Highly controllable optical bistability effect in a 2 μm Tm:YAG ceramic laser at room temperature Xuan Liu,1 Haitao Huang,2,3 Deyuan Shen,1,* Heyuan Zhu,1 Jian Zhang2,3 and Dingyuan Tang2,3 1 Department of Optical Science and Engineering, Fudan University, Shanghai 200433, China School of Physics and Electronic Engineering, Jiangsu Normal University, Xuzhou 221116, China 3 Jiangsu Collaborative Innovation center of Advanced Laser Technology and Emerging Industry, Jiangsu Normal University, Xuzhou 221116, China * [email protected] 2
Abstract: A highly controllable optical bistability in a Tm:YAG ceramic laser system is reported, which is attributed to the thermal-induced change in the stability of the resonator. The width of the bistable region can be tuned in a large scale from 0.8 W to 6.3 W. At nearly semi-confocal cavity configuration, a second lasing condition was observed in the bistable region with a modulated shape of the laser beam and a broadened laser spectrum. The influence of the temperature on the bistable laser operation was also discussed in detail. To our knowledge, this is the first report on the optical bistability effect in Tm:YAG ceramic lasers. ©2015 Optical Society of America OCIS codes: (140.3580) Lasers, solid-state; (190.1450) Bistability; effects.
(140.6810) Thermal
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
T. S. Kubo and T. J. Kane, “Diode-pumped lasers at five eye-safe wavelengths,” IEEE J. Quantum Electron. 28(4), 1033–1040 (1992). R. Targ, B. C. Steakley, J. G. Hawley, L. L. Ames, P. Forney, D. Swanson, R. Stone, R. G. Otto, V. Zarifis, P. Brockman, R. S. Calloway, S. H. Klein, and P. A. Robinson, “Coherent lidar airborne wind sensor II: flight-test results at 2 and 10 µm,” Appl. Opt. 35(36), 7117–7127 (1996). D. Theisen, V. Ott, H. W. Bernd, V. Danicke, R. Keller, and R. Brinkmann, “Cw high power IR-laser at 2μm for minimally invasive surgery,” Proc. SPIE 5142, 96–100 (2003). L. S. Yan, A. E. Willner, X. X. Wu, A. L. Yi, A. Bogoni, Z. Y. Chen, and H. Y. Jiang, “All-optical signal processing for ultra high speed optical systems and networks,” J. Lightwave Technol. 30(24), 3760–3770 (2012). G. Assanto, Z. Wang, D. J. Hagan, and E. W. Vanstryland, “All-optical modulation via nonlinear cascading in type II second-harmonic generation,” Appl. Phys. Lett. 67(15), 2120 (1995). D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel’kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91(21), 213903 (2003). H. Nihei and A. Okamoto, “Photonic crystal systems for high-speed optical memory device on an atomic scale,” Proc. SPIE 4416, 470–473 (2001). H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic, 1985) Y. Shen and G. P. Wang, “Optical bistability in metal gap waveguide nanocavities,” Opt. Express 16(12), 8421– 8426 (2008). A. Shinya, S. Matsuo, T. Yosia, E. Tanabe, T. Kuramochi, T. Sato, Kakitsuka, and M. Notomi, “All-optical onchip bit memory based on ultra high Q InGaAsP photonic crystal,” Opt. Express 16(23), 19382–19387 (2008). J. H. Liu, H. J. Zhang, X. Mateos, W. J. Han, and V. Petrov, “Bistable laser operation of a Yb0.0054:Y0.3481Gd0.6465VO4 mixed crystal,” Opt. Lett. 33(16), 1810–1812 (2008). X. L. Zhang and Y. Z. Wang, “Optical bistability effects in a Tm,Ho:YLF laser at room temperature,” Opt. Lett. 32(16), 2333–2335 (2007). Ph. Goldner, O. Guillot-Noël, and P. Higel, “Optical bistability in Yb3+:YCa4O(BO3)3 crystal,” Opt. Mater. 26(3), 281–286 (2004). V. E. Hartwell, H. Nakajima, and N. Djeu, “Pump interference and optical bistability effects in a Tm,Ho:YAG microlaser,” Opt. Lett. 20(21), 2210–2212 (1995). X. Liu, H. T. Huang, H. Y. Zhu, Y. Wang, L. Wang, D. Y. Shen, J. Zhang, and D. Y. Tang, “A modified model for the LD pumped 2μm Tm:YAG laser: thermal behavior and laser performance,” Opt. Commun. 332, 332–338 (2014).
#230675 - $15.00 USD (C) 2015 OSA
Received 18 Dec 2014; revised 30 Jan 2015; accepted 2 Feb 2015; published 16 Mar 2015 23 Mar 2015 | Vol. 23, No. 6 | DOI:10.1364/OE.23.007619 | OPTICS EXPRESS 7619
16. J. Frauchiger, P. Albers, and H. P. Weber, “Modeling of thermal lensing and higher order ring mode oscillation in end-pumped cw Nd:YAG lasers,” IEEE J. Quantum Electron. 28(4), 1046–1056 (1992). 17. X. Fu, Q. Liu, and M. L. Gong, “Distributed-side-pumped slab lasers: theoretical design and modeling,” IEEE J. Quantum Electron. 47(4), 479–485 (2011). 18. V. Sazegari, M. R. J. Milani, and A. K. Jafari, “Structural and optical behavior due to thermal effects in endpumped Yb:YAG disk lasers,” Appl. Opt. 49(36), 6910–6916 (2010).
1. Introduction Due to the eye safe nature, lasers in 2μm region have attracted much attention in many fields, such as medical operation, remote sensing, lidar and industrial processing [1–3]. As a promising alternative to their electronic counterpart, all optical signal processing system possesses the advantages of ultra-high bandwidth and the absence of optical-to-electrical conversion [4]. Optical bistability (OB) is a feasible approach to achieve many key components including optical transistor, all optical switching and optical memory [5–7]. One of the classical configurations to achieve optical bistability is using a passive Fabry-Perot cavity containing nonlinear medium [8]. Y. Shen et al. realized the OB effect in a nanocavity by filling a piece of non-linear optical medium into a metal gap waveguide [9]. A. Shinya et. al. utilized the refractive index modulation caused by carrier-plasma dispersion in InGaAsP photonic crystal to achieve optical bistability and all-optical bit memory operation [10]. Another configuration is laser systems with intracavity saturable absorber. In Yb-doped systems, the resonant loss act as an inherent effective saturable absorber and result in the optical bistability under certain circumstances [11]. While for Tm and Ho doped laser systems, the combination of the excited state absorption and energy transfer upconversion processes lead to the observation of optical bistability [12]. Intrinsic optical bistabilities was also reported in some active optical materials [13]. However, for the reported optical bistabilities in laser systems in 2 μm region, the typical bistable regions are rather small and the tunabilities are limited [12, 14]. In addition, the two stable conditions of the laser systems are only differentiated by the laser powers, while other properties of the laser beam are the same. This has limited their applications in all optical signal processing systems because the embedded information is limited. In this paper, a thermal induced optical bistability in Tm:YAG ceramic laser is reported. The width of the bistable region can be tuned in a large scale by deliberately changing the cavity length, from a minimum width of only 0.8 W to a maximum width of around 6.3 W. In addition to the difference in laser power, a discrepancy in the mode distribution was also observed between the two stable conditions under certain cavity configuration. Different from the Gaussian distribution of the laser beam in normal lasing condition, obvious high order modes oscillation was observed in the second lasing condition and the shape of the output laser beam was highly dependent on the shape of the pump beam. The influence of temperature on the optical bistability was also analyzed in detail. This phenomenon provides not only a novel method to achieve optical bistability in 2 μm region, but also an efficient tool to investigate the interaction between the pump field and high order laser field. As the shape of the high order modes are subjected to the shape of the pump beam, this phenomenon could be used to generate optical bistable modulation in all optical signal processing systems.
#230675 - $15.00 USD (C) 2015 OSA
Received 18 Dec 2014; revised 30 Jan 2015; accepted 2 Feb 2015; published 16 Mar 2015 23 Mar 2015 | Vol. 23, No. 6 | DOI:10.1364/OE.23.007619 | OPTICS EXPRESS 7620
2. Experimental setup
Fig. 1. Experimental setup for the bistable laser operation.
The experiment configuration is shown in Fig. 1. The pump source used in this experiment was a laser diode stack consisting of five horizontal cascaded diode bars. The central wavelength of laser diode was around 784.5 nm with a spectral width (FWHM) of 2.8 nm. The beam qualities of the diode stack were Mx2 = 153 and My2 = 83.8 with the definition of the axes shown in Fig. 1. Micro-lens arrays were used for the beam shaping of the laser diode. A plano-convex lens with a focal length of 50 mm was used to focus the pump beam into the Tm:YAG ceramic sample with a spot size of ~0.6 mm (x) × 0.35 mm (y) on the beam waist. The Tm:YAG ceramic sample used in the experiment was 1.67 mm thick (y), 10mm wide (x) and 10 mm long with a doping concentration of 3 at %. Both end surfaces of the sample were antireflection (AR) coated at 760-810 nm and 1750-2050 nm. The sample was sandwiched by two copper micro-channel heat sinks for efficient heat removal. Indium foils of about 0.1 mm thick were used to provide even thermal contact. A concave-plane resonator was used to generate laser oscillation. The rear mirror M1 had a radius of curvature of 200 mm and was antireflection (AR) coated at 760-810 nm and high-reflection (HR) coated at 1890-2170 nm. A plane mirror M2 acted as the output coupler and the transmissivity at 1890-2170 nm was 10%. An external reflecting mirror M3 that was AR coated at 760-810 nm and HR coated at 1930-2100 nm was used to separate the 2-μm laser from the residual pump laser. 3. Result and discussion 3.1 Tunability of the optical bistability
Fig. 2. Bistable laser operation at different physical cavity lengths.
#230675 - $15.00 USD (C) 2015 OSA
Received 18 Dec 2014; revised 30 Jan 2015; accepted 2 Feb 2015; published 16 Mar 2015 23 Mar 2015 | Vol. 23, No. 6 | DOI:10.1364/OE.23.007619 | OPTICS EXPRESS 7621
Laser performances at different physical cavity lengths are shown in Fig. 2. In these experiments, the physical length of L1 was kept at 37 mm and the length of L2 was changed (see Fig. 1). When the absorbed pump power increased from zero, the 2 μm laser power increased correspondingly until a critical point, which is referred to as Pdown, was reached and then the oscillation of 2 μm laser terminated. For simplicity, we termed the condition in which the output laser power increased linearly with the absorbed pump power as the normal lasing condition. Significant saturation in output power was observed around Pdown, as can be seen in Fig. 2. If the absorbed pump power was decreased from this point, the 2 μm laser would no longer oscillate until another critical point, which is referred to as Pup, was reached. Then the output power jumped from zero to a substantial level and the normal lasing condition was retrieved. Further reduction of the pump power would lead to a decrease in the output power with nearly the same slope efficiency. Therefore a hysteresis loop with sizable width in the dependence of output power on the pump power was presented. The bistable region was defined by Pup < Pabs < Pdown, in which the output power at a given pump level was dependent on the way this pump level was reached. The Pup and Pdown for L2 = 52 mm were marked in Fig. 2 for a better illustration. By changing the physical length of L2, the width of the bistable region could be tuned in large scale, from 0.8 W at L2 = 75 mm to 6.3 W at L2 = 52 mm. Traditional causes of laser termination included the cavity misalignment and the thermallens-induced change in the cavity stability. In order to address the major cause of the bistability, a plane-parallel resonator, which was more sensitive to the cavity misalignment than a plano-concave cavity, was used to achieve bistable laser operation. The pitch and yaw angles of the mirrors for optimal cavity alignment, at which a maximum output power was achieved, kept unchanged during the process of increasing the pump power from zero to Pdown. And once the laser oscillation was terminated, it could not be retrieved by tuning the mirrors. Only by reducing the absorbed pump power to a level lower than Pup or reducing the cavity length, the laser oscillation could be retrieved. Hence the influence of the cavity misalignment was excluded.
Fig. 3. Change of the thermal focal length during the bistable laser operation.
The bistable operation of the Tm:YAG ceramic laser could then be explained by the abrupt change of the thermal focal length when the laser resonator was operating at the margin of the stable region, as can be seen in Fig. 3. The accumulation of the heat load became heavier with the increase in the pump power, leading to a decrease in the thermal focal length. Once the absorbed pump power surpassed Pdown, the thermal lens effect was so severe that the resonator became unstable and the laser oscillation was terminated. Then the pump power that was extracted by the 2 μm laser radiation during the normal lasing condition
#230675 - $15.00 USD (C) 2015 OSA
Received 18 Dec 2014; revised 30 Jan 2015; accepted 2 Feb 2015; published 16 Mar 2015 23 Mar 2015 | Vol. 23, No. 6 | DOI:10.1364/OE.23.007619 | OPTICS EXPRESS 7622
was converted into additional heat load in the non-lasing condition, which resulted in an abrupt increase in the thermal accumulation and hence a decrease in the thermal focal length. Only when the absorbed pump power decreased to a pump level that was much lower than Pdown, then the thermal focal length in non-lasing condition became large enough so that the resonator turned into a stable one and the laser oscillation was restarted. The discrepancy between the thermal focal lengths in normal lasing condition and nonlasing condition was proportional to the output power in normal lasing condition at Pdown, which represented the energy that was transformed into heat in the non-lasing condition. If the output power at Pdown was higher, the pump power should decrease by a larger extent to offset the additional heat load generated in non-lasing condition, leading to a wider bistable region. When the physical length of the cavity was increased, the critical thermal focal length, which turned the stable resonator into an unstable one, became larger, and the value of Pdown as well as the output power at Pdown were reduced correspondingly, leading to a narrower bistable region. Thus a wide tuning range of the width of the bistable region could be achieved by simply changing the physical length of the resonator. The critical value of the thermal focal length fcr beyond which the laser cavity became unstable was calculated with the following method. If the thermal lens in a gain medium in a laser resonator can be assumed to be an ideal thin lens, as shown in Fig. 4, the round-trip matrix of the resonator can be written as follows: A B T = = TR1Tl 1TfTl 2TR 2Tl 2TfTl 1 C D
(1)
1 0 Tf = 1 (2) − 1 f In which the TR1, Tl1, Tf, Tl2, TR2 were the transmission matrixes for each element shown in Fig. 4. f was the focal length of the thermal lens. As the value of (A + D)/2 reduced with a decreasing value of thermal focal length f, the boundary condition for the cavity stability should be (A + D)/2 = −1, and the value of fcr was calculated correspondingly.
Fig. 4. Transformation of the output beam for a stable resonator containing a thermal lens f.
In order to verify the explanation for the optical bistability, we’ve measured the thermal focal length at pump powers around Pdown at normal lasing condition for each cavity length and compared the measured values with the critical values fcr that were calculated using the equations above. The experimental setup for the measurement is illustrated in Fig. 4. The beam waist radius of the TEM00 Gaussian beam at position d2 could be denoted as
ω = 0
ω M
2
(3)
where ω was the measured beam waist and M2 was the beam quality factor. According to the Gaussian beam propagation theory, the TEM00 beam radius at the output mirror ωM was
#230675 - $15.00 USD (C) 2015 OSA
Received 18 Dec 2014; revised 30 Jan 2015; accepted 2 Feb 2015; published 16 Mar 2015 23 Mar 2015 | Vol. 23, No. 6 | DOI:10.1364/OE.23.007619 | OPTICS EXPRESS 7623
deduced then. At the same time, the fundamental mode beam radius at the output mirror can be calculated through the following equations:
ω = 2 M
L ' = l1 + l 2 −
g '2 λL' π g '1(1 − g '1 g ' 2)
(4)
l1 ⋅ l 2 L ' l2 L ' l1 , g '1 = 1 − − , g ' 2 = 1 − − f R1 f R2 f
(5)
where R1 and R2 were the radiuses of curvature of M1 and M2, respectively. In our measurement, the value of R2 was set to be ∞. l1 and l2 were the distances from the thermal lens to M1 and M2, respectively. Then the thermal focal length f can then be deduced. A comparison between the measured value f around the stable margin and the critical value fcr was shown in Table 1. Table 1. Measured and Calculated Thermal Focal Lengths L2/mm
Absorbed Pump power for measurement / W
Measured thermal focal length f / mm
Pdown / W
52 62 67 75
29 21.1 17.2 12.5
109 130 141 156
30.2 22 17.8 13.3
Calculated critical thermal focal length fcr /mm 88 115 129 160
It could be seen from Table 1 that the thermal focal length at the pump power around Pdown at lasing condition was close to the calculated critical value. As the saturation at the margin of the stable region was severe, which can be clearly seen from Fig. 2, the thermal accumulation was greatly aggravated in this region. Further increase in the pump power from the measured point to Pdown leaded to a drastic decrease in the thermal focal length from the measured value and finally resulted in the termination of the laser oscillation. As most of the calculated critical thermal focal lengths were smaller than the measured ones under the pump power only a little lower than Pdown, this may imply that apart from the thermal induced cavity stability change, the change in the three-level lasing regime in Tm ions doped crystals, which was highly temperature dependent, also played an important role in this bistable laser operation. Further study is required for more detailed discussion and this will be conducted in our future work.
#230675 - $15.00 USD (C) 2015 OSA
Received 18 Dec 2014; revised 30 Jan 2015; accepted 2 Feb 2015; published 16 Mar 2015 23 Mar 2015 | Vol. 23, No. 6 | DOI:10.1364/OE.23.007619 | OPTICS EXPRESS 7624
3.2. Existence of second lasing condition
Fig. 5. Bistable laser operation with the existence of the second lasing condition.
When the resonator was deliberately tuned to nearly semi-confocal, a second lasing condition was observed in the bistable region, as can be seen in Fig. 5. When the pump power decreased from Pdown, no output laser power was observed at the beginning. However, once the absorbed pump power reduced to certain level, which was termed as Pmml and marked in Fig. 5 for the blue line, laser output was observed with the laser power to be significantly smaller than that in normal lasing condition. Further reduction in absorbed pump power leaded to a decrease in the laser power and normal lasing condition was finally retrieved when the absorbed pump power was less than Pup. The shapes of the output beams in the two lasing conditions were monitored with a beam profiler (NanoScan, Photon Inc.), and the results are shown in the following figure.
Fig. 6. Shapes of the laser beams in region 1 and region 2.
As shown in Fig. 6, instead of the Gausssian distribution of the laser beam in region 1, the laser output beam in region 2 was clearly separated. The M2 factors for the laser beam in region 1 were calculated to be 2.92 and 3.03 in the x and y directions, respectively, while that of the laser beam in region 2 were 5.84 and 6.45 in the x and y directions, respectively. This
#230675 - $15.00 USD (C) 2015 OSA
Received 18 Dec 2014; revised 30 Jan 2015; accepted 2 Feb 2015; published 16 Mar 2015 23 Mar 2015 | Vol. 23, No. 6 | DOI:10.1364/OE.23.007619 | OPTICS EXPRESS 7625
proved that higher order modes were oscillating in region 2. The corresponding laser spectrum was also measured by an optical spectrum analyzer (AQ6375, Yokogawa) with a resolution of 0.05 nm and the results are shown in Fig. 7. The spectrum width of the laser in region 2 was around 0.6 nm larger than that in region 1.
Fig. 7. Spectrums of the lasers in region 1 and region 2.
The influence of the cooling water temperature on the bistable laser operations are also shown in Fig. 5. For a better illustration, the temperature dependence of the width of the bistable region is listed in the following Table. Table 2. Temperature dependence of the width of the bistable region Temperature / °C 10°C 15°C 20°C
Pdown - Pmml / W 3.5 2.4 2.0
Pmml- Pup / W 1.2 2.0 2.4
It could be seen in Table 2 that the width of region 2, which is represented by the value of Pmml- Pup, increased with temperature. Thermal accumulation at the center of the pump area became much heavier with higher cooling water temperature, leading to a much larger discrepancy between the focusing levels of high order modes and the fundamental mode. The difference between the critical point for the oscillation of high order modes and that of the fundamental mode (Pmml- Pup) became much larger as a consequence.
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Received 18 Dec 2014; revised 30 Jan 2015; accepted 2 Feb 2015; published 16 Mar 2015 23 Mar 2015 | Vol. 23, No. 6 | DOI:10.1364/OE.23.007619 | OPTICS EXPRESS 7626
3.3 Explanation and verification
Fig. 8. The OPD profile on x direction with five horizontal cascade diode bars and the parabolic approximation.
As the shape of the laser beam clearly showed a separated nature, we’ve calculated the temperature distribution in the sample under non-lasing condition when five horizontal cascade diode bars were used as the pump source. The method is the same as that used in our previously reported work [15]. According to the thermal lens theory, the optical phase difference (OPD) estimated by a thermally induced spherical lens is given by a parabolic approximation: ( x − x 0) 2 (6) 2f Figure 8 showed the calculated OPD profile on x direction at 50 W pump power when the five horizontal bars were used as the pump source and the corresponding parabolic approximation using a single value of f. It could be seen that the actual thermally induced optical phase difference profile deviated substantially from the parabolic shape at the outer region. This strongly aberrative thermal lensing was assumed to govern the periodic spatial filtering of the resonator which leaded to a preferential higher mode oscillation when the fundamental mode oscillation was suppressed in region 2. Laser field at the center of the pump area experienced much more focusing than that distributed at the margin of the pump area. With the pump power in region 2, the resonator was unstable for fundamental mode due to the much more severe focusing at the center of the pump area and the oscillation of fundamental mode was inhibited. However, for lasers of high order modes, the resonator was still in stable region and a preferential higher mode oscillation occurred. As the diffraction losses of high order modes were higher than that of fundamental mode, the laser output power in region 2 was much smaller than that in region 1. The aberration was mainly caused by two reasons. One of them was the logarithmic OPD profile of the outer region, as was well illustrated in Frauchiger’s work [16]. Another cause of the aberration was assumed to be the strong non-Gaussian shape of the pump beam, which made the aberration in this laser system severer than that in a Gaussian pump. A distributed thermal focal length on the horizontal direction, which represented the focusing level of local position, was calculated according to the following equation for a better illustration [17]: OPD( x) = OPD 0 −
#230675 - $15.00 USD (C) 2015 OSA
Received 18 Dec 2014; revised 30 Jan 2015; accepted 2 Feb 2015; published 16 Mar 2015 23 Mar 2015 | Vol. 23, No. 6 | DOI:10.1364/OE.23.007619 | OPTICS EXPRESS 7627
( x − x 0) ( x − x 0) f ( x) = − =− dn 2[OPD( x) - OPD( x0 )] 2 [T ( x) - T ( x0 )]dz dT 2
2
(7)
where x0 represented the coordinate of the center of the pump beam, and T was the local temperature calculated in the former stage. The value of the thermal-optic coefficient dn/dT was set to be 7.3 × 10−6 K−1 [18]. The results were presented in Fig. 9 together with the distribution of the pump beam. A thermal focal length distribution with a Gaussian pump distribution assumption was also provided for comparison.
Fig. 9. Distributions of the pump laser field and the thermal focal lengths for different pump distributions.
As can be seen in Fig. 9, laser beams propagating through the central part of the pumped region experienced much severer thermal focusing when the pump source was five bars than that in Gaussian pump. Hence the strong non-Gaussian shape of the pump beam, together with the logarithmic OPD profile of the outer region, was assumed to be the major causes. In order to verify our explanation, a fiber-coupled laser diode was used as the pump source to achieve the second lasing condition in the bistable region. The distribution of the pump beam was measured to be in Gaussian shape with the radius of the beam waist to be 100 μm. The Tm:YAG ceramic sample used in the experiment was 2 mm thick (y), 3 mm wide (x) and 4 mm long with a doping concentration of 4 at %. Limited by the available absorbed pump power, the laser power in the second lasing condition was too low to be monitored by the beam profiler. A mid-infrared detector card (VRC6, Thorlabs) was used instead and the results were shown in the following figure:
#230675 - $15.00 USD (C) 2015 OSA
Received 18 Dec 2014; revised 30 Jan 2015; accepted 2 Feb 2015; published 16 Mar 2015 23 Mar 2015 | Vol. 23, No. 6 | DOI:10.1364/OE.23.007619 | OPTICS EXPRESS 7628
Fig. 10. Shapes of the laser beams in region 1 and region 2 with the fiber coupled LD.
As depicted in Fig. 10, in comparison with the filled laser beam spot in region 1, the shape of the laser beam in region 2 was a ring. This not only proved the existence of the second lasing condition was caused by the strong aberrative thermal lens effect, but also revealed that the shape of the laser beams in second lasing condition was controlled by the shape of the pump beam. From the description above, it could be noticed that the shape of the laser beam in region 2 was highly dependent on the distribution of the thermal focal lens, which was controlled by the shape of the pump beam. This bistable laser operation not only provides sufficient information about the interaction between the high order modes and the pump field, but also adds a new controllable degree of freedom to traditional optical bistabilities. The information that could be conveyed in the shape of the laser beam, combined with the nature that this information could only be revealed by changing the pump power in a specific way, would largely expand the applications of optical bistabilities in all-optical signal processing systems. 4. Conclusion In summary, we have observed a highly controllable optical bistability in a Tm:YAG ceramic laser system, which was attributed to the thermal-induced change in the stability of the resonator. The width of the bistable region could be tuned in large scale, from a minimum width of 0.8 W to a maximum width of 6.3 W, by changing the physical length of the resonator. A second lasing condition was observed in the bistable region under certain resonator configurations. The shape of the laser beam in the second lasing condition was obviously separated and the corresponding spectrum was around 0.6 nm wider than that in normal lasing condition. This was attributed to the thermal-induced discrimination between lasers of fundamental mode and high order modes. This bistable laser operation not only provides sufficient information about the interaction between the high order modes and the pump field, but also adds a new controllable degree of freedom to traditional 2 μm optical bistabilities, and would largely expand the applications of optical bistabilities in all-optical signal processing systems. Acknowledgments This work is supported by the National Natural Science Foundation of China ((Grant No. 61177045, 61308047, and 11274144), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 13KJB510008), and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).
#230675 - $15.00 USD (C) 2015 OSA
Received 18 Dec 2014; revised 30 Jan 2015; accepted 2 Feb 2015; published 16 Mar 2015 23 Mar 2015 | Vol. 23, No. 6 | DOI:10.1364/OE.23.007619 | OPTICS EXPRESS 7629
Abstract: A highly controllable optical bistability in a Tm:YAG ceramic laser system is reported, which is attributed to the thermal-induced change in the stability of the resonator. The width of the bistable region can be tuned in a large scale from 0.8 W to 6.3 W. At nearly semi-confocal cavity configuration, a second lasing condition was observed in the bistable region with a modulated shape of the laser beam and a broadened laser spectrum. The influence of the temperature on the bistable laser operation was also discussed in detail. To our knowledge, this is the first report on the optical bistability effect in Tm:YAG ceramic lasers. ©2015 Optical Society of America OCIS codes: (140.3580) Lasers, solid-state; (190.1450) Bistability; effects.
(140.6810) Thermal
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
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Received 18 Dec 2014; revised 30 Jan 2015; accepted 2 Feb 2015; published 16 Mar 2015 23 Mar 2015 | Vol. 23, No. 6 | DOI:10.1364/OE.23.007619 | OPTICS EXPRESS 7619
16. J. Frauchiger, P. Albers, and H. P. Weber, “Modeling of thermal lensing and higher order ring mode oscillation in end-pumped cw Nd:YAG lasers,” IEEE J. Quantum Electron. 28(4), 1046–1056 (1992). 17. X. Fu, Q. Liu, and M. L. Gong, “Distributed-side-pumped slab lasers: theoretical design and modeling,” IEEE J. Quantum Electron. 47(4), 479–485 (2011). 18. V. Sazegari, M. R. J. Milani, and A. K. Jafari, “Structural and optical behavior due to thermal effects in endpumped Yb:YAG disk lasers,” Appl. Opt. 49(36), 6910–6916 (2010).
1. Introduction Due to the eye safe nature, lasers in 2μm region have attracted much attention in many fields, such as medical operation, remote sensing, lidar and industrial processing [1–3]. As a promising alternative to their electronic counterpart, all optical signal processing system possesses the advantages of ultra-high bandwidth and the absence of optical-to-electrical conversion [4]. Optical bistability (OB) is a feasible approach to achieve many key components including optical transistor, all optical switching and optical memory [5–7]. One of the classical configurations to achieve optical bistability is using a passive Fabry-Perot cavity containing nonlinear medium [8]. Y. Shen et al. realized the OB effect in a nanocavity by filling a piece of non-linear optical medium into a metal gap waveguide [9]. A. Shinya et. al. utilized the refractive index modulation caused by carrier-plasma dispersion in InGaAsP photonic crystal to achieve optical bistability and all-optical bit memory operation [10]. Another configuration is laser systems with intracavity saturable absorber. In Yb-doped systems, the resonant loss act as an inherent effective saturable absorber and result in the optical bistability under certain circumstances [11]. While for Tm and Ho doped laser systems, the combination of the excited state absorption and energy transfer upconversion processes lead to the observation of optical bistability [12]. Intrinsic optical bistabilities was also reported in some active optical materials [13]. However, for the reported optical bistabilities in laser systems in 2 μm region, the typical bistable regions are rather small and the tunabilities are limited [12, 14]. In addition, the two stable conditions of the laser systems are only differentiated by the laser powers, while other properties of the laser beam are the same. This has limited their applications in all optical signal processing systems because the embedded information is limited. In this paper, a thermal induced optical bistability in Tm:YAG ceramic laser is reported. The width of the bistable region can be tuned in a large scale by deliberately changing the cavity length, from a minimum width of only 0.8 W to a maximum width of around 6.3 W. In addition to the difference in laser power, a discrepancy in the mode distribution was also observed between the two stable conditions under certain cavity configuration. Different from the Gaussian distribution of the laser beam in normal lasing condition, obvious high order modes oscillation was observed in the second lasing condition and the shape of the output laser beam was highly dependent on the shape of the pump beam. The influence of temperature on the optical bistability was also analyzed in detail. This phenomenon provides not only a novel method to achieve optical bistability in 2 μm region, but also an efficient tool to investigate the interaction between the pump field and high order laser field. As the shape of the high order modes are subjected to the shape of the pump beam, this phenomenon could be used to generate optical bistable modulation in all optical signal processing systems.
#230675 - $15.00 USD (C) 2015 OSA
Received 18 Dec 2014; revised 30 Jan 2015; accepted 2 Feb 2015; published 16 Mar 2015 23 Mar 2015 | Vol. 23, No. 6 | DOI:10.1364/OE.23.007619 | OPTICS EXPRESS 7620
2. Experimental setup
Fig. 1. Experimental setup for the bistable laser operation.
The experiment configuration is shown in Fig. 1. The pump source used in this experiment was a laser diode stack consisting of five horizontal cascaded diode bars. The central wavelength of laser diode was around 784.5 nm with a spectral width (FWHM) of 2.8 nm. The beam qualities of the diode stack were Mx2 = 153 and My2 = 83.8 with the definition of the axes shown in Fig. 1. Micro-lens arrays were used for the beam shaping of the laser diode. A plano-convex lens with a focal length of 50 mm was used to focus the pump beam into the Tm:YAG ceramic sample with a spot size of ~0.6 mm (x) × 0.35 mm (y) on the beam waist. The Tm:YAG ceramic sample used in the experiment was 1.67 mm thick (y), 10mm wide (x) and 10 mm long with a doping concentration of 3 at %. Both end surfaces of the sample were antireflection (AR) coated at 760-810 nm and 1750-2050 nm. The sample was sandwiched by two copper micro-channel heat sinks for efficient heat removal. Indium foils of about 0.1 mm thick were used to provide even thermal contact. A concave-plane resonator was used to generate laser oscillation. The rear mirror M1 had a radius of curvature of 200 mm and was antireflection (AR) coated at 760-810 nm and high-reflection (HR) coated at 1890-2170 nm. A plane mirror M2 acted as the output coupler and the transmissivity at 1890-2170 nm was 10%. An external reflecting mirror M3 that was AR coated at 760-810 nm and HR coated at 1930-2100 nm was used to separate the 2-μm laser from the residual pump laser. 3. Result and discussion 3.1 Tunability of the optical bistability
Fig. 2. Bistable laser operation at different physical cavity lengths.
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Received 18 Dec 2014; revised 30 Jan 2015; accepted 2 Feb 2015; published 16 Mar 2015 23 Mar 2015 | Vol. 23, No. 6 | DOI:10.1364/OE.23.007619 | OPTICS EXPRESS 7621
Laser performances at different physical cavity lengths are shown in Fig. 2. In these experiments, the physical length of L1 was kept at 37 mm and the length of L2 was changed (see Fig. 1). When the absorbed pump power increased from zero, the 2 μm laser power increased correspondingly until a critical point, which is referred to as Pdown, was reached and then the oscillation of 2 μm laser terminated. For simplicity, we termed the condition in which the output laser power increased linearly with the absorbed pump power as the normal lasing condition. Significant saturation in output power was observed around Pdown, as can be seen in Fig. 2. If the absorbed pump power was decreased from this point, the 2 μm laser would no longer oscillate until another critical point, which is referred to as Pup, was reached. Then the output power jumped from zero to a substantial level and the normal lasing condition was retrieved. Further reduction of the pump power would lead to a decrease in the output power with nearly the same slope efficiency. Therefore a hysteresis loop with sizable width in the dependence of output power on the pump power was presented. The bistable region was defined by Pup < Pabs < Pdown, in which the output power at a given pump level was dependent on the way this pump level was reached. The Pup and Pdown for L2 = 52 mm were marked in Fig. 2 for a better illustration. By changing the physical length of L2, the width of the bistable region could be tuned in large scale, from 0.8 W at L2 = 75 mm to 6.3 W at L2 = 52 mm. Traditional causes of laser termination included the cavity misalignment and the thermallens-induced change in the cavity stability. In order to address the major cause of the bistability, a plane-parallel resonator, which was more sensitive to the cavity misalignment than a plano-concave cavity, was used to achieve bistable laser operation. The pitch and yaw angles of the mirrors for optimal cavity alignment, at which a maximum output power was achieved, kept unchanged during the process of increasing the pump power from zero to Pdown. And once the laser oscillation was terminated, it could not be retrieved by tuning the mirrors. Only by reducing the absorbed pump power to a level lower than Pup or reducing the cavity length, the laser oscillation could be retrieved. Hence the influence of the cavity misalignment was excluded.
Fig. 3. Change of the thermal focal length during the bistable laser operation.
The bistable operation of the Tm:YAG ceramic laser could then be explained by the abrupt change of the thermal focal length when the laser resonator was operating at the margin of the stable region, as can be seen in Fig. 3. The accumulation of the heat load became heavier with the increase in the pump power, leading to a decrease in the thermal focal length. Once the absorbed pump power surpassed Pdown, the thermal lens effect was so severe that the resonator became unstable and the laser oscillation was terminated. Then the pump power that was extracted by the 2 μm laser radiation during the normal lasing condition
#230675 - $15.00 USD (C) 2015 OSA
Received 18 Dec 2014; revised 30 Jan 2015; accepted 2 Feb 2015; published 16 Mar 2015 23 Mar 2015 | Vol. 23, No. 6 | DOI:10.1364/OE.23.007619 | OPTICS EXPRESS 7622
was converted into additional heat load in the non-lasing condition, which resulted in an abrupt increase in the thermal accumulation and hence a decrease in the thermal focal length. Only when the absorbed pump power decreased to a pump level that was much lower than Pdown, then the thermal focal length in non-lasing condition became large enough so that the resonator turned into a stable one and the laser oscillation was restarted. The discrepancy between the thermal focal lengths in normal lasing condition and nonlasing condition was proportional to the output power in normal lasing condition at Pdown, which represented the energy that was transformed into heat in the non-lasing condition. If the output power at Pdown was higher, the pump power should decrease by a larger extent to offset the additional heat load generated in non-lasing condition, leading to a wider bistable region. When the physical length of the cavity was increased, the critical thermal focal length, which turned the stable resonator into an unstable one, became larger, and the value of Pdown as well as the output power at Pdown were reduced correspondingly, leading to a narrower bistable region. Thus a wide tuning range of the width of the bistable region could be achieved by simply changing the physical length of the resonator. The critical value of the thermal focal length fcr beyond which the laser cavity became unstable was calculated with the following method. If the thermal lens in a gain medium in a laser resonator can be assumed to be an ideal thin lens, as shown in Fig. 4, the round-trip matrix of the resonator can be written as follows: A B T = = TR1Tl 1TfTl 2TR 2Tl 2TfTl 1 C D
(1)
1 0 Tf = 1 (2) − 1 f In which the TR1, Tl1, Tf, Tl2, TR2 were the transmission matrixes for each element shown in Fig. 4. f was the focal length of the thermal lens. As the value of (A + D)/2 reduced with a decreasing value of thermal focal length f, the boundary condition for the cavity stability should be (A + D)/2 = −1, and the value of fcr was calculated correspondingly.
Fig. 4. Transformation of the output beam for a stable resonator containing a thermal lens f.
In order to verify the explanation for the optical bistability, we’ve measured the thermal focal length at pump powers around Pdown at normal lasing condition for each cavity length and compared the measured values with the critical values fcr that were calculated using the equations above. The experimental setup for the measurement is illustrated in Fig. 4. The beam waist radius of the TEM00 Gaussian beam at position d2 could be denoted as
ω = 0
ω M
2
(3)
where ω was the measured beam waist and M2 was the beam quality factor. According to the Gaussian beam propagation theory, the TEM00 beam radius at the output mirror ωM was
#230675 - $15.00 USD (C) 2015 OSA
Received 18 Dec 2014; revised 30 Jan 2015; accepted 2 Feb 2015; published 16 Mar 2015 23 Mar 2015 | Vol. 23, No. 6 | DOI:10.1364/OE.23.007619 | OPTICS EXPRESS 7623
deduced then. At the same time, the fundamental mode beam radius at the output mirror can be calculated through the following equations:
ω = 2 M
L ' = l1 + l 2 −
g '2 λL' π g '1(1 − g '1 g ' 2)
(4)
l1 ⋅ l 2 L ' l2 L ' l1 , g '1 = 1 − − , g ' 2 = 1 − − f R1 f R2 f
(5)
where R1 and R2 were the radiuses of curvature of M1 and M2, respectively. In our measurement, the value of R2 was set to be ∞. l1 and l2 were the distances from the thermal lens to M1 and M2, respectively. Then the thermal focal length f can then be deduced. A comparison between the measured value f around the stable margin and the critical value fcr was shown in Table 1. Table 1. Measured and Calculated Thermal Focal Lengths L2/mm
Absorbed Pump power for measurement / W
Measured thermal focal length f / mm
Pdown / W
52 62 67 75
29 21.1 17.2 12.5
109 130 141 156
30.2 22 17.8 13.3
Calculated critical thermal focal length fcr /mm 88 115 129 160
It could be seen from Table 1 that the thermal focal length at the pump power around Pdown at lasing condition was close to the calculated critical value. As the saturation at the margin of the stable region was severe, which can be clearly seen from Fig. 2, the thermal accumulation was greatly aggravated in this region. Further increase in the pump power from the measured point to Pdown leaded to a drastic decrease in the thermal focal length from the measured value and finally resulted in the termination of the laser oscillation. As most of the calculated critical thermal focal lengths were smaller than the measured ones under the pump power only a little lower than Pdown, this may imply that apart from the thermal induced cavity stability change, the change in the three-level lasing regime in Tm ions doped crystals, which was highly temperature dependent, also played an important role in this bistable laser operation. Further study is required for more detailed discussion and this will be conducted in our future work.
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Received 18 Dec 2014; revised 30 Jan 2015; accepted 2 Feb 2015; published 16 Mar 2015 23 Mar 2015 | Vol. 23, No. 6 | DOI:10.1364/OE.23.007619 | OPTICS EXPRESS 7624
3.2. Existence of second lasing condition
Fig. 5. Bistable laser operation with the existence of the second lasing condition.
When the resonator was deliberately tuned to nearly semi-confocal, a second lasing condition was observed in the bistable region, as can be seen in Fig. 5. When the pump power decreased from Pdown, no output laser power was observed at the beginning. However, once the absorbed pump power reduced to certain level, which was termed as Pmml and marked in Fig. 5 for the blue line, laser output was observed with the laser power to be significantly smaller than that in normal lasing condition. Further reduction in absorbed pump power leaded to a decrease in the laser power and normal lasing condition was finally retrieved when the absorbed pump power was less than Pup. The shapes of the output beams in the two lasing conditions were monitored with a beam profiler (NanoScan, Photon Inc.), and the results are shown in the following figure.
Fig. 6. Shapes of the laser beams in region 1 and region 2.
As shown in Fig. 6, instead of the Gausssian distribution of the laser beam in region 1, the laser output beam in region 2 was clearly separated. The M2 factors for the laser beam in region 1 were calculated to be 2.92 and 3.03 in the x and y directions, respectively, while that of the laser beam in region 2 were 5.84 and 6.45 in the x and y directions, respectively. This
#230675 - $15.00 USD (C) 2015 OSA
Received 18 Dec 2014; revised 30 Jan 2015; accepted 2 Feb 2015; published 16 Mar 2015 23 Mar 2015 | Vol. 23, No. 6 | DOI:10.1364/OE.23.007619 | OPTICS EXPRESS 7625
proved that higher order modes were oscillating in region 2. The corresponding laser spectrum was also measured by an optical spectrum analyzer (AQ6375, Yokogawa) with a resolution of 0.05 nm and the results are shown in Fig. 7. The spectrum width of the laser in region 2 was around 0.6 nm larger than that in region 1.
Fig. 7. Spectrums of the lasers in region 1 and region 2.
The influence of the cooling water temperature on the bistable laser operations are also shown in Fig. 5. For a better illustration, the temperature dependence of the width of the bistable region is listed in the following Table. Table 2. Temperature dependence of the width of the bistable region Temperature / °C 10°C 15°C 20°C
Pdown - Pmml / W 3.5 2.4 2.0
Pmml- Pup / W 1.2 2.0 2.4
It could be seen in Table 2 that the width of region 2, which is represented by the value of Pmml- Pup, increased with temperature. Thermal accumulation at the center of the pump area became much heavier with higher cooling water temperature, leading to a much larger discrepancy between the focusing levels of high order modes and the fundamental mode. The difference between the critical point for the oscillation of high order modes and that of the fundamental mode (Pmml- Pup) became much larger as a consequence.
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Received 18 Dec 2014; revised 30 Jan 2015; accepted 2 Feb 2015; published 16 Mar 2015 23 Mar 2015 | Vol. 23, No. 6 | DOI:10.1364/OE.23.007619 | OPTICS EXPRESS 7626
3.3 Explanation and verification
Fig. 8. The OPD profile on x direction with five horizontal cascade diode bars and the parabolic approximation.
As the shape of the laser beam clearly showed a separated nature, we’ve calculated the temperature distribution in the sample under non-lasing condition when five horizontal cascade diode bars were used as the pump source. The method is the same as that used in our previously reported work [15]. According to the thermal lens theory, the optical phase difference (OPD) estimated by a thermally induced spherical lens is given by a parabolic approximation: ( x − x 0) 2 (6) 2f Figure 8 showed the calculated OPD profile on x direction at 50 W pump power when the five horizontal bars were used as the pump source and the corresponding parabolic approximation using a single value of f. It could be seen that the actual thermally induced optical phase difference profile deviated substantially from the parabolic shape at the outer region. This strongly aberrative thermal lensing was assumed to govern the periodic spatial filtering of the resonator which leaded to a preferential higher mode oscillation when the fundamental mode oscillation was suppressed in region 2. Laser field at the center of the pump area experienced much more focusing than that distributed at the margin of the pump area. With the pump power in region 2, the resonator was unstable for fundamental mode due to the much more severe focusing at the center of the pump area and the oscillation of fundamental mode was inhibited. However, for lasers of high order modes, the resonator was still in stable region and a preferential higher mode oscillation occurred. As the diffraction losses of high order modes were higher than that of fundamental mode, the laser output power in region 2 was much smaller than that in region 1. The aberration was mainly caused by two reasons. One of them was the logarithmic OPD profile of the outer region, as was well illustrated in Frauchiger’s work [16]. Another cause of the aberration was assumed to be the strong non-Gaussian shape of the pump beam, which made the aberration in this laser system severer than that in a Gaussian pump. A distributed thermal focal length on the horizontal direction, which represented the focusing level of local position, was calculated according to the following equation for a better illustration [17]: OPD( x) = OPD 0 −
#230675 - $15.00 USD (C) 2015 OSA
Received 18 Dec 2014; revised 30 Jan 2015; accepted 2 Feb 2015; published 16 Mar 2015 23 Mar 2015 | Vol. 23, No. 6 | DOI:10.1364/OE.23.007619 | OPTICS EXPRESS 7627
( x − x 0) ( x − x 0) f ( x) = − =− dn 2[OPD( x) - OPD( x0 )] 2 [T ( x) - T ( x0 )]dz dT 2
2
(7)
where x0 represented the coordinate of the center of the pump beam, and T was the local temperature calculated in the former stage. The value of the thermal-optic coefficient dn/dT was set to be 7.3 × 10−6 K−1 [18]. The results were presented in Fig. 9 together with the distribution of the pump beam. A thermal focal length distribution with a Gaussian pump distribution assumption was also provided for comparison.
Fig. 9. Distributions of the pump laser field and the thermal focal lengths for different pump distributions.
As can be seen in Fig. 9, laser beams propagating through the central part of the pumped region experienced much severer thermal focusing when the pump source was five bars than that in Gaussian pump. Hence the strong non-Gaussian shape of the pump beam, together with the logarithmic OPD profile of the outer region, was assumed to be the major causes. In order to verify our explanation, a fiber-coupled laser diode was used as the pump source to achieve the second lasing condition in the bistable region. The distribution of the pump beam was measured to be in Gaussian shape with the radius of the beam waist to be 100 μm. The Tm:YAG ceramic sample used in the experiment was 2 mm thick (y), 3 mm wide (x) and 4 mm long with a doping concentration of 4 at %. Limited by the available absorbed pump power, the laser power in the second lasing condition was too low to be monitored by the beam profiler. A mid-infrared detector card (VRC6, Thorlabs) was used instead and the results were shown in the following figure:
#230675 - $15.00 USD (C) 2015 OSA
Received 18 Dec 2014; revised 30 Jan 2015; accepted 2 Feb 2015; published 16 Mar 2015 23 Mar 2015 | Vol. 23, No. 6 | DOI:10.1364/OE.23.007619 | OPTICS EXPRESS 7628
Fig. 10. Shapes of the laser beams in region 1 and region 2 with the fiber coupled LD.
As depicted in Fig. 10, in comparison with the filled laser beam spot in region 1, the shape of the laser beam in region 2 was a ring. This not only proved the existence of the second lasing condition was caused by the strong aberrative thermal lens effect, but also revealed that the shape of the laser beams in second lasing condition was controlled by the shape of the pump beam. From the description above, it could be noticed that the shape of the laser beam in region 2 was highly dependent on the distribution of the thermal focal lens, which was controlled by the shape of the pump beam. This bistable laser operation not only provides sufficient information about the interaction between the high order modes and the pump field, but also adds a new controllable degree of freedom to traditional optical bistabilities. The information that could be conveyed in the shape of the laser beam, combined with the nature that this information could only be revealed by changing the pump power in a specific way, would largely expand the applications of optical bistabilities in all-optical signal processing systems. 4. Conclusion In summary, we have observed a highly controllable optical bistability in a Tm:YAG ceramic laser system, which was attributed to the thermal-induced change in the stability of the resonator. The width of the bistable region could be tuned in large scale, from a minimum width of 0.8 W to a maximum width of 6.3 W, by changing the physical length of the resonator. A second lasing condition was observed in the bistable region under certain resonator configurations. The shape of the laser beam in the second lasing condition was obviously separated and the corresponding spectrum was around 0.6 nm wider than that in normal lasing condition. This was attributed to the thermal-induced discrimination between lasers of fundamental mode and high order modes. This bistable laser operation not only provides sufficient information about the interaction between the high order modes and the pump field, but also adds a new controllable degree of freedom to traditional 2 μm optical bistabilities, and would largely expand the applications of optical bistabilities in all-optical signal processing systems. Acknowledgments This work is supported by the National Natural Science Foundation of China ((Grant No. 61177045, 61308047, and 11274144), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 13KJB510008), and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).
#230675 - $15.00 USD (C) 2015 OSA
Received 18 Dec 2014; revised 30 Jan 2015; accepted 2 Feb 2015; published 16 Mar 2015 23 Mar 2015 | Vol. 23, No. 6 | DOI:10.1364/OE.23.007619 | OPTICS EXPRESS 7629
