Abstract

We develop a hybrid optofluidic microcavity by placing a microsphere with a diameter ranging from 1 to 4 μm in liquid-filled plano-plano Fabry–Perot (FP) cavities, which can provide an extremely low effective mode volume down to 0.35.1  μm3 while maintaining a high Q-factor up to 1×1045×104 and a finesse of 2000. Compared to the pure plano-plano FP cavities that are known to suffer from the lack of mode confinement, diffraction, and geometrical walk-off losses as well as being highly susceptible to mirror misalignment, our microsphere-integrated FP (MIFP) cavities show strong optical confinement in the lateral direction with a tight mode radius of only 0.4–0.9 μm and high tolerance to mirror misalignment as large as 2°. With the microsphere serving as a waveguide, the MIFP is advantageous over a fiber-sandwiched FP cavity due to the open-cavity design for analytes/liquids to interact strongly with the resonant mode, the ease of assembly, and the possibility to replace the microsphere. In this work, the main characteristics of the MIFP, including Q-factor, finesse, effective mode radius and volume, and their dependence on the surrounding medium’s refractive index, mirror spacing, microsphere position inside the FP cavity, and mirror misalignment, are systematically investigated using a finite-element method. Then, by inserting dye-doped polystyrene microspheres of various sizes into the FP cavity filled with water, we experimentally realize single-mode MIFP optofluidic lasers that have a lasing threshold as low as a few microjoules per square millimeter and a lasing spot radius of only 0.5  μm. Our results suggest that the MIFP cavities provide a promising technology platform for novel photonic devices and biological/chemical detection with ultra-small detection volumes.

© 2018 Chinese Laser Press

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2018 (1)

C.-Y. Gong, Y. Gong, W.-L. Zhang, Y. Wu, Y.-J. Rao, G.-D. Peng, and X. Fan, “Fiber optofluidic microlaser with lateral single mode emission,” IEEE J. Sel. Top. Quantum Electron. 24, 0900206 (2018).
[Crossref]

2017 (4)

Q. Chen, Y. C. Chen, Z. Zhang, B. Wu, R. Coleman, and X. Fan, “An integrated microwell array platform for cell lasing analysis,” Lab Chip 17, 2814–2820 (2017).
[Crossref]

Y. C. Chen, Q. Chen, T. Zhang, W. Wang, and X. Fan, “Versatile tissue lasers based on high-Q Fabry–Perot microcavities,” Lab Chip 17, 538–548 (2017).
[Crossref]

M. Humar, A. Dobravec, X. Zhao, and S. H. Yun, “Biomaterial microlasers implantable in the cornea, skin, and blood,” Optica 4, 1080–1085 (2017).
[Crossref]

F. Abolmaali, A. Brettin, A. Green, N. I. Limberopoulos, A. M. Urbas, and V. N. Astratov, “Photonic jets for highly efficient mid-IR focal plane arrays with large angle-of-view,” Opt. Express 25, 31174–31185 (2017).
[Crossref]

2016 (1)

A. A. Trichet, P. R. Dolan, D. James, G. M. Hughes, C. Vallance, and J. M. Smith, “Nanoparticle trapping and characterization using open microcavities,” Nano Lett. 16, 6172–6177 (2016).
[Crossref]

2015 (3)

W. Wang, C. Zhou, T. Zhang, J. Chen, S. Liu, and X. Fan, “Optofluidic laser array based on stable high-Q Fabry–Perot microcavities,” Lab Chip 15, 3862–3869 (2015).
[Crossref]

M. Humar and S. H. Yun, “Intracellular microlasers,” Nat. Photonics 9, 572–576 (2015).
[Crossref]

M. Humar, M. C. Gather, and S. H. Yun, “Cellular dye lasers: lasing thresholds and sensing in a planar resonator,” Opt. Express 23, 27865–27879 (2015).
[Crossref]

2014 (3)

A. Jonáš, M. Aas, Y. Karadag, S. Manioğlu, S. Anand, D. McGloin, H. Bayraktar, and A. Kiraz, “In vitro and in vivo biolasing of fluorescent proteins suspended in liquid microdroplet cavities,” Lab Chip 14, 3093–3100 (2014).
[Crossref]

X. Fan and S. H. Yun, “The potential of optofluidic biolasers,” Nat. Methods 11, 141–147 (2014).
[Crossref]

K. W. Allen, A. Darafsheh, F. Abolmaali, N. Mojaverian, N. I. Limberopoulos, A. Lupu, and V. N. Astratov, “Microsphere-chain waveguides: focusing and transport properties,” Appl. Phys. Lett. 105, 021112 (2014).
[Crossref]

2013 (2)

Q. Chen, X. Zhang, Y. Sun, M. Ritt, S. Sivaramakrishnan, and X. Fan, “Highly sensitive fluorescent protein FRET detection using optofluidic lasers,” Lab Chip 13, 2679–2681 (2013).
[Crossref]

S. Nizamoglu, M. C. Gather, and S. H. Yun, “All-biomaterial laser using vitamin and biopolymers,” Adv. Mater. 25, 5943–5947 (2013).
[Crossref]

2012 (1)

Y. Sun and X. Fan, “Distinguishing DNA by analog-to-digital-like conversion by using optofluidic lasers,” Angew. Chem. Int. Ed. 51, 1236–1239 (2012).
[Crossref]

2011 (5)

X. Fan and I. M. White, “Optofluidic microsystems for chemical and biological analysis,” Nat. Photonics 5, 591–597 (2011).
[Crossref]

G. Aubry, Q. Kou, J. Soto-Velasco, C. Wang, S. Meance, J. J. He, and A. M. Haghiri-Gosnet, “A multicolor microfluidic droplet dye laser with single mode emission,” Appl. Phys. Lett. 98, 111111 (2011).
[Crossref]

M. C. Gather and S. H. Yun, “Single-cell biological lasers,” Nat. Photonics 5, 406–410 (2011).
[Crossref]

Y. Yang, A. Q. Liu, L. Lei, L. K. Chin, C. D. Ohl, Q. J. Wang, and H. S. Yoon, “A tunable 3D optofluidic waveguide dye laser via two centrifugal Dean flow streams,” Lab Chip 11, 3182–3187 (2011).
[Crossref]

A. Martinez and S. Yamashita, “Multi-gigahertz repetition rate passively modelocked fiber lasers using carbon nanotubes,” Opt. Express 19, 6155–6163 (2011).
[Crossref]

2010 (4)

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

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

D. Hunger, T. Steinmetz, Y. Colombe, C. Deutsch, T. W. Hänsch, and J. Reichel, “A fiber Fabry–Perot cavity with high finesse,” New J. Phys. 12, 065038 (2010).
[Crossref]

Y. Sun, S. I. Shopova, C.-S. Wu, S. Arnold, and X. Fan, “Bioinspired optofluidic FRET lasers via DNA scaffolds,” Proc. Natl. Acad. Sci. USA 107, 16039–16042 (2010).
[Crossref]

2009 (1)

A. Heifetz, S. C. Kong, A. V. Sahakian, A. Taflove, and V. Backman, “Photonic nanojets,” J. Comput. Theor. Nanosci. 6, 1979–1992 (2009).
[Crossref]

2008 (3)

S. Yang and V. N. Astratov, “Photonic nanojet-induced modes in chains of size-disordered microspheres with an attenuation of only 0.08 dB per sphere,” Appl. Phys. Lett. 92, 261111 (2008).
[Crossref]

J. Schafer, J. Mondia, R. Sharma, Z. Lu, A. Susha, A. Rogach, and L. Wang, “Quantum dot microdrop laser,” Nano Lett. 8, 1709–1712 (2008).
[Crossref]

S.-S. Wang, J. Fu, M. Qiu, K.-J. Huang, Z. Ma, and L.-M. Tong, “Modeling endface output patterns of optical micro/nanofibers,” Opt. Express 16, 8887–8895 (2008).
[Crossref]

2007 (2)

2006 (3)

2005 (2)

2004 (2)

S. M. Buck, H. Xu, M. Brasuel, M. A. Philbert, and R. Kopelman, “Nanoscale probes encapsulated by biologically localized embedding (PEBBLEs) for ion sensing and imaging in live cells,” Talanta 63, 41–59 (2004).
[Crossref]

Z. Chen, A. Taflove, and V. Backman, “Photonic nanojet enhancement of backscattering of light by nanoparticles: a potential novel visible-light ultramicroscopy technique,” Opt. Express 12, 1214–1220 (2004).
[Crossref]

2000 (1)

H.-J. Moon, Y.-T. Chough, and K. An, “Cylindrical microcavity laser based on the evanescent-wave-coupled gain,” Phys. Rev. Lett. 85, 3161–3164 (2000).
[Crossref]

1996 (1)

J. M. Gérard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, and T. Rivera, “Quantum boxes as active probes for photonic microstructures: the pillar microcavity case,” Appl. Phys. Lett. 69, 449–451 (1996).
[Crossref]

1974 (1)

J. Arnaud, A. Saleh, and J. Ruscio, “Walk-off effects in Fabry–Perot diplexers,” IEEE Trans. Microw. Theory. Tech. 22, 486–493 (1974).
[Crossref]

1966 (1)

1963 (1)

A. Fox and T. Li, “Modes in a maser interferometer with curved and tilted mirrors,” Proc. IEEE 51, 80–89 (1963).
[Crossref]

1961 (1)

A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Labs Tech. J. 40, 453–488 (1961).
[Crossref]

Aas, M.

A. Jonáš, M. Aas, Y. Karadag, S. Manioğlu, S. Anand, D. McGloin, H. Bayraktar, and A. Kiraz, “In vitro and in vivo biolasing of fluorescent proteins suspended in liquid microdroplet cavities,” Lab Chip 14, 3093–3100 (2014).
[Crossref]

Abolmaali, F.

F. Abolmaali, A. Brettin, A. Green, N. I. Limberopoulos, A. M. Urbas, and V. N. Astratov, “Photonic jets for highly efficient mid-IR focal plane arrays with large angle-of-view,” Opt. Express 25, 31174–31185 (2017).
[Crossref]

K. W. Allen, A. Darafsheh, F. Abolmaali, N. Mojaverian, N. I. Limberopoulos, A. Lupu, and V. N. Astratov, “Microsphere-chain waveguides: focusing and transport properties,” Appl. Phys. Lett. 105, 021112 (2014).
[Crossref]

Allen, K. W.

K. W. Allen, A. Darafsheh, F. Abolmaali, N. Mojaverian, N. I. Limberopoulos, A. Lupu, and V. N. Astratov, “Microsphere-chain waveguides: focusing and transport properties,” Appl. Phys. Lett. 105, 021112 (2014).
[Crossref]

An, K.

H.-J. Moon, Y.-T. Chough, and K. An, “Cylindrical microcavity laser based on the evanescent-wave-coupled gain,” Phys. Rev. Lett. 85, 3161–3164 (2000).
[Crossref]

Anand, S.

A. Jonáš, M. Aas, Y. Karadag, S. Manioğlu, S. Anand, D. McGloin, H. Bayraktar, and A. Kiraz, “In vitro and in vivo biolasing of fluorescent proteins suspended in liquid microdroplet cavities,” Lab Chip 14, 3093–3100 (2014).
[Crossref]

Arnaud, J.

J. Arnaud, A. Saleh, and J. Ruscio, “Walk-off effects in Fabry–Perot diplexers,” IEEE Trans. Microw. Theory. Tech. 22, 486–493 (1974).
[Crossref]

Arnold, S.

Y. Sun, S. I. Shopova, C.-S. Wu, S. Arnold, and X. Fan, “Bioinspired optofluidic FRET lasers via DNA scaffolds,” Proc. Natl. Acad. Sci. USA 107, 16039–16042 (2010).
[Crossref]

Astratov, V.

Astratov, V. N.

F. Abolmaali, A. Brettin, A. Green, N. I. Limberopoulos, A. M. Urbas, and V. N. Astratov, “Photonic jets for highly efficient mid-IR focal plane arrays with large angle-of-view,” Opt. Express 25, 31174–31185 (2017).
[Crossref]

K. W. Allen, A. Darafsheh, F. Abolmaali, N. Mojaverian, N. I. Limberopoulos, A. Lupu, and V. N. Astratov, “Microsphere-chain waveguides: focusing and transport properties,” Appl. Phys. Lett. 105, 021112 (2014).
[Crossref]

S. Yang and V. N. Astratov, “Photonic nanojet-induced modes in chains of size-disordered microspheres with an attenuation of only 0.08 dB per sphere,” Appl. Phys. Lett. 92, 261111 (2008).
[Crossref]

Aubry, G.

G. Aubry, Q. Kou, J. Soto-Velasco, C. Wang, S. Meance, J. J. He, and A. M. Haghiri-Gosnet, “A multicolor microfluidic droplet dye laser with single mode emission,” Appl. Phys. Lett. 98, 111111 (2011).
[Crossref]

Backman, V.

Balslev, S.

Barrier, D.

J. M. Gérard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, and T. Rivera, “Quantum boxes as active probes for photonic microstructures: the pillar microcavity case,” Appl. Phys. Lett. 69, 449–451 (1996).
[Crossref]

Bayraktar, H.

A. Jonáš, M. Aas, Y. Karadag, S. Manioğlu, S. Anand, D. McGloin, H. Bayraktar, and A. Kiraz, “In vitro and in vivo biolasing of fluorescent proteins suspended in liquid microdroplet cavities,” Lab Chip 14, 3093–3100 (2014).
[Crossref]

Borselli, M.

Brasuel, M.

S. M. Buck, H. Xu, M. Brasuel, M. A. Philbert, and R. Kopelman, “Nanoscale probes encapsulated by biologically localized embedding (PEBBLEs) for ion sensing and imaging in live cells,” Talanta 63, 41–59 (2004).
[Crossref]

Brettin, A.

Buck, S. M.

S. M. Buck, H. Xu, M. Brasuel, M. A. Philbert, and R. Kopelman, “Nanoscale probes encapsulated by biologically localized embedding (PEBBLEs) for ion sensing and imaging in live cells,” Talanta 63, 41–59 (2004).
[Crossref]

Chen, J.

W. Wang, C. Zhou, T. Zhang, J. Chen, S. Liu, and X. Fan, “Optofluidic laser array based on stable high-Q Fabry–Perot microcavities,” Lab Chip 15, 3862–3869 (2015).
[Crossref]

Chen, Q.

Q. Chen, Y. C. Chen, Z. Zhang, B. Wu, R. Coleman, and X. Fan, “An integrated microwell array platform for cell lasing analysis,” Lab Chip 17, 2814–2820 (2017).
[Crossref]

Y. C. Chen, Q. Chen, T. Zhang, W. Wang, and X. Fan, “Versatile tissue lasers based on high-Q Fabry–Perot microcavities,” Lab Chip 17, 538–548 (2017).
[Crossref]

Q. Chen, X. Zhang, Y. Sun, M. Ritt, S. Sivaramakrishnan, and X. Fan, “Highly sensitive fluorescent protein FRET detection using optofluidic lasers,” Lab Chip 13, 2679–2681 (2013).
[Crossref]

Chen, Y. C.

Q. Chen, Y. C. Chen, Z. Zhang, B. Wu, R. Coleman, and X. Fan, “An integrated microwell array platform for cell lasing analysis,” Lab Chip 17, 2814–2820 (2017).
[Crossref]

Y. C. Chen, Q. Chen, T. Zhang, W. Wang, and X. Fan, “Versatile tissue lasers based on high-Q Fabry–Perot microcavities,” Lab Chip 17, 538–548 (2017).
[Crossref]

Chen, Z.

Chin, L. K.

Y. Yang, A. Q. Liu, L. Lei, L. K. Chin, C. D. Ohl, Q. J. Wang, and H. S. Yoon, “A tunable 3D optofluidic waveguide dye laser via two centrifugal Dean flow streams,” Lab Chip 11, 3182–3187 (2011).
[Crossref]

Chough, Y.-T.

H.-J. Moon, Y.-T. Chough, and K. An, “Cylindrical microcavity laser based on the evanescent-wave-coupled gain,” Phys. Rev. Lett. 85, 3161–3164 (2000).
[Crossref]

Coleman, R.

Q. Chen, Y. C. Chen, Z. Zhang, B. Wu, R. Coleman, and X. Fan, “An integrated microwell array platform for cell lasing analysis,” Lab Chip 17, 2814–2820 (2017).
[Crossref]

Colombe, Y.

D. Hunger, T. Steinmetz, Y. Colombe, C. Deutsch, T. W. Hänsch, and J. Reichel, “A fiber Fabry–Perot cavity with high finesse,” New J. Phys. 12, 065038 (2010).
[Crossref]

Costard, E.

J. M. Gérard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, and T. Rivera, “Quantum boxes as active probes for photonic microstructures: the pillar microcavity case,” Appl. Phys. Lett. 69, 449–451 (1996).
[Crossref]

Darafsheh, A.

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Y. C. Chen, Q. Chen, T. Zhang, W. Wang, and X. Fan, “Versatile tissue lasers based on high-Q Fabry–Perot microcavities,” Lab Chip 17, 538–548 (2017).
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Figures (10)

Fig. 1.
Fig. 1. Schematic of an MIFP cavity, in which an MS is inserted in an FP cavity filled with liquid.
Fig. 2.
Fig. 2. (a) and (b), (d)–(g) Schematic and representative electrical field distribution of the fundamental resonant mode of (a) and (b) MIFP, (d) and (e) finite PPFP, and (f) and (g) WGM cavities, respectively. d is the diameter of the MSs and also the diameter of the circular mirrors. L is the mirror spacing. For the MIFP cavity, the MS is assumed in the center of the two mirrors. In (b), (e), and (g), the parameters are d = 3    μm , L = 3.06    μm , and n a = 1.33 . The symmetrical axis is set in the 2D-axisymmetric model, indicating the geometry on the right side is assumed to rotate around the axis, rendering a quasi-3D model. PMLs are boundaries where the calculation is terminated. Integration line R in (b) is plotted across the vertical center of the freestanding wave node closest to the bottom mirror and is used to calculate the effective mode radius. (c) Reflectance spectra of 7-, 11-, and 15-dielectric-layer mirrors across a wavelength range of 400 to 800 nm. (h)  Q -factor of MIFP, finite PPFP, and WGM cavities as a function of d . There are two variables ( d and L ) for the MIFP cavity and the PPFP cavity. For a given d , L is chosen to be as close to d as possible and with maximum calculated Q -factor for the MIFP cavity in a range of L from d + 0.02 to d + 0.28    μm , since the Q -factor oscillates over L with a period of about 0.28 μm.
Fig. 3.
Fig. 3. (a)–(d) Electrical field distribution of the (a)  HE 11 , (b)  TM 01 , (c)  TE 01 , and (d)  HE 21 modes of an MIFP cavity with a 2-μm diameter MS placed in a 2.04-μm-long FP cavity ( d = 2    μm , L = 2.04    μm , n a = 1.5 ). Upper and lower panels are the cross-sectional and vertical-sectional view, respectively. White arrows indicate the in-plane electrical field vector in the cross-sectional view. (e)–(g)  Q -factor of the HE 11 , TM 01 , TE 01 , and HE 21 modes as a function of surrounding medium RI n a for three different MIFP structures: (e) 1-μm MS in 1.04-μm-long cavity ( d = 1    μm , L = 1.04    μm ), (f) 2-μm MS in 2.04-μm-long cavity ( d = 2    μm , L = 2.04    μm ), and (g) 4-μm MS in 4.06-μm-long cavity ( d = 4    μm , L = 4.06    μm ). The diameter of the mirrors is set to be 2 μm larger than that of the corresponding MS.
Fig. 4.
Fig. 4. Electrical field distribution of the HE 21 mode of the MIFP cavity in Fig. 3(e) ( d = 1    μm , L = 1.04    μm ) (a) before and (b) after the Q -factor drop as the surrounding medium RI n a increases from (a) 1.5 to (b) 1.52. It can be seen that the mode confinement in (b) becomes quite weak with a large portion of the eletrical field leaking into the PML layer, leading to an extra spillover loss and a decreased Q -factor.
Fig. 5.
Fig. 5. (a) Schematic of an MIFP cavity with the cavity length L larger than the MS diameter d . b 0 is the distance from the MS center to the bottom mirror. (b) Electrical field amplitude distribution of the HE 11 mode for MIFP cavities ( d = 4    μm , b 0 = 2.03    μm ) with cavity lengths L = 6    μm and 8 μm under a surrounding medium RI of 1.33, 1.4, and 1.5, respectively. (c)–(e) Calculated Q -factor of HE 11 mode for MIFP cavities ( d = 4    μm , b 0 = 2.03    μm ) as a function of cavity length L at (c)  n a = 1.33 , (d)  n a = 1.4 , and (e)  n a = 1.5 , respectively. In the observation window of 520–560 nm for the resonance wavelength, there are usually two modes with consecutive longitudinal mode numbers but different Q . For clarity, we divide them into two groups. The red circle line corresponds to even longitudinal mode numbers ( m = 2 N ), and the blue circle line corresponds to odd longitudinal mode numbers ( m = 2 N + 1 ). (f)–(h) Calculated Q -factor of the TM 01 , TE 01 , and HE 21 modes for MIFP cavities ( d = 4    μm , b 0 = 2.03    μm ) as a function of cavity length L at (f)  n a = 1.33 , (g)  n a = 1.4 , and (h)  n a = 1.5 , respectively.
Fig. 6.
Fig. 6. (a)–(c) Photonic nanojet formation by a 4-μm diameter polystyrene MS illuminated by a Guassian beam ( radius = 3    μm ) with a surrounding medium RI of (a)  n a = 1.33 , (b)  n a = 1.4 , and (c)  n a = 1.5 . The point with the maximal electric field amplitude is chosen to be the focusing point. The focal length here is defined as the distance from the bottom of the MS to the focusing point. (d) Reflected light field distribution when the “nanojet” formed in (a) is incident on a mirror placed within the focusing length of the MS at n a = 1.33 . Most of the light field is reflected back into the MS. (e) Reflected light field distribution when the “nanojet” formed in (a) is incident on a mirror placed beyond the focusing length of the MS at n a = 1.33 . A large portion of the light field misses the MS. For a better understanding, the nanojet formation is simplified as a focusing lens in ray optics, as shown in insets of (d) and (e). Schematics show how light propagates when the mirror is placed within [inset of (d)] and outside [inset of (e)] the focusing plane.
Fig. 7.
Fig. 7. (a)–(c) Calculated Q -factors of the HE 11 , TM 01 , TE 01 , and HE 21 modes as a function of b 0 [the distance from the MS center to the bottom mirror, illustrated in Fig. 5(a)] at (a)  n a = 1.33 , (b)  n a = 1.4 , and (c)  n a = 1.5 for the MIFP cavity with fixed d = 4    μm and L = 6    μm . (d)–(f) Calculated Q -factors of the HE 11 , TM 01 , TE 01 , and HE 21 modes as a function of b 0 at (d)  n a = 1.33 , (e)  n a = 1.4 , and (f)  n a = 1.5 for the MIFP cavity with fixed d = 4    μm and L = 10    μm . Insets in (d) and (e) show the HE 11 mode profiles at b 0 = 4.9    μm and 4.48 μm, respectively.
Fig. 8.
Fig. 8. (a) Schematic of an MIFP cavity with the top mirror tilted by θ with respect to the bottom mirror. (b) Fundamental mode profile of an MIFP cavity ( d = 4    μm , L = 6.18    μm , n a = 1.4 , θ = 2 ° ). (c)–(e) Comparison of the Q -factor of the fundamental mode under different tilting angles ( θ = 0 ° , 1°, and 2°), and cavity length L is set to be 1, 1.5, and 2 times the MS diameter d at (c)  n a = 1.33 , (d)  n a = 1.4 , and (e)  n a = 1.5 .
Fig. 9.
Fig. 9. (a) Lasing spectra for MIFP-based lasers constructed by inserting 4-μm (red line), 2-μm (blue line), and 1-μm (green line) diameter polystyrene MSs between the two mirrors. Insets show the images of the lasing modes. Scale bar, 2 μm. (b) Spectrally integrated laser output as a function of pump energy density for the 4-μm diameter MIFP (red) and 2-μm diameter MIFP (blue) cavity, respectively. (c) Spectrally integrated laser output as a function of pump energy density for the 1-μm diameter MIFP cavity.
Fig. 10.
Fig. 10. (a) Lasing spectra under different pump intensity for MIFP-based lasers constructed by inserting a 4-μm diameter polystyrene MS (indicated by the dashed circle in the inset) into a 6-μm length FP cavity. The cavity spacing is controlled by using 6-μm diameter non-fluorescent MSs (indicated by the dashed circles in the inset). Scale bar, 4 μm. (b) Spectrally integrated laser output as a function of pump energy density for the MIFP-based laser in (a). Error bars are obtained by 3 measurements.

Tables (2)

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Table 1. Q -Factor, Finesse, Mode Radius, and Mode Volume ( HE 11 Mode) of MIFP Cavity at a Wavelength around 540 nma

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Table 2. Parameters Used for the Calculation of Q -Factor Q 0 from Measured Lasing Threshold P th

Equations (8)

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V eff = V ϵ ( r ) | E ( r ) | 2 d 3 r max [ ϵ ( r ) | E ( r ) | 2 ] ,
r m = R ϵ ( r ) | E ( r ) | 2 d r max [ ϵ ( r ) | E ( r ) | 2 ] ,
F = Q m λ / 2 n eff L = Q m / m .
Q i = 4 π n a L / [ λ In ( R 1 R 2 ) ] ,
P th = 8 π h c 2 n sp 2 Δ t λ L 4 λ p E ( λ L ) × A ( 1 + C ) 1 B C ,
A = σ a ( λ L ) / σ a ( λ p ) ,
B = σ a ( λ L ) / σ e ( λ L ) ,
C = Q abs / Q 0 = 2 π n sp λ L N σ a ( λ L ) · 1 Q 0 ,

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