28

28. W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227–6244 (1996). [CrossRef]

30

30. M. J. A. de Dood, E. F. C. Driessen, D. Stolwijk, and M. P. van Exter, “Observation of coupling between surface plasmons in index-matched hole arrays,” Phys. Rev. B 77, 115437 (2008). [CrossRef]

]. This is a result of the coupling between the modes via external radiation [31

31. J. Wiersig, “Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities,” Phys. Rev. Lett. 97, 253901 (2006). [CrossRef]

, 32

32. Q. H. Song and H. Cao, “Improving optical confinement in nanostructures via external mode coupling,” Phys. Rev. Lett. 105, 053902 (2010). [CrossRef] [PubMed]

]. In this case the radiation of the subradiant mode into the surrounding is suppressed by destructive interference and the quality factor is considerably enhanced, while the radiation of the superradiant mode is increased via constructive interference. The destructive interference effect on the subradiant mode can be used to gain insight into what limits the linewidth of these resonances after the transfer to the gel, since it is decoupled from radiative losses to the environment.

Figure 4 contains the relevant transmission spectra for angles of incidence between 10° and 40° for s- (left) and p-polarization (right), which clearly demonstrates the avoided crossing between the s-polarized modes. Data are plotted for every 2° and are offset vertically for clarity. The solid lines through the data are fits using the Fano model with a double resonance for s-polarized data and a single Fano resonance for the p-polarized data. The fits are in excellent agreement with the data and were used to extract the center frequency and quality factor of each of the resonances. Figure 5 shows the frequencies of the three modes (a) and the quality factors of the two s-polarized modes (b). At the avoided crossing, the quality factor of the lower energy (1,0) mode increases to a value of ∼300, while the mode amplitude decreases. The quality factor of the p-polarized mode Qp ≈ 100 is constant for wavevectors between 0.1 and 0.36×2π/a, and the data has been omitted from Fig. 5 for clarity.

Fig. 4 Measured transmission spectra (dots) as a function of frequency showing the avoided crossing of the (1,0) and (−1,±1) modes. Data are shown for angles of incidence from 10° to 40° for every 2°, for both s-polarization (left) and p-polarization (right). Each measured spectrum is offset vertically for clarity. The solid lines are fits of a Fano model using either a double or a single resonance to the data.
Fig. 5 Dispersion relation of the avoided crossing of the (1,0) and (−1,±1) modes obtained from the Fano fits in Fig. 4. The center frequencies of the modes (a) and quality factors (b) are plotted as a function of the in-plane wavevector k ||. The triangles in (a) correspond to the (−1,±1) mode that couples to p-polarized light, while the filled and open circles are the center frequencies of the (1,0) and (−1,±1) modes that couple to s-polarized light. The solid lines in (a) are fits to the data using a coupled mode theory (see text). The maximum achievable quality factor for the subradiant mode is close to 300 and is limited by the finite size of the structure.

We describe coupling of the modes using a relatively simple coupled mode theory with only three modes to gain insight in the dispersion of the modes. The interaction between the three coupled modes can be described by a 3 × 3 matrix Hamiltonian of the following form:
H=(ν1κ1κ1κ1ν2+κ2κ2κ1κ2ν2+κ2).
The coupling constant κ 1 characterizes the interaction between the s-polarized (1,0) and (−1,±1) mode, while the coupling constant κ 2 describes the coupling between the two degenerate (−1,±1) modes. The coupling of the waves leads to a standing wave pattern and creates an energy difference at the avoided crossing. This coupling is due to Bragg reflection with a (2,±1) and a (0,2) reciprocal lattice vector, respectively. The resulting dispersion relations of the three coupled modes are given by the Eigenvalues of the matrix H in terms of the frequencies ν 1 and ν 2 of the uncoupled modes. In order to describe the uncoupled modes we use a first order Taylor expansion of the propagation constant β(ν) of the fundamental TE waveguide mode of the slab that we fold back to the first Brillouin zone. This Taylor expansion contains the phase velocity vp and group velocity vg at the avoided crossing as adjustable parameters. Details of this coupled mode theory are given in the supporting information.

The solid lines in Fig. 5a are the result of fitting the coupled mode theory using vp, vg, κ 1, and κ 2 as free parameters, and show excellent agreement with the experimental data. The dashed lines in the figure are the dispersion of the uncoupled modes ν 1 and ν 2. From the fit we obtain a phase velocity vp = 0.4864 ± 0.0002 × c and a group velocity vg = 0.307 ± 0.005 × c, where c is the speed of light in vacuum. The effective refractive index neff = c/vp = 2.056 ± 0.001. This large difference between phase and group velocity is consistent with the dispersion relation of a slab waveguide with a large refractive index (n ≈ 3.0) for the guiding layer. The value of the coupling constants are κ 1 = 0.0096 ± 0.0005 × c/a and κ 2 = 0.0110 ± 0.0005 × c/a, respectively. The corresponding splittings are 22κ1/νc=5.6% and 2κ 2/νc = 3.6% of the center frequency νc = 0.6080 × c/a.

Figure 5b compares the quality factor Q of the s-polarized modes (symbols) obtained from the Fano fits to an estimate of the quality factors based on the numerically calculated quality factors Qideal. The variation in Qideal with parallel wavevector k || was extracted from a scattering matrix calculation for an infinitely large photonic crystal structure with parameters identical to that of the experimental structure. In the experimental structure these quality factor are never reached due to a combination of absorption, imperfections, and finite size effects, which we incorporate by introducing a quality factor Qloss. The total quality factor Q is then given by
1Q=1Qideal+1Qloss.
(2)
The solid lines in Fig. 5b are obtained by using a constant value of Qloss = 250 (dashed line). To improve the quality of the fit for the subradiant mode a value of Qloss that is a function k || could be envisaged. Such a model would reflect the fact that the field distribution in the slab depends on k ||, making losses due to Rayleigh scattering and imperfections in the structure a function of k ||. Using the simple picture of an avoided crossing of two modes to explain the subradiant mode, we find that the data for k || < 0.25 × 2π/a ((1,0) mode) are best described by Qloss ∼ 175, and by Qloss ∼ 325 for k || > 0.25 × 2π/a ((−1,±1) mode). To estimate what limits measured quality factors of the subradiant mode we use the highest value in Fig. 5b, close to 300. The corresponding distance is 0/neff ≈ 200 μm, which suggests that it is the finite size of the sample that limits the quality factor. The finite size aperture of the membrane leads to a diffraction limited spread in wavevector k ||, which in turn limits the Q value in the frequency domain via the photonic dispersion relation. For our sample covering an area of ∼ 300 × 300 μm2, we conclude that the quality factor is mainly limited by the finite size of the sample, and not so much by the optical quality of the structure after the transfer to the gel. We emphasize that the quality factors before and after transfer are very similar and that we expect a similar behavior for the quality factor of the subradiant mode before transfer to the gel. However, in this case the amplitude of the subradiant mode becomes too small to resolve these resonances in the experimental reflection spectra.

For the superradiant mode (blue circles), the agreement between the calculated and measured Q is less good. We believe that this is due to an interaction with the leaky modes originating from the fundamental TM waveguide mode. While the presence of this mode does not affect the calculated Q for ideal holes with straight sidewalls, we speculate that small imperfections and tapering of the holes enable a weak coupling between modes.

5. Conclusion

We have shown that it is possible to transfer photonic crystal membranes with sizes up to ∼ 425 × 425 μm2 to a transparent gel substrate without compromising the optical properties. The transfer process eliminates the buckling of the membrane caused by compressive strain from the 0.05% lattice mismatch between the Al0.35Ga0.65As membrane and the GaAs substrate. We studied the subradiant mode in the avoided crossing between the (1,0) and (−1,±1) leaky modes of the square lattice in detail and found quality factors up to ∼ 300. These quality factors are limited by the finite size of the experimental structure, demonstrating the excellent optical quality of the nanostructures after the transfer to the gel substrate. We believe that our method is applicable to other photonic crystal structures with different lattice symmetries, other membrane structures and to photonic crystal cavities. This makes such structures attractive for experimental study of nonlinear resonant effects that benefit from the field enhancement [5

5. J. P. Mondia, H. M. van Driel, W. Jiang, A. R. Cowan, and J. F. Young, “Enhanced second-harmonic generation from planar photonic crystals,” Opt. Lett. 28, 2500–2502 (2003). [CrossRef] [PubMed]

, 34

34. A. R. Cowan and Jeff F. Young, “Mode matching for second-harmonic generation in photonic crystal waveguides,” Phys. Rev. B 65, 085106 (2002). [CrossRef]

, 35

35. J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. Le Vassor d’Yerville, E. Centeno, D. Cassagne, and J. P. Albert, “Giant second-harmonic generation in a one-dimensional gan photonic crystal,” Phys. Rev. B 69, 085105 (2004). [CrossRef]

], for light extraction in light emitting diodes [4

4. J. J. Wierer, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency with high extraction efficiency,” Nat. Photonics 3, 163–169 (2009). [CrossRef]

], or to enhance the coupling to nitrogen-vacancy centers in diamond [12

12. T. van der Sar, E. C. Heeres, G. M. Dmochowski, G. de Lange, L. Robledo, T. H. Oosterkamp, and R. Hanson, “Nanopositioning of a diamond nanocrystal containing a single nitrogen-vacancy defect center,” Appl. Phys. Lett. 94, 173104 (2009). [CrossRef]

, 13

13. D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vučkovič, H. Park, and M. D. Lukin, “Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity,” Nano Lett. 10, 3922–3926 (2010). [CrossRef] [PubMed]

, 36

36. F. Jelezko, A. Volkmer, I. Popa, K. K. Rebane, and J. Wrachtrup, “Coherence length of photons from a single quantum system,” Phys. Rev. A 67, 041802 (2003). [CrossRef]

].

Acknowledgments

The photonic crystals in this study were fabricated in the Nanofacility of the Kavli Nanolab at the Delft University of Technology. This research was made possible by financial support from the Dutch Association for Scientifc Research (NWO) and the Foundation for Fundamental Research of Matter (FOM).

References and links

1.

M. Notomi, “Manipulating light with strongly modulated photonic crystals,” Rep. Prog. Phys. 73, 096501 (2010). [CrossRef]

2.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 9–12 (2004). [CrossRef]

3.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system.” Nature 445, 896–899 (2007). [CrossRef] [PubMed]

4.

J. J. Wierer, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency with high extraction efficiency,” Nat. Photonics 3, 163–169 (2009). [CrossRef]

5.

J. P. Mondia, H. M. van Driel, W. Jiang, A. R. Cowan, and J. F. Young, “Enhanced second-harmonic generation from planar photonic crystals,” Opt. Lett. 28, 2500–2502 (2003). [CrossRef] [PubMed]

6.

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Mériadec, and A. Levenson, “Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length,” Phys. Rev. Lett. 89, 043901 (2002). [CrossRef] [PubMed]

7.

A. D. Bristow, J. P. Mondia, and H. M. van Driel, “Sum and difference frequency generation as diagnostics for leaky eigenmodes in two-dimensional photonic crystal waveguides,” J. Appl. Phys. 99, 023105 (2006). [CrossRef]

8.

P. Kopperschmidt, S. Senz, G. Kästner, D. Hesse, and U. M. Gösele, “Materials integration of gallium arsenide and silicon by wafer bonding,” Appl. Phys. Lett. 72, 3181–3183 (1998). [CrossRef]

9.

Z. Hatzopoulos, D. Cenghera, G. Deligeorgisa, M. Androulidakia, E. Aperathitisa, and G. H. A. Georgakilas, “Molecular beam epitaxy of GaAs/AlGaAs epitaxial structures for integrated optoelectronic devices on Si using GaAs-Si wafer bonding,” J. Cryst. Growth 227–228, 193–196 (2001). [CrossRef]

10.

P. Kopperschmidt, G. Kästner, S. Senz, D. Hesse, and U. Gösele, “Wafer bonding of gallium arsenide on sapphire,” Appl. Phys. A 64, 533–537 (1997). [CrossRef]

11.

E. Chow, A. Grot, L. W. Mirkarimi, M. Sigalas, and G. Girolami, “Ultracompact biochemical sensor built with two-dimensional photoniccrystal microcavity,” Opt. Lett. 29, 1093–1095 (2004). [CrossRef] [PubMed]

12.

T. van der Sar, E. C. Heeres, G. M. Dmochowski, G. de Lange, L. Robledo, T. H. Oosterkamp, and R. Hanson, “Nanopositioning of a diamond nanocrystal containing a single nitrogen-vacancy defect center,” Appl. Phys. Lett. 94, 173104 (2009). [CrossRef]

13.

D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vučkovič, H. Park, and M. D. Lukin, “Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity,” Nano Lett. 10, 3922–3926 (2010). [CrossRef] [PubMed]

14.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990). [CrossRef] [PubMed]

15.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Existence of a photonic band gap in two dimensions,” Appl. Phys. Lett. 61, 495–497 (1992). [CrossRef]

16.

C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, “A7 structure: a family of photonic crystals,” Phys. Rev. B 50, 1988–1991 (1994). [CrossRef]

17.

T. Maeda, J. Lee, R. Shul, J. Han, J. Hong, E. Lambers, S. Pearton, C. Abernathy, and W. Hobson, “Inductively coupled plasma etching of III–V semiconductors in BCl3-based chemistries. I. GaAs, GaN, GaP, GaSb and AlGaAs,” Appl. Surf. Sci. 143, 174–182 (1999). [CrossRef]

18.

E. F. C. Driessen, D. Stolwijk, and M. J. A. de Dood, “Asymmetry reversal in the reflection from a two-dimensional photonic crystal,” Opt. Lett. 32, 3137–3139 (2007). [CrossRef] [PubMed]

19.

L. Babić and M. J. A. de Dood, “Interpretation of the fano lineshape reversal in the reflectivity spectra of photonic crystal slabs,” Opt. Express 18, 26569–26582 (2011). [CrossRef]

20.

Detailed information and technical datasheets are available via the manufacturers website: http://www.gelpak.com

21.

http://www.ioffe.ru/SVA/NSM/Semicond/AlGaAs/index.html.

22.

The force Fs to peel off the membrane breaking all gel-membrane bonds on the surface is proportional to L × (1 – π(r/a)2)). The force needed to break the membrane free Fb is given by the work needed to peel free the membranes along the sides and gives Fbd × (a – 2r). The ratio between the two forces Fs/Fb is then proportional to Ld×1π(r/a)2a2r, where the second term is a geometrical factor that accounts for the square lattice of air holes in the membrane.

23.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70, 1438–1440 (1997). [CrossRef]

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–R16258 (1999). [CrossRef]

25.

S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the fano resonance in optical resonators,” J. Opt. Soc. Am. A 20, 569–572 (2003). [CrossRef]

26.

T. Ochiai and K. Sakoda, “Nearly free-photon approximation for two-dimensional photonic crystal slabs,” Phys. Rev. B 64, 045108 (2001). [CrossRef]

27.

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006). [CrossRef]

28.

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227–6244 (1996). [CrossRef]

29.

C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, “Femtosecond light transmission and subradiant damping in plasmonic crystals,” Phys. Rev. Lett. 94, 113901 (2005). [CrossRef] [PubMed]

30.

M. J. A. de Dood, E. F. C. Driessen, D. Stolwijk, and M. P. van Exter, “Observation of coupling between surface plasmons in index-matched hole arrays,” Phys. Rev. B 77, 115437 (2008). [CrossRef]

31.

J. Wiersig, “Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities,” Phys. Rev. Lett. 97, 253901 (2006). [CrossRef]

32.

Q. H. Song and H. Cao, “Improving optical confinement in nanostructures via external mode coupling,” Phys. Rev. Lett. 105, 053902 (2010). [CrossRef] [PubMed]

33.

P. Paddon and J. Young, “Two-dimensional vector-coupled-mode theory for textured planar waveguides,” Phys. Rev. B 61, 2090–2101 (2000). [CrossRef]

34.

A. R. Cowan and Jeff F. Young, “Mode matching for second-harmonic generation in photonic crystal waveguides,” Phys. Rev. B 65, 085106 (2002). [CrossRef]

35.

J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. Le Vassor d’Yerville, E. Centeno, D. Cassagne, and J. P. Albert, “Giant second-harmonic generation in a one-dimensional gan photonic crystal,” Phys. Rev. B 69, 085105 (2004). [CrossRef]

36.

F. Jelezko, A. Volkmer, I. Popa, K. K. Rebane, and J. Wrachtrup, “Coherence length of photons from a single quantum system,” Phys. Rev. A 67, 041802 (2003). [CrossRef]

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(220.4000) Optical design and fabrication : Microstructure fabrication
(260.5740) Physical optics : Resonance
(050.5298) Diffraction and gratings : Photonic crystals

ToC Category:
Photonic Crystals

History
Original Manuscript: July 19, 2011
Revised Manuscript: August 16, 2011
Manuscript Accepted: August 29, 2011
Published: September 22, 2011

Citation
Lj. Babić, R. Leijssen, E.F.C. Driessen, and M.J.A. de Dood, "Transfer of photonic crystal membranes to a transparent gel substrate," Opt. Express 19, 19532-19541 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-20-19532


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References

  1. M. Notomi, “Manipulating light with strongly modulated photonic crystals,” Rep. Prog. Phys.73, 096501 (2010). [CrossRef]
  2. T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature432, 9–12 (2004). [CrossRef]
  3. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system.” Nature445, 896–899 (2007). [CrossRef] [PubMed]
  4. J. J. Wierer, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency with high extraction efficiency,” Nat. Photonics3, 163–169 (2009). [CrossRef]
  5. J. P. Mondia, H. M. van Driel, W. Jiang, A. R. Cowan, and J. F. Young, “Enhanced second-harmonic generation from planar photonic crystals,” Opt. Lett.28, 2500–2502 (2003). [CrossRef] [PubMed]
  6. Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Mériadec, and A. Levenson, “Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length,” Phys. Rev. Lett.89, 043901 (2002). [CrossRef] [PubMed]
  7. A. D. Bristow, J. P. Mondia, and H. M. van Driel, “Sum and difference frequency generation as diagnostics for leaky eigenmodes in two-dimensional photonic crystal waveguides,” J. Appl. Phys.99, 023105 (2006). [CrossRef]
  8. P. Kopperschmidt, S. Senz, G. Kästner, D. Hesse, and U. M. Gösele, “Materials integration of gallium arsenide and silicon by wafer bonding,” Appl. Phys. Lett.72, 3181–3183 (1998). [CrossRef]
  9. Z. Hatzopoulos, D. Cenghera, G. Deligeorgisa, M. Androulidakia, E. Aperathitisa, and G. H. A. Georgakilas, “Molecular beam epitaxy of GaAs/AlGaAs epitaxial structures for integrated optoelectronic devices on Si using GaAs-Si wafer bonding,” J. Cryst. Growth227–228, 193–196 (2001). [CrossRef]
  10. P. Kopperschmidt, G. Kästner, S. Senz, D. Hesse, and U. Gösele, “Wafer bonding of gallium arsenide on sapphire,” Appl. Phys. A64, 533–537 (1997). [CrossRef]
  11. E. Chow, A. Grot, L. W. Mirkarimi, M. Sigalas, and G. Girolami, “Ultracompact biochemical sensor built with two-dimensional photoniccrystal microcavity,” Opt. Lett.29, 1093–1095 (2004). [CrossRef] [PubMed]
  12. T. van der Sar, E. C. Heeres, G. M. Dmochowski, G. de Lange, L. Robledo, T. H. Oosterkamp, and R. Hanson, “Nanopositioning of a diamond nanocrystal containing a single nitrogen-vacancy defect center,” Appl. Phys. Lett.94, 173104 (2009). [CrossRef]
  13. D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vučkovič, H. Park, and M. D. Lukin, “Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity,” Nano Lett.10, 3922–3926 (2010). [CrossRef] [PubMed]
  14. K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett.65, 3152–3155 (1990). [CrossRef] [PubMed]
  15. R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Existence of a photonic band gap in two dimensions,” Appl. Phys. Lett.61, 495–497 (1992). [CrossRef]
  16. C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, “A7 structure: a family of photonic crystals,” Phys. Rev. B50, 1988–1991 (1994). [CrossRef]
  17. T. Maeda, J. Lee, R. Shul, J. Han, J. Hong, E. Lambers, S. Pearton, C. Abernathy, and W. Hobson, “Inductively coupled plasma etching of III–V semiconductors in BCl3-based chemistries. I. GaAs, GaN, GaP, GaSb and AlGaAs,” Appl. Surf. Sci.143, 174–182 (1999). [CrossRef]
  18. E. F. C. Driessen, D. Stolwijk, and M. J. A. de Dood, “Asymmetry reversal in the reflection from a two-dimensional photonic crystal,” Opt. Lett.32, 3137–3139 (2007). [CrossRef] [PubMed]
  19. L. Babić and M. J. A. de Dood, “Interpretation of the fano lineshape reversal in the reflectivity spectra of photonic crystal slabs,” Opt. Express18, 26569–26582 (2011). [CrossRef]
  20. Detailed information and technical datasheets are available via the manufacturers website: http://www.gelpak.com
  21. http://www.ioffe.ru/SVA/NSM/Semicond/AlGaAs/index.html .
  22. The force Fs to peel off the membrane breaking all gel-membrane bonds on the surface is proportional to L × (1 – π(r/a)2)). The force needed to break the membrane free Fb is given by the work needed to peel free the membranes along the sides and gives Fb ∝ d × (a – 2r). The ratio between the two forces Fs/Fb is then proportional to Ld×1−π(r/a)2a−2r, where the second term is a geometrical factor that accounts for the square lattice of air holes in the membrane.
  23. M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett.70, 1438–1440 (1997). [CrossRef]
  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. B60, R16255–R16258 (1999). [CrossRef]
  25. S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the fano resonance in optical resonators,” J. Opt. Soc. Am. A20, 569–572 (2003). [CrossRef]
  26. T. Ochiai and K. Sakoda, “Nearly free-photon approximation for two-dimensional photonic crystal slabs,” Phys. Rev. B64, 045108 (2001). [CrossRef]
  27. K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B73, 115126 (2006). [CrossRef]
  28. W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B54, 6227–6244 (1996). [CrossRef]
  29. C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, “Femtosecond light transmission and subradiant damping in plasmonic crystals,” Phys. Rev. Lett.94, 113901 (2005). [CrossRef] [PubMed]
  30. M. J. A. de Dood, E. F. C. Driessen, D. Stolwijk, and M. P. van Exter, “Observation of coupling between surface plasmons in index-matched hole arrays,” Phys. Rev. B77, 115437 (2008). [CrossRef]
  31. J. Wiersig, “Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities,” Phys. Rev. Lett.97, 253901 (2006). [CrossRef]
  32. Q. H. Song and H. Cao, “Improving optical confinement in nanostructures via external mode coupling,” Phys. Rev. Lett.105, 053902 (2010). [CrossRef] [PubMed]
  33. P. Paddon and J. Young, “Two-dimensional vector-coupled-mode theory for textured planar waveguides,” Phys. Rev. B61, 2090–2101 (2000). [CrossRef]
  34. A. R. Cowan and Jeff F. Young, “Mode matching for second-harmonic generation in photonic crystal waveguides,” Phys. Rev. B65, 085106 (2002). [CrossRef]
  35. J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. Le Vassor d’Yerville, E. Centeno, D. Cassagne, and J. P. Albert, “Giant second-harmonic generation in a one-dimensional gan photonic crystal,” Phys. Rev. B69, 085105 (2004). [CrossRef]
  36. F. Jelezko, A. Volkmer, I. Popa, K. K. Rebane, and J. Wrachtrup, “Coherence length of photons from a single quantum system,” Phys. Rev. A67, 041802 (2003). [CrossRef]

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