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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 5 — Feb. 27, 2012
  • pp: 5204–5212
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GaAs-based air-slot photonic crystal nanocavity for optomechanical oscillators

Masahiro Nomura  »View Author Affiliations


Optics Express, Vol. 20, Issue 5, pp. 5204-5212 (2012)
http://dx.doi.org/10.1364/OE.20.005204


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Abstract

We theoretically investigate an optomechanical structure consisting of two parallel GaAs membranes with an air-slot type photonic crystal nanocavity. The optical cavity has a quality factor of 4.8 × 106 at 1.52 μm and an extremely small modal volume of 0.015 of a cubic wavelength for the fundamental mode in a vacuum. The localized electric field near the air/dielectric-object boundary provides a large optomechanical coupling factor of ~990 GHz/nm. The fundamental mechanical mode resonance is 95 MHz and a quality factor is 83,800 at room temperature, nearly seven times higher than that for a similar Si-based structure. This high mechanical quality factor of a GaAs-based structure stems from low thermoelastic loss and leads to more effective optical control of nanomechanical oscillators.

© 2012 OSA

1. Introduction

It has been known that atoms and ions can be mechanically manipulated by a nearly resonant laser beam [1

1. F. Diedrich, J. C. Bergquist, W. M. Itano, and D. J. Wineland, “Laser cooling to the zero-point energy of motion,” Phys. Rev. Lett. 62(4), 403–406 (1989). [CrossRef] [PubMed]

3

3. S. Chu, “Laser manipulation of atoms and particles,” Science 253(5022), 861–866 (1991). [CrossRef] [PubMed]

] and even massive dielectric objects can be optically manipulated via the radiation-pressure and the optical gradient force [4

4. V. Braginsky and A. Manukin, Measurement of Weak Forces in Physics Experiments (Univ. Chicago Press, 1977).

]. Recently, the optical manipulation of micro and nanomechanical structures has been intensively investigated due to interests in both the fundamental physics and a variety of potential applications, including highly sensitive mass and weak force detections. In experimental investigations, cavity-assisted schemes are used to enhance the interaction between a mechanical oscillator and a resonant electric field. Optomechanical experiments using the radiation pressure [5

5. T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008). [CrossRef] [PubMed]

] or the optical gradient force [6

6. D. Van Thourhout and J. Roels, “Optomechanical Device actuation through the optical gradient force,” Nat. Photonics 4(4), 211–217 (2010). [CrossRef]

] have been performed using a microlever with a micromirror [7

7. D. Kleckner and D. Bouwmeester, “Sub-kelvin optical cooling of a micromechanical resonator,” Nature 444(7115), 75–78 (2006). [CrossRef] [PubMed]

, 8

8. C. H. Metzger and K. Karrai, “Cavity cooling of a microlever,” Nature 432(7020), 1002–1005 (2004). [CrossRef] [PubMed]

], a thin membrane in or as an optical cavity [9

9. J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452(7183), 72–75 (2008). [CrossRef] [PubMed]

, 10

10. O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, “Radiation-pressure cooling and optomechanical instability of a micromirror,” Nature 444(7115), 71–74 (2006). [CrossRef] [PubMed]

], a micro toroid [11

11. G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Riviere, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5(12), 909–914 (2009). [CrossRef]

], a microsphere [12

12. Y.-S. Park and H. Wang, “Resolved-sideband and cryogenic cooling of an optomechanical resonator,” Nat. Phys. 5(7), 489–493 (2009). [CrossRef]

], and a photonic crystal (PhC) [13

13. M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009). [CrossRef] [PubMed]

, 14

14. J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011). [CrossRef] [PubMed]

] structure. The optical gradient force, which is the basic operation principle of optical tweezers, can provide a much larger force per photon when strong field gradients are available. Therefore, the optical gradient force can be used for efficient manipulation of optomechanical systems. The origin of the optical gradient force can be understood interaction between the gradient field and an electric dipole in a structure induced by the gradient field.

In this paper, we theoretically investigate optomechanical coupling between a pair of GaAs membranes with an air-slot mode-gap PhC nanocavity and the optical mode. Numerically estimated optical properties, mechanical properties, and optomechanical properties of a designed structure are shown. We analyzed the motion of the nanomechanical oscillator controlled by a slightly detuned single-frequency pump laser. Then, we show the advantage of a GaAs-based structure over a Si-based structure in mechanical property and the importance of the mechanical property in optomechanical control of damping and amplification of the mechanical oscillator.

2. Structure of nanomechanical oscillator

Figure 1
Fig. 1 (a) Computed cavity electric field distribution in the air-slot PhC nanocavity structure. The long-term (Q = 4.8 × 106) and localized (V = 0.015λ3) electric field confinement around the air/semiconductor boundary results in extremely strong optomechanical interaction. (b) Color plot of the absolute displacement in y direction for the investigated fundamental mechanical oscillation mode (95 MHz). This oscillation can be optically controlled by the cavity field in the PhC nanocavity.
shows a schematic of the investigated nanostructure consisting of two parallel GaAs membrane separated by an air-slot with a width s = 80 nm, which is located at the center of a line defect (W1) of a triangular lattice of air-holes. The period of the lattice a and the radius of the air-hole r are 490 nm and 140 nm, respectively. The thickness, length and width of the membrane are 204 nm, 7.84 μm (16a), and 2.08 μm (2.53as/2 ). The nanomechanical structure possesses a mode-gap type photonic crystal (PhC) cavity with a high Q [22

22. E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultra-high-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006). [CrossRef]

] to enhance the optomechanical coupling by a long cavity photon lifetime. The air-holes are slightly shifted outward as indicated in the inset by arrows in Fig. 1(a) to create a mode-gap PhC nanocavity. The amounts of shifts are 3δ, 2δ, and δ for the air-holes as respectively indicated by red, blue, and green arrows, where δ = 0.0095a. This cavity design was proposed by Yamamoto et al. for the study of cavity quantum electrodynamics in free space with Si-based structures [23

23. T. Yamamoto, M. Notomi, H. Taniyama, E. Kuramochi, Y. Yoshikawa, Y. Torii, and T. Kuga, “Design of a high-Q air-slot cavity based on a width-modulated line-defect in a photonic crystal slab,” Opt. Express 16(18), 13809–13817 (2008). [CrossRef] [PubMed]

]. We note that air-slot type cavities are also useful for optomechanics, and actually, possibility of operation in a resolved-sideband limit is theoretically reported in [15

15. Y. Li, J. Zheng, J. Gao, J. Shu, M. S. Aras, and C. W. Wong, “Design of dispersive optomechanical coupling and cooling in ultrahigh-Q/V slot-type photonic crystal cavities,” Opt. Express 18(23), 23844–23856 (2010). [CrossRef] [PubMed]

]. In this structure, photons are localized at the air-semiconductor boundary. Therefore, the cavity field is sensitive to the motion of the semiconductor membranes, and the optomechanical coupling strength is expected to be very high.

3. Simulation results and discussions

In this section, we report optical properties of the air-slot mode-gap PhC nanocavity, mechanical properties of the doubly clamped GaAs membrane, and optomechanical coupling of the GaAs nanomechanical oscillator with the PhC nanocavity. The motion of the GaAs membrane is analyzed by the estimated parameters. Then, the performance as an optomechanical oscillator of a GaAs-based structure is compared with that of a similar Si-based structure.

3.1 Optical properties

3.2 Mechanical properties

The mechanical property of the structure was studied by finite-element-method (FEM). In the numerical simulations, the beams are clamped at both ends using the fixed boundary conditions. The mechanical motions of the beam are categorized into in-plane and out-of-plane motions. In this study, the fundamental in-plane mode is investigated. Figure 1(b) shows a color plot of the absolute displacement in y-direction of the mode. The deformation of the structure is exaggerated for clear visibility. The part colored by red indicates the absolute displacement of the structure is large. The mechanical frequency of the mode is calculated to be Ωm/2π = 95 MHz with GaAs material properties: density ρ of 5316 kg/m3, Young’s modulus E of 85.9 GPa, thermal expansion coefficient α of 5.7 × 10−6 1/K, specific heat capacity Cp of 550 J/(kg·K), and thermal conductivity κth of 33 W/(m·K). The resonant frequency is lower than that of a similar Si structure (175 MHz) due to larger ρ and smaller E. This mode has the maximum displacement at x = 0, where the optical cavity mode has the electric field maximum. Therefore, the mechanical motion in y-direction efficiently couples to the fundamental optical cavity mode shown in Fig. 1(a).

The investigated doubly clamped beam structure has several dissipative processes. These damping processes are caused by thermoelastic loss, clamping loss, surrounding gas, and so on. The damping of the vibrating structure in air is very large and leads to a very low Qm of the order of 100. We assume that the optomechanical system is in high vacuum where the gas damping is negligible as this is the regime where most experimental investigations have been performed. Thermoelastic loss is often the main damping mechanism in the mechanical structure and limits the value of Qm at room temperature [27

27. C. Zener, “Internal Friction in Solids. I. Theory of Internal Friction in Reeds,” Phys. Rev. 52(3), 230–235 (1937). [CrossRef]

, 28

28. T. H. Metcalf, B. B. Pate, D. M. Photiadis, and B. H. Houston, “Thermoelastic damping in micromechanical resonators,” Appl. Phys. Lett. 95(6), 061903 (2009). [CrossRef]

]. The value of Qm is calculated by Zener’s theory of thermoelastic damping with the following expression
Qm=CpρEαT(1+Ωmτth)2Ωmτth
(1)
where, τth is the thermal relaxation time τth=Cpρw/π2κthof 40 ns for this system. We obtained very high value of Qm = 83,800, which is higher than that for a Si-based same structure by nearly seven times. The details and reason will be discussed in subsection 3.4.

3.3 Optomechanical coupling properties

In this subsection, we discuss the optomechanical coupling between the fundamental optical mode and the in-plane fundamental mechanical mode. The optomechanical coupling factor gOM is the perturbed optical cavity resonance Δωc induced by small displacement Δy of the structure and expressed as dωc/dy. One can parameterize the optomechanical coupling strength by an effective coupling length LOM, which is described by LOM1=1ωcdωcdy. The coupling length can be obtained by perturbation theory for Maxwell’s equations with displacement of material boundaries and described by the following expression

LOM1=12(q(r)·n)[Δε12(r)|E(0)(r)|2Δ(ε121(r))|D(0)(r)|2]dAε(r)|E(r)|2dV.
(2)

In this equation, q(r) is a normalized displacement field defined by q(r) = Q(r)/Δymax, where Δymax is the largest displacement amplitude in the structure. n is the unit normal vector at the surface of the membrane in the static condition. Δε12and Δ(ε121) are defined as ε1ε2 andε11ε21, respectively. E(0)and D(0) are the electric field parallel to and the electric displacement normal to the air/semiconductor boundary. The value of gOM is calculated by the electric field distribution and displacement field and estimated to be 991 GHz/nm, which corresponds to LOM ~200 nm. The obtained coupling strength is about one order of magnitude larger than that obtained in other optomechanical coupling systems without air-slot. The stronger optomechanical coupling stems from the enhancement of the electric field in the narrow air-slot and it clearly indicates great advantage of an air-slot cavity for an optomechanically coupled structures.

3.4 Optical control of a GaAs-based nanomechanical oscillator

We investigated the motion of the nanomechanical oscillator and the time-dependent intensity of the optical cavity mode by numerically solving the coupled equations for the stored energy in the optical cavity |a|2 and the input power |s|2
dadt=iΔω(y)a(12τ0+12τex)a+1τexs
(3)
d2ydt2+Ωm2Qmdydt+Ωm2=FOMmeff=gOMωc |a|2meff
(4)
where Δω(y) = ΔωgOMy: Δω is the detuning of the pump laser frequency with respect to the cavity resonance . The cavity field decay rate κ is given by 12τ0+12τex, where the first term is the intrinsic cavity field decay rate and the second term is the coupling rate to the external system for pumping. The effective mass meff is computed from the following equation
meff=(rr0) 2(rr0)max2ρdV,
(5)
where, r is the position of each segment used in the FEM simulation and (r-r0) is the displacement of the segment from the original position of r0 at the static condition. The integral is taken over the whole beams and meff is calculated to be ~6 pg. The motion of the optomechanically coupled structure can be simulated by Eqs. (3) and (4) with the obtained parameters. Δω is crucial parameter to determine how the mechanical system is optically controlled. It is known that blue detuning (Δω > 0) and red detuning (Δω < 0) respectively amplifies and damps the motion of mechanical oscillators. In this work, we mainly discuss the case of the red detuning. The optomechanical coupling modifies the intrinsic mechanical resonator damping rate Γ. In the weak retardation regime (κ >> Ωm), in our case, the modified damping rate Γom induced by laser beam with pump power P can be calculated by the following equation [15

15. Y. Li, J. Zheng, J. Gao, J. Shu, M. S. Aras, and C. W. Wong, “Design of dispersive optomechanical coupling and cooling in ultrahigh-Q/V slot-type photonic crystal cavities,” Opt. Express 18(23), 23844–23856 (2010). [CrossRef] [PubMed]

].

Γom=ωc2ΩmLom2meff(2κexκ2+4Δ(y)2)[κ/2(Δ(y)Ωm)2+(κ/2)2κ/2(Δ(y)+Ωm)2+(κ/2)2]P.
(6)

Figure 2
Fig. 2 Enhanced damping rate at various laser frequency detuning with respect to the cavity resonance Δω. The lateral axis is normalized by the optical cavity decay rate κ.
shows the enhanced damping rate defined by (Γom+Γ)/Γ at various Δω in the case of P = 1 nW and Q = 5 × 105 as an example. Although at zero and very large detuning, the pumping laser does not couple with the mechanical mode, when Δω ~κ/2 the motion of the oscillator becomes sensitive to the cavity electric field. In the investigated structure, the result indicates that the optimal Δω for optomechanical control is ~0.35κ. The value of Δω is fixed at 0.35κ or −0.35κ in this study.

The cavity field amplitude and the motions of the membrane in the in-plane direction were simulated for the fundamental mode and the results are shown in Figs. 3(a)
Fig. 3 Time evolution of the velocity of the membrane (y>0) and the cavity field amplitude (a) at the detuning of −0.35κ (red detuning, cooling case) and (b) at the detuning of 0.35κ (blue detuning, heating case).
and 3(b) for the cases of Δω = −0.35κ and 0.35κ. One can see that the cavity field amplitude oscillate at the frequency of the mechanical mode of 95 MHz and there is a π-phase-shift in the cavity field amplitude between the two detuning cases. The right vertical axis is the velocity of the membrane (y > 0). When the velocity v is positive, the membrane moves to + y direction and the slit width becomes wider. In Fig. 3(a), for the case of red-detuning, the integrated cavity field amplitude over the time period of v > 0 is larger than that taken over v < 0. This behavior indicates that the cavity field pulls the membrane to –y direction when the membrane moves to + y direction and results in damping of the mechanical oscillation of the membrane. On the other hand, for the blue-detuning case in Fig. 3(b), the integrated cavity field amplitude over v > 0 is smaller than that taken over v < 0. Therefore, the amplitude of the mechanical oscillation is amplified by the laser. These results clearly show the laser-induced cooling and amplification of the mechanical motions.

The displacement dependent cavity field amplitude leads to optically induced stiffening of the mechanical system, which can be observed as the modification in mechanical eigenfrequency. Figure 4(a)
Fig. 4 (a) Mechanical frequency change induced by optical stiffening and (b) cooling factor at various detunings and values of cavity Q at an input power of 1 nW.
shows calculated mechanical frequencies at various Qs and Δωs. The mechanical frequency is modified on the order of 10 kHz, which corresponds to ~10−4 of Ωm. Figure 4(b) shows cooling factor Fc=(Γom+Γ)/Γ at various Qs and Δωs. It is clearly shown that a high-Q optical cavity is essential for optical control of a mechanical oscillator based on the cavity enhanced scheme and the motion of the oscillator can be optically controlled by precise detuning of Δω.

3.5 Comparison with a Si-based structure

Most of the theoretical and experimental investigations of optomechanics have been done with Si or SiN based structures, because Si-based structures can be processed more precisely compared with III-V semiconductor materials such as GaAs and higher optical cavity Q can be achieved. We also calculated optical and mechanical properties of the investigated structure for Si-based material in the same manner as GaAs-based material. In numerical simulations, the optical property of a GaAs-based and a Si-based air-slot mode-gap PhC nanocavity are about the same due to the similar refractive indices of GaAs (~3.4) and Si (~3.5) at 1.5 μm range. Here, we note that GaAs has advantageous mechanical properties, which is crucial for optomechanical systems, over Si at room temperature, where thermoelastic loss is the dominant damping mechanism in this system. The value of Qm was estimated by Zener’s theory using Eq. (1) with material parameters summarized in Table 1

Table 1. Summary of the parameters used to estimate Qm and values of Qm for GaAs and Si-based structures.

table-icon
View This Table
.

The values of Qm for the GaAs-based and the Si-based structures of the investigated design are 83,800 and 13,300, respectively. In the estimation, we found that the higher Qm of the GaAs-based structure stemmed from a longer thermal relaxation time in a GaAs material. The difference in thermal relaxation times, τth=Cpρw/π2κth, between GaAs and Si is mainly caused by κth, which is different by a factor of 8. This thermal feature leads to less thermoelastic loss in the GaAs structure and to better mechanical property.

We calculated cooling factors of the investigated structure at various Qms in the case of P = 1 nW and Q = 5 × 105, and the result is shown in Fig. 5
Fig. 5 Color map of the calculated cooling factors at various detunings and values of Qm at an input power of 1 nW. Cavity Q is fixed at 5 × 105.
. The parameters used in the estimation are those of GaAs material besides Qm. One can see that Fc strongly depends on Qm. This result indicates the importance of mechanical property for optomechanical structures. Currently, we fabricate the designed GaAs-based structures and the experimental results will be reported elsewhere.

4. Summary

A GaAs-based optomechanical nanostructure with an air-slot mode-gap PhC nanocavity is theoretically investigated. The GaAs-based structure provides better mechanical property than that of a Si-based structure at room temperature due to lower thermoelastic loss. The importance of less mechanical damping in optical control of nanomechanical oscillators is clearly shown in the simulation. In addition, the GaAs-based structure provides excellent optical property as a Si-based structure due to the similar refractive indices at 1.5 μm wavelength range. Although most of the experimental investigations have adopted Si material to fabricate optomechanical oscillators, obtained simulation results indicate that GaAs also can be a good material for optomechanical structures: the difficulty in the fabrication process is compensated by the superior mechanical properties of GaAs.

Acknowledgments

The author would like to thank K. Hirakawa, W. Shimizu and E. Harbord for helpful discussions. This work was partly supported by Nippon Sheet Glass Foundation for Materials Science and Engineering, the Mitsubishi Foundation, and Project for Developing Innovation Systems of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.

References and links

1.

F. Diedrich, J. C. Bergquist, W. M. Itano, and D. J. Wineland, “Laser cooling to the zero-point energy of motion,” Phys. Rev. Lett. 62(4), 403–406 (1989). [CrossRef] [PubMed]

2.

C. N. Cohen-Tannoudji and W. D. Phillips, “New mechanisms for laser cooling,” Phys. Today 43(10), 33–40 (1990). [CrossRef]

3.

S. Chu, “Laser manipulation of atoms and particles,” Science 253(5022), 861–866 (1991). [CrossRef] [PubMed]

4.

V. Braginsky and A. Manukin, Measurement of Weak Forces in Physics Experiments (Univ. Chicago Press, 1977).

5.

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008). [CrossRef] [PubMed]

6.

D. Van Thourhout and J. Roels, “Optomechanical Device actuation through the optical gradient force,” Nat. Photonics 4(4), 211–217 (2010). [CrossRef]

7.

D. Kleckner and D. Bouwmeester, “Sub-kelvin optical cooling of a micromechanical resonator,” Nature 444(7115), 75–78 (2006). [CrossRef] [PubMed]

8.

C. H. Metzger and K. Karrai, “Cavity cooling of a microlever,” Nature 432(7020), 1002–1005 (2004). [CrossRef] [PubMed]

9.

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452(7183), 72–75 (2008). [CrossRef] [PubMed]

10.

O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, “Radiation-pressure cooling and optomechanical instability of a micromirror,” Nature 444(7115), 71–74 (2006). [CrossRef] [PubMed]

11.

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Riviere, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5(12), 909–914 (2009). [CrossRef]

12.

Y.-S. Park and H. Wang, “Resolved-sideband and cryogenic cooling of an optomechanical resonator,” Nat. Phys. 5(7), 489–493 (2009). [CrossRef]

13.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009). [CrossRef] [PubMed]

14.

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011). [CrossRef] [PubMed]

15.

Y. Li, J. Zheng, J. Gao, J. Shu, M. S. Aras, and C. W. Wong, “Design of dispersive optomechanical coupling and cooling in ultrahigh-Q/V slot-type photonic crystal cavities,” Opt. Express 18(23), 23844–23856 (2010). [CrossRef] [PubMed]

16.

J. Gao, J. F. McMillan, M.-C. Wu, J. Zheng, S. Assefa, and C. W. Wong, “Demonstration of an air-slot modegap confined photonic crystal slab nanocavity with ultrasmall mode volumes,” Appl. Phys. Lett. 96(5), 051123 (2010). [CrossRef]

17.

A. H. Safavi-Naeini, T. P. M. Alegre, M. Winger, and O. Painer, “Optomechanics in an ultrahigh-Q two-dimensional photonic crystal cavity,” Appl. Phys. Lett. 97(18), 181106 (2010). [CrossRef]

18.

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(7014), 200–203 (2004). [CrossRef] [PubMed]

19.

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single quantum dot-nanocavity system,” Nat. Phys. 6(4), 279–283 (2010). [CrossRef]

20.

L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “High frequency GaAs nano-optomechanical disk resonator,” Phys. Rev. Lett. 105(26), 263903 (2010). [CrossRef] [PubMed]

21.

H. Okamoto, D. Ito, K. Onomitsu, H. Sanada, H. Gotoh, T. Sogawa, and H. Yamaguchi, “Vibration amplification, damping, and self-oscillations in micromechanical resonators induced by optomechanical coupling through carrier excitation,” Phys. Rev. Lett. 106(3), 036801 (2011). [CrossRef] [PubMed]

22.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultra-high-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006). [CrossRef]

23.

T. Yamamoto, M. Notomi, H. Taniyama, E. Kuramochi, Y. Yoshikawa, Y. Torii, and T. Kuga, “Design of a high-Q air-slot cavity based on a width-modulated line-defect in a photonic crystal slab,” Opt. Express 16(18), 13809–13817 (2008). [CrossRef] [PubMed]

24.

Z. Zhang and M. Qiu, “Small-volume waveguide-section high Q microcavities in 2D photonic crystal slabs,” Opt. Express 12(17), 3988–3995 (2004). [CrossRef] [PubMed]

25.

H. S. Ee, K. Y. Jeong, M. K. Seo, Y. H. Lee, and H. G. Park, “Ultrasmall square-lattice zero-cell photonic crystal laser,” Appl. Phys. Lett. 93(1), 011104 (2008). [CrossRef]

26.

M. Nomura, K. Tanabe, S. Iwamoto, and Y. Arakawa, “High-Q design of semiconductor-based ultrasmall photonic crystal nanocavity,” Opt. Express 18(8), 8144–8150 (2010). [CrossRef] [PubMed]

27.

C. Zener, “Internal Friction in Solids. I. Theory of Internal Friction in Reeds,” Phys. Rev. 52(3), 230–235 (1937). [CrossRef]

28.

T. H. Metcalf, B. B. Pate, D. M. Photiadis, and B. H. Houston, “Thermoelastic damping in micromechanical resonators,” Appl. Phys. Lett. 95(6), 061903 (2009). [CrossRef]

OCIS Codes
(140.3320) Lasers and laser optics : Laser cooling
(140.3945) Lasers and laser optics : Microcavities
(050.5298) Diffraction and gratings : Photonic crystals
(120.4880) Instrumentation, measurement, and metrology : Optomechanics

ToC Category:
Photonic Crystals

History
Original Manuscript: December 5, 2011
Revised Manuscript: February 8, 2012
Manuscript Accepted: February 10, 2012
Published: February 16, 2012

Citation
Masahiro Nomura, "GaAs-based air-slot photonic crystal nanocavity for optomechanical oscillators," Opt. Express 20, 5204-5212 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-5-5204


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References

  1. F. Diedrich, J. C. Bergquist, W. M. Itano, and D. J. Wineland, “Laser cooling to the zero-point energy of motion,” Phys. Rev. Lett.62(4), 403–406 (1989). [CrossRef] [PubMed]
  2. C. N. Cohen-Tannoudji and W. D. Phillips, “New mechanisms for laser cooling,” Phys. Today43(10), 33–40 (1990). [CrossRef]
  3. S. Chu, “Laser manipulation of atoms and particles,” Science253(5022), 861–866 (1991). [CrossRef] [PubMed]
  4. V. Braginsky and A. Manukin, Measurement of Weak Forces in Physics Experiments (Univ. Chicago Press, 1977).
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