- Email: [email protected]
Tailoring emission spectra by using microcavities
Results in Physics 13 (2019) 102138
Contents lists available at ScienceDirect
Results in Physics journal homepage: www.elsevier.com/locate/rinp
Tailoring emission spectra by using microcavities Muhammad Hanif Ahmed Khan Khushik, Chun Jiang
⁎
T
State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
ARTICLE INFO
ABSTRACT
Keywords: Emission spectrum Emitter Microcavity Local density of states
We present a theoretical model to describe emission spectrum of an emitter in a micro-cavity. Our model proposes that the spectrum in a metal micro-cavity depends on the product of the emission spectrum in free space and the local density of states (LDOS) in the cavity which the emitter is placed in. Since Purcell effect can enhance LDOS of a micro-cavity, the emission intensity of an emitter is directly proportional to LDOS depending on the geometry of microcavity. Thus, the model predicts that the spectrum of an emitter can be modified as a narrow spectrum in microcavity possessing sharp LDOS spectrum, also can be modified as broadband spectrum with broadband LDOS spectrum. Finite-difference time-domain (FDTD) numerical simulations support our prediction.
Introduction Spectrum of an emitter (e.g. rare-earth ion, quantum dot) in crystals and glasses play an important role in its application for optoelectronics and information technology areas. Erbium-doped glasses, thuliumdoped glasses, and neodymium-doped glasses have emission peak wavelengths around 1530 nm, 1470 nm and 1300 nm in telecommunication windows region respectively [1–3]. On the first hand, for optical signal amplification, the wavelength width of emission spectra is hoped to be as broad as possible because broader emission spectra have wider gain bandwidth, thus more channels can be amplified in an optical fiber amplifier [4]. On the other hand, for optical fiber laser, the width of emission spectra is hoped to be as narrow as possible, as narrower emission width has larger gain coefficient, leading to lower lasing threshold. Moreover, in order to explore new quantum optics applications, a suitably modified dielectric surrounding is indispensable having vacuums fluctuations controlling spontaneous emission [5]. Spontaneous emission (SE) is the basic natural property of the material involved in the generation of light [6]. Therefore, it has been very important to control and tailor the behavior of spontaneous emission when designing some devices for optical communication, quantum-information systems, displays and solar energy conversion technologies [6]. Quantum theory suggests that SE results from the transition of an excited state electron toward its available ground state [7]. Recently photonic cavities have got great improvements and found their applications in ultrahigh efficiency single photon emitters and thresholdless nano lasers [8]. The direction-dependent emission spectra and radiative transitions
⁎
rate are highly affected by the surrounding of emitter [7]. LDOS have played an important role in the development of novel photonic devices [9]. At the specific location of the emitter, LDOS determines the number of electromagnetic modes available for the emission of photons. Therefore, it is very important to analyze LDOS of different microcavity structure geometry. In this paper, we design several different microcavities and calculate their LDOS using finite-different time domain method to study emission spectra from emitters embedded in circular/elliptical-metal cavity and square/rectangular cavities. We show that the emission spectra in a free space can be tailored by using different microcavity geometry surrounding it and show the relationship between LDOS and the emission spectrum of the luminescent ion. Theoretical consideration It is known that amount of power radiated by a given current is affected by surrounding geometry. Mathematically it can be given as
P = I 2Rra
(1)
where I is current, Rra is radiation resistance, which is a function of the geometry surrounding the current. Frequency-dependent waveguide impedance suggests that at the frequency below cut-off frequency the power radiated by a dipole source should be suppressed in a hollow metallic cavity [10]. The amount of power at the frequency over cutoff frequency is directly related to LDOS of the geometry [11]. The surrounding of the emitter has a large effect on the properties of spontaneously emitted light. The direction-dependent emission spectra
Corresponding author. E-mail addresses: [email protected] (M.H.A.K. Khushik), [email protected] (C. Jiang).
https://doi.org/10.1016/j.rinp.2019.02.074 Received 29 January 2019; Received in revised form 21 February 2019; Accepted 22 February 2019 Available online 23 February 2019 2211-3797/ © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/BY/4.0/).
Results in Physics 13 (2019) 102138
M.H.A.K. Khushik and C. Jiang
Fig. 1. The microcavities with different geometries. A: square cavity and rectangular cavity, B: circular cavity and elliptical cavity.
and emission rate depend on the surrounding of the emitter. The Fermi’s golden rule describes the radiative rate involving LDOS [12]. The available modes for the emitted photon at the particular location of the emitter depends on LDOS. The emission rate and LDOS are functions of location of the emitter and emission frequency ω [9]. Fermi’s golden mathematical rule governs the spontaneous emission transition rate between u and v states [12].
R u, v =
2
[Tu, v ]2 D ( )
width are 1.4a, 1.2a, thickness is 0.2a. For the circular cavity, the radius is 0.6a and thickness is 0.2a. For the elliptical cavity, the long axis and short axis lengths are 1.2a, 0.8a, respectively, and thickness is 0.2a, where a is a length unit, e.g. one micrometer. We use Gaussian-like emission spectra as emission spectra in freespace (P0 (r , ) ) and use it as the source of FDTD simulation (with MEEP package) and calculate the LDOS and emission spectra (flux from MEEP) of circular and elliptical metallic microcavities with FDTD, and then calculate the theoretical emission spectra (theoretical flux) according to Eq.4. The theoretical flux and flux from MEEP are shown in Fig. 2 (a) and (b). It is illustrated from the figures that our theoretical calculation is in good agreement with the numerical results. The dash lines in Fig. 2 (c), (d), (e) and (f) illustrate the emission spectra in free space, and the solid lines present the power spectral density flowing through the monitors of the square, circular, rectangular and elliptical metallic cavities. It is shown from Fig. 2 that in the square metal and circular metal cavities, the emission spectra recorded at the notch are similar to that in free-space environment. However, in the rectangular metal and elliptical metal cavities, the spectra are much narrower compared to that in free-space environment, thus the emission spectra can be modified as sharp spectra, which will have potential applications for designing low threshold solid lasers and gas lasers. Fig. 3 illustrates the emission spectra in free space, square, circular, rectangular and elliptical silicon cavities. It is shown in Fig. 3 that in the square silicon and rectangular silicon cavities, the emission spectra recorded at the notch is a convolution of three smaller emission spectra, and the main spectra is much higher than other spectra and its width is narrower than that in a free-space environment, especially, the width in square cavity is much narrower. In the circular silicon cavity, the spectra is a sharp spectrum, which is much narrower than that in free-space environment, thus a broad emission spectra in free-space can be modified as a sharp spectra by using this circular silicon microcavity. However, in the elliptical silicon cavity, the emission spectrum recorded at the notch includes two intense peaks. The central frequency of one peak is much smaller than the frequency of free-space environment, its line width is much narrower compared to the free-space environment. The central frequency of other peak is much larger than the frequency of free-space environment, and its line width is more narrower compared to the free-space environment. Thus, the emission spectra in free space can be modified as broadband spectra by further tailoring the elliptical silicon cavity
(2)
Here [Tu, v ] represents transition matrix between u and v states, D ( ) is frequency-dependent LDOS. If the microcavity is a spherical cavity whose radius is R, and a photonic emitter is placed in the sphere as an analog to the practical luminescent point source. The LDOS in the cavity can be expressed as [12]
D( ) =
1 (
0
0 /2Q ) 2 + ( 0 /2Q)2
(3)
where is the oscillating frequency of emitter, ω0is the resonance frequency of cavity and Q is the quality factor of cavity. As we can see, the eigenmodes of cavity give high densities of states at the resonant frequencies while at frequencies between two eigenfrequencies the densities of states are quite low. Here, we propose that the relationship between the radiated power spectrum P(r , ) in a microcavity and LDOS of microcavity may be expressed with
P(r , ) = P0 (r , ) × D (r , )
(4)
where P0 (r , ) is the emission power spectrum of an emitter in free space. Result and discussion Fig. 1 shows the microcavities with different geometries. A: square cavity and rectangular cavity, B: circular cavity and ellipse cavity. In order to allow the fields to propagate away from the cavity the structures have a small notch on one side. FDTD simulations are used to calculate the LDOS and emission spectrum. The numerical resolution is 100 pixels/a. A Gaussian source in time is lunched at the center of the microcavities, and the monitor for power flux is recorded at the notch to observe the emission spectrum. For the square-cavity, the side length is 1.2a and thickness is 0.2a. For the rectangular-cavity, the length and 2
Results in Physics 13 (2019) 102138
M.H.A.K. Khushik and C. Jiang
Fig. 2. The emission spectra in free space and square, circular, rectangular and elliptical metallic cavities.
3
Results in Physics 13 (2019) 102138
M.H.A.K. Khushik and C. Jiang
Fig. 3. The emission spectra in free space, square, circular, rectangular and elliptical silicon cavities.
Fig. 4. The fields inside square, rectangular, elliptical and circular metallic cavities.
4
Results in Physics 13 (2019) 102138
M.H.A.K. Khushik and C. Jiang
Fig. 5. (a) The microcavity for manipulating emission spectrum. (b) Electromagnetic fields inside the double-square silicon microcavity. (c) Emission spectra from a double-square silicon cavity. (d) Emission spectra from a double-square metallic cavity.
geometry, which will have potential application for designing broadband optical devices such as fiber amplifiers and fiber sources. The fields inside square, rectangular, elliptical and circular metallic cavities are shown in Fig. 4. Fig. 5 (a) and (b) show the structure and field of double-square silicon microcavities and (c) and (d) illustrates the emission spectra of the double-square silicon and double-square metal microcavities. For the silicon microcavity, the spectra is convolution of two emission spectra, and the main peak is much higher than second peak, and the whole spectra width is much wider than that in a free-space environment. For metal microcavity, the spectra includes one peak, and its width is nearly equal to the spectra in a free-space environment. The structure and field of double-elliptical silicon microcavities are shown in Fig. 6 (a) and (b), and the emission spectra of the doubleelliptical silicon and metal microcavities are shown in Fig. 6 (c) and (d). For double-elliptical silicon microcavity the emission spectrum comprises of two peaks. Double-elliptical silicon microcavity has high-order modes and possess two peaks of emission spectrum in opposite directions. The positive peak is due to the positive electric field and the negative peak is due to opposite direction. The double-elliptical silicon cavity halves the emission spectra of the luminescent ion. The metallic elliptical double-cavities has one sharp peak. The metallic cavity can be used for designing low threshold solid lasers and gas lasers.
luminescent ions by using geometrical microcavities and describe the mathematical relationship between emission spectrum of luminescent ion in free space and embedded in the microcavity. The numerical results show that the emission spectrum of an active ion from a metallic cavity is equivalent to the dot product of its emission spectrum in free space and the geometrical dependent LDOS of the cavity. Furthermore, the numerical results show that metallic rectangular, metallic elliptical, metallic double-elliptical cavities and circular silicon cavity can modify spectra as sharp spectra, enabling the luminescent ions to be used for designing low threshold solid lasers and gas lasers. Square and rectangular silicon cavities modify the emission spectra as convolution of different emission spectra of different widths. Elliptical silicon cavity and double-square silicon cavity can modify spectra as wider spectra, enabling the luminescent ion to be used for designing broadband waveguide amplifiers and sources. Square, circular and double-square metallic cavities do not produce considerable change in the emission spectra of luminescent ion. Double-elliptical silicon microcavity halves the emission spectra of luminescent ion. These microcavity geometries will be key for the development of new luminescent materials with more useful spectral properties than conventional bulk materials. Acknowledgement We acknowledge the useful contributions of distinguished members of the state key laboratory of advanced optical communication systems and networks in the department of electronic engineering at Shanghai Jiao Tong University.
Conclusion We discover the possibilities of tailoring the emission spectra of 5
Results in Physics 13 (2019) 102138
M.H.A.K. Khushik and C. Jiang
Fig. 6. (a) A double-elliptical cavity structure for manipulating emission spectrum. (b) Electromagnetic fields inside double-elliptical silicon microcavity. (c) emission spectra from a double-elliptical silicon cavity. (d) Emission spectra from a double-elliptical metallic cavity.
Funding [5]
National Natural Science Foundation of China (60377023, 60672017); New Century Excellent Talents Universities (NCET); Shanghai Optical Science and Technology project (05DZ22009).
[6] [7] [8]
References
[9]
[1] Jayarajan P, Kuppusammy PG, et al. Analysis of temperature based power spectrum in EDFA and YDFA with different pump power for THz applications. Results Phys 2018;10:160–3. [2] Singh Rajandeep, Singh Maninder Lal. Performance evaluation of S-band Thulium doped silica fiber amplifier employing multiple pumping schemes. Optik-Int J Light Electron Optics 2017;140:565–70. [3] Turkiewicz Jarosław Piotr. Cost-effective n× 25 Gbit/s DWDM transmission in the 1310 nm wavelength domain. Opt Fiber Technol 2011;17(3):179–84. [4] Lei C, Jin A, Song R, Chen Z, Hou J. Theoretical and experimental research of
[10] [11] [12]
6
supercontinuum generation in an ytterbium-doped fiber amplifier. Opt Express 2016;24(9):9237–50. Hog TB, Akselrde GM, et al. Ultrafast spontaneous emission source using plasmonic nanoantennas. Nat Commun 2015;6:7788. Lodahl P, et al. Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals. Nature 2004;430(7000):654. Loudon R. The quantum theory of light. New York: Oxford Univ. Press; 2000. Englund D, et al. Controlling the spontaneous emission rate of single quantum dots in a two -dimensional photonic crystal. Phys Rev Lett 2005;95(1). Naz ESG, Jorgensen MR, Schmidt OG. Density of optical states in rolled-up photonic crystals and quasi crystals. Comput Phys Commun 2017;214:117–27. Wang S, Teixeria FL. An equivalent electric field source for wideband FDTD simulations of waveguide discontinuities. IEEE Microwave Wireless Compon Lett 2003;13(1):27–9. A. Taflove A. Oskooi S.G. Johnson Advances in FDTD computational electrodynamics: photonics and nanotechnology Artech House 2013. Lee M, Zworski M. A Fermi golden rule for quantum graphs. J. Math. Phys. 2016;57(9).
Contents lists available at ScienceDirect
Results in Physics journal homepage: www.elsevier.com/locate/rinp
Tailoring emission spectra by using microcavities Muhammad Hanif Ahmed Khan Khushik, Chun Jiang
⁎
T
State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
ARTICLE INFO
ABSTRACT
Keywords: Emission spectrum Emitter Microcavity Local density of states
We present a theoretical model to describe emission spectrum of an emitter in a micro-cavity. Our model proposes that the spectrum in a metal micro-cavity depends on the product of the emission spectrum in free space and the local density of states (LDOS) in the cavity which the emitter is placed in. Since Purcell effect can enhance LDOS of a micro-cavity, the emission intensity of an emitter is directly proportional to LDOS depending on the geometry of microcavity. Thus, the model predicts that the spectrum of an emitter can be modified as a narrow spectrum in microcavity possessing sharp LDOS spectrum, also can be modified as broadband spectrum with broadband LDOS spectrum. Finite-difference time-domain (FDTD) numerical simulations support our prediction.
Introduction Spectrum of an emitter (e.g. rare-earth ion, quantum dot) in crystals and glasses play an important role in its application for optoelectronics and information technology areas. Erbium-doped glasses, thuliumdoped glasses, and neodymium-doped glasses have emission peak wavelengths around 1530 nm, 1470 nm and 1300 nm in telecommunication windows region respectively [1–3]. On the first hand, for optical signal amplification, the wavelength width of emission spectra is hoped to be as broad as possible because broader emission spectra have wider gain bandwidth, thus more channels can be amplified in an optical fiber amplifier [4]. On the other hand, for optical fiber laser, the width of emission spectra is hoped to be as narrow as possible, as narrower emission width has larger gain coefficient, leading to lower lasing threshold. Moreover, in order to explore new quantum optics applications, a suitably modified dielectric surrounding is indispensable having vacuums fluctuations controlling spontaneous emission [5]. Spontaneous emission (SE) is the basic natural property of the material involved in the generation of light [6]. Therefore, it has been very important to control and tailor the behavior of spontaneous emission when designing some devices for optical communication, quantum-information systems, displays and solar energy conversion technologies [6]. Quantum theory suggests that SE results from the transition of an excited state electron toward its available ground state [7]. Recently photonic cavities have got great improvements and found their applications in ultrahigh efficiency single photon emitters and thresholdless nano lasers [8]. The direction-dependent emission spectra and radiative transitions
⁎
rate are highly affected by the surrounding of emitter [7]. LDOS have played an important role in the development of novel photonic devices [9]. At the specific location of the emitter, LDOS determines the number of electromagnetic modes available for the emission of photons. Therefore, it is very important to analyze LDOS of different microcavity structure geometry. In this paper, we design several different microcavities and calculate their LDOS using finite-different time domain method to study emission spectra from emitters embedded in circular/elliptical-metal cavity and square/rectangular cavities. We show that the emission spectra in a free space can be tailored by using different microcavity geometry surrounding it and show the relationship between LDOS and the emission spectrum of the luminescent ion. Theoretical consideration It is known that amount of power radiated by a given current is affected by surrounding geometry. Mathematically it can be given as
P = I 2Rra
(1)
where I is current, Rra is radiation resistance, which is a function of the geometry surrounding the current. Frequency-dependent waveguide impedance suggests that at the frequency below cut-off frequency the power radiated by a dipole source should be suppressed in a hollow metallic cavity [10]. The amount of power at the frequency over cutoff frequency is directly related to LDOS of the geometry [11]. The surrounding of the emitter has a large effect on the properties of spontaneously emitted light. The direction-dependent emission spectra
Corresponding author. E-mail addresses: [email protected] (M.H.A.K. Khushik), [email protected] (C. Jiang).
https://doi.org/10.1016/j.rinp.2019.02.074 Received 29 January 2019; Received in revised form 21 February 2019; Accepted 22 February 2019 Available online 23 February 2019 2211-3797/ © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/BY/4.0/).
Results in Physics 13 (2019) 102138
M.H.A.K. Khushik and C. Jiang
Fig. 1. The microcavities with different geometries. A: square cavity and rectangular cavity, B: circular cavity and elliptical cavity.
and emission rate depend on the surrounding of the emitter. The Fermi’s golden rule describes the radiative rate involving LDOS [12]. The available modes for the emitted photon at the particular location of the emitter depends on LDOS. The emission rate and LDOS are functions of location of the emitter and emission frequency ω [9]. Fermi’s golden mathematical rule governs the spontaneous emission transition rate between u and v states [12].
R u, v =
2
[Tu, v ]2 D ( )
width are 1.4a, 1.2a, thickness is 0.2a. For the circular cavity, the radius is 0.6a and thickness is 0.2a. For the elliptical cavity, the long axis and short axis lengths are 1.2a, 0.8a, respectively, and thickness is 0.2a, where a is a length unit, e.g. one micrometer. We use Gaussian-like emission spectra as emission spectra in freespace (P0 (r , ) ) and use it as the source of FDTD simulation (with MEEP package) and calculate the LDOS and emission spectra (flux from MEEP) of circular and elliptical metallic microcavities with FDTD, and then calculate the theoretical emission spectra (theoretical flux) according to Eq.4. The theoretical flux and flux from MEEP are shown in Fig. 2 (a) and (b). It is illustrated from the figures that our theoretical calculation is in good agreement with the numerical results. The dash lines in Fig. 2 (c), (d), (e) and (f) illustrate the emission spectra in free space, and the solid lines present the power spectral density flowing through the monitors of the square, circular, rectangular and elliptical metallic cavities. It is shown from Fig. 2 that in the square metal and circular metal cavities, the emission spectra recorded at the notch are similar to that in free-space environment. However, in the rectangular metal and elliptical metal cavities, the spectra are much narrower compared to that in free-space environment, thus the emission spectra can be modified as sharp spectra, which will have potential applications for designing low threshold solid lasers and gas lasers. Fig. 3 illustrates the emission spectra in free space, square, circular, rectangular and elliptical silicon cavities. It is shown in Fig. 3 that in the square silicon and rectangular silicon cavities, the emission spectra recorded at the notch is a convolution of three smaller emission spectra, and the main spectra is much higher than other spectra and its width is narrower than that in a free-space environment, especially, the width in square cavity is much narrower. In the circular silicon cavity, the spectra is a sharp spectrum, which is much narrower than that in free-space environment, thus a broad emission spectra in free-space can be modified as a sharp spectra by using this circular silicon microcavity. However, in the elliptical silicon cavity, the emission spectrum recorded at the notch includes two intense peaks. The central frequency of one peak is much smaller than the frequency of free-space environment, its line width is much narrower compared to the free-space environment. The central frequency of other peak is much larger than the frequency of free-space environment, and its line width is more narrower compared to the free-space environment. Thus, the emission spectra in free space can be modified as broadband spectra by further tailoring the elliptical silicon cavity
(2)
Here [Tu, v ] represents transition matrix between u and v states, D ( ) is frequency-dependent LDOS. If the microcavity is a spherical cavity whose radius is R, and a photonic emitter is placed in the sphere as an analog to the practical luminescent point source. The LDOS in the cavity can be expressed as [12]
D( ) =
1 (
0
0 /2Q ) 2 + ( 0 /2Q)2
(3)
where is the oscillating frequency of emitter, ω0is the resonance frequency of cavity and Q is the quality factor of cavity. As we can see, the eigenmodes of cavity give high densities of states at the resonant frequencies while at frequencies between two eigenfrequencies the densities of states are quite low. Here, we propose that the relationship between the radiated power spectrum P(r , ) in a microcavity and LDOS of microcavity may be expressed with
P(r , ) = P0 (r , ) × D (r , )
(4)
where P0 (r , ) is the emission power spectrum of an emitter in free space. Result and discussion Fig. 1 shows the microcavities with different geometries. A: square cavity and rectangular cavity, B: circular cavity and ellipse cavity. In order to allow the fields to propagate away from the cavity the structures have a small notch on one side. FDTD simulations are used to calculate the LDOS and emission spectrum. The numerical resolution is 100 pixels/a. A Gaussian source in time is lunched at the center of the microcavities, and the monitor for power flux is recorded at the notch to observe the emission spectrum. For the square-cavity, the side length is 1.2a and thickness is 0.2a. For the rectangular-cavity, the length and 2
Results in Physics 13 (2019) 102138
M.H.A.K. Khushik and C. Jiang
Fig. 2. The emission spectra in free space and square, circular, rectangular and elliptical metallic cavities.
3
Results in Physics 13 (2019) 102138
M.H.A.K. Khushik and C. Jiang
Fig. 3. The emission spectra in free space, square, circular, rectangular and elliptical silicon cavities.
Fig. 4. The fields inside square, rectangular, elliptical and circular metallic cavities.
4
Results in Physics 13 (2019) 102138
M.H.A.K. Khushik and C. Jiang
Fig. 5. (a) The microcavity for manipulating emission spectrum. (b) Electromagnetic fields inside the double-square silicon microcavity. (c) Emission spectra from a double-square silicon cavity. (d) Emission spectra from a double-square metallic cavity.
geometry, which will have potential application for designing broadband optical devices such as fiber amplifiers and fiber sources. The fields inside square, rectangular, elliptical and circular metallic cavities are shown in Fig. 4. Fig. 5 (a) and (b) show the structure and field of double-square silicon microcavities and (c) and (d) illustrates the emission spectra of the double-square silicon and double-square metal microcavities. For the silicon microcavity, the spectra is convolution of two emission spectra, and the main peak is much higher than second peak, and the whole spectra width is much wider than that in a free-space environment. For metal microcavity, the spectra includes one peak, and its width is nearly equal to the spectra in a free-space environment. The structure and field of double-elliptical silicon microcavities are shown in Fig. 6 (a) and (b), and the emission spectra of the doubleelliptical silicon and metal microcavities are shown in Fig. 6 (c) and (d). For double-elliptical silicon microcavity the emission spectrum comprises of two peaks. Double-elliptical silicon microcavity has high-order modes and possess two peaks of emission spectrum in opposite directions. The positive peak is due to the positive electric field and the negative peak is due to opposite direction. The double-elliptical silicon cavity halves the emission spectra of the luminescent ion. The metallic elliptical double-cavities has one sharp peak. The metallic cavity can be used for designing low threshold solid lasers and gas lasers.
luminescent ions by using geometrical microcavities and describe the mathematical relationship between emission spectrum of luminescent ion in free space and embedded in the microcavity. The numerical results show that the emission spectrum of an active ion from a metallic cavity is equivalent to the dot product of its emission spectrum in free space and the geometrical dependent LDOS of the cavity. Furthermore, the numerical results show that metallic rectangular, metallic elliptical, metallic double-elliptical cavities and circular silicon cavity can modify spectra as sharp spectra, enabling the luminescent ions to be used for designing low threshold solid lasers and gas lasers. Square and rectangular silicon cavities modify the emission spectra as convolution of different emission spectra of different widths. Elliptical silicon cavity and double-square silicon cavity can modify spectra as wider spectra, enabling the luminescent ion to be used for designing broadband waveguide amplifiers and sources. Square, circular and double-square metallic cavities do not produce considerable change in the emission spectra of luminescent ion. Double-elliptical silicon microcavity halves the emission spectra of luminescent ion. These microcavity geometries will be key for the development of new luminescent materials with more useful spectral properties than conventional bulk materials. Acknowledgement We acknowledge the useful contributions of distinguished members of the state key laboratory of advanced optical communication systems and networks in the department of electronic engineering at Shanghai Jiao Tong University.
Conclusion We discover the possibilities of tailoring the emission spectra of 5
Results in Physics 13 (2019) 102138
M.H.A.K. Khushik and C. Jiang
Fig. 6. (a) A double-elliptical cavity structure for manipulating emission spectrum. (b) Electromagnetic fields inside double-elliptical silicon microcavity. (c) emission spectra from a double-elliptical silicon cavity. (d) Emission spectra from a double-elliptical metallic cavity.
Funding [5]
National Natural Science Foundation of China (60377023, 60672017); New Century Excellent Talents Universities (NCET); Shanghai Optical Science and Technology project (05DZ22009).
[6] [7] [8]
References
[9]
[1] Jayarajan P, Kuppusammy PG, et al. Analysis of temperature based power spectrum in EDFA and YDFA with different pump power for THz applications. Results Phys 2018;10:160–3. [2] Singh Rajandeep, Singh Maninder Lal. Performance evaluation of S-band Thulium doped silica fiber amplifier employing multiple pumping schemes. Optik-Int J Light Electron Optics 2017;140:565–70. [3] Turkiewicz Jarosław Piotr. Cost-effective n× 25 Gbit/s DWDM transmission in the 1310 nm wavelength domain. Opt Fiber Technol 2011;17(3):179–84. [4] Lei C, Jin A, Song R, Chen Z, Hou J. Theoretical and experimental research of
[10] [11] [12]
6
supercontinuum generation in an ytterbium-doped fiber amplifier. Opt Express 2016;24(9):9237–50. Hog TB, Akselrde GM, et al. Ultrafast spontaneous emission source using plasmonic nanoantennas. Nat Commun 2015;6:7788. Lodahl P, et al. Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals. Nature 2004;430(7000):654. Loudon R. The quantum theory of light. New York: Oxford Univ. Press; 2000. Englund D, et al. Controlling the spontaneous emission rate of single quantum dots in a two -dimensional photonic crystal. Phys Rev Lett 2005;95(1). Naz ESG, Jorgensen MR, Schmidt OG. Density of optical states in rolled-up photonic crystals and quasi crystals. Comput Phys Commun 2017;214:117–27. Wang S, Teixeria FL. An equivalent electric field source for wideband FDTD simulations of waveguide discontinuities. IEEE Microwave Wireless Compon Lett 2003;13(1):27–9. A. Taflove A. Oskooi S.G. Johnson Advances in FDTD computational electrodynamics: photonics and nanotechnology Artech House 2013. Lee M, Zworski M. A Fermi golden rule for quantum graphs. J. Math. Phys. 2016;57(9).