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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 20 — Sep. 26, 2011
  • pp: 18903–18909
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High-finesse cavities fabricated by buckling self-assembly of a-Si/SiO2 multilayers

T. W. Allen, J. Silverstone, N. Ponnampalam, T. Olsen, A. Meldrum, and R. G. DeCorby  »View Author Affiliations


Optics Express, Vol. 19, Issue 20, pp. 18903-18909 (2011)
http://dx.doi.org/10.1364/OE.19.018903


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Abstract

Arrays of half-symmetric Fabry-Perot micro-cavities were fabricated by controlled formation of circular delamination buckles within a-Si/SiO2 multilayers. Cavity height scales approximately linearly with diameter, in reasonable agreement with predictions based on elastic buckling theory. The measured finesse (F > 103) and quality factors (Q > 104 in the 1550 nm range) are close to reflectance limited predictions, indicating that the cavities have low roughness and few defects. Degenerate Hermite-Gaussian and Laguerre-Gaussian modes were observed, suggesting a high degree of cylindrical symmetry. Given their silicon-based fabrication, these cavities hold promise as building blocks for integrated optical sensing systems.

© 2011 OSA

1. Introduction and background

MEMS-based Fabry-Perot cavities have many applications in fiber and sensing systems and for fundamental physics studies. However, the quality factor (Q) and finesse (F) of flat-mirror cavities has typically been limited by defects such as surface roughness and non-parallelism or uncontrolled curvature of the mirrors [1

1. E. J. Eklund and A. M. Shkel, “Factors affecting the performance of micromachined sensors based on Fabry-Perot interferometry,” J. Micromech. Microeng. 15(9), 1770–1776 (2005). [CrossRef]

,2

2. W. Liu and J. J. Talghader, “Thermally invariant dielectric coatings for micromirrors,” Appl. Opt. 41(16), 3285–3293 (2002). [CrossRef] [PubMed]

]. Furthermore, to mitigate finesse reduction arising from walk-off of non-collimated beams, flat-mirror cavities typically must operate in a low mode order with relatively large lateral dimensions [3

3. R. R. A. Syms, “Principles of free-space optical microelectromechanical systems,” in Part C: Journal of Mechanical Engineering Science, Vol. 222 of Proceedings of the Institution of Mechanical Engineers (Sage Publications, 2008), pp. 1–17.

]. Tayebati et al. [4

4. P. Tayebati, P. Wang, M. Azimi, L. Maflah, and D. Vakhshoori, “Microelectromechanical tunable filter with stable half symmetric cavity,” Electron. Lett. 34(20), 1967–1968 (1998). [CrossRef]

] demonstrated half-symmetric cavities with improved stability and finesse, by using thin-film stress to control the curvature of a tethered mirror in a surface micromachining process. Similar results were obtained by Halbritter et al. [5

5. H. Halbritter, M. Aziz, F. Riemenschneider, and P. Meissner, “Electrothermally tunable two-chip optical filter with very low-cost and simple concept,” Electron. Lett. 38(20), 1201–1202 (2002). [CrossRef]

], using a bulk (two-wafer) micromachining process. Half-symmetric cavities with F ~3×103 are reportedly used in commercial MEMS-based micro-spectrometers [6

6. R. Crocombe, “MEMS technology moves process spectroscopy into a new dimension,” Spectroscopy Europe 16–19 (June–July 2004).

].

Here, we describe a method that employs standard silicon processing steps (film deposition, lithography) to produce variable-size micro-cavities on a single chip. Circular regions of low adhesion were embedded within Si/SiO2 multilayer stacks, and delamination buckles were subsequently induced to form in these regions. The resulting structures closely resemble half-symmetric resonators with one flat mirror and one nearly spherical mirror, and their optical properties were found to be in excellent agreement with the well-known predictions (derived from the paraxial wave equation) for macroscopic cavities of that type. Due to the nearly perfect symmetry of the cavities, modes from both the Laguerre-Gaussian and Hermite-Gaussian basis sets could be coupled and observed. The cavities exhibit F as high as 3×103 and Q as high as 4×104.

2. Fabrication and morphology of buckled dome micro-cavities

General details of the fabrication process were provided elsewhere [13

13. E. Epp, N. Ponnampalam, W. Newman, B. Drobot, J. N. McMullin, A. F. Meldrum, and R. G. DeCorby, “Hollow Bragg waveguides fabricated by controlled buckling of Si/SiO2 multilayers,” Opt. Express 18(24), 24917–24925 (2010). [CrossRef] [PubMed]

] in the context of aircore waveguide channels, but a brief summary is as follows. First, a Bragg mirror (4 periods of SiO2 and a-Si) was deposited by reactive magnetron sputtering onto a double-side-polished Si wafer. Next, a low adhesion, vapor-phase deposited fluorocarbon layer (~10 nm thick) was patterned on the top (a-Si) surface of this mirror. Subsequently, a second 4-period mirror (starting with a-Si), capped by a double-thickness a-Si layer, was deposited. All layers in both the upper and lower mirror were targeted as quarter-wave layers at 1550 nm, except for the half-wavelength (latent) capping layer. The capping layer was added to increase the stiffness of the upper mirror, thereby improving the thermal stability as discussed below. The total thickness of the upper mirror with capping layer is ~1.7 μm. Sputtering parameters were as described previously [13

13. E. Epp, N. Ponnampalam, W. Newman, B. Drobot, J. N. McMullin, A. F. Meldrum, and R. G. DeCorby, “Hollow Bragg waveguides fabricated by controlled buckling of Si/SiO2 multilayers,” Opt. Express 18(24), 24917–24925 (2010). [CrossRef] [PubMed]

], except that here we used a slightly lower background pressure (3 mTorr) for the a-Si layers and a slightly higher substrate temperature (170 °C). For magnetron sputtered a-Si, these conditions have been associated with higher film density, higher index, and lower loss [14

14. S. Bruynooghe, N. Schmidt, M. Sundermann, H. W. Becker, S. Spinzig, “Optical and structural properties of amorphous silicon coatings deposited by magnetron sputtering,” in Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2010), paper ThA9.

]. Our process produced a-Si layers with refractive index ~3.7 and extinction coefficient ~0.001 at 1550 nm, as estimated from VASE (variable-angle spectroscopic ellipsometry) measurements. The SiO2 layers were estimated to have refractive index ~1.47 in the same range. Using well-known formulae [15

15. A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th ed. (Oxford University Press, 2007), Chap. 4.

] (and confirmed by transfer matrix results), these values imply a best-case reflectance R ~0.999 for the 4-period mirrors, corresponding to a best-case (reflectance-limited) finesse FR ~3140 in the absence of defects.

After deposition of the upper mirror, samples were placed on a hot plate and subjected to an empirically optimized heating process, to induce loss of adhesion between the upper and lower Bragg mirrors in the regions of the embedded fluorocarbon. The multilayers exhibit an effective medium compressive stress ~200 MPa immediately after deposition, and this stress reduces with subsequent annealing [13

13. E. Epp, N. Ponnampalam, W. Newman, B. Drobot, J. N. McMullin, A. F. Meldrum, and R. G. DeCorby, “Hollow Bragg waveguides fabricated by controlled buckling of Si/SiO2 multilayers,” Opt. Express 18(24), 24917–24925 (2010). [CrossRef] [PubMed]

]. From numerous trials, delamination buckles formed at a sample-dependent temperature, typically in the 250 to 350 °C range. Variation in the buckling temperature is likely due to uncontrolled variation in the properties (i.e. thickness, roughness) of the fluorocarbon layer. In any case, it results in uncertainty regarding the effective stress at the time of buckle formation, which is the subject of ongoing work.

As shown schematically in Fig. 1(a)
Fig. 1 Buckled dome micro-cavities: (a) schematic cross-section showing optimized coupling to the fundamental cavity mode by a nearly Gaussian beam (with waist radius ω0) from a lensed fiber. For most cavities tested, the fiber mode field diameter was actually larger than 2ω0, resulting in the excitation of multiple modes. (b) Microscope image of pairs of 150, 200, and 250 μm diameter domes. Some dust particles are also visible.
, the compressive stress causes the upper Bragg mirror to buckle away from the substrate, producing a hollow cavity between a curved mirror and a flat mirror. Within a certain range of diameter for a given net stress, the circular delamination produced a dome-shaped buckle with a nearly spherical shape at its center. The cavities have diameters in the 100 to 800 μm range and peak heights in the ~2 to 25 μm range. However, larger buckles exhibited greater deviation from a spherical shape, such as partial collapse or flattening of the central region. In the following, we focus mainly on buckles with diameters of 400 μm or less (see Fig. 1(b)), which exhibited the best morphology and optical properties.

Neglecting plastic deformation, the theory for elastic buckling of a clamped circular plate can be used to predict the preconditions and height of a circular delamination buckle [16

16. J. W. Hutchinson, M. D. Thouless, and E. G. Liniger, “Growth and configurational stability of circular, buckling-driven film delaminations,” Acta Metall. Mater. 40(2), 295–308 (1992). [CrossRef]

]. The critical buckling stress is σc = 1.2235[E/(1-ν 2)](h/a)2, where E is Young’s modulus, ν is Poisson’s ratio, and h and a = D/2 are the thickness and radius of the plate. For a given stress and assuming fixed E, ν, and h, this implies a minimum diameter (Dmin) for buckling to occur. For D > Dmin, the peak deflection of the plate can be approximated as:
δ=h[1.9(σσC1)]1/2[1.9σ(1ν2)1.2235E]1/2D2,
(1)
where σ is the biaxial compressive stress, and the last approximation holds for σ >>σc (i.e. for D >> Dmin). Thus, for a given σ, ν, and E, and for D >> Dmin, Eq. (1) predicts that buckle height will increase approximately linearly with diameter. Equation (1) is an approximate closed-form solution to a nonlinear problem [16

16. J. W. Hutchinson, M. D. Thouless, and E. G. Liniger, “Growth and configurational stability of circular, buckling-driven film delaminations,” Acta Metall. Mater. 40(2), 295–308 (1992). [CrossRef]

], and is expected to over-estimate the height for large σ/σc (i.e. for large D). In fact, bifurcation to a nonaxisymmetric buckling mode is predicted at high values of stress (for σ/σc > 56 when ν = 1/3 [16

16. J. W. Hutchinson, M. D. Thouless, and E. G. Liniger, “Growth and configurational stability of circular, buckling-driven film delaminations,” Acta Metall. Mater. 40(2), 295–308 (1992). [CrossRef]

]).

3. Optical properties and characterization

Assuming a spherical shape for the buckled upper mirror, the domes form half-symmetric Fabry-Perot cavities [4

4. P. Tayebati, P. Wang, M. Azimi, L. Maflah, and D. Vakhshoori, “Microelectromechanical tunable filter with stable half symmetric cavity,” Electron. Lett. 34(20), 1967–1968 (1998). [CrossRef]

]. Depending on the degree of cylindrical symmetry, mode-fields for such cavities are traditionally described using one of two alternative sets of orthogonal basis functions [15

15. A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th ed. (Oxford University Press, 2007), Chap. 4.

,18

18. A. E. Siegman, Lasers (University Science Books, 1986).

]. In a rectangular coordinate system, the solutions are Hermite-Gaussian (HG) functions Hm,n(x,y,z), where m and n are integer mode indices for the x and y transverse coordinates. In a cylindrical coordinate system, the solutions are Laguerre-Gaussian (LG) functions Lp,l(r,ϕ,z), where p and l are integer mode indices for the radial and azimuthal coordinate directions, respectively. In most macroscopic cavities, deviation from cylindrical symmetry is significant so that it is predominately HG modes that are observed experimentally [18

18. A. E. Siegman, Lasers (University Science Books, 1986).

]. However, a predominance of LG modes has been reported for some micro-cavities [19

19. R. C. Pennington, G. D’Alessandro, J. J. Baumberg, and M. Kaczmarek, “Tracking spatial modes in nearly hemispherical microcavities,” Opt. Lett. 32(21), 3131–3133 (2007). [CrossRef] [PubMed]

].

Each family of solutions forms a complete set of orthogonal basis functions, so that a given HG mode can be expressed as a linear weighted sum of degenerate LG modes, or vice-versa [20

20. I. Kimel and L. R. Elias, “Relations between Hermite and Laguerre Gaussian modes,” IEEE J. Quantum Electron. 29(9), 2562–2567 (1993). [CrossRef]

]. The degeneracy condition requires that the modes have equivalent Gouy phase shift, and is expressed as follows:
g=m+n=2p+l.
(3)
For example, the HG1,1, LG1,0, and LG0,2 modes form a nominally degenerate set. Degenerate modes are expected to share the same resonance frequency, although slight imperfections (such as deviations from spherical mirror symmetry) will perturb this degeneracy [10

10. P. R. Dolan, G. M. Hughes, F. Grazioso, B. R. Patton, and J. M. Smith, “Femtoliter tunable optical cavity arrays,” Opt. Lett. 35(21), 3556–3558 (2010). [CrossRef] [PubMed]

]. For RC >> δ, the nominal wavelength spacing between non-degenerate transverse spatial modes can be approximated [15

15. A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th ed. (Oxford University Press, 2007), Chap. 4.

] as:
ΔλT=λ22πz0Δg,
(4)
where λ is the resonant wavelength, and z0 is the Rayleigh range, of the fundamental cavity mode. Table 1

Table 1. Predicted and Measured Optical Properties for Representative Microcavitiesa

table-icon
View This Table
shows predicted and measured mode properties for 4 representative cavities, where the predictions are based on the RC fit described above (+/− 20 μm from the peak).

Optical properties of the cavities were tested using the experimental setup illustrated in Fig. 1(a). Light from a tunable laser was coupled into the cavities via lensed optical fiber with focal spot diameter ~20 μm, somewhat larger than the fundamental mode field diameter for most of the cavities tested. This resulted in significant coupling to higher-order spatial modes. However, lower-order modes could be isolated and imaged by tuning the laser to the corresponding resonant wavelength of a given mode. Transmitted light was captured by either an infrared camera or a cooled photodetector.

Representative results for a 250 μm diameter dome are shown in Fig. 3
Fig. 3 The plot shows the transmission spectrum for a 250 μm diameter cavity, with peak height (mirror spacing) ~7.5 μm. The broad peak near 1522 nm is due to a transmission resonance outside the buckled areas. The inset plot shows the fundamental resonance line in greater detail. Mode-field images were captured with the laser tuned near one of the resonance lines, as indicated. Images for the four nominally degenerate modes associated with the third-order resonance were captured by making fine adjustments to the laser wavelength.
. Transverse modes exhibited fixed spacing with values in good agreement with the predictions from paraxial theory, as summarized in Table 1. As mentioned, associated with each higher-order resonance line is a set of nominally degenerate HG and LG modes, whose degeneracy is perturbed by any deviation from cylindrical/spherical symmetry, such as spherical aberration or astigmatism [10

10. P. R. Dolan, G. M. Hughes, F. Grazioso, B. R. Patton, and J. M. Smith, “Femtoliter tunable optical cavity arrays,” Opt. Lett. 35(21), 3556–3558 (2010). [CrossRef] [PubMed]

,19

19. R. C. Pennington, G. D’Alessandro, J. J. Baumberg, and M. Kaczmarek, “Tracking spatial modes in nearly hemispherical microcavities,” Opt. Lett. 32(21), 3131–3133 (2007). [CrossRef] [PubMed]

]. Such perturbations are apparent from the multiple sub-peaks within the g = 2 and g = 3 resonant lines in Fig. 3. By making fine adjustments (typically on the order of a few picometers) to the laser wavelength, it was possible to isolate individual HG and LG modes within a given resonant line. As an example, the H3,0, H2,1, L0,3, and L1,1 modes shown represent the complete set of HG and LG modes possessing g = 3 degeneracy. To our knowledge, such direct experimental evidence for the intrinsic relationship between LG and HG modes is rarely reported. We believe it is made possible, in part, by the near-cylindrical symmetry and geometrical perfection of the self-assembled microcavities.

For the smallest cavities, the LG modes were dominant and it was in fact more difficult to isolate HG modes. Moreover, there was less evidence for the existence of multiple peaks within the high-order resonance lines, suggesting a higher degree of symmetry. As an example, Fig. 4
Fig. 4 The plot shows the transmission spectrum for a 200 μm diameter dome, with peak height (mirror spacing) ~5.7 μm. Representative LP ,1 mode images are shown; they were captured by tuning the laser source to one of the resonance lines as indicated.
shows the transmission spectrum for a 200 μm diameter cavity. Also shown are representative images of Lp ,1 modes, which were found to be dominant in this case. As predicted by (3), this family of modes occupies the odd-order (g = 1,3,5 …) resonance lines. The mismatch between the incident beam and the fundamental cavity mode is particularly large here, resulting in significant coupling to higher order modes. As above, these modes exhibit a fixed spacing in good agreement with paraxial theory. Finally, the effective fundamental mode volume is on the order of Vm ~100λ3 for the smallest cavities, comparable to values reported for similar cavities [10

10. P. R. Dolan, G. M. Hughes, F. Grazioso, B. R. Patton, and J. M. Smith, “Femtoliter tunable optical cavity arrays,” Opt. Lett. 35(21), 3556–3558 (2010). [CrossRef] [PubMed]

,11

11. A. Muller, E. B. Flagg, J. R. Lawall, and G. S. Solomon, “Ultrahigh-finesse, low-mode-volume Fabry-Perot microcavity,” Opt. Lett. 35(13), 2293–2295 (2010). [CrossRef] [PubMed]

].

4. Summary and conclusions

The reflectance-limited optical properties of the cavity modes can be taken as evidence that the ‘defect finesse’ [1

1. E. J. Eklund and A. M. Shkel, “Factors affecting the performance of micromachined sensors based on Fabry-Perot interferometry,” J. Micromech. Microeng. 15(9), 1770–1776 (2005). [CrossRef]

] of the cavities is high. This suggests that cavities formed by buckling can have very low roughness and a highly regular geometric shape. In principle, the finesse could be improved by using higher reflectance mirrors. For example, reflectance of the present mirrors is mainly limited by absorption in the a-Si layers, which could be reduced by the use of hydrogenated a-Si. Furthermore, operation at shorter wavelengths might be possible by replacing a-Si with TiO2 or similar, provided compressively stressed layers are possible.

Acknowledgments

The work was supported by the National Sciences and Engineering Research Council of Canada.

References and links

1.

E. J. Eklund and A. M. Shkel, “Factors affecting the performance of micromachined sensors based on Fabry-Perot interferometry,” J. Micromech. Microeng. 15(9), 1770–1776 (2005). [CrossRef]

2.

W. Liu and J. J. Talghader, “Thermally invariant dielectric coatings for micromirrors,” Appl. Opt. 41(16), 3285–3293 (2002). [CrossRef] [PubMed]

3.

R. R. A. Syms, “Principles of free-space optical microelectromechanical systems,” in Part C: Journal of Mechanical Engineering Science, Vol. 222 of Proceedings of the Institution of Mechanical Engineers (Sage Publications, 2008), pp. 1–17.

4.

P. Tayebati, P. Wang, M. Azimi, L. Maflah, and D. Vakhshoori, “Microelectromechanical tunable filter with stable half symmetric cavity,” Electron. Lett. 34(20), 1967–1968 (1998). [CrossRef]

5.

H. Halbritter, M. Aziz, F. Riemenschneider, and P. Meissner, “Electrothermally tunable two-chip optical filter with very low-cost and simple concept,” Electron. Lett. 38(20), 1201–1202 (2002). [CrossRef]

6.

R. Crocombe, “MEMS technology moves process spectroscopy into a new dimension,” Spectroscopy Europe 16–19 (June–July 2004).

7.

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom-field coupling for Bose-Einstein condensates in an optical cavity on a chip,” Nature 450(7167), 272–276 (2007). [CrossRef] [PubMed]

8.

I. Favero and K. Karrai, “Optomechanics of deformable optical cavities,” Nat. Photonics 3(4), 201–205 (2009). [CrossRef]

9.

C. Toninelli, Y. Delley, T. Stoferle, A. Renn, S. Gotzinger, and V. Sandoghdar, “A scanning microcavity for in situ control of single-molecule emission,” Appl. Phys. Lett. 97(2), 021107 (2010). [CrossRef]

10.

P. R. Dolan, G. M. Hughes, F. Grazioso, B. R. Patton, and J. M. Smith, “Femtoliter tunable optical cavity arrays,” Opt. Lett. 35(21), 3556–3558 (2010). [CrossRef] [PubMed]

11.

A. Muller, E. B. Flagg, J. R. Lawall, and G. S. Solomon, “Ultrahigh-finesse, low-mode-volume Fabry-Perot microcavity,” Opt. Lett. 35(13), 2293–2295 (2010). [CrossRef] [PubMed]

12.

M. Trupke, E. A. Hinds, S. Eriksson, E. A. Curtis, Z. Moktadir, E. Kukharenka, and M. Kraft, “Microfabricated high-finesse optical cavity with open access and small volume,” Appl. Phys. Lett. 87(21), 211106 (2005). [CrossRef]

13.

E. Epp, N. Ponnampalam, W. Newman, B. Drobot, J. N. McMullin, A. F. Meldrum, and R. G. DeCorby, “Hollow Bragg waveguides fabricated by controlled buckling of Si/SiO2 multilayers,” Opt. Express 18(24), 24917–24925 (2010). [CrossRef] [PubMed]

14.

S. Bruynooghe, N. Schmidt, M. Sundermann, H. W. Becker, S. Spinzig, “Optical and structural properties of amorphous silicon coatings deposited by magnetron sputtering,” in Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2010), paper ThA9.

15.

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th ed. (Oxford University Press, 2007), Chap. 4.

16.

J. W. Hutchinson, M. D. Thouless, and E. G. Liniger, “Growth and configurational stability of circular, buckling-driven film delaminations,” Acta Metall. Mater. 40(2), 295–308 (1992). [CrossRef]

17.

L. Freund and S. Suresh, Thin Film Materials, Stress, Defect Formation, and Surface Evolution (Cambridge University Press, 2003), Chap. 5.

18.

A. E. Siegman, Lasers (University Science Books, 1986).

19.

R. C. Pennington, G. D’Alessandro, J. J. Baumberg, and M. Kaczmarek, “Tracking spatial modes in nearly hemispherical microcavities,” Opt. Lett. 32(21), 3131–3133 (2007). [CrossRef] [PubMed]

20.

I. Kimel and L. R. Elias, “Relations between Hermite and Laguerre Gaussian modes,” IEEE J. Quantum Electron. 29(9), 2562–2567 (1993). [CrossRef]

21.

E. Epp, N. Ponnampalam, J. N. McMullin, and R. G. Decorby, “Thermal tuning of hollow waveguides fabricated by controlled thin-film buckling,” Opt. Express 17(20), 17369–17375 (2009). [CrossRef] [PubMed]

22.

E. Garmire, “Theory of quarter-wave-stack dielectric mirrors used in a thin fabry-perot filter,” Appl. Opt. 42(27), 5442–5449 (2003). [CrossRef] [PubMed]

OCIS Codes
(120.2230) Instrumentation, measurement, and metrology : Fabry-Perot
(130.3120) Integrated optics : Integrated optics devices
(230.4170) Optical devices : Multilayers
(130.7408) Integrated optics : Wavelength filtering devices

ToC Category:
Integrated Optics

History
Original Manuscript: July 6, 2011
Revised Manuscript: August 20, 2011
Manuscript Accepted: August 23, 2011
Published: September 14, 2011

Citation
T. W. Allen, J. Silverstone, N. Ponnampalam, T. Olsen, A. Meldrum, and R. G. DeCorby, "High-finesse cavities fabricated by buckling self-assembly of a-Si/SiO2 multilayers," Opt. Express 19, 18903-18909 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-20-18903


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References

  1. E. J. Eklund and A. M. Shkel, “Factors affecting the performance of micromachined sensors based on Fabry-Perot interferometry,” J. Micromech. Microeng.15(9), 1770–1776 (2005). [CrossRef]
  2. W. Liu and J. J. Talghader, “Thermally invariant dielectric coatings for micromirrors,” Appl. Opt.41(16), 3285–3293 (2002). [CrossRef] [PubMed]
  3. R. R. A. Syms, “Principles of free-space optical microelectromechanical systems,” in Part C: Journal of Mechanical Engineering Science, Vol. 222 of Proceedings of the Institution of Mechanical Engineers (Sage Publications, 2008), pp. 1–17.
  4. P. Tayebati, P. Wang, M. Azimi, L. Maflah, and D. Vakhshoori, “Microelectromechanical tunable filter with stable half symmetric cavity,” Electron. Lett.34(20), 1967–1968 (1998). [CrossRef]
  5. H. Halbritter, M. Aziz, F. Riemenschneider, and P. Meissner, “Electrothermally tunable two-chip optical filter with very low-cost and simple concept,” Electron. Lett.38(20), 1201–1202 (2002). [CrossRef]
  6. R. Crocombe, “MEMS technology moves process spectroscopy into a new dimension,” Spectroscopy Europe16–19 (June–July 2004).
  7. Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom-field coupling for Bose-Einstein condensates in an optical cavity on a chip,” Nature450(7167), 272–276 (2007). [CrossRef] [PubMed]
  8. I. Favero and K. Karrai, “Optomechanics of deformable optical cavities,” Nat. Photonics3(4), 201–205 (2009). [CrossRef]
  9. C. Toninelli, Y. Delley, T. Stoferle, A. Renn, S. Gotzinger, and V. Sandoghdar, “A scanning microcavity for in situ control of single-molecule emission,” Appl. Phys. Lett.97(2), 021107 (2010). [CrossRef]
  10. P. R. Dolan, G. M. Hughes, F. Grazioso, B. R. Patton, and J. M. Smith, “Femtoliter tunable optical cavity arrays,” Opt. Lett.35(21), 3556–3558 (2010). [CrossRef] [PubMed]
  11. A. Muller, E. B. Flagg, J. R. Lawall, and G. S. Solomon, “Ultrahigh-finesse, low-mode-volume Fabry-Perot microcavity,” Opt. Lett.35(13), 2293–2295 (2010). [CrossRef] [PubMed]
  12. M. Trupke, E. A. Hinds, S. Eriksson, E. A. Curtis, Z. Moktadir, E. Kukharenka, and M. Kraft, “Microfabricated high-finesse optical cavity with open access and small volume,” Appl. Phys. Lett.87(21), 211106 (2005). [CrossRef]
  13. E. Epp, N. Ponnampalam, W. Newman, B. Drobot, J. N. McMullin, A. F. Meldrum, and R. G. DeCorby, “Hollow Bragg waveguides fabricated by controlled buckling of Si/SiO2 multilayers,” Opt. Express18(24), 24917–24925 (2010). [CrossRef] [PubMed]
  14. S. Bruynooghe, N. Schmidt, M. Sundermann, H. W. Becker, S. Spinzig, “Optical and structural properties of amorphous silicon coatings deposited by magnetron sputtering,” in Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2010), paper ThA9.
  15. A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th ed. (Oxford University Press, 2007), Chap. 4.
  16. J. W. Hutchinson, M. D. Thouless, and E. G. Liniger, “Growth and configurational stability of circular, buckling-driven film delaminations,” Acta Metall. Mater.40(2), 295–308 (1992). [CrossRef]
  17. L. Freund and S. Suresh, Thin Film Materials, Stress, Defect Formation, and Surface Evolution (Cambridge University Press, 2003), Chap. 5.
  18. A. E. Siegman, Lasers (University Science Books, 1986).
  19. R. C. Pennington, G. D’Alessandro, J. J. Baumberg, and M. Kaczmarek, “Tracking spatial modes in nearly hemispherical microcavities,” Opt. Lett.32(21), 3131–3133 (2007). [CrossRef] [PubMed]
  20. I. Kimel and L. R. Elias, “Relations between Hermite and Laguerre Gaussian modes,” IEEE J. Quantum Electron.29(9), 2562–2567 (1993). [CrossRef]
  21. E. Epp, N. Ponnampalam, J. N. McMullin, and R. G. Decorby, “Thermal tuning of hollow waveguides fabricated by controlled thin-film buckling,” Opt. Express17(20), 17369–17375 (2009). [CrossRef] [PubMed]
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