Abstract

Metal-clad subwavelength lasers have recently become excellent candidates for light sources in densely packed chip-scale photonic circuits. In this review, we summarize recent research efforts in the theory, design, fabrication, and characterization of such lasers. We detail advancements of both the metallo-dielectric and the coaxial type lasers: for the metallo-dielectric type, we discuss operation with both optical pumping and electrical pumping. For the coaxial type, we discuss operation with all spontaneous emission coupled into the lasing mode, as well as the smallest metal-clad lasers to date operating at room temperature. A formal treatment of the Purcell effect, the modification of the spontaneous emission rate by a subwavelength cavity, is then presented to assist in better understanding the quantum effects in these nanoscale semiconductor lasers. This formalism is developed for the transparent medium condition, using the emitter-field-reservoir model in the quantum theory of damping. We show its utility through the analysis and design of subwavelength lasers. Finally, we discuss future research directions toward high-efficiency nanolasers and potential applications, such as creating planar arrays of uncoupled lasers with emitter densities near the resolution limit.

© 2014 Optical Society of America

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2014

J. S. Smalley, Q. Gu, and Y. Fainman, “Temperature dependence of the spontaneous emission factor in subwavelength semiconductor lasers,” IEEE J. Quantum Electron. 50, 175–185 (2014).

2013

C. Sauvan, J. Hugonin, I. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013).
[CrossRef]

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8, 506–511 (2013).
[CrossRef]

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493, 195–199 (2013).
[CrossRef]

P. Bhattacharya, B. Xiao, A. Das, S. Bhowmick, and J. Heo, “Solid state electrically injected exciton-polariton laser,” Phys. Rev. Lett. 110, 206403 (2013).
[CrossRef]

C. Ning, “What is Laser Threshold?” IEEE J. Sel. Top. Quantum Electron. 19, 1503604 (2013).
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C. Chen, C. Chiu, S. Chang, M. Shih, M. Kuo, J. Huang, H. Kuo, S. Chen, L. Lee, and M. Jeng, “Large-area ultraviolet GaN-based photonic quasicrystal laser with high-efficiency green color emission of semipolar {10-11} In 0.3  Ga 0.7  N/GaN multiple quantum wells,” Appl. Phys. Lett. 102, 011134 (2013).
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W. Zhou and Z. Ma, “Breakthroughs in nanomembranes and nanomembrane lasers,” IEEE Photonics J. 5, 700707 (2013).
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O. Bondarenko, Q. Gu, J. Shane, A. Simic, B. Slutsky, and Y. Fainman, “Wafer bonded distributed feedback laser with sidewall modulated Bragg gratings,” Appl. Phys. Lett. 103, 043105 (2013).
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K. Ding, M. Hill, Z. Liu, L. Yin, P. van Veldhoven, and C. Ning, “Record performance of electrical injection sub-wavelength metallic-cavity semiconductor lasers at room temperature,” Opt. Express 21, 4728–4733 (2013).
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Z. Wang, B. Tian, and D. van Thourhout, “Design of a novel micro-laser formed by monolithic integration of a III-V pillar with a silicon photonic crystal cavity,” J. Lightwave Technol. 31, 1475–1481 (2013).
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Q. Gu, B. Slutsky, F. Vallini, J. S. Smalley, M. P. Nezhad, N. C. Frateschi, and Y. Fainman, “Purcell effect in sub-wavelength semiconductor lasers,” Opt. Express 21, 15603–15617 (2013).
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2012

C. A. Ni and S. L. Chuang, “Theory of high-speed nanolasers and nanoLEDs,” Opt. Express 20, 16450–16470 (2012).
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J. Y. Suh, C. H. Kim, W. Zhou, M. D. Huntington, D. T. Co, M. R. Wasielewski, and T. W. Odom, “Plasmonic bowtie nanolaser arrays,” Nano Lett. 12, 5769–5774 (2012).
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A. A. High, J. R. Leonard, A. T. Hammack, M. M. Fogler, L. V. Butov, A. V. Kavokin, K. L. Campman, and A. C. Gossard, “Spontaneous coherence in a cold exciton gas,” Nature 483, 584–588 (2012).
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A. A. Saleh and J. A. Dionne, “Waveguides with a silver lining: low threshold gain and giant modal gain in active cylindrical and coaxial plasmonic devices,” Phys. Rev. B 85, 045407 (2012).
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2011

S. Strauf and F. Jahnke, “Single quantum dot nanolaser,” Laser Photonics Rev. 5, 607–633 (2011).

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H. Abe, M. Narimatsu, S. Kita, A. Tomitaka, Y. Takemura, and T. Baba, “Live cell imaging using photonic crystal nanolaser array,” Micro-TAS 593, 2011 (2011).

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J. H. Lee, M. Khajavikhan, A. Simic, Q. Gu, O. Bondarenko, B. Slutsky, M. P. Nezhad, and Y. Fainman, “Electrically pumped sub-wavelength metallo-dielectric pedestal pillar lasers,” Opt. Express 19, 21524–21531 (2011).
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2010

2009

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2008

2007

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M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, and T. J. Eijkemans, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1, 589–594 (2007).
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2006

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, “Optical coupling of whispering-gallery modes of two identical microdisks and its effect on photonic molecule lasing,” IEEE J. Sel. Top. Quantum Electron. 12, 78–85 (2006).
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S. Noda, “Seeking the ultimate nanolaser,” Science 314, 260–261 (2006).
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G. Khitrova, H. Gibbs, M. Kira, S. Koch, and A. Scherer, “Vacuum Rabi splitting in semiconductors,” Nat. Phys. 2, 81–90 (2006).
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2005

2004

M. P. Nezhad, K. Tetz, and Y. Fainman, “Gain assisted propagation of surface plasmon polaritons on planar metallic waveguides,” Opt. Express 12, 4072–4079 (2004).
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T. Baba, D. Sano, K. Nozaki, K. Inoshita, Y. Kuroki, and F. Koyama, “Observation of fast spontaneous emission decay in GaInAsP photonic crystal point defect nanocavity at room temperature,” Appl. Phys. Lett. 85, 3989–3991 (2004).
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2003

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K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
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T. Baba and D. Sano, “Low-threshold lasing and Purcell effect in microdisk lasers at room temperature,” IEEE J. Sel. Top. Quantum Electron. 9, 1340–1346 (2003).
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2002

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2001

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1999

L. M. Pedrotti, M. Sokol, and P. R. Rice, “Linewidth of four-level microcavity lasers,” Phys. Rev. A 59, 2295–2301 (1999).
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1998

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1997

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1994

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1992

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1990

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1989

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1988

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1987

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1985

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1982

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1978

1972

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1958

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1946

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S. Sweeney, A. Phillips, A. Adams, E. O’Reilly, and P. Thijs, “The effect of temperature dependent processes on the performance of 1.5-μm compressively strained InGaAs (P) MQW semiconductor diode lasers,” IEEE Photonics Technol. Lett. 10, 1076–1078 (1998).
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H. Abe, M. Narimatsu, S. Kita, A. Tomitaka, Y. Takemura, and T. Baba, “Live cell imaging using photonic crystal nanolaser array,” Micro-TAS 593, 2011 (2011).

T. Baba, D. Sano, K. Nozaki, K. Inoshita, Y. Kuroki, and F. Koyama, “Observation of fast spontaneous emission decay in GaInAsP photonic crystal point defect nanocavity at room temperature,” Appl. Phys. Lett. 85, 3989–3991 (2004).
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M. Glauser, G. Rossbach, G. Cosendey, J. Levrat, M. Cobet, J. Carlin, J. Besbas, M. Gallart, P. Gilliot, and R. Butté, “Investigation of InGaN/GaN quantum wells for polariton laser diodes,” Phys. Stat. Solidi C 9, 1325–1329 (2012).
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G. Bjork, A. Karlsson, and Y. Yamamoto, “On the linewidth of microcavity lasers,” Appl. Phys. Lett. 60, 304–306 (1992).
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Figures (23)

Figure 1
Figure 1

The M=4 whispering gallery resonance for a thick semiconductor disk (a) is shown in (b). (rc=460nm, hc=480nm, nsemi=3.4). Note the spatial spread of the mode compared to the actual disk size. (c) The same disk encased in an optically thick (dm=100nm) gold shield will have well-confined (d) reflective and (e) surface plasmon polariton modes but with much higher mode losses. |E| is shown in all cases, and the section plane is horizontal and through the middle of the cylinder. (Reprinted from [33].)

Figure 2
Figure 2

(a) Cross section of the metal-coated composite gain waveguide. (b) Cylindrical closed 3D resonator. (c) Cylindrical open 3D resonator. (Reprinted from [37].)

Figure 3
Figure 3

(a) Threshold gain εg as a function of the shield thickness Δ for the TE01 mode with Rout=460nm. (b) Minimal threshold gain as a function of Rout. The vertical lines show the cutoff of each mode in the 3D resonator plug region. (Reprinted from [37].)

Figure 4
Figure 4

Cross section of a closed cylindrical 3D subwavelength laser resonator. The electric field intensity |E|2 normalized to its maximal value of the TE012 mode is shown. The inset shows a similar open structure. (Reprinted from [37].)

Figure 5
Figure 5

(a) Schematic view of a practical realization of the laser cavity, compatible with planar fabrication techniques. The air gap at the bottom of the laser is formed after selective etch of the InP substrate. In the designed cavity the values for h1, h2, and h3 are 200, 550, and 250 nm, respectively. (b) Cross sections of |E| for the TE012 mode of the cavity. (Reprinted from [33].)

Figure 6
Figure 6

Various stages of the fabrication process: (a) array of e-beam patterned HSQ resist dots. (b) RIE etched pillar after oxygen plasma and BOE cleaning. The faint bump in the middle indicates the boundary between the InGaAsP and InP layers. (c) Etched pillar after PECVD of silica. The outline of the semiconductor pillar can be seen through the silica layer. (d) Silica covered pillar after undergoing aluminum sputtering (70 nm). (e) Tilted bottom view of one of the samples after selective InP etch with HCL. The surface is composed of the PECVD deposited silica. (f) Contrast-enhanced normal bottom view of a cavity. The circular outline around the air hole is due to the dielectric shield and agrees well with the target dielectric-shield thickness of 200 nm. (Reprinted from [33].)

Figure 7
Figure 7

(a) Light–light curve for a nanolaser with major and minor core diameters of 490 and 420 nm (blue dotted curve). The same data set is shown as a log–log plot (red dotted inset) together with the slopes for the PL, ASE, and lasing regions. Also shown are the images of the defocused emitted beam cross section (taken at about 10 μm away from the nanolaser exit aperture) for (I) CW pumping and (II) pulsed pumping. The appearance of the higher contrast fringes indicates increased coherence due to lasing. (b) Evolution of the emission spectra from PL to lasing. (c) Effective refractive indices (green data points) of the pumped MQW gain medium at lasing wavelengths, back-calculated from lasing spectra obtained from an array of nanolasers. Error bars were calculated assuming ±5nm error in measuring the disk diameters from the scanning electron microscopes. The dashed red curve shows the effective refractive index of the unpumped MQW layer, as measured by a Filmetrics interferometric analyzer. The blue curve is offset down from the red by a constant amount (0.102 RIU), which was chosen for best fit to the lasing data. The index reduction is consistent with the estimated free carrier effects. (Reprinted from [33].)

Figure 8
Figure 8

(a) Lasing mode’s electric field profile, and the three spectra in the evaluation of the Purcell factor: (b) cavity lineshape, (c) homogeneous broadening lineshape, and (d) PL spectra. Dashed red, measured at low pump powers; solid blue, datasheet provided by OEpic Inc. (Reprinted from [41].)

Figure 9
Figure 9

Simulated mode distribution of all modes that fall within the spectral window of PL and have cavity Q>20. Also shown are Purcell factors for each mode, Fcav, calculated using two different sources of PL spectra. (Reprinted from [41].)

Figure 10
Figure 10

(a) Transparent wavelength versus carrier density and (b) spontaneous emission factor versus temperature for a 10 nm MQW-InGaAsP-metal-clad nanolaser similar to that of Section 2, but with 250 and 350 nm core and total radii, respectively. The cases of positive and effectively negative thermo-optic coefficients are denoted by dnr/dT>0 and dnr/dT<0, respectively. (Reprinted from [75].)

Figure 11
Figure 11

Nanoscale coaxial laser cavity. (a) Schematic of a coaxial laser cavity. (b), (c) SEM micrographs of the constituent rings in structure A and structure B, respectively. The side view of the rings comprising the coaxial structures is seen. The rings consist of SiO2 on top, and a quantum well gain region underneath. (Reprinted from [13].)

Figure 12
Figure 12

Electromagnetic simulation of nanoscale coaxial cavities. (a) Modal spectrum of the cavity of structure A at a temperature of 4.5 K. This cavity supports a pair of HE11 degenerate modes and the fundamental TEM-like mode in the gain bandwidth. (b) Modal spectrum of the cavity of structure B. This cavity supports only the fundamental TEM-like mode in the gain bandwidth of the quantum wells. In the figures, Q is the quality factor of the mode, Γ is the energy confinement factor to the semiconductor region, and Vmode is the effective modal volume. The color bar shows normalized |E|2. Nominal permittivity values are used in this simulation. (Reprinted from [13].)

Figure 13
Figure 13

Cross section of the cavity, based on structure B, with an inner core radius of Rcore=100nm at a temperature of 4.5 K. On the left side, the refractive index map is shown; on the right side, the TEM-like mode is depicted. The table gives the central wavelength of the mode, the Q factor of the mode, and the mode confinement factor to the wells (In0.56Ga0.44As0.94P0.06 layers), for different values of silver permittivity. The real part of the silver permittivity is 126 in all cases. (Reprinted from [13].)

Figure 14
Figure 14

Optical characterization of high-β-factor nanoscale coaxial cavities, light–light curve, linewidth versus pump power, and spectral evolution diagram for lasers with threshold. Lasing in structure A. (a) Light–light curve. (b) Spectral evolution. (c) Linewidth evolution at room temperature. The pump power is calculated as the fraction of power incident on the laser aperture. The solid curves in (a) are the best fit of the rate-equation model. The resolution of the monochromator was set to 3.3 nm. (Reprinted from [13].)

Figure 15
Figure 15

Optical characterization of unity β-factor nanoscale coaxial cavities, light–light curve, linewidth versus pump power, and spectral evolution diagram for unity β-factor lasing in structure B. (a) Light–light curve. (b) Spectral evolution. (c) Linewidth evolution at 4.5 K. The pump power is calculated as the fraction of the power incident on the laser aperture. The solid curve in (a) is the best fit of the rate-equation model. The resolution of the monochromator was set to 1.6 nm. (Reprinted from [13].)

Figure 16
Figure 16

Measured data (red dots) and simulation curves for structure B, with an inner core radius of Rcore=100nm, and a gain medium ring with a thickness of Δ=100nm at a temperature of 4.5 K. β-factors are β=1 for the black top curve (ideal unity β-factor laser), β=0.95 for the blue middle curve (best fit to data), and β=0.86 for the green bottom curve. (Reprinted from [13].)

Figure 17
Figure 17

(a) Transverse cross section of the insulated coaxial waveguide for electrical pumping. The different regions are characterized by their electrical permittivities, εM, εD, and εG, for the metal cladding, dielectric insulator, and gain (semiconductor) annulus, respectively. The four parameters that determine the geometry are a1, a2, a3, and a4. (b) Longitudinal cross section of same waveguide, with the inner and outer insulating layer widths defined as Δi=a2a1 and Δo=a4a3, respectively.

Figure 18
Figure 18

Threshold gain as an explicit function of a2 and a3, and implicitly of the inner and outer insulating layer (shield) widths. Both shield widths are varied from 0 to 23 nm, while a1 and a4 are fixed at 100 and 200 nm, respectively. The blue and red ends of the color spectrum correspond to minimal and maximal threshold gains, respectively. The inset boxes list the minimum and maximum threshold gains for this parameter space as εgth=0.410 (gth=4890cm1) and εgth=1.835 (gth=21,980cm1), respectively, and the level step of the contours is 0.2.

Figure 19
Figure 19

(a) Contour plot, |E(x,y)|, of the TEM-like mode for the coaxial waveguide without insulating layers, where a1=100nm and a4=200nm. (b) Contour plot of the same mode for the insulated coaxial waveguide, where a1, a2, a3, and a4, are 100, 110, 190, and 200 nm, respectively. The threshold gain of the latter is εgth=0.811 (gth=9770cm1), while that of the former is εgth=0.410 (gth=4890cm2). (c) Cross-sectional plot, |E(x)|, of the same mode corresponding to the uninsulated waveguide, and (d) insulated waveguide.

Figure 20
Figure 20

(a) Schematic of the subwavelength pedestal pillar laser where rcore is the radius of the InGaAs gain layer, and rclad is the radius of the InP cladding. Δr is the difference between rcore and rclad. dshield is the thickness of the SiO2 shield layer, and hcore is the height of the InGaAs gain medium. (b) Horizontal cross section of the electric field intensity when rcore is 750 nm, rclad is 690 nm (Δr=60nm), and dshield is 150 nm with silver coating. (Reprinted from [34].)

Figure 21
Figure 21

Numerical simulation results of the cavity Q factor and threshold gain for various pedestal sizes. Δr (rcorerclad) is the pedestal undercut depth. (a) rcore=750nm, dshield=150nm, and rclad is varied from 750 to 600 nm (Δr=0150nm). The blue curve represents the cavity Q and the red curve represents the threshold gain. (b) rcore=220nm, dshield=150nm, and rclad is varied from 220 to 70 nm (Δr=0150nm). (c) Vertical cross section of the resonant mode field (TE011) intensity when rcore, rclad=220nm (Δr=0nm, cylinder type), and dshield=150nm. (d) Resonant mode field (TE011) intensity when rcore=220nm, rclad=100nm (Δr=120nm, pedestal type), and dshield=150nm. (Reprinted from [34].)

Figure 22
Figure 22

SEM micrographs of subwavelength pillar laser structure during fabrication procedure. (a) Pillar (rcore=395nm) structure after dry etching. (b) Pedestal pillar is formed by selective InP wet etching. (c) Thin SiO2 layer (150 nm) is deposited on the pillar structure by PECVD. (d) N-contact metal (Ti/Pd/Au) layer deposited on the top of the pillar. (e) Silver is deposited on whole pillar structure. Scale bar in each image represents 500 nm. (Reprinted from [34].)

Figure 23
Figure 23

Lasing characteristics of rcore=750nm pedestal subwavelength pillar laser device. (a) SEM micrograph of rcore=750nm pedestal pillar structure. (b) Spectral evolution graphs with increasing injection currents. (c) LI curve of this device. (d) Linewidth measurement by a monochromator with 0.35 nm resolution. (e) Lasing spectrum measured at 140 K. Inset shows LI curve at 140 K. (Reprinted from [34].)

Tables (1)

Tables Icon

Table 1. Evaluation of the Purcell Factor Fcav(TE012) Using Different Methods (Reprinted from [41])

Equations (25)

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Fpτbulkτcav=[34π2QVa(λn)3][|d·f(re)|2|d|2][Δωc24(ωeωc)2+Δωc2],
Fp=[34π2QVa(λn)3].
H^=H^A+H^F+H^AF+H^R+H^FR,
P21,|00materialω2133πεr(c/nr)3τcoll|P12(ω21)|2D(ω21)dω21ω¯2133πεr(c/nr)3τcoll|P12(ω¯21)|2,
P21,equilibriumcav=kωk(n¯(ωk)+1)|P12(ω21)·ek(re)|2D(ω21)Lk(ωωk)R(ωω21,τcoll)dωdω21,
Lk(ωωk)1π12Ck(12Ck)2+(ωωk)2=2π·Qωk(12Δωk)2(12Δωk)2+(ωωk)2,whereCk=Δωk,
FcavP21,equilibriumcavP21,|00material=k3πεr(c/nr)3τcollωkω¯2131|P12(ω¯21)|2|P12(ω21)·ek(re)|2D(ω21)Lk(ωωk)R(ωω21,τcoll)dωdω21k3πεr(c/nr)3τcollωkω¯213|P12(ω¯21)·ek(re)|2|P12(ω¯21)|2D(ω21)Lk(ωωk)R(ωω21,τcoll)dωdω21.
|P12(ω¯21)·ek(re)|213|P12(ω¯21)|21VaVa|ek(r)|2d3r,
Fp=kπ(c/nr)3τcollωkω¯2131Va{εrVa|Ek(r)|2d3r[((ωεR(r,ω))ω|ω=ωk+εR(r,ωk))Ek2(r)]d3r}×D(ω21)Lk(ωωk)R(ωω21,τcoll)dωdω21=kπ(c/nr)3τcollωkω¯2131Va{Γk}D(ω21)Lk(ωωk)R(ωω21,τcoll)dωdω21=kFcav(k),
β=Fcav(1)kFcav(k),
Fcav(k)(T)=π(c/nr)3τcollωk(T)ω¯213ΓkVaZSP(ω21,T)L(ωωk,T)R(ωω21,τcoll,T)dωdω21.
βmax(T)=Fcavlasing(T)kFcav(k)(T).
dSidt=(Γig(n,ω)L(ωωi)dωωiQi)Si+Γie(n,ω)L(ωωi)dωdNdt=αp(n,ωp)Pi(Γig(n,ω)L(ωωi)dω)SiiΓie(n,ω)L(ωωi)dωNτrNτnr.
τr1=1Fpn2ω2π2c2e(n,ω)dω,
E^(r,t)=k,εωk2ε0L3i(a^k,ε(t)eik·ra^k,ε(t)eik·r)ε.
a^k,ε(t)=a^k,ε(0)·eiωkt;a^k,ε(t)=a^k,ε(0)·eiωkt,
E^(r,t)=E^+(r,t)+E^(r,t),E^+(r,t)=k,εωk2ε0L3ia^k,ε(t)eik·rε,E^(r,t)=(E^+(r,t))=k,εωk2ε0L3ia^k,ε(t)eik·rε.
E^u(r,t)=E^u+(r,t)+E^u(r,t)=ωk>0iωk(a^k(t)a^k(t))·ek(r),
ek(r)=Ek(r)Nk,NkV[ε(r)Ek2(r)+μ(r)Hk2(r)]d3r,
Nk=V[(ωεR(r,ω))ω|ω=ωkEk2(r)+μ(r)Hk2(r)]d3r=V[((ωεR(r,ω))ω|ω=ωk+εR(r,ωk))Ek2(r)]d3r,
ddt[a^k(t)a^k(t+τ)]R=Ck[a^k(t)a^k(t+τ)]R+Ckn¯(ωk)e12Ck|τ|eiωkτ,ddt[a^k(t)a^k(t+τ)]R=Ck[a^k(t)a^k(t+τ)]R+Ck(n¯(ωk)+1)e12Ck|τ|eiωkτ,
[a^k(t)a^k(t+τ)]R=n¯(ωk)e12Ck|τ|eiωkτ,[a^k(t)a^k(t+τ)]R=(n¯(ωk)+1)e12Ck|τ|eiωkτ.
P21,i(t)=12t0t0+τcollt0t0+τcolleiω21(tt)i|(P12*(ω21)·E^+(r,t))·(P12(ω21)·E^(r,t))|iD(ω21)dω21dtdt,
P21,|00free=12t0t0+τcollt0t0+τcolleiω21(tt)00|(P12*(ω21)·k,εωk2ε0L3εa^k,ε(t)eik·re)×(P12(ω21)·k,εωk2ε0L3εa^k,ε(t)eik·re)|00D(ω21)dω21dtdt=k,εωk2ε0L3|P12(ω21)·ε|2D(ω21)R(ωkω21,τcoll)dω21ω2133πε0c3τcoll|P12(ω21)|2D(ω21)dω21.
P21,|00cav=kωk|P12(ω21)·ek(re)|2D(ω21)R(ωkω21,τcoll)dω21.

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