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We develop a versatile integrated opto-fluidic ring resonator (OFRR) dye laser that can be operated regardless of the refractive index (RI) of the liquid. The OFRR is a micro-sized glass capillary with a wall thickness of a few micrometers. When the liquid in the core has an RI lower than that of the capillary wall (n=1.45), the capillary circular cross-section forms the ring resonator and supports the whispering gallery modes (WGMs) that interact evanescently with the gain medium in the core. When the core RI is higher than that of the wall, the WGMs exist at the core/wall interface. In both cases, the WGMs can have extremely high Q-factor (>109), providing excellent optical feedback for low-threshold lasing. In this paper, we analyze the OFRR laser for various core RI’s and then we demonstrate the R6G laser when the dye is in ethanol (n=1.36), chloroform (n=1.445), and quinoline (n=1.626). The lasing threshold of 25 nJ/mm2 is achieved, two to three orders of magnitude lower than the previous work in microfluidic lasers. We further show that the laser emission can be efficiently out-coupled via an optical waveguide in touch with the OFRR for both high and low RI liquid core, allowing for easy guiding and delivery of the laser light.
©2007 Optical Society of America
1. Introduction
Microfluidic lasers have recently been under intensive investigation for micro-total-analysis systems and compact light sources [1–7]. They belong to an important emerging field of optofluidics [8,9], in which photonics and microfluidics are integrated to achieve new functionalities. In those lasers, the optical feedback is provided by embedded distributed feedback (DFB) gratings [2,5,7] or integrated Fabry-Pérot-type resonators [1,3,4,6]. Optical ring resonators have also been utilized in microfluidics lasers [10–14]. In a ring resonator, the whispering gallery modes (WGMs) form at the boundary of high and low refractive index (RI) media [15]. The WGMs generally have high Q-factors, leading to low lasing thresholds. There are two types of ring resonator microfluidic lasers. In the first type, as exemplified by a microdroplet or a glass capillary filled with the liquid whose RI is higher than that of the wall (n=1.45), the ring resonator is formed by the liquid itself and the WGM is predominantly confined within the high index liquid [10,11,14]. In the second type of ring resonator microfluidics lasers, the WGM is confined in a solid dielectric ring resonator and its evanescent field protrudes into the surrounding liquid of low RI [12,13].
In microfluidic lasers, especially in the ring resonator based lasers, selection of a liquid with an appropriate RI is critical. For example, high RI liquid is needed in DFB lasers and liquid waveguide lasers [4,5,7]. High index core is also necessary to achieve lasing in a capillary with a thick wall (tens to hundreds of micrometers) and no lasing is observed when the core RI is lower than that of the wall [11,14]. On the other hand, for the ring resonator lasers that rely on the evanescent gain in the surrounding medium, the low RI liquid is imperative, as no WGM would exist when the RI of the liquid is larger than that of the ring resonator. The requirement of the liquid RI has significantly limited the flexibility and practicality of microfluidic lasers.
In this paper, we develop a versatile opto-fluidic ring resonator (OFRR) dye laser that can be operated with liquids of any RI. The OFRR, illustrated in Fig. 1(A), is based on a thin-walled fused silica (n=1.45) capillary with an outer diameter (OD) of a few tens to a few hundreds of micrometers and a wall thickness of a few micrometers [16,17]. It naturally integrates the ring resonator with microfluidics. When the RI of the liquid core is low, the circular cross-section of the capillary wall forms the ring resonator. The WGMs are mainly confined at the boundary between the wall and the surrounding medium (typically, air). The thin wall ensures that the WGMs of high Q-factors have sufficient exposure to the core to support the dye lasing through the evanescent gain [16]. When the liquid RI increases, the WGM gradually shifts towards the core. A new set of the WGMs form at the liquid/wall interface when the core RI becomes higher than that of the wall. As a result, the OFRR can support the microfluidic lasers regardless of the core RI.
We use R6G dissolved in ethanol (n=1.36), chloroform (n=1.445), and quinoline (n=1.626) to demonstrate the OFRR lasing performance. First, theoretical analysis is performed to analyze the OFRR laser with various core RI’s and then we show that an unprecedented lasing threshold on the order of 10 nJ/mm2 can be achieved due to extremely high Q-factors (> 109). Furthermore, the laser emission can be efficiently coupled out through a waveguide in touch with the OFRR for both low and high liquid RI, which provides an excellent mechanism for light guiding and delivery.
2. Theory
We first investigate the behavior of the WGM in the OFRR when the liquid core RI varies. Detailed analysis can be found in our previous work [18]. Figure 2 plots the WGM intensity distribution for the core RI (n1) of 1.36, 1.445, and 1.626. When the core RI is lower than that of the wall, the WGM is mainly confined within the wall and has an evanescent field exposed to the core, which provides the feedback for lasing [Fig. 2(A)]. It should be emphasized that the wall thickness is crucial in low-threshold lasers, as the thick wall prevents the low order WGMs, which have high Q-factors, from being exposed to the core. As reported in Refs. [11,14], no lasing is observed when the thick-walled capillary is filled with ethanol.
When the core RI is 1.445 [Fig. 2(B)], the OFRR becomes virtually a homogeneous cylindrical ring resonator; and more light is pulled towards the core. When the core RI becomes higher than that of the wall, the core itself becomes the ring resonator and the WGMs exist at the core/wall boundary, as shown by the ripple-like structure in Fig. 2(C). Meanwhile, another set of WGMs exist at the boundary between the wall and air. Since the wall is thin, the WGMs in these two boundaries interact and form bonding and anti-bonding modes [18,19]. Figure 2(C) shows a new hybrid mode formed by the 4th order WGM in the core interacting strongly with the 6th order WGM in the wall. These new modes have large presence in both core and wall and also have sufficient exposure outside the ring for the coupling to the waveguide, as discussed later.
Fig. 2. WGM distribution for an OFRR with OD = 75 μm and wall thickness, t = 5 μm when the core RI (n1) is 1.36 (A), 1.445 (B), and 1.626 (C). The wall RI (n2) is 1.45 and the RI for the surrounding medium (n3) is 1.0. The WGM spectral position, λ, and the corresponding angular momentum, l, are labeled in the figure. All modes are polarized along the OFRR longitudinal direction. The fraction of light in the core (η1) and outside the resonator (η3) is: (A) η1 = 0.2%, η3 = 0.6%. (B) η1 = 0.9%, η3 = 0.6%. (C) η1 = 4.7%, η3 = 0.53%. Dashed lines indicate the OFRR inner and outer surface.
Note that in this thin-walled OFRR, extremely high radiation Q-factors persist even for relatively high order WGMs due to the large RI contrast between the wall and the air (1.45/1.0). For example, all WGMs shown in Fig. 2 have a Q-factor in excess of 1011. For a comparison, for the thick-walled capillary that uses the liquid core as the resonator, Q-factors are on the order of 106 when the RI is (1.626/1.45) [11,20,21]. For those second-type ring resonators that rely on the contrast between the resonator and the surrounding dye solution, the Q-factor will be completely destroyed when the liquid RI approaches that of the wall because of radiation loss.
In an OFRR, WGMs reside in both core and wall. Therefore, only a fraction of the WGM interacts with the gain medium. The lasing behavior of this partially interacting system has been analyzed by Moon et al. [12]. For a given dye concentration, the minimum fraction of the excited molecules, γ(λ), is given by:
where σa and σe are the absorption and emission cross section, respectively. Qdye is the Q-factor related to the dye absorption, i.e., Qdye = 2πn2/λσaρ. n2 is the RI of the wall, λ is the WGM wavelength, and ρ is the dye concentration. η1 is the fraction of the WGM in the core. Qempty is the empty cavity Q-factor when the ring resonator is filled with the solvent in the absence of dye. Qempty is determined by:
where Qrad, Q wall, and Qsca are the Q-factor determined by the radiation loss, loss in the wall medium, and loss resulting from the surface scattering. Qsol = 2πn2/λαsol, where αsol is the absorption coefficient of the solvent.
When η1Qempty >> Qdye, all WGMs have nearly the same lasing threshold with the lasing position determined by σa/σe. The lasing threshold and its spectral position are insensitive to the change in Qempty. On the other hand, when η1Qempty << Qdye, the lasing threshold depends on η1Qempty and the lasing wavelength is determined by l/σe, as shown later. Another special case is when Qempty in Eq. (2) is limited by the solvent absorption,
suggesting that the lasing threshold is independent of η1 and that all modes should have the same lasing threshold, regardless of the value of Qempty relative to Qdye.
3. Experiment
The OFRR up to 50 cm long is fabricated with a computer controlled pulling station where a fused silica capillary preform (Polymicro TSP530660, OD = 616 μm and wall thickness: t = 40 μm) is stretched under heat. The resulting OFRR has an OD of 75 μm and a wall thickness of 5 μm, as shown in Fig. 1(B), suggesting that the original aspect ratio (OD:t) can be well maintained. Previously, the thin-walled OFRR was obtained by using HF etching, which is time consuming and may decrease the Q-factor due to the increased surface roughness [16,22]. With our current method, fabrication is completed in a few minutes and the OFRR size can be adjusted during the fabrication. Additionally, extremely high Q-factors can be obtained, as discussed later. Therefore, the OFRR offers a very promising microfluidic laser technology that rivals other types of microfluidic dye lasers that require more sophisticated microfabrication facilities and techniques [1–7].
The experimental setup is illustrated in Fig. 1(A). Both ends of the 3-cm long OFRR are connected to plastic tubing and the dye solution is circulated through the OFRR at a flow rate of 10 μL/min. A pulsed laser (Opolette, 532 nm, 10 ns pulse width, 20 Hz repetition rate) is loosely focused onto the side of the OFRR through a cylindrical lens so that a 1 mm portion of the capillary is excited. The pump power is adjusted by a neutral density filter. The dye emission is collected through free space or by an optical fiber taper of approximately 2 μm in diameter in touch with the OFRR, and then is sent to a spectrometer (Ocean Optics USB4000, spectral resolution of 3.7 nm), as shown in Fig. 1(A).
Figure 3(A) shows the lasing emission spectra for R6G in ethanol. The peak is at 602 nm. Figure 3(B) plots the lasing peak as a function of the pump intensity. It is shown that the lasing threshold is approximately 25 nJ/mm2, two to three orders of magnitude lower than that in previously reported microfluidic dye lasers [1–7,16], reflecting the excellent performance of the OFRR as a laser cavity.
The laser threshold and the spectral position of the first lasing peak can be analyzed using the equations and discussion in the previous section. We have performed a detailed analysis on the Q-factors of the WGMs and found that all WGMs (up to 15th order) have Qrad>>1011. For ethanol, Qsol ~ 108, since αsol ~ 0.001 cm-1 [23, 24]. The fraction of the evanescent light in the core, η1, can be assumed to be 1% (see Fig. 2). Fused silica absorption and surface roughness induced losses have been investigated in detail with microspheres, which show a Q-factor as high as 8×109 [25,26]. Therefore, the OFRR that uses the same material and is fabricated under the similar heating condition as for microspheres should have a Qempty well above 109. This result represents two orders of magnitude improvement in the Q-factor over our previous OFRR, in which the Q-factor is measured to be 107, limited by the surface roughness resulting from the HF etching [16].
Fig. 3. (A) Laser emission spectra of the 2 mM R6G in ethanol. (B) Peak intensity at 602.5 nm vs pump power density (triangle). The linear fit (solid line) shows the lasing threshold is approximately 25 nJ/mm2.
Figure 4(A) shows the lasing spectra for various R6G concentrations. When R6G is 1–2 mM, the Qdye is about 106 at 600 nm. According to Eq. (1), when η1Qempty >> Qdye, the lasing threshold minimum is broad around 600 nm, as shown by Curve 1 and 2 in Fig. 4(B). Further increase in η1Qempty does not lead to any significant change in the predicted spectral position of the laser emission. One way to estimate η1Qempty is to reduce the dye concentration, hence increasing Qdye, such that the lasing spectral position becomes sensitive to η1Qempty, as shown experimentally and theoretically in Figs. 4(A) and 4(B), respectively. When η1Qempty < Qdye, a decrease in η1Qempty will result in a blue shift in the lasing wavelength, The lowest concentration to achieve lasing is 0.002 mM [Curve 4 in both Figs. 4(A) and 4(B)] and the lasing wavelength is at 562 nm, indicating that η1Qempty ~ 4×106. When η1Qempty = 4×105, the lasing peak is expected to be below 560 nm. No lasing can be achieved when the η1Qempty is further decreased, as γ should be less than unity. η1Qempty = 4×106 can indeed be achieved in the OFRR. One of the WGMs is given in Fig. 2(A), in which η1 is 0.2%, which corresponds to Qempty=2×109. Furthermore, comparison between Curve 1 (current laser condition) and 3 (for the laser in Ref. [16]), the γ value or lasing threshold is reduced by 40 fold, consistent with what is observed experimentally.
Fig. 4. (A) Laser emission spectra for R6G in ethanol when the pump power is slightly above the threshold. R6G concentration for Curve 1–4 is: 2 mM, 1 mM, 0.01 mM, and 0.002 mM. Curves are vertically shifted for clarity. (B) γ value for various η1Qempty and R6G concentrations. Curve 1: η1Qempty = 4×106, ρ = 2 mM; Curve 2: η1Qempty = 4×106, ρ = 1 mM; Curve 3: η1Qempty = 4×106, ρ= 0.01 mM (or η1Qempty = 4×104, ρ= 1 mM); Curve 4: η1Qempty = 4×106, ρ = 0.002 mM; Curve 5: η1Qempty = 4×105, ρ = 0.002 mM; Curve 6: η1Qempty = 4×104, ρ = 0.002 mM;
To demonstrate that the lasing can also be achieved with a larger core RI, in Fig. 5(A) and (B), ethanol is replaced by chloroform (n1=1.445) and quinoline (n1=1.626), respectively. Chloroform has absorption on the order of 10-4 cm-1 [24], therefore, η1Qempty for chloroform is similar to that for ethanol. For quinoline, our absorption measurement shows that Qsol is approximately 106 at 600 nm. According to Eq. (2), Qempty is limited by the solvent absorption. Figure 5(C) plots the γ value using Eq. (3), which still has a broad minimum around 600 nm.
Fig. 5. Laser emission spectra at various excitation power levels for R6G in chloroform (A) and quinoline (B). (C) γ values for R6G in quinoline that is used in Eq. (3). R6G concentration: 2 mM.
This laser peak position is confirmed by the experimental results in Fig. 5(B). In addition, the γ value for quinoline is twice the value for ethanol [Curve 1 in Fig. 4(B)], in agreement with the higher lasing threshold observed experimentally for R6G in quinoline.
The laser emission can be out-coupled by an optical fiber taper or a waveguide in touch with the OFRR. The coupling efficiency is determined by:
where Qfiber is the Q-factor related to the fiber coupling loss. Note that during lasing the dye absorption does not contribute to the cavity Q-factor degradation due to the inversion achieved in the dye molecules. This evanescent coupling through a fiber or waveguide coupling can be very efficient. For example, at the critical coupling where Qfiber = Qempty, 50% of the light can be coupled out. Figure 6 shows the spectra of the laser emission out-coupled by an optical fiber taper (approximately 2 μm in diameter) when the pump is well above the R6G lasing threshold. This shows that the light can be coupled out even when the core RI is greater than that of the wall. Also note that the pump light and the broad spontaneous emission are significantly suppressed in the output signal.
It should be emphasized once again that the wall thickness plays an important role in efficient light out-coupling. Although a thick-walled capillary supports the lasing oscillation (when the core RI is higher than that of capillary) [11,21], the laser emission can not be coupled out via a tapered fiber or a waveguide since those core modes at the core/wall interface are completely shielded by the thick wall [18]. Additionally, due to large phase mismatch between the core WGMs and the fiber or waveguide, the coupling strength decreases extremely fast with the increased wall thickness [18].
Fig. 6. Spectra of the laser emission coupled through the same optical fiber taper. R6G is in ethanol (A), chloroform (B), and quinoline (C). R6G concentration: 2 mM.
4. Summary and future work
We have analyzed and demonstrated a versatile microfluidic dye laser based on the OFRR that can be operated with the liquid in the core having either lower or higher RI than that of the ring resonator. Extremely low lasing threshold on the order of 10 nJ/mm2 has been achieved due to extremely high Q-factors (>109). The laser emission can be efficiently coupled out through a waveguide in touch with the OFRR, thus providing convenient light delivery. All of these meritorious features, together with the advantage of extremely simple OFRR fabrication, make the OFRR a very promising technology in microfluidic laser development.
Future work will be focused on indirect excitation through resonant energy transfer to achieve an even lower lasing threshold [17], tuning the OFRR laser, and obtaining single mode lasing [27]. Additionally, embedding the OFRR into a low-index polymer is another very interesting area to explore, which enables the OFRR based laser to be integrated with polymer based microfluidics [28]. Furthermore, OFRRs with a thinner wall will be pursued to expose more light to the core. Finally, using OFRR in actual biosensing will also be investigated.
Acknowledgments
This work is sponsored by the 3M Non-Tenured Faculty Award and the Wallace H. Coulter Foundation. SL is a visiting professor from Franklin & Marshall College and is supported by an award from Research Corporation.
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