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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 12, Iss. 7 — Apr. 5, 2004
  • pp: 1458–1463
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Fabrication-tolerant high quality factor photonic crystal microcavities

Kartik Srinivasan, Paul E. Barclay, and Oskar Painter  »View Author Affiliations


Optics Express, Vol. 12, Issue 7, pp. 1458-1463 (2004)
http://dx.doi.org/10.1364/OPEX.12.001458


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Abstract

A two-dimensional photonic crystal microcavity design supporting a wavelength-scale volume resonant mode with a calculated quality factor (Q) insensitive to deviations in the cavity geometry at the level of Q≳2×104 is presented. The robustness of the cavity design is confirmed by optical fiber-based measurements of passive cavities fabricated in silicon. For microcavities operating in the λ=1500 nm wavelength band, quality factors between 1.3–4.0×104 are measured for significant variations in cavity geometry and for resonant mode normalized frequencies shifted by as much as 10% of the nominal value.

© 2004 Optical Society of America

Fig. 1. (a) FDTD calculated magnetic field amplitude (|B|) in the center of the optically thin membrane for the fundamental A20 mode. (b) Scanning electron microscope image of a fabricated Si PC microcavity with a graded defect design (PC-5 described below).

1. Introduction

Fig. 2. Grade in the normalized hole radius (r/a) along the central and ŷ axes of square lattice PC cavities such as those shown in Fig. 1. Cavity r/a profiles for (a,b) FDTD cavity designs and (c,d) microfabricated Si cavities.

Use of an odd symmetry mode to suppress vertical radiation loss is, at a basic level, independent of changes in the size of the holes defining the defect cavity. This feature has been confirmed in simulations of simple defect cavity designs in square lattice photonic crystals[8

8. K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express 10, 670–684 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-15-670. [CrossRef] [PubMed]

], where Q did not degrade below 104, despite significant changes (as much as 40%) in the size of the (two) central defect holes. Perturbations that cause the cavity to be asymmetric create a mode which, though not strictly odd, will be a perturbation to an odd mode, and hence will still largely suppress DC Fourier components and exhibit high Q. However, for the square lattice photonic crystal structures considered here, perturbations to the central defect hole geometry can result in a degradation in Q , due in part to the lack of a complete in-plane bandgap within the square lattice. This lack of a complete bandgap requires the defect geometry to be tailored so as to eliminate the presence of Fourier components in directions where the lattice is no longer reflective.

This tailoring was achieved in Ref. [8

8. K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express 10, 670–684 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-15-670. [CrossRef] [PubMed]

] by a grade in the hole radius moving from the center of the cavity outwards. The grade, shown in Fig. 1, serves to help eliminate couplings to in-plane radiation modes along the diagonal axes of the square lattice (the M-point of the reciprocal lattice) where the PC is no longer highly reflective, while simultaneously providing a means to keep the in-plane reflectivity high along the ŷ axis (the direction of the mode’s dominant Fourier components). The use of a large number of holes to define the defect region ensures that no single hole is responsible for creating the potential well that confines the resonant mode, making the design less susceptible to fluctuations in the size of individual holes. Instead, the continuous change in the position of the conduction band-edge resulting from the grade in hole radius creates an approximately harmonic potential well[13

13. O. Painter, K. Srinivasan, and P. Barclay, “A Wannier-like Equation for Photon States of Locally Perturbed Photonic Crystals,” Phys. Rev. B 68, 035214 (2003). [CrossRef]

]. This smooth change in the position of the band-edge creates a robust way to mode-match between the central portion of

Table 1. Theoretical (PC-A through PC-E) and experimental (PC-1 through PC-7) normalized frequency (a/λo ) and quality factor (Q) values for the A20 mode of cavities with profiles shown in Fig. 2.

table-icon
View This Table

the cavity (where the mode sits) and its exterior. In other work[11

11. Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003). [CrossRef] [PubMed]

], softening of this transition is achieved by adjusting the position of two holes surrounding the central cavity region (which consists of three removed air holes in a hexagonal lattice). This method can achieve high-Q, but as mode-matching is achieved by tailoring only two holes it is more sensitive to perturbations than the adiabatic transition created by a grade in the hole radius. Finally, we note that even though a relatively large number of holes are modified to create the graded lattice, V eff is still wavelength-scale, and remains between 0.8–1.4(λ/n) 3 in all of the devices considered in this work. In addition, the methods used here to achieve robustness in Q are general and can be applied to cavities in other PC lattices[14

14. K. Srinivasan and O. Painter, “Fourier space design of high-Q cavities in standard and compressed hexagonal lattice photonic crystals,” Opt. Express 11, 579–593 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-6-579. [CrossRef] [PubMed]

].

To test the sensitivity of the design to perturbations experimentally, cavities were fabricated in a d=340 nm thick silicon membrane through a combination of electron beam lithography, inductively-coupled plasma reactive ion etching, and wet etching. Figure 2(c)-(d) shows the values of r/a along the central and ŷ axes for a number of fabricated devices (PC-1 through PC-7), as measured with a scanning electron microscope (SEM). Cavities are passively tested[12

12. K. Srinivasan, P. E. Barclay, M. Borselli, and O. Painter, “Optical fiber based measurement of an ultra-small volume, high-Q photonic crystal microcavity,” submitted to Phys. Rev. Lett., Sept. 2003 (available at http://arxiv.org/quant-ph/abs/0309190).

] using an optical fiber taper[15

15. J. Knight, G. Cheung, F. Jacques, and T. Birks, “Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper,” Opt. Lett. 22, 1129–1131 (1997). [CrossRef] [PubMed]

], which consists of a standard single mode optical fiber that has been heated and stretched to a minimum diameter of 1–2 µm. At such sizes, the evanescent field of the fiber mode extends into the surrounding air, providing a means by which the cavity modes can be sourced and out-coupled. The fiber taper is spliced to the output of a fiber-pigtailed scanning tunable laser (1565–1625 nm) with 1 pm resolution, and is mounted (Fig. 3(a)) above and parallel to an array of PC cavities (Fig. 3(b)). When it is brought into close proximity (~500 nm) to the sample surface, and the polarization of the fiber taper is adjusted (via polarization-controlling padddle wheels) to be TE-polarized relative to the slab, evanescent coupling between the taper and cavity modes occurs.

Fig. 3. (a) Schematic illustrating the fiber taper probe measurement setup. (b) SEM image of an array of undercut PC cavities (white box indicates position of one device within the array). (c) Measured data (blue dots) and exponential fit (red curve) for linewidth vs. taper-PC gap of the A20 mode in PC-5. (Inset) Taper transmission for this device when the taper-PC gap is 350 nm. (d) Same as (c) for PC-6 (here, the taper transmission in the inset is shown when Δz=650 nm). The transmission curves are normalized relative to transmission in the absence of the PC cavity.

Figure 3(c)-(d) shows measurements for devices PC-5 and PC-6, which have significantly different r/a profiles (Fig. 2(c)-(d)). The inset of Fig. 3(c) shows the normalized taper transmission as a function of wavelength when the taper is 350 nm above cavity PC-5. By measuring the dependence of cavity mode linewidth (γ) on the vertical taper-PC gap (Δz) (Fig. 3(c)), an estimate of the true cold-cavity linewidth (γ 0) is given by the asymptotic value of γ reached when the taper is far from the cavity. For PC-5, γ0 ~0.065 nm, corresponding to Q~2.5×104. Figure 3(d) shows the linewidth measurement for PC-6. For this device, γ 0~0.041 nm, corresponding to a Q~4.0×104. As described in Ref. [12

12. K. Srinivasan, P. E. Barclay, M. Borselli, and O. Painter, “Optical fiber based measurement of an ultra-small volume, high-Q photonic crystal microcavity,” submitted to Phys. Rev. Lett., Sept. 2003 (available at http://arxiv.org/quant-ph/abs/0309190).

], the strength of the taper-PC coupling as a function of taper position can be used to estimate the spatial localization of the cavity field; these measurements closely correspond with calculations and for PC-6 are consistent with an FDTD-predictedV eff~0.9(λ/n)3. These PC microcavities thus simultaneously exhibit a high-Q factor that is insensitive to perturbations, and an ultra-small V eff.

Linewidth measurements for each of the cavities PC-1 through PC-7 are compiled in Table 1. The robustness of the Q to non-idealities in fabrication is clearly evident. Though all of the devices exhibit a general grade in r/a, the steepness of the grade and the average hole radius (r̄/a) vary considerably without reducing Q below 1.3×104. These high-Q values are exhibited despite the fact that many cavities are not symmetric (the odd boundary condition is thus only approximately maintained), and the frequency of the cavity resonance varies over a 10% range, between a/λo =0.243-0.270.

In summary, the robustness in Q to errors in the in-plane design of a PC microcavity consisting of a graded square lattice of air holes is discussed. This property is confirmed both by FDTD simulations of devices where the steepness of the grade and the average hole radius are varied without degrading Q below 2×104, and in measurements of microfabricated Si cavities that exhibit Q factors between 1.3-4.0×104 over a wide range of device parameters. For these high-Q cavities, current limitations on the Q factor appear to stem principally from slightly angled sidewalls and etched surface roughness, as opposed to errors in the in-plane shape or size of holes.

This work was partly supported by the Charles Lee Powell Foundation. The authors thank M. Borselli for his contributions in building the taper test setup. K.S. thanks the Hertz Foundation for its financial support.

Footnotes

1This label refers to the mode’s symmetry classification and to it being the lowest frequency mode in the bandgap.

References and links

1.

O. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819–1824 (1999). [CrossRef] [PubMed]

2.

T. Yoshie, J. Vučković, A. Scherer, H. Chen, and D. Deppe, “High quality two-dimensional photonic crystal slab cavities,” Appl. Phys. Lett. 79, 4289–4291 (2001). [CrossRef]

3.

Optical Processes in Microcavities, R. K. Chang and A. J. Campillo, eds., (World Scientific, Singapore, 1996).

4.

H. J. Kimble, “Strong Interactions of Single Atoms and Photons in Cavity QED,” Physica Scripta T76, 127–137 (1998). [CrossRef]

5.

P. Michler, A. Kiraz, C. Becher, W. Schoenfeld, P. Petroff, L. Zhang, E. Hu, and A. Imomoglu, “A Quantum Dot Single-Photon Turnstile Device,” Science 290, 2282–2285 (2000). [CrossRef] [PubMed]

6.

C. Santori, M. Pelton, G. Solomon, Y. Dale, and Y. Yamamoto, “Triggered Single Photons from a Quantum Dot,” Phys. Rev. Lett. 86, 1502–1505 (2001). [CrossRef] [PubMed]

7.

J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E65(2002).

8.

K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express 10, 670–684 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-15-670. [CrossRef] [PubMed]

9.

H.-Y. Ryu, M. Notomi, and Y.-H. Lee, “High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities,” Appl. Phys. Lett. 83, 4294–4296 (2003). [CrossRef]

10.

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, “Experimental demonstration of a high quality factor photonic crystal microcavity,” Appl. Phys. Lett. 83, 1915–1917 (2003). [CrossRef]

11.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003). [CrossRef] [PubMed]

12.

K. Srinivasan, P. E. Barclay, M. Borselli, and O. Painter, “Optical fiber based measurement of an ultra-small volume, high-Q photonic crystal microcavity,” submitted to Phys. Rev. Lett., Sept. 2003 (available at http://arxiv.org/quant-ph/abs/0309190).

13.

O. Painter, K. Srinivasan, and P. Barclay, “A Wannier-like Equation for Photon States of Locally Perturbed Photonic Crystals,” Phys. Rev. B 68, 035214 (2003). [CrossRef]

14.

K. Srinivasan and O. Painter, “Fourier space design of high-Q cavities in standard and compressed hexagonal lattice photonic crystals,” Opt. Express 11, 579–593 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-6-579. [CrossRef] [PubMed]

15.

J. Knight, G. Cheung, F. Jacques, and T. Birks, “Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper,” Opt. Lett. 22, 1129–1131 (1997). [CrossRef] [PubMed]

16.

Y. Tanaka, T. Asano, Y. Akahane, B.-S. Song, and S. Noda, “Theoretical investigation of a two-dimensional photonic crystal slab with truncated air holes,” Appl. Phys. Lett. 82, 1661–1663 (2003). [CrossRef]

OCIS Codes
(140.5960) Lasers and laser optics : Semiconductor lasers
(230.5750) Optical devices : Resonators
(270.5580) Quantum optics : Quantum electrodynamics

ToC Category:
Research Papers

History
Original Manuscript: March 2, 2004
Revised Manuscript: March 30, 2004
Published: April 5, 2004

Citation
Kartik Srinivasan, Paul Barclay, and Oskar Painter, "Fabrication-tolerant high quality factor photonic crystal microcavities," Opt. Express 12, 1458-1463 (2004)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-7-1458


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References

  1. O. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O�??Brien, P. D. Dapkus, and I. Kim, �??Two-Dimensional Photonic Band-Gap Defect Mode Laser,�?? Science 284, 1819�??1824 (1999). [CrossRef] [PubMed]
  2. T. Yoshie, J. Vu¡ckovic, A. Scherer, H. Chen, and D. Deppe, �??High quality two-dimensional photonic crystal slab cavities,�?? Appl. Phys. Lett. 79, 4289�??4291 (2001). [CrossRef]
  3. Optical Processes in Microcavities, R. K. Chang and A. J. Campillo, eds., (World Scientific, Singapore, 1996).
  4. H. J. Kimble, �??Strong Interactions of Single Atoms and Photons in Cavity QED,�?? Physica Scripta T76, 127�??137 (1998). [CrossRef]
  5. P. Michler, A. Kiraz, C. Becher, W. Schoenfeld, P. Petroff, L. Zhang, E. Hu, and A. Imomoglu, �??A Quantum Dot Single-Photon Turnstile Device,�?? Science 290, 2282�??2285 (2000). [CrossRef] [PubMed]
  6. C. Santori, M. Pelton, G. Solomon, Y. Dale, and Y. Yamamoto, �??Triggered Single Photons from a Quantum Dot,�?? Phys. Rev. Lett. 86, 1502�??1505 (2001). [CrossRef] [PubMed]
  7. J. Vu¡ckovic, M. Lon¡car, H. Mabuchi, and A. Scherer, �??Design of photonic crystal microcavities for cavity QED,�?? Phys. Rev. E 65 (2002).
  8. K. Srinivasan and O. Painter, �??Momentum space design of high-Q photonic crystal optical cavities,�?? Opt. Express 10, 670�??684 (2002), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-15-670">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-15-670</a>. [CrossRef] [PubMed]
  9. H.-Y. Ryu, M. Notomi, and Y.-H. Lee, �??High-quality-factor and small-mode-volume hexapole modes in photoniccrystal-slab nanocavities,�?? Appl. Phys. Lett. 83, 4294�??4296 (2003). [CrossRef]
  10. K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, �??Experimental demonstration of a high quality factor photonic crystal microcavity,�?? Appl. Phys. Lett. 83, 1915�??1917 (2003). [CrossRef]
  11. Y. Akahane, T. Asano, B.-S. Song, and S. Noda, �??High-Q photonic nanocavity in a two-dimensional photonic crystal,�?? Nature 425, 944�??947 (2003). [CrossRef] [PubMed]
  12. K. Srinivasan, P. E. Barclay, M. Borselli, and O. Painter, �??Optical fiber based measurement of an ultrasmall volume, high-Q photonic crystal microcavity,�?? submitted to Phys. Rev. Lett., Sept. 2003 (available at <a href="http://arxiv.org/quant-ph/abs/0309190">http://arxiv.org/quant-ph/abs/0309190</a>).
  13. O. Painter, K. Srinivasan, and P. Barclay, �??A Wannier-like Equation for Photon States of Locally Perturbed Photonic Crystals,�?? Phys. Rev. B 68, 035214 (2003). [CrossRef]
  14. K. Srinivasan and O. Painter, �??Fourier space design of high-Q cavities in standard and compressed hexagonal lattice photonic crystals,�?? Opt. Express 11, 579�??593 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-6-579">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-6-579</a>. [CrossRef] [PubMed]
  15. J. Knight, G. Cheung, F. Jacques, and T. Birks, �??Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper,�?? Opt. Lett. 22, 1129�??1131 (1997). [CrossRef] [PubMed]
  16. Y. Tanaka, T. Asano, Y. Akahane, B.-S. Song, and S. Noda, �??Theoretical investigation of a two-dimensional photonic crystal slab with truncated air holes,�?? Appl. Phys. Lett. 82, 1661�??1663 (2003). [CrossRef]

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