Abstract

The laser cooling of vibrational states of solids has been achieved through photoluminescence in rare-earth elements, optical forces in optomechanics, and Brillouin scattering light–sound interaction. The net cooling of solids through spontaneous Raman scattering and the laser refrigeration of indirect band gap semiconductors both remain unsolved challenges. Here, we show analytically that photonic density of states (DoS) engineering can address the two fundamental requirements for achieving spontaneous Raman cooling: suppressing the dominance of Stokes (heating) transitions and the enhancement of anti-Stokes (cooling) efficiency beyond the natural optical absorption of the material. We develop a general model for the DoS modification to spontaneous Raman scattering probabilities, and elucidate the necessary and minimum condition required for achieving net Raman cooling. With a suitably engineered DoS, we establish the enticing possibility of the refrigeration of intrinsic silicon by annihilating phonons from all its Raman-active modes simultaneously, through a single telecom wavelength pump. This result points to a highly flexible approach for the laser cooling of any transparent semiconductor, including indirect band gap semiconductors, far away from significant optical absorption, band-edge states, excitons, or atomic resonances.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
  38. M. Campbell, D. Sharp, M. Harrison, R. Denning, and A. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53–56 (2000).
    [Crossref]
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    [Crossref]
  40. E. C. Nelson, N. L. Dias, K. P. Bassett, S. N. Dunham, V. Verma, M. Miyake, P. Wiltzius, J. A. Rogers, J. J. Coleman, X. Li, and P. V. Braun, “Epitaxial growth of three-dimensionally architectured optoelectronic devices,” Nat. Mater. 10, 676–681 (2011).
    [Crossref]
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    [Crossref]
  44. D. Fenner, D. Biegelsen, and R. Bringans, “Silicon surface passivation by hydrogen termination: a comparative study of preparation methods,” J. Appl. Phys. 66, 419–424 (1989).
    [Crossref]
  45. A. G. Aberle, “Surface passivation of crystalline silicon solar cells: a review,” Prog. Photovoltaics 8, 473–487 (2000).
    [Crossref]
  46. P. Schmid, “Optical absorption in heavily doped silicon,” Phys. Rev. B 23, 5531–5536 (1981).
    [Crossref]
  47. D. K. Schroder, N. R. Thomas, and J. C. Swartz, “Free carrier absorption in silicon,” IEEE J. Solid-State Circuits 13, 180–187 (1978).
    [Crossref]
  48. M. Ma, F. W. Mont, X. Yan, J. Cho, E. F. Schubert, G. B. Kim, and C. Sone, “Effects of the refractive index of the encapsulant on the light-extraction efficiency of light-emitting diodes,” Opt. Express 19, A1135–A1140 (2011).
    [Crossref]

2014 (1)

2013 (3)

S. D. Melgaard, D. V. Seletskiy, A. Di Lieto, M. Tonelli, and M. Sheik-Bahae, “Optical refrigeration to 119  K, below National Institute of Standards and Technology cryogenic temperature,” Opt. Lett. 38, 1588–1590 (2013).
[Crossref]

J. Zhang, D. Li, R. Chen, and Q. Xiong, “Laser cooling of a semiconductor by 40 kelvin,” Nature 493, 504–508 (2013).
[Crossref]

S. C. Rand, “Raman laser cooling of solids,” J. Lumin. 133, 10–14 (2013).
[Crossref]

2012 (3)

G. Bahl, M. Tomes, F. Marquardt, and T. Carmon, “Observation of spontaneous Brillouin cooling,” Nat. Phys. 8, 203–207 (2012).
[Crossref]

Y. J. Ding and J. B. Khurgin, “From anti-Stokes photoluminescence to resonant Raman scattering in GaN single crystals and GaN-based heterostructures,” Laser Photon. Rev. 6, 660–677 (2012).
[Crossref]

D. V. Seletskiy, M. P. Hehlen, R. I. Epstein, and M. Sheik-Bahae, “Cryogenic optical refrigeration,” Adv. Opt. Photon. 4, 78–107 (2012).
[Crossref]

2011 (3)

M. Ma, F. W. Mont, X. Yan, J. Cho, E. F. Schubert, G. B. Kim, and C. Sone, “Effects of the refractive index of the encapsulant on the light-extraction efficiency of light-emitting diodes,” Opt. Express 19, A1135–A1140 (2011).
[Crossref]

R. Aggarwal, L. Farrar, S. Saikin, A. Aspuru-Guzik, M. Stopa, and D. Polla, “Measurement of the absolute Raman cross section of the optical phonon in silicon,” Solid State Commun. 151, 553–556 (2011).
[Crossref]

E. C. Nelson, N. L. Dias, K. P. Bassett, S. N. Dunham, V. Verma, M. Miyake, P. Wiltzius, J. A. Rogers, J. J. Coleman, X. Li, and P. V. Braun, “Epitaxial growth of three-dimensionally architectured optoelectronic devices,” Nat. Mater. 10, 676–681 (2011).
[Crossref]

2010 (1)

D. V. Seletskiy, S. D. Melgaard, S. Bigotta, A. Di Lieto, M. Tonelli, and M. Sheik-Bahae, “Laser cooling of solids to cryogenic temperatures,” Nat. Photonics 4, 161–164 (2010).
[Crossref]

2009 (2)

2008 (1)

M. A. Green, “Self-consistent optical parameters of intrinsic silicon at 300  K including temperature coefficients,” Sol. Energy Mater. Sol. Cells 92, 1305–1310 (2008).
[Crossref]

2007 (1)

Y. Chen, J. Geddes Iii, J. Lee, P. Braun, and P. Wiltzius, “Holographically fabricated photonic crystals with large reflectance,” Appl. Phys. Lett. 91, 241103 (2007).
[Crossref]

2006 (4)

J. B. Khurgin, “Band gap engineering for laser cooling of semiconductors,” J. Appl. Phys. 100, 113116 (2006).
[Crossref]

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

S. Gigan, H. Böhm, M. Paternostro, F. Blaser, G. Langer, J. Hertzberg, K. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67–70 (2006).
[Crossref]

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

2004 (1)

M. Sheik-Bahae and R. I. Epstein, “Can laser light cool semiconductors?” Phys. Rev. Lett. 92, 247403 (2004).
[Crossref]

2002 (1)

S. Gaponenko, “Effects of photon density of states on Raman scattering in mesoscopic structures,” Phys. Rev. B 65, 140303 (2002).
[Crossref]

2001 (2)

Y. A. Vlasov, X.-Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414, 289–293 (2001).
[Crossref]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[Crossref]

2000 (3)

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405, 437–440 (2000).
[Crossref]

M. Campbell, D. Sharp, M. Harrison, R. Denning, and A. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53–56 (2000).
[Crossref]

A. G. Aberle, “Surface passivation of crystalline silicon solar cells: a review,” Prog. Photovoltaics 8, 473–487 (2000).
[Crossref]

1995 (3)

M. A. Green and M. J. Keevers, “Optical properties of intrinsic silicon at 300  K,” Prog. Photovoltaics 3, 189–192 (1995).
[Crossref]

M. Keevers and M. Green, “Absorption edge of silicon from solar cell spectral response measurements,” Appl. Phys. Lett. 66, 174–176 (1995).
[Crossref]

R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnell, and C. E. Mungan, “Observation of laser-induced fluorescent cooling of a solid,” Nature 377, 500–503 (1995).
[Crossref]

1994 (2)

K. M. Ho, C. Chan, C. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413–416 (1994).
[Crossref]

H. Sözüer and J. P. Dowling, “Photonic band calculations for woodpile structures,” J. Mod. Opt. 41, 231–239 (1994).
[Crossref]

1992 (1)

C. A. Klein, T. M. Hartnett, and C. J. Robinson, “Critical-point phonon frequencies of diamond,” Phys. Rev. B 45, 12854–12863 (1992).
[Crossref]

1991 (1)

E. Yablonovitch, T. Gmitter, and K. Leung, “Photonic band structure: the face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67, 2295–2298 (1991).
[Crossref]

1990 (1)

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

1989 (1)

D. Fenner, D. Biegelsen, and R. Bringans, “Silicon surface passivation by hydrogen termination: a comparative study of preparation methods,” J. Appl. Phys. 66, 419–424 (1989).
[Crossref]

1983 (1)

J. Wagner and M. Cardona, “Absolute efficiency and dispersion of Raman scattering by phonons in silicon,” Solid State Commun. 48, 301–303 (1983).
[Crossref]

1981 (1)

P. Schmid, “Optical absorption in heavily doped silicon,” Phys. Rev. B 23, 5531–5536 (1981).
[Crossref]

1978 (1)

D. K. Schroder, N. R. Thomas, and J. C. Swartz, “Free carrier absorption in silicon,” IEEE J. Solid-State Circuits 13, 180–187 (1978).
[Crossref]

1970 (1)

T. Hart, R. Aggarwal, and B. Lax, “Temperature dependence of Raman scattering in silicon,” Phys. Rev. B 1, 638–642 (1970).
[Crossref]

1967 (1)

J. Parker, D. Feldman, and M. Ashkin, “Raman scattering by silicon and germanium,” Phys. Rev. 155, 712–714 (1967).
[Crossref]

1964 (1)

R. Loudon, “The Raman effect in crystals,” Adv. Phys. 13, 423–482 (1964).
[Crossref]

1963 (1)

J. Waugh and G. Dolling, “Crystal dynamics of gallium arsenide,” Phys. Rev. 132, 2410–2412 (1963).
[Crossref]

1946 (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 37–38 (1946).
[Crossref]

1929 (1)

P. Pringsheim, “Zwei bemerkungen über den unterschied von lumineszenz-und temperaturstrahlung,” Z. Phys. 57, 739–746 (1929).
[Crossref]

Aberle, A. G.

A. G. Aberle, “Surface passivation of crystalline silicon solar cells: a review,” Prog. Photovoltaics 8, 473–487 (2000).
[Crossref]

Aggarwal, R.

R. Aggarwal, L. Farrar, S. Saikin, A. Aspuru-Guzik, M. Stopa, and D. Polla, “Measurement of the absolute Raman cross section of the optical phonon in silicon,” Solid State Commun. 151, 553–556 (2011).
[Crossref]

T. Hart, R. Aggarwal, and B. Lax, “Temperature dependence of Raman scattering in silicon,” Phys. Rev. B 1, 638–642 (1970).
[Crossref]

Arcizet, O.

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

Ashcroft, N.

N. Ashcroft and N. Mermin, Solid State Physics (Saunders College, 1976), Chap. 23.

Ashkin, M.

J. Parker, D. Feldman, and M. Ashkin, “Raman scattering by silicon and germanium,” Phys. Rev. 155, 712–714 (1967).
[Crossref]

Asmerom, Y.

Aspelmeyer, M.

S. Gigan, H. Böhm, M. Paternostro, F. Blaser, G. Langer, J. Hertzberg, K. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67–70 (2006).
[Crossref]

Aspuru-Guzik, A.

R. Aggarwal, L. Farrar, S. Saikin, A. Aspuru-Guzik, M. Stopa, and D. Polla, “Measurement of the absolute Raman cross section of the optical phonon in silicon,” Solid State Commun. 151, 553–556 (2011).
[Crossref]

Bahl, G.

G. Bahl, M. Tomes, F. Marquardt, and T. Carmon, “Observation of spontaneous Brillouin cooling,” Nat. Phys. 8, 203–207 (2012).
[Crossref]

Bassett, K. P.

E. C. Nelson, N. L. Dias, K. P. Bassett, S. N. Dunham, V. Verma, M. Miyake, P. Wiltzius, J. A. Rogers, J. J. Coleman, X. Li, and P. V. Braun, “Epitaxial growth of three-dimensionally architectured optoelectronic devices,” Nat. Mater. 10, 676–681 (2011).
[Crossref]

Bäuerle, D.

S. Gigan, H. Böhm, M. Paternostro, F. Blaser, G. Langer, J. Hertzberg, K. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67–70 (2006).
[Crossref]

Biegelsen, D.

D. Fenner, D. Biegelsen, and R. Bringans, “Silicon surface passivation by hydrogen termination: a comparative study of preparation methods,” J. Appl. Phys. 66, 419–424 (1989).
[Crossref]

Bigotta, S.

D. V. Seletskiy, S. D. Melgaard, S. Bigotta, A. Di Lieto, M. Tonelli, and M. Sheik-Bahae, “Laser cooling of solids to cryogenic temperatures,” Nat. Photonics 4, 161–164 (2010).
[Crossref]

Biswas, R.

K. M. Ho, C. Chan, C. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413–416 (1994).
[Crossref]

Blanco, A.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405, 437–440 (2000).
[Crossref]

Blaser, F.

S. Gigan, H. Böhm, M. Paternostro, F. Blaser, G. Langer, J. Hertzberg, K. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67–70 (2006).
[Crossref]

Bo, X.-Z.

Y. A. Vlasov, X.-Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414, 289–293 (2001).
[Crossref]

Böhm, H.

S. Gigan, H. Böhm, M. Paternostro, F. Blaser, G. Langer, J. Hertzberg, K. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67–70 (2006).
[Crossref]

Boucaud, P.

Bouwmeester, D.

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

Braun, P.

Y. Chen, J. Geddes Iii, J. Lee, P. Braun, and P. Wiltzius, “Holographically fabricated photonic crystals with large reflectance,” Appl. Phys. Lett. 91, 241103 (2007).
[Crossref]

Braun, P. V.

E. C. Nelson, N. L. Dias, K. P. Bassett, S. N. Dunham, V. Verma, M. Miyake, P. Wiltzius, J. A. Rogers, J. J. Coleman, X. Li, and P. V. Braun, “Epitaxial growth of three-dimensionally architectured optoelectronic devices,” Nat. Mater. 10, 676–681 (2011).
[Crossref]

Briant, T.

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

Bringans, R.

D. Fenner, D. Biegelsen, and R. Bringans, “Silicon surface passivation by hydrogen termination: a comparative study of preparation methods,” J. Appl. Phys. 66, 419–424 (1989).
[Crossref]

Buchwald, M. I.

R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnell, and C. E. Mungan, “Observation of laser-induced fluorescent cooling of a solid,” Nature 377, 500–503 (1995).
[Crossref]

Campbell, M.

M. Campbell, D. Sharp, M. Harrison, R. Denning, and A. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53–56 (2000).
[Crossref]

Cardona, M.

J. Wagner and M. Cardona, “Absolute efficiency and dispersion of Raman scattering by phonons in silicon,” Solid State Commun. 48, 301–303 (1983).
[Crossref]

P. Y. Yu and M. Cardona, Fundamentals of Semiconductors (Springer, 1996), Chap. 7.

Carmon, T.

G. Bahl, M. Tomes, F. Marquardt, and T. Carmon, “Observation of spontaneous Brillouin cooling,” Nat. Phys. 8, 203–207 (2012).
[Crossref]

Chan, C.

K. M. Ho, C. Chan, C. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413–416 (1994).
[Crossref]

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

Checoury, X.

Chen, R.

J. Zhang, D. Li, R. Chen, and Q. Xiong, “Laser cooling of a semiconductor by 40 kelvin,” Nature 493, 504–508 (2013).
[Crossref]

Chen, Y.

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Figures (4)

Fig. 1.
Fig. 1.

Concept of DoS engineering for Raman cooling of an arbitrary number of phonon modes. (a) Stokes scattering (red) dominates anti-Stokes scattering (blue) from any chosen phonon mode ω0,i in bulk media. (b) It is proposed that an engineered photonic DoS with a complete band gap can be used to (c) suppress Stokes scattering while simultaneously enhancing anti-Stokes scattering intensity, as demonstrated previously with Brillouin cooling [13].

Fig. 2.
Fig. 2.

Band structure and DoS of a diamond-structure photonic crystal consisting of air spheres in silicon. The refractive index of silicon is n=3.44 in the calculation; the radii of the air spheres are r=0.3a, where a is the lattice constant of the photonic crystal. The yellow-shaded region denotes the range of the photonic band gap. The frequency (ωa/2πc) is in nondimensional units.

Fig. 3.
Fig. 3.

Cooling all Raman-active phonons in silicon. (a) Raman efficiencies per unit length SAS and SS (in intrinsic crystalline silicon patterned with the Fig. 2 diamond photonic crystal) as functions of pump frequency. The contributions from all three Raman-active phonon modes are included. The yellow-shaded region denotes the band gap for the pump. Band-edge absorption, not included, will become significant at pump frequencies higher than 260 THz (approximately the band gap energy). (b) Calculated cooling and heating efficiency per unit length. The Stokes process is suppressed over a wide range, resulting in net phonon energy removal and the simultaneous cooling of all Raman-active phonons.

Fig. 4.
Fig. 4.

Net Raman cooling is achievable in silicon: the net cooling efficiency per unit length (ω0ωASSASω0ωSSS) can exceed the absorption coefficient for the design presented. The absorption coefficient for silicon is extracted from [27,28]. Near 210 THz (1427 nm), the net cooling overcomes the absorption.

Equations (18)

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W(ωi,ω)=2π22ωiωNi14πD(ω)|M|2,
D3(ω)=ω22π2c3,
SΩWωNiωiD(ω).
(SΩ)Stokes=(ωSc)4NMω0(1+n0)|RS(Ω)|2,
(SΩ)Anti-Stokes=(ωASc)4NMω0n0|RAS(Ω)|2,
SS=(ωSc)4NMω0(1+n0)Ω|RS(Ω)|2dΩ,
SAS=(ωASc)4NMω0n0Ω|RAS(Ω)|2dΩ.
SS=(ωSc)4NMω0(1+n0)ΩD(ωS,Ω)D3(ωS)/4π|RS(Ω)|2dΩ
SAS=(ωASc)4NMω0n0ΩD(ωAS,Ω)D3(ωAS)/4π|RAS(Ω)|2dΩ,
Pnet=Pabs+Pph,SPph,AS,
Pph,S=ω0PSωS=A·L·ω0ωSSSIpump,
Pph,AS=ω0PASωAS=A·L·ω0ωASSASIpump.
Pnet=A·L·Ipump(α+ω0ωSSSω0ωASSAS)<0,
α<ω0ωASSASω0ωSSS.
α<all modes(ω0ωASSASω0ωSSS).
Rx^=(00000d0d0),Ry^=(00d000d00),Rz^=(0d0d00000),
|R|2=|e^i·Rξ^·e^s|2,
D(ω)=iFBZdk⃗(2π)3δ(ωωi(k⃗)),

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