Open Access
Add to BibSonomy
Abstract
A three-dimensional notched-elliptical microdisk with a wavelength-size notch on the boundary is proposed as a multi-wavelength and unidirectional emission lasing source. The device contains multiple properly designed two-dimensional whispering gallery mode-based polymer notched microdisks with different dimensions for use as a multi-wavelength source. It can have a relatively high optical quality factor of 4000, unidirectional emission with low far-field divergence ∼4°, and the efficiency of emission is as high as 84.2%. The effect of the notch size on the far-field divergence is analyzed, and the multi-wavelength lasing performance is characterized, demonstrating that the resonator is robust and reliable. This work paves a unique but generic way for the design of compact multi-wavelength microlasers.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Distinguished by a small footprint, low threshold, and low power consumption, the whispering-gallery-mode (WGM) microresonator holds great promise for photonic applications [1–3], especially for microlasers [4–6]. However, most microlasers only generate one single lasing wavelength. Recently, multi-wavelength lasing has been paid more attention on the applications in wavelength division-multiplexed communication systems, optical signal processing and biomedical researches [7–9]. Traditionally, multi-wavelength microlasers are usually made from electrically pumped multiple cascaded microdisks coupled to a waveguide. For example, four-, eight-, and sixteen-wavelength lasers have been demonstrated where WGM microdisks are either tangentially or radially coupled out through the bus waveguide [10–13]. Microdisks with slightly different cavity lengths integrated onto the same waveguide will have different resonance wavelengths, which is appealing to multi-wavelength lasers. Other kinds of WGM microcavities have also been proposed for multi-wavelength lasing, such as a microrod symmetrically coated by dye and polymer as a dual-wavelength laser [14], multiple terrace-microspheres working as a spherical cavity laser for multi-wavelength emission [15], and a crystalline microdisk resonator as a multi-wavelength coherent source due to Kerr nonlinear interaction [16]. However, it is difficult to regulate the light coupling efficiency by precisely controlling the gaps between microdisks and waveguide. Additionally, the lasing at different wavelengths are nonuniform, which is mainly attributed to coupling losses. The solution to this issue is to apply different bias currents to the microdisk lasers, but it might be difficult for multi-wavelength lasers with a large number of wavelength channels, as the nonuniformity scales directly relate to the quantity of microdisks [17]. Additionally, the size and space occupied by the aforementioned multi-wavelength lasers are relatively large, which is also a major hurdle in the realization of compact devices. Lately, a type of WGM microbubble based on hybrid colloidal quantum dots (QD) with inorganic nanocomposites was demonstrated to be a multi-wavelength laser [18]. However, the preparation of well dispersed QD−polymer composites is challenging, primarily relating to large-scale phase separation, which results in QD aggregation and high optical scattering and losses. Moreover, this methodology is not easily adaptable to patterning, as structures are limited to hemispherical droplets, providing limited control over the cavity geometry. Therefore, it is necessary and urgent to develop a highly integrated, easily controllable, and high-performance microresonator for multi-wavelength applications.
It is known that deformed microcavities by breaking the rotational symmetry can increase the directionality of emission and power emission efficiency [19]. Various materials are predicted and confirmed experimentally to have a unidirectional emission with a low beam divergence [20,21]. Among these materials, polymers are very attractive for applications in on-chip photonics and environmental monitoring [22], due to cheap and easy fabrication as well as chemical resistance. In addition, it is demonstrated that the unidirectional emission can be adjusted to the targeted wavelength through conveniently upsizing or downsizing a deformed polymer microdisk, with the purpose of adding to the suite of cost-effective three-dimensional (3D) polymer optical devices [23]. Following this approach, through combining multiple deformed microdisk resonators creatively within a certain range of the deformation parameter, a multi-wavelength WGM microresonator can be expected.
In this paper, we design and numerically characterize a novel 3D multi-wavelength WGM polymer microresonator based on multiple crossed notched-elliptical microdisks (CNEMs). All the angles between every two adjacent crossed microdisks are equal. It is demonstrated that the near- and far-field profiles of each microdisk are separated with little cross-talk from each other. Therefore, it bears unidirectional emissions with a low far-field divergence ∼4° and the highest emission efficiency can reach 84.2%. The effect of the notch size on the far-field unidirectional emission is analyzed, demonstrating that the resonator is robust and relatively insensitive to deviations caused by fabrication uncertainties. Consequently, the proposed devices can be utilized for establishing a unique but generic method of cost-effective, easily controllable, and high-performance microlasers, which not only can be functionalized as an excellent platform to explore light-matter interaction, but also explore the new development of practical multi-wavelength microlasers.
2. Structure and basic theory
The schematic view and ray simulation of a notched-elliptical polymer microdisk is shown in Fig. 1(a). According to the focusing property of the ellipse [24], the notch on the boundary, whose size is at the scale of the wavelength, is located exactly on the foci of an auxiliary ellipse, leading the injecting light refracted into parallel rays on the opposite boundary. Here, ɛ=b/a is defined as the deformation parameter, where a and b are the lengths of the semi-major axis and semi-minor axis, respectively [Fig. 1(a)]. Using Snell’s law, we can achieve the relationship between the deformation parameter ɛ and the refractive index n of the notched ellipse, which is given by [25]
For a microresonator with a specific material whose refractive index is n, the WGM resonance condition can be given by [26] wherein r and C are the radius and circumference of the resonator, respectively, and m is the azimuthal mode number, an integer representing the WGM angular momentum. Here, we select a polymer material with n=1.52 [27], and ɛ=0.819, which represents the optimal deformation parameter for unidirectional emission [23]. Equation (2) demonstrates that the resonance occurs for wavelengths when an integer multiple of that wavelength matches the circumference. The microdisks with different ɛ lead to changes in the circumference C, which in turn changes the WGM resonance condition, as indicated by Eq. (2). Therefore, if several microdisks with different ɛ are combined productively, a multi-wavelength microresonator can be easily anticipated.
Fig. 1. (a) Schematic view and ray simulation of a notched-elliptical microdisk. Inset: Zoomed in cross section view of the white rectangle to illustrate the notch dimensions with w, d, and h, respectively. (b) Schematic view of one to four CNEMs.
The basic idea here is that the deformed microcavities based on multiple crossed notched-elliptical microdisks by breaking the rotational symmetry can increase the directionality of emission and power emission efficiency [19]. The circumference of every microdisk is slightly different with each other, causing unidirectional emission with multiple different wavelengths. The main advantages of this type of properly designed multiple microdisks are highly integrated and easily controllable compared to those by using several microdisks either tangentially or radially coupled out through the bus waveguide [10], and the microresonator based on hybrid colloidal quantum dots (QD) with inorganic nanocomposites [18]. Hence it bears the potential to be a compact 3D multi-wavelength WGM lasing source. The schematic views from one to four CNEMs, on which WGM is formed respectively, are shown in Fig. 1(b). The two, three and four CNEMs share the same major axis a, but different minor axis b due to different deformation parameters. Consequently, the circumference of each microdisk is different. All the angles between every two adjacent crossed microdisks are equal. It can be noted that the bigger deformation parameter is, the larger circumference of the microdisk is, and the longer resonance wavelength for the same mode can be obtained accordingly. In order to minimize the beam divergence and have the rotational symmetry according to x axis, the notch is made as an oblate spheroid, whose size is optimized to be w = 0.3µm and d = h=0.25µm, wherein w refers to the semi major axis along x axis, d and h refer to the semi minor axes along y and z axes, respectively, as shown in the inset of Fig. 1(a). The reason for making the notch as an oblate spheroid is to make sure each cross section of it through the central axis is the same ellipse with the same scale.
3. Simulation results
The field properties and emission performances of the proposed CNEM are studied with 3D finite-difference-time-domain (FDTD) method via Lumerical software. A perfectly matched layer (PML) with a thickness of 1µm is constructed on all surfaces of the computational domain as the boundary conditions, for simulating an infinite domain while minimizing spurious reflections. Dipole sources are used to excite WGM in each microdisk of CNEMs simultaneously.
The intensity spectra from one to four CNEMs are shown in Figs. 2(a)–2(d). It should be noted that CNEM is sensitive to polarization of the lighting sources. The peaks with the highest intensity are the TM modes formed by CNEMs. As illustrated in Fig. 1(a), these modes are modulated and formed due to the notched-elliptical geometry of each microdisk. Consistent with Eq. (2), the peaks in Figs. 2(a)–2(d) represent the resonance wavelengths for microdisks with different ɛ, respectively. The resonance wavelengths red shift linearly with the increase of ɛ. When ɛ changes from ɛ1=0.799 to ɛ4=0.829 (with a step of 0.01), the circumferences of the microdisks enlarges accordingly from 26.09µm to 26.48µm (with a step of 0.13µm), the resonance wavelength eventually redshifts across a wide range of 7.89 nm (with a step of 2.63nm). The mode profiles in Fig. 2(e) show WGM can be propagated in each microdisk for four CNEMs at four resonance wavelengths respectively, without disturbing each other.
Fig. 2. (a)-(d) Intensity spectra, schematic views (left panels of insets), far-field patterns in logarithmically scales (right panels of insets) from one to four CNEMs, respectively. Right bottom panel of insets in (a) shows the zoom-in peak in the blue rectangle. (e) Vertical cross-sectional mode profiles of four CNEMs under four resonance wavelengths, respectively.
It should be noted that the wavelength spacing can be tunable and exactly designed. With slight variations in the circumference, we can achieve the spectral channel spacing of ∼3nm. And spacing of ∼8nm can be further obtained if two microdisks with the first and fourth resonance wavelengths are chosen for CNEMs. To further analyze the spectra, the quality (Q) factor of CNEM, widely used to characterize a WGM resonance, can be estimated according to the relation of Q = λres/δλ, where λres is the resonance wavelength and δλ is the full width at half maximum (FWHM) of resonant peak, respectively [17]. Therefore, Q factor is around 4000 with δλ of 0.13nm for all the resonant wavelengths from one to four CNEMs. Such a polymer device can be fabricated using the advanced lithography and can act as a multi-wavelength laser source around 530 nm, when suitably doped with active materials such as dye Coumarin 540 A [28].
As discussed above, along with the quantity of CNEMs increasing from one to four, the angle between two nearest CNEMs is decreasing. On the contrary, the possibility of interference with each other increases. Therefore, if good performance can be obtained in the condition of four CNEMs, it can be assumed that all work well for one to three CNEMs. To this end, the simulated far-field spectral responses of the four CNEMs under four different resonance wavelengths are shown in Fig. 3, wherein λres1 to λres4 represent four resonance wavelengths [in Fig. 2(d)] under deformation parameters ɛ1 to ɛ4. A unidirectional emission is strongly peaked around the far-field angle 0°. The in-plane beam divergence of four CNEMs for respective wavelengths is still very narrow, instead of interfering with each other. Good agreement can be observed between the far-field intensity profiles (insets in Fig. 3) and the far-field angle polar plots (Fig. 3). The fact that such multi-wavelength unidirectional emissions can be obtained with such a miniature structure is attractive for the design and fabrication of multi-wavelength microlasers.
Fig. 3. Comparison of the far-field profiles for four CNEMs with different notch sizes. Insets: Far-field profiles for the highest intensity in the hemispheres above the CNEMs.
In order to further investigate the characteristics of CNEM, the effect due to the notch sizes on the far-field profiles is considered. The notch on the boundary of the studied four CNEMs acts as the scatterer and is critical for the unidirectional emission, which is shown in Fig. 3. It can be seen that the unidirectional emission is totally spoiled without a notch for all the four microdisks. Variations from w=0.3µm, h = d=0.25µm; w=0.35µm, h = d=0.25µm; to w=0.35µm, h = d=0.3µm do not appreciably affect the far-field emission distribution. Far-filed profiles (top insets) of the highest intensities for four microdisks show good agreements with the far-field angle plots (bottom insets). Therefore, CNEM is robust and relatively insensitive to deviations caused by fabrication uncertainties.
Additionally, in order to quantify the directionality of the emission, a measure of directionality is introduced,
where I(θ) represents the angular intensity distribution in the far-field [23]. In the following, θ=30° is set. The ratio between the intensity emitted into a ±30° window around 0° and the total emission intensity is studied. The detailed illustration of emission efficiency and FWHM with different resonance wavelengths for one CNEM is illustrated in Table 1 and Fig. 4(a). As it is shown, both the peaks of the emission efficiency and the valleys of the FWHM are mostly within the range of resonance wavelengths for one to four CNEMs, which is preferable for lasing applications. In addition, an inverse trend of emission efficiency and FWHM with wavelength can be seen, meaning the lowest FWHM contributes the best emission efficiency, which is 84.2%. With the increase of numbers of CNEMs, illustrated in Fig. 4(b), the emission efficiency and FWHM are still stabilized, meaning the whole structure is robust without cross-talk.Fig. 4. Emission efficiency and FWHM versus resonance wavelengths for one CNEM (a) and No. of CNEMs (b). The dashed line in (a) represents the range of resonance wavelengths of four CNEMs.
Table 1. Illustration of circumferences and emission wavelengths with different deformation parameters from one to four CNEMs.
4. Conclusion
In conclusion, a novel type of multi-wavelength WGM resonator from CNEM was realized through combining multiple deformed microdisk resonators creatively within a certain range of the deformation parameter. It is demonstrated that the near- and far-field profiles of each CNEM are separated without interfering with each other. It exhibits a relatively high optical quality factor of 4000, unidirectional emissions with low far-field divergence ∼4° and the highest emission efficiency can reach 84.2% in visible wavelength region. Additionally, the unidirectional emission can be adjusted to the targeted wavelength through conveniently upsizing or downsizing a deformed polymer microdisk. The effect of the notch size on the far-field emission is analyzed, demonstrating that the resonator is robust and relatively insensitive to deviations caused by fabrication uncertainties. This letter demonstrates a unique but generic scheme of cost-effective, easily controllable, and high-performance microresonators, which not only provides an excellent platform to explore light-matter interaction, but also has great potential for the new practical multi-wavelength microlasers.
Funding
Shanghai Young Oriental Scholar Project (QD2019); Higher Education Discipline Innovation Project (D20031); Natural Science Foundation of Shandong Province (ZR2017MF038).
Disclosures
The authors declare no conflicts of interest.
References
1. M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482(7384), 204–207 (2012). [CrossRef]
2. X. Ma, S. Fan, H. Wei, Z. Zuo, S. Krishnaswamy, and J. Fang, “Miniature resonator sensor based on a hybrid plasmonic nanoring,” Opt. Express 27(23), 33051–33060 (2019). [CrossRef]
3. H. Wei and S. Krishnaswamy, “Polymer micro-ring resonator integrated with a fiber ring laser for ultrasound detection,” Opt. Lett. 42(13), 2655–2658 (2017). [CrossRef]
4. Y. Deng, R. K. Jain, and M. Hossein-Zadeh, “Demonstration of a cw room temperature mid-IR microlaser,” Opt. Lett. 39(15), 4458–4461 (2014). [CrossRef]
5. J. Feng, X. Jiang, X. Yan, Y. Wu, B. Su, H. Fu, J. Yao, and L. Jiang, “'Capillary-Bridge Lithography’ for Patterning Organic Crystals toward Mode-Tunable Microlaser Arrays,” Adv. Mater. 29(1), 1603652 (2017). [CrossRef]
6. G. Y. Zhu, J. T. Li, Z. S. Tian, J. Dai, Y. Y. Wang, P. L. Li, and C. X. Xu, “Electro-pumped whispering gallery mode ZnO microlaser array,” Appl. Phys. Lett. 106(2), 021111 (2015). [CrossRef]
7. H. Wei and S. Krishnaswamy, “Adaptive fiber-ring lasers based on an optical fiber Fabry-Perot cavity for high-frequency dynamic strain sensing,” Appl. Opt. 59(2), 530–535 (2020). [CrossRef]
8. H. Wei, A. K. Amrithanath, and S. Krishnaswamy, “Multi-wavelength erbium-doped fiber ring lasers based on an optical fiber tip interferometer,” In Optical Components and Materials XVI, (International Society for Optics and Photonics, 2019), p. 1091420.
9. L. He, Ş. K. Özdemir, and L. Yang, “Whispering gallery microcavity lasers,” Laser Photonics Rev. 7(1), 60–82 (2013). [CrossRef]
10. L. Zou, X. Lv, Y. Huang, H. Long, Q. Yao, J. Xiao, and Y. Du, “Four-wavelength microdisk laser array laterally coupled with a bus waveguide,” Opt. Lett. 38(19), 3807–3810 (2013). [CrossRef]
11. J. V. Campenhout, L. Liu, P. R. Romeo, D. V. Thourhout, C. Seassal, P. Regreny, L. D. Cioccio, J. Fedeli, and R. Baets, “A compact SOI-integrated multiwavelength laser source based on cascaded InP microdisks,” IEEE Photonics Technol. Lett. 20(16), 1345–1347 (2008). [CrossRef]
12. S. J. Choi, Z. Peng, Q. Yang, S. J. Choi, and P. D. Dapkus, “Eight-channel microdisk CW laser arrays vertically coupled to common output bus waveguides,” IEEE Photonics Technol. Lett. 16(2), 356–358 (2004). [CrossRef]
13. S. Sui, M. Tang, Y. Yang, J. Xiao, Y. Du, and Y. Huang, “Sixteen-wavelength hybrid AlGaInAs/Si microdisk laser array,” IEEE J. Quantum Electron. 51(4), 1–8 (2015). [CrossRef]
14. G. Zhu, J. Li, P. Li, Z. Tian, J. Dai, Y. Wang, Z. Shi, and C. Xu, “Different wavelength ranges’ WGM lasing from a ZnO microrod/R6G: PMMA microcavity,” Europhys. Lett. 110(6), 67007 (2015). [CrossRef]
15. H. Uehara, T. Yano, and S. Shibata, “Terrace-microsphere lasers: spherical cavity lasers for multiwavelength emission,” In Optical Components and Materials VII (International Society for Optics and Photonics, 2010), p. 75981E.
16. J. Pfeifle, A. Coillet, R. I. Henriet, K. Saleh, P. Schindler, C. Weimann, W. Freude, I. V. Balakireva, L. Larger, C. Koos, and Y. K. Chembo, “Optimally coherent Kerr combs generated with crystalline whispering gallery mode resonators for ultrahigh capacity fiber communications,” Phys. Rev. Lett. 114(9), 093902 (2015). [CrossRef]
17. J. V. Campenhout, P. R. Romeo, D. V. Thourhout, C. Seassal, P. Regreny, L. D. Cioccio, J. Fedeli, and R. Baets, “Design and optimization of electrically injected InP-based microdisk lasers integrated on and coupled to a SOI waveguide circuit,” J. Lightwave Technol. 26(1), 52–63 (2008). [CrossRef]
18. Y. Wang, V. D. Ta, K. S. Leck, B. H. I. Z. Wang, T. He, C. Ohl, H. V. Demir, and H. Sun, “Robust whispering-gallery-mode microbubble lasers from colloidal quantum dots,” Nano Lett. 17(4), 2640–2646 (2017). [CrossRef]
19. H. Cao and J. Wiersig, “Dielectric microcavities: Model systems for wave chaos and non-Hermitian physics,” Rev. Mod. Phys. 87(1), 61–111 (2015). [CrossRef]
20. J. Wiersig and M. Hentschel, “Combining directional light output and ultralow loss in deformed microdisks,” Phys. Rev. Lett. 100(3), 033901 (2008). [CrossRef]
21. F. Albert, C. Hopfmann, A. Eberspächer, F. Arnold, M. Emmerling, C. Schneider, S. Höfling, A. Forchel, M. Kamp, J. Wiersig, and S. Reitzenstein, “Directional whispering gallery mode emission from Limaçon-shaped electrically pumped quantum dot micropillar lasers,” Appl. Phys. Lett. 101(2), 021116 (2012). [CrossRef]
22. M. Schermer, S. Bittner, G. Singh, C. Ulysse, M. Lebental, and J. Wiersig, “Unidirectional light emission from low-index polymer microlasers,” Appl. Phys. Lett. 106(10), 101107 (2015). [CrossRef]
23. X. Ma, S. Fan, H. Wei, A. Amrithanath, J. Fang, and S. Krishnaswamy, “Notched-elliptical polymer microdisk resonator for unidirectional emission at visible and near-infrared wavelengths,” Appl. Phys. Express 13(5), 052002 (2020). [CrossRef]
24. R. K. Luneburg, “Mathematical theory of optics,” Univ of California Press, Chap 3, (1964).
25. Q. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Dieh, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. 107(52), 22407–22412 (2010). [CrossRef]
26. Y. Sun and X. Fan, “Optical ring resonators for biochemical and chemical sensing,” Anal. Bioanal. Chem. 399(1), 205–211 (2011). [CrossRef]
27. S. Dottermusch, D. Busk, M. Langenhorst, U. W. Paetzold, and B. S. Richards, “Exposure-dependent refractive index of Nanoscribe IP-Dip photoresist layers,” Opt. Lett. 44(1), 29–32 (2019). [CrossRef]
28. V. Ta, S. Yang, Y. Wang, Y. Gao, T. He, R. Chen, H. Demir, and H. Sun, “Multicolor lasing prints,” Appl. Phys. Lett. 107(22), 221103 (2015). [CrossRef]
