1. Introduction

One of the trends in modern photonics is the development of miniature devices based on microresonators with whispering gallery modes (WGMs) [1,2]. Such WGM resonators have huge Q-factors and enormous nonlinear coefficients, which allows exploiting nonlinear and laser effects at very low pump powers. Microresonators are in demand for a variety of applications such as spectroscopy, telecommunications, sensors, optical filters and switches, quantum communications, and many others [1,2].

Chalcogenide glasses are very attractive and promising materials for use in various photonic devices [3], including microresonators [4–7]. Chalcogenide glasses have huge values of cubic Kerr and Raman nonlinearities, two-three orders of magnitude higher than the corresponding values for silica glass [3]. Chalcogenide glasses are transparent in the mid-IR range, therefore they are actively used for this spectral region [3]. Currently, fibers based on As₂S₃ and As₂Se₃ glasses are commercially available. Microspheres with Q factors > 7×10⁷ can be made of such fibers [4]. Note that chalcogenide microresonators can be also fabricated on-chip [8,9] which also corresponds to current trends [10].

Raman lasing in a chalcogenide microsphere was demonstrated for the first time in Ref. [4] with a pump at a wavelength of 1550 nm and an ultra-low coupled pump power threshold of 13 μW. In Ref. [5], the authors reported multimode cascade Raman lasing in an As₂S₃ microsphere with a maximum order of five when pumped at 1557 nm and with a number of orders of three when pumped at 1880 nm, the longest achieved Raman wavelength was almost 2400 nm. In cascade processes, under the action of continuous wave (CW) pump, initially the first-order Raman radiation is generated which serves as the pump for the second-order Raman radiation, then the second-order radiation is the pump for the third-order Raman radiation, and so on.

Potentially, Raman generation in chalcogenide microspheres can be obtained in the mid-IR range, which is inaccessible, for example, for silica microresonators. However, even in the telecommunication range, chalcogenide microspheres made of As₂S₃ glass can have certain advantages. The maximum of the Raman response function for As₂S₃ glass corresponds to 10.3 THz [11]. This enables Raman lasing in the L-band with a C-band pump, which may be important for some applications. Note that since the maximum of the Raman response function for silica glass corresponds to 13.2 THz, using a quite standard C-band pump leads to Raman lasing in the longer-wavelength U-band [12]. Moreover, the Raman gain bandwidth is twice narrower for As₂S₃ glass compared with silica glass [11], which can be beneficial for development of single-mode Raman microlasers including cascade operated, since fewer WGMs can be effectively amplified. However, to date, we are not aware of the achievement of single-mode lasing in As₂S₃ microspheres.

Here, we demonstrate single-mode Raman lasing with a more than 50-nm wavelength tuning achieved solely by a pump wavelength tuning in an As₂S₃ glass microsphere, for the first time to the best of our knowledge, in chalcogenide microresonators. When a pump power in the C-band is relatively low, single-mode Raman generation in the L-band and the U-band is attained. When the pump power significantly exceeds the threshold, multimode cascade Raman lasing up to the fourth order with the longest wavelength >2 μm is achieved. Note that in previous demonstrations of Raman lasing in chalcogenide glass microspheres specially designed self-frequency locked lasers were used that gave no control over generation wavelengths [5]. Here we use a commercially available tunable telecommunication laser module allowing us to control Raman wavelengths in a simple scheme. The numerical simulation of the Lugiato-Lefever equation is also performed for better understanding of observed Raman lasing. A good agreement between experimental and numerical results is demonstrated.

In addition, it is known that different processes based on high Kerr nonlinearity is extensively studied in chalcogenide glass waveguides and fibers [3]. But we do not know about experimental demonstrations of Kerr-based new wavelength generation in chalcogenide microspheres. Here, generation of up-converted radiation in the O-band at 1.38 μm interpreted as a result of four-wave mixing due to the Kerr nonlinearity between the pump wave and the second-order Raman wave is also reported, for the first time to the best of our knowledge, in chalcogenide microresonators.

2. Experimental details

Chalcogenide glass microspheres were fabricated in air atmosphere from As₂S₃-based commercially available fiber (IRflex Corporation, IRF-S-5, step-index fiber with 5/100/280 μm core/cladding/coating diameters and 0.3 numerical aperture). We believe that the step-index profile does not affect WGM properties since the field is confined near a surface and the glass of thin core remains inside a sample. The protective polymer coating was removed and after that a piece of a chalcogenide fiber was softened and gradually stretched to form a taper with a minimum diameter of about 20 μm using a home-made resistive micro-heater. This stage is shown in the photo in Fig. 1(a). Then the chalcogenide taper was divided into two parts by an abrupt increase of the heater power and fast pulling of the taper. Next, one end of the tapered As₂S₃ fiber was inserted vertically into the wire coil of the micro-heater near the upper edge of the coil [see Fig. 1(b)]. The thin end of the chalcogenide taper was heated and melted by radiative heat transfer as a result of which a microsphere was formed under the influence of surface tension forces. The process was monitored by an optical microscope and the heater power could be adjusted in real time. The microsphere diameter controlled by changing the heating duration. We produced samples with diameters ranging from 34 μm to 320 μm but Raman lasing was observed only in the smallest one with the Q-factor of 10⁶. The image of the microsphere with diameter d ∼ 34 μm obtained with an optical microscope (Motic BA310) is presented in Fig. 1(c). We calculated a free spectral range (FSR = 1.15 THz) for the TE fundamental modes of this microsphere similarly to [13] with the linear refractive index for As₂S₃ glass taken from Ref. [14]. We also calculated the second-order dispersion β₂ ≈ 550 ps²/km, the effective mode volume of 210 μm², and the nonlinear Kerr coefficient of 4.5·10³ (W·km)⁻¹ for the fundamental TE mode family at pump wavelengths.

 

Fig. 1. Two stages of manufacturing As₂S₃ chalcogenide glass microsphere from a fiber: (a) softening and stretching a piece of chalcogenide fiber with a resistive micro-heater; (b) forming a microsphere under the influence of surface tension forces from a tapered As₂S₃ fiber end. (c) Image of As₂S₃ microsphere obtained with an optical microscope. (d) Simplified experimental scheme.

Download Full Size | PDF

The experiments on Raman lasing in the produced As₂S₃ microsphere were performed according to the scheme presented in Fig. 1(d). The study was conducted in an acrylic glove box (with working chamber dimensions 900×500×500 mm) to protect the As₂S₃ microsphere and fiber taper against dust and airflows from the conditioning air system. The As₂S₃ microsphere was pumped by a tunable CW C-band laser (Pure Photonics, PPCL550-180-60, tuning range 1.516-1.576 μm, line width 10 kHz). Coupling of the CW pump to the As₂S₃ microsphere and outcoupling of the generated Raman radiation were realized with a silica fiber taper as also shown in Fig. 1(d). The silica fiber taper was made of a commercially available fiber SMF28e by softening and stretching it in the flame of a gas burner. The waist diameter of the fabricated silica taper was about 2 μm. Coarse adjustment of relative position of the As₂S₃ microsphere and fiber taper was done manually using two CCD cameras also placed in the acrylic glove box. These CCD cameras showed images in perpendicular planes. The relative position between the As₂S₃ microsphere and the silica taper was adjusted with sub-100 nm accuracy by means of a computer-controlled three-axis translation stage with precision piezo actuators (Thorlabs MAX312D). By varying the relative positions we changed in experiment the coupling efficiency and the total Q-factor Q_total, since 1/Q_total = 1/Q_int + 1/Q_coupl, where Q_int is the intrinsic Q-factor and Q_coupl is the coupling Q-factor. Note that these characteristics affect Raman lasing dramatically.

The output spectra of the transmitted pump light and the generated Raman radiation in the telecommunication range were recorded by the Optical Spectrum Analyzer (OSA, Yokogawa AQ6370D, operating range 0.6–1.7 μm). Raman lasing in the range beyond the telecommunication one was also attained in experiments. As the OSA operating range is limited by 1.7 μm, the measurement scheme had to be modified to detect this kind of optical spectra. For this, we used an amplified PbSe detector (PDA20H, Thorlabs) together with a scanning grating monochromator (MS2004i, SOL Instruments Ltd.) integrated to the computer controlled scheme [see Fig. 1(d)].

3. Single-mode Raman lasing in L-band and U-band

In the first experimental series we aimed at obtaining wavelength-tunable single-mode Raman lasing by tuning a pump wavelength throughout the operating range of the C-band laser. The measured spectra are plotted in Fig. 2 (left column). These spectra also contain unconverted pump which goes through the silica fiber taper without coupling into the microsphere [see Fig. 1(d)]. The broad pedestals originate from the pump laser.

 

Fig. 2. Experimental spectra of tunable single-mode Raman lasing (left column) and the corresponding numerically simulated spectra (right column).

Download Full Size | PDF

To attain single-mode Raman lasing, the regime of sweeping the laser frequency near a certain value was turned on. The laser frequency changed in a sawtooth manner over time. When sweeping near a resonant WGM, bursts of Raman generation were observed periodically. Further we stopped the sweeping regime on the frequency descending branch, and after that the laser frequency was constant. Then a steady-state Raman lasing was often observed due to mode pulling [15]. Sometimes we observed multi-mode Raman lasing in different mode families (a distance between the generated modes was smaller than the FSR), which can be explained by a significant excess of the pump over the threshold. But frequently single-mode Raman lasing occurred. We could repeatedly initiate the same single mode generation regime by performing the frequency sweep with fixed start and end frequencies. For this series, the pump power was about 3 mW before the silica taper, but we did not know pump cavity detuning from the nearest WGM and the mode family to which this WGM belonged. Note that the effective volumes of the excited WGMs, the overlap integrals for pump and Raman fields, and the Q-factors depend on the mode family. We also adjusted the relative position of the As₂S₃ microsphere and the silica fiber taper for each pump wavelength which led to changing Q_coupl. So, we obtained tunable single-mode Raman lasing in the 1.610-1.663 μm range when the pump laser wavelength changed in the 1.522-1.574 μm range (see Fig. 2, left column). In the bottom subplot in Fig. 2 (left column) there are two Raman orders.

For better understanding of the observed effects, the nonlinear dynamics of the intracavity field leading to Raman lasing was simulated numerically. We modeled the dimensionless Lugiato-Lefever equation in the form given in Ref. [16] with the Raman response function for the As₂S₃ glass taken from Ref. [11]. We used home-made software based on the Split-step Fourier method as in Ref. [13]. The critical coupling was set (Q_int = Q_coupl). In the framework of the numerical model, we were able to obtain steady-state single-mode Raman spectra similar to the experimental ones (compare the left and right columns in Fig. 2). We set the constant pump power (|S|² = 200 dimensionless units [16]) but varied the dimensionless detuning Δ from the cavity resonance closest to the pump frequency [16]. The experimental and numerical results shown in Fig. 2 agree well. A slight difference between the experimental and simulated Raman wavelengths can be explained by the fact that in the experiment WGM not only from the fundamental TE family could be excited, whereas in the modeling we considered only the fundamental TE WGMs with FSR = 1.15 THz.

To demonstrate that detuning is an important parameter in the process under consideration, we studied theoretically the Δ dependence of the dimensionless intracavity powers at a pump wavelength and at wavelengths corresponding to the first and second Raman orders (see Fig. 3). For the chosen value |S|² = 200 and zero detuning Δ = 0, there are two single-mode Raman orders with comparable intracavity powers. As the detuning modulus increases, the power of the second-order Raman wave begins to decrease, while the intensity of the first-order Raman wave remains almost unchanged. When the second Raman order is below the generation threshold, the first Raman order intensity begins to decrease until it is also below the threshold. Note that wavelength tunability by changing pump wavelength is extended to the second-order cascade Raman lasing.

 

Fig. 3. Numerical dependence of dimensionless intracavity powers on detuning.

Download Full Size | PDF

4. Multimode cascade Raman lasing in the 1.6-2 μm range

When the pump power significantly exceeded the threshold, Raman lasing became multimode, and different families of WGMs were excited. Moreover, cascade processes were observed. In our experiments, we observed several orders of Raman generation for the maximum pump power of 25 mW before the taper. For recording Raman spectra in the range beyond 1.7 μm we used the monochromator plus the PbSe photodetector [see Fig. 1(d)]. Unfortunately, due to low detector sensitivity we had to use signal averaging and set large entrance and exit slits of the monochromator which resulted in poor spectral resolution. Thus we could not resolve various generated WGMs within the same Raman order and observed only broadened peaks.

When the pump wavelength was 1.53 μm, we obtained three orders of cascade Raman lasing, the central wavelengths of which were about 1.62 μm, 1.72 μm, and 1.83 μm, respectively. The composite Raman spectrum is shown in Fig. 4. The frequency difference between the CW pump and the first-order Raman peak was about 10.9 THz, the difference between the first and the second orders was about 10.8 THz, and the difference between the second and the third orders was about 10.5 THz. The spectrum of the first-order multimode Raman lasing was recorded both by the OSA (Fig. 4, dark blue curve) and by the PbSe detector plus monochromator (Fig. 4, light blue curve). Note an interesting feature in the spectrum. In addition to the down-converted spectral peaks due to Raman lasing, there is an up-converted spectral peak at a wavelength of 1.38 μm which corresponds to a frequency of 217.4 THz. We believe that this peak is generated due to FWM between the pump wave at a frequency of 196.1 THz and the wave corresponding to Raman lasing at a frequency of 2×196.1 − 217.4 = 174.8 THz (1.72 μm) in the WGM belonging to the second Raman order. We believe that the pump wave, the Raman wave and the high-frequency wave belong to different families of modes, which allows meeting the phase matching condition. Note that this condition cannot be satisfied for all three modes belonging to the fundamental family, since the dispersion in the entire considered range is normal for As₂S₃ microsphere. As far as we know, this is the first report on the generation of radiation at a frequency higher than the pump frequency in chalcogenide microresonators, which should undoubtedly be studied in more detail in future works.

 

Fig. 4. Experimental spectrum of three-cascade Raman lasing recorded by OSA (dark blue curve) and by PbSe detector plus monochromator (light blue curve) for a pump wavelength of 1.53 μm.

Download Full Size | PDF

Then we tuned the wavelength of the CW pump laser to 1.57 μm and attained four orders of Raman lasing at the central wavelengths of about 1.66 μm, 1.76 μm, 1.88 μm, and 2.01 μm (see Fig. 5). The frequency difference between the pump and the first-order Raman lasing, between the first and second orders, between the second and the third orders, and between the third and the fourth orders was about 10.4 THz, 10.3 THz, 10.9 THz, and 10.3 THz, respectively.

 

Fig. 5. Experimental spectrum of four-cascade Raman lasing recorded by OSA (dark blue curve) and by PbSe detector plus monochromater (light blue curve) for a pump wavelength of 1.57 μm.

Download Full Size | PDF

5. Conclusion

To conclude, we demonstrated experimentally Raman lasing in a home-made As₂S₃ chalcogenide glass microsphere with a diameter of 34 μm pumped through a silica fiber taper by a commercially available C-band narrow-line laser module. When the pump power excess over the threshold was not very high, we attained single-mode Raman lasing tunable in the L-band and the U-band from 1.610 μm to 1.663 μm by tuning the pump wavelength in the 1.522-1.574 μm range, for the first time to the best of our knowledge. When the pump power significantly exceeded the threshold, multimode cascade Raman lasing was achieved. For the pump wavelength of 1.57 μm, we attained four orders of Raman lasing at the central wavelengths of about 1.66 μm, 1.76 μm, 1.88 μm, and 2.01 μm. For the pump wavelength of 1.53 μm, we obtained three orders of cascade Raman lasing, the central wavelengths of which were about 1.62 μm, 1.72 μm, and 1.83 μm. In this case, in addition to down-converted spectral peaks due to Raman lasing, there was an up-converted spectral peak at 217.4 THz (1.38 μm). We believe that this peak was generated due to FWM between the pump wave at 196.1 THz and the wave corresponding to the second-order Raman lasing at 2×196.1 − 217.4 = 174.8 THz (1.72 μm).

The numerical simulation of the Lugiato-Lefever equation was also performed for qualitative understanding of Raman lasing. We demonstrated a good agreement between the experimental and the theoretical results for tunable single-mode Raman lasing. It was also shown theoretically that detuning of the pump wave from the nearest resonant WGM strongly affected the intracavity powers and a number of the generated Raman orders.