Abstract

Non-traditional whispering gallery modes are studied in a glass microsphere. Geometrical ray tracing is used to explain and calculate these modes. Thermal emission and Raman scattering are used as an internal light source to excite these modes inside the glass microsphere. The thermal and Raman emission spectra are modified due to the existence of these modes. Fourier analysis is then used to distinguish the individual modes. The understanding of these non-traditional WGM may lead to alternative design strategies for sensor applications or laser cavity configurations.

© 2017 Optical Society of America

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References

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    [PubMed]
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    [PubMed]
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2017 (2)

A. Bozzola, S. Perotto, and F. De Angelis, “Hybrid plasmonic-photonic whispering gallery mode resonators for sensing: a critical review,” Analyst (Lond.) 142(6), 883–898 (2017).
[PubMed]

F. J. Timmermans, L. Chang, H. A. G. M. van Wolferen, A. T. M. Lenferink, and C. Otto, “Observation of whispering gallery modes through electron beam-induced deposition,” Opt. Lett. 42(7), 1337–1340 (2017).
[PubMed]

2016 (1)

F. J. Timmermans, B. Liszka, A. T. M. Lenferink, H. A. G. M. van Wolferen, and C. Otto, “Integration of correlative Raman microscopy in a dualbeam FIB SEM,” J. Raman Spectrosc. 47, 956–962 (2016).

2015 (3)

M. Humar and S. H. Yun, “Intracellular microlasers,” Nat. Photonics 9, 572 (2015).

T. Kumagai, T. Kishi, and T. Yano, “Low threshold lasing of bubble-containing glass microspheres by non-whispering gallery mode excitation over a wide wavelength range,” J. Appl. Phys. 117, 113104 (2015).

M. R. Foreman, J. D. Swaim, and F. Vollmer, “Whispering gallery mode sensors,” Adv. Opt. Photonics 7(2), 168–240 (2015).
[PubMed]

2013 (1)

R. C. Gauthier, “Whispering-gallery modes of mu-optic silicon bottle resonator examined using a Fourier-Bessel eigen-state approach,” J. Micro-Nanolith. Mem. 12, 043007 (2013).

2010 (1)

T. Ioppolo, N. Das, and M. V. Otugen, “Whispering gallery modes of microspheres in the presence of a changing surrounding medium: A new ray-tracing analysis and sensor experiment,” J. Appl. Phys. 107, 103105 (2010).

2006 (1)

M. L. Gorodetsky and A. E. Fomin, “Geometrical theory of whispering-gallery modes,” Ieee J. Sel. Top. Quant. 12, 33–39 (2006).

2000 (1)

1998 (1)

1994 (1)

1992 (1)

L. G. Guimaraes and H. M. Nussenzveig, “Theory of Mie Resonances and Ripple Fluctuations,” Opt. Commun. 89, 363–369 (1992).

1989 (1)

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-Factor and Nonlinear Properties of Optical Whispering-Gallery Modes,” Phys. Lett. A 137, 393–397 (1989).

1986 (1)

V. Scheuer, H. Koops, and T. Tschudi, “Electron beam decomposition of carbonyls on silicon,” Microelectron. Eng. 5, 423–430 (1986).

1960 (1)

J. B. Keller, “Asymptotic Solution of Eigenvalue Problems,” Ann. Phys. 9, 24–75 (1960).

Bozzola, A.

A. Bozzola, S. Perotto, and F. De Angelis, “Hybrid plasmonic-photonic whispering gallery mode resonators for sensing: a critical review,” Analyst (Lond.) 142(6), 883–898 (2017).
[PubMed]

Braginsky, V. B.

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-Factor and Nonlinear Properties of Optical Whispering-Gallery Modes,” Phys. Lett. A 137, 393–397 (1989).

Chang, L.

Chang, R. K.

Chowdhury, D. Q.

Das, N.

T. Ioppolo, N. Das, and M. V. Otugen, “Whispering gallery modes of microspheres in the presence of a changing surrounding medium: A new ray-tracing analysis and sensor experiment,” J. Appl. Phys. 107, 103105 (2010).

De Angelis, F.

A. Bozzola, S. Perotto, and F. De Angelis, “Hybrid plasmonic-photonic whispering gallery mode resonators for sensing: a critical review,” Analyst (Lond.) 142(6), 883–898 (2017).
[PubMed]

Fomin, A. E.

M. L. Gorodetsky and A. E. Fomin, “Geometrical theory of whispering-gallery modes,” Ieee J. Sel. Top. Quant. 12, 33–39 (2006).

Foreman, M. R.

M. R. Foreman, J. D. Swaim, and F. Vollmer, “Whispering gallery mode sensors,” Adv. Opt. Photonics 7(2), 168–240 (2015).
[PubMed]

Gauthier, R. C.

R. C. Gauthier, “Whispering-gallery modes of mu-optic silicon bottle resonator examined using a Fourier-Bessel eigen-state approach,” J. Micro-Nanolith. Mem. 12, 043007 (2013).

Gorodetsky, M. L.

M. L. Gorodetsky and A. E. Fomin, “Geometrical theory of whispering-gallery modes,” Ieee J. Sel. Top. Quant. 12, 33–39 (2006).

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-Factor and Nonlinear Properties of Optical Whispering-Gallery Modes,” Phys. Lett. A 137, 393–397 (1989).

Guimaraes, L. G.

L. G. Guimaraes and H. M. Nussenzveig, “Theory of Mie Resonances and Ripple Fluctuations,” Opt. Commun. 89, 363–369 (1992).

Humar, M.

M. Humar and S. H. Yun, “Intracellular microlasers,” Nat. Photonics 9, 572 (2015).

Ilchenko, V. S.

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-Factor and Nonlinear Properties of Optical Whispering-Gallery Modes,” Phys. Lett. A 137, 393–397 (1989).

Ioppolo, T.

T. Ioppolo, N. Das, and M. V. Otugen, “Whispering gallery modes of microspheres in the presence of a changing surrounding medium: A new ray-tracing analysis and sensor experiment,” J. Appl. Phys. 107, 103105 (2010).

Kaiser, T.

Keller, J. B.

J. B. Keller, “Asymptotic Solution of Eigenvalue Problems,” Ann. Phys. 9, 24–75 (1960).

Kishi, T.

T. Kumagai, T. Kishi, and T. Yano, “Low threshold lasing of bubble-containing glass microspheres by non-whispering gallery mode excitation over a wide wavelength range,” J. Appl. Phys. 117, 113104 (2015).

Koops, H.

V. Scheuer, H. Koops, and T. Tschudi, “Electron beam decomposition of carbonyls on silicon,” Microelectron. Eng. 5, 423–430 (1986).

Kumagai, T.

T. Kumagai, T. Kishi, and T. Yano, “Low threshold lasing of bubble-containing glass microspheres by non-whispering gallery mode excitation over a wide wavelength range,” J. Appl. Phys. 117, 113104 (2015).

Lange, S.

Leach, D. H.

Lenferink, A. T. M.

F. J. Timmermans, L. Chang, H. A. G. M. van Wolferen, A. T. M. Lenferink, and C. Otto, “Observation of whispering gallery modes through electron beam-induced deposition,” Opt. Lett. 42(7), 1337–1340 (2017).
[PubMed]

F. J. Timmermans, B. Liszka, A. T. M. Lenferink, H. A. G. M. van Wolferen, and C. Otto, “Integration of correlative Raman microscopy in a dualbeam FIB SEM,” J. Raman Spectrosc. 47, 956–962 (2016).

Liszka, B.

F. J. Timmermans, B. Liszka, A. T. M. Lenferink, H. A. G. M. van Wolferen, and C. Otto, “Integration of correlative Raman microscopy in a dualbeam FIB SEM,” J. Raman Spectrosc. 47, 956–962 (2016).

Nussenzveig, H. M.

L. G. Guimaraes and H. M. Nussenzveig, “Theory of Mie Resonances and Ripple Fluctuations,” Opt. Commun. 89, 363–369 (1992).

Otto, C.

F. J. Timmermans, L. Chang, H. A. G. M. van Wolferen, A. T. M. Lenferink, and C. Otto, “Observation of whispering gallery modes through electron beam-induced deposition,” Opt. Lett. 42(7), 1337–1340 (2017).
[PubMed]

F. J. Timmermans, B. Liszka, A. T. M. Lenferink, H. A. G. M. van Wolferen, and C. Otto, “Integration of correlative Raman microscopy in a dualbeam FIB SEM,” J. Raman Spectrosc. 47, 956–962 (2016).

Otugen, M. V.

T. Ioppolo, N. Das, and M. V. Otugen, “Whispering gallery modes of microspheres in the presence of a changing surrounding medium: A new ray-tracing analysis and sensor experiment,” J. Appl. Phys. 107, 103105 (2010).

Perotto, S.

A. Bozzola, S. Perotto, and F. De Angelis, “Hybrid plasmonic-photonic whispering gallery mode resonators for sensing: a critical review,” Analyst (Lond.) 142(6), 883–898 (2017).
[PubMed]

Roll, G.

Scheuer, V.

V. Scheuer, H. Koops, and T. Tschudi, “Electron beam decomposition of carbonyls on silicon,” Microelectron. Eng. 5, 423–430 (1986).

Schweiger, G.

Swaim, J. D.

M. R. Foreman, J. D. Swaim, and F. Vollmer, “Whispering gallery mode sensors,” Adv. Opt. Photonics 7(2), 168–240 (2015).
[PubMed]

Timmermans, F. J.

F. J. Timmermans, L. Chang, H. A. G. M. van Wolferen, A. T. M. Lenferink, and C. Otto, “Observation of whispering gallery modes through electron beam-induced deposition,” Opt. Lett. 42(7), 1337–1340 (2017).
[PubMed]

F. J. Timmermans, B. Liszka, A. T. M. Lenferink, H. A. G. M. van Wolferen, and C. Otto, “Integration of correlative Raman microscopy in a dualbeam FIB SEM,” J. Raman Spectrosc. 47, 956–962 (2016).

Tschudi, T.

V. Scheuer, H. Koops, and T. Tschudi, “Electron beam decomposition of carbonyls on silicon,” Microelectron. Eng. 5, 423–430 (1986).

van Wolferen, H. A. G. M.

F. J. Timmermans, L. Chang, H. A. G. M. van Wolferen, A. T. M. Lenferink, and C. Otto, “Observation of whispering gallery modes through electron beam-induced deposition,” Opt. Lett. 42(7), 1337–1340 (2017).
[PubMed]

F. J. Timmermans, B. Liszka, A. T. M. Lenferink, H. A. G. M. van Wolferen, and C. Otto, “Integration of correlative Raman microscopy in a dualbeam FIB SEM,” J. Raman Spectrosc. 47, 956–962 (2016).

Vollmer, F.

M. R. Foreman, J. D. Swaim, and F. Vollmer, “Whispering gallery mode sensors,” Adv. Opt. Photonics 7(2), 168–240 (2015).
[PubMed]

Yano, T.

T. Kumagai, T. Kishi, and T. Yano, “Low threshold lasing of bubble-containing glass microspheres by non-whispering gallery mode excitation over a wide wavelength range,” J. Appl. Phys. 117, 113104 (2015).

Yun, S. H.

M. Humar and S. H. Yun, “Intracellular microlasers,” Nat. Photonics 9, 572 (2015).

Adv. Opt. Photonics (1)

M. R. Foreman, J. D. Swaim, and F. Vollmer, “Whispering gallery mode sensors,” Adv. Opt. Photonics 7(2), 168–240 (2015).
[PubMed]

Analyst (Lond.) (1)

A. Bozzola, S. Perotto, and F. De Angelis, “Hybrid plasmonic-photonic whispering gallery mode resonators for sensing: a critical review,” Analyst (Lond.) 142(6), 883–898 (2017).
[PubMed]

Ann. Phys. (1)

J. B. Keller, “Asymptotic Solution of Eigenvalue Problems,” Ann. Phys. 9, 24–75 (1960).

Ieee J. Sel. Top. Quant. (1)

M. L. Gorodetsky and A. E. Fomin, “Geometrical theory of whispering-gallery modes,” Ieee J. Sel. Top. Quant. 12, 33–39 (2006).

J. Appl. Phys. (2)

T. Kumagai, T. Kishi, and T. Yano, “Low threshold lasing of bubble-containing glass microspheres by non-whispering gallery mode excitation over a wide wavelength range,” J. Appl. Phys. 117, 113104 (2015).

T. Ioppolo, N. Das, and M. V. Otugen, “Whispering gallery modes of microspheres in the presence of a changing surrounding medium: A new ray-tracing analysis and sensor experiment,” J. Appl. Phys. 107, 103105 (2010).

J. Micro-Nanolith. Mem. (1)

R. C. Gauthier, “Whispering-gallery modes of mu-optic silicon bottle resonator examined using a Fourier-Bessel eigen-state approach,” J. Micro-Nanolith. Mem. 12, 043007 (2013).

J. Opt. Soc. Am. A (3)

J. Raman Spectrosc. (1)

F. J. Timmermans, B. Liszka, A. T. M. Lenferink, H. A. G. M. van Wolferen, and C. Otto, “Integration of correlative Raman microscopy in a dualbeam FIB SEM,” J. Raman Spectrosc. 47, 956–962 (2016).

Microelectron. Eng. (1)

V. Scheuer, H. Koops, and T. Tschudi, “Electron beam decomposition of carbonyls on silicon,” Microelectron. Eng. 5, 423–430 (1986).

Nat. Photonics (1)

M. Humar and S. H. Yun, “Intracellular microlasers,” Nat. Photonics 9, 572 (2015).

Opt. Commun. (1)

L. G. Guimaraes and H. M. Nussenzveig, “Theory of Mie Resonances and Ripple Fluctuations,” Opt. Commun. 89, 363–369 (1992).

Opt. Lett. (1)

Phys. Lett. A (1)

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-Factor and Nonlinear Properties of Optical Whispering-Gallery Modes,” Phys. Lett. A 137, 393–397 (1989).

Other (1)

L. Chang, Chip Based Common-path Swept-source Optical Coherence Tomography Device (Universiteit Twente, 2016).

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Figures (7)

Fig. 1
Fig. 1 Side view of the ray picture of the second 1x2π-mode. R is the radius of the circle. θi is the incident angle (the same as the reflection angle). Lbr is the length between adjacent reflection points. θr is the refraction angle (in case of θi is smaller than the critical angle). θchange is the change in propagation direction between reflections. n1 and n2 are the refractive index of the sphere and surrounding material respectively.
Fig. 2
Fig. 2 Mode characterization system. The light paths (rays) of a few modes are shown (side view) as examples. N indicates the number of cycles before the light path overlaps with itself for the first time. Each N corresponds to a set of modes. Number M is used to identify every unique individual mode inside a given Nx2π-mode set, in the order of an increasing number of reflections.
Fig. 3
Fig. 3 Experimental setup and sample. (a) Figure of the setup and sample. The FIB head is behind the SEM end lens and not shown in this figure. The sample can be moved between FIB, SEM and Raman with a stage within the vacuum chamber. C paste is carbon paste. The C-paste in between the heater and copper foil is used to improve the heat conductivity. (b) Top view of the whole sample. (c) Optical image of the measured glass sphere, top view. (d) SEM image of the measured glass sphere, top view.
Fig. 4
Fig. 4 (a) Example of measured thermal spectrum (black trace) and Raman + thermal spectrum (red trace) after carbon deposition by SEM and FIB operation. The thermal spectrum is measured at the center of the sphere. The Raman + thermal spectrum is measured on the edge of the sphere (in top view). The top relative wavenumber axis is used to help to read the glass Raman signal. (b) The Fourier transform of the spectra in (a). The identified modes are marked. Modes with suffix of ‘_r2’ or ‘_r3′ are the same modes as the one without the suffix. The suffix is used to indicate the optical path length of 2 or 3 times of the Lop. This is caused by the light interference in that mode with itself after 2 or 3 times round trip.
Fig. 5
Fig. 5 An overview of all 12 measured modes. The column at the extreme right has the name of the modes, their incident angle and the calculated and measured optical path length. Three modes with gray background are the modes detected also with multiple round trip. The second right column is the ray pictures (side view) of corresponding modes. The little arrows in mode 1_1, 1_2, 2_2 and 3_4 are used to indicate the location and direction of the detected refracted light. All the other images are the corresponding mode images (top view) constructed by integration over the Lop peak in the Fourier transform spectra of each mode at all scanned locations. The sphere is not perfectly round in the scanned top view. This is due to a small drift in the electron microscope scan stage during the long measurement time of ~10 hours.
Fig. 6
Fig. 6 Averaged FT spectra over the area of the detected modes. The insert is a binary top view image of all detected modes area. The 1_1 mode is located at the center. The 1_2 mode is located in between the center and the edge. All the other modes are located on or very close to the edge. The main plot is an average of all the FT plots in the white area of the inserted image.
Fig. 7
Fig. 7 Calculated normalized round trip optical path length as a function of incident angle for different modes. Normalized optical path length considers the Rn1 as unit one. Therefore, all the calculated modes can be universally applied to any spherical sample regardless the size and refractive index. All the modes measured in our sample are marked with a red circle. The dashed vertical line indicates the critical angle (~41°) in our sample.

Equations (6)

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θ c h a n g e = 360 ° J ,
θ i = 180 ° θ c h a n g e 2 .
L b r = 2 R cos ( θ i ) ,
L o p = J L b r n 1 ,
θ c h a n g e = N 360 ° J ,
L o p = 2 J R n 1 cos ( 90 ° N 180 ° J ) .

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