Control of spontaneous emission coupling factor β in fiber-coupled microsphere resonators

Abstract

The spontaneous emission coupling factor ␤ is studied for fiber-coupled microspheres with a thin gain layer of phosphorus codoped sol-gel erbium silica-aluminum glass. From the input-output characteristics of the lasing, ␤ = 0.039 is estimated for a sample with a gain layer on the sphere surface. ␤ is estimated to increase to 0.19 when an additional silica glass thin layer is overcoated to improve the overlap between the gain layer and the optical mode of the lasing inside the sphere. [4][5][6][7][8][9] In addition to Q values and coupling efficiency, a crucial parameter for its applications is the spontaneous emission coupling factor ␤, defined as the fraction of spontaneous emission coupled into a cavity mode with respect to the spontaneous emission into all modes. 10 To realize microsphere lasers with a low lasing threshold, it is essential to improve ␤. Moreover, ␤ is important for the realization of optical quantum information devices, such as single photon sources 11 and quantum phase gates. 12,13 The ␤ factor has been investigated in sole liquid microdroplets and polymer microspheres ͑without tapered-fiber coupling͒. Chang and Campillo measured the stimulated Raman scattering in carbon disulfide microdroplets of 8 m diameter. 14 They observed an absence of a clear threshold and estimated ␤ to be about 0.42. Kuwata-Gonokami and Takeda demonstrated lasing in a 5 m diameter polystyrene microsphere with a dye doped surface layer. 15 From the input and output characteristics near the lasing threshold, they estimated ␤ to be 0.3. However, these studies were for sole microspheres using free-space laser pumping and ␤ factors for fiber-coupled microspheres have not been fully investigated.In this letter, we report the estimation of ␤ factors for fiber-coupled microspheres. We also study the change of ␤ factor according to the location of the gain layer inside the sphere. For this study, the thickness of the gain layer has to be sufficiently smaller than the distribution of the optical mode in the sphere. For this purpose, we used a method to fabricate a fiber-coupled microsphere laser with a submicron thickness gain layer. 9 By overcoating an undoped sol-gel silica glass thin layer to improve the overlap between the gain layer and the optical mode in the sphere, ␤ of a sample with a gain layer on the sphere surface was increased from 0.039 to 0.19.Overcoating of an undoped sol-gel silica glass on a precoated gain layer produces optimal coupling between the gain layer and the optical mode in a microsphere. Figure 1 shows the calculated distribution of the thin gain layer and the optical mode in a 40 m diameter microsphere at 1535.7 nm wavelength, corresponding to the emission wavelength of Er. The calculation of the optical mode was based on the Lorenz-Mie theory. 16 The optical mode is confined in the region about 600 nm inside from the surface with full width at half maximum of about 1000 nm. To realize a large ␤, it is essential to locate the gain layer at the peak of the optical mode. Considering the thickness...

Photonic atoms and molecules

“…4a and b). Much of the work being done on WGM microcavities has been to achieve the ultimate quality factors [45,46] required for investigations of cavity quantum electrodynamics [23], quantum informatics applications [47][48][49] and nonlinear optics [50,51] in a regime of strong coupling. The typical value of Q-factor for composite CdTe QDs/microcavity of 3 µm size is $ 3500, which corresponds to the value of average photon storage time $ 1 ps.…”

WGM microresonators: sensing, lasing and fundamental optics with microspheres

“…For example, Yang and Vahala [25] used the sol-gel method to cover the surface of SiO 2 microspheres with a 1-μm thick erbium-doped layer from which 1530-nm lasing was observed with a threshold of 26 μW. Recently, Takashima et al [84] showed that by overcoating the sol gel layer with a layer of SiO 2 to a total thickness of 200 nm the coupling coefficient of the lasing emission into selected WGM can be increased from 0.039 to 0. old of 65 nW at 1050 nm was observed from a SiO 2 sphere coated with neodymium-doped gadolinium oxide nanocrystals [85]. In another novel approach, a SiO 2 microsphere was coated with a layer of erbium-doped phosphate glass.…”

Optical Characterization and Lasing in Three-Dimensional Opal-Structures

“…Weak fluorescence of Rh6G still remained, since the energy transfer efficiency is not 100%. The dependence of a lasing threshold on donor-acceptor concentrations can be quantified via a spontaneous emission coupling ratio β (Horowicz et al, 1992;Takashima et al, 2008). To determine the β value, defined as the fraction of spontaneous emission coupled into a lasing mode with respect to the spontaneous emission into all modes, the input-output power relationship was modeled using a rate equation (Yokoyama and Brorson, 1989;Kippenberg et al, 2006):…”