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We report an Nd:YAG laser pumped by light emission diodes (LEDs) at 750 nm. With 1% output coupling from a linear cavity containing a 2-cm long Nd:YAG crystal, the laser generated 37.5 μJ pulse energy at 1064 nm with M2 = 1.1 when pumped by 2.73-mJ LED energy in a 1-ms pulse at a 10 Hz rate. The measured optical and slope efficiencies for this linear-cavity laser are 1.36, and 9%, respectively. With 1 and 5% output couplings from a Z-cavity containing the same laser crystal, the lasers generated 346 and 288 μJ pulse energy with an optical efficiency of 3.4 and 2.8% and slope efficiency of 6.6 and 14%, respectively, for the same 1-ms pump pulse repeating at a 10 Hz rate. At the highest output from the Z-cavity, the measured M2 for the beam is 3.6.
© 2016 Optical Society of America
1. Introduction
Light-emitting-diode (LED) pumped laser was demonstrated shortly after the invention of a laser in the 1960s ([1–5]). Most of the early-day LED pumped lasers required operation at cryogenic temperatures. The debut of much brighter diode lasers quickly demises LED as a laser pump. However, when using a diode laser to pump another laser, to achieve the highest efficiency, one often carefuly tunes the emission line of the diode laser to match the strongest absorption line of the laser gain material. Instability of a diode-pumped laser could therefore result from drift of the narrow pump line due to, for instance, temperature or pump-current variation. On the other hand, a flash-lamp pumped laser has a relatively low optical efficiency, as the emission spectrum of a flash lamp is too broadband for most laser materials. An LED emission spectrum, however, is moderately broad and yet much narrower than that of a flash lamp, often overlapping well with a group of high absorption lines in a laser material. This moderately broadband pumping from LED is expected to offer both high efficiency and good stability for laser operation.
Recently, the performance of LED has been greatly improved and yet the cost of it has been drastically reduced by massive civilian applications. For example, the lighting industry has developed highly efficient high-power LEDs in the visible spectrum, and the surveillance industry has developed similar LEDs in the near infrared spectrum. Although the brightness of an LED, including temporal and spectral coherence, can never match that of an ordinary laser, the low cost and long lifetime of an LED have generated renewed interest in using modern high-power LEDs as laser pump sources. As high-power high-efficiency LED for lighting is widely available now, Lee et al. [6] carried out some simulation study on several laser gain materials with white and blue LEDs pumping. The investigated materials include Nd-doped laser gain media, Ti:sapphire crystal, and solid dye. However experimental realization of the study in [6] is yet to be accomplished.
Materials containing Nd3+ ions are popular gain media for diode pumped solid-state lasers. For example, Nd:YAG, Nd:YVO4, and Nd:GdVO4 are often pumped by diode lasers near 810 nm to emit laser radiations at 0.97, 1.06, or 1.3 μm. To reduce thermal loading on the gain crystal, it is also possible to directly pump an Nd3+ laser to the emitting level by using a diode laser at 880 nm [7]. In the infrared band, an LED emitting at 810 or 880 nm is just emerging from the market but not widely available yet. Recently Barbet et al. reported a broadband 850-nm LED pumped Nd:YVO4 laser with 0.5% optical efficiency [8], driving the LED by a pulsed current 8 times higher than in the continuous-wave (CW) operation. To take advantage of highly efficient blue LED, Villars et al. [9] just reported a Ce3+ doped Nd:YAG laser pumped by blue LED at 460 nm with 0.4 and 6% optical efficiency for single and multi-transverse mode operations, respectively. In the demonstration, the blue LED was cooled to 0° C and driven by a pulsed current approximately 14 times higher than in the CW operation. The fluorescence of Ce3+ between 500 and 600 nm was strongly absorbed by Nd3+, resulting in an efficient output from the laser. An optical efficiency of 0.8% was also reported in Ref [9]. for single-transverse-mode operation of the Nd laser pumped by 810-nm LEDs. In fact, the transitions between 4I9/2 and [4S3/2, 4F7/2] levels of Nd3+ ions also provide a broad absorption band centered at 750 nm, which is quite suitable for LED pumping. Indeed, a 750-nm dye laser pumped Nd:YAG laser [10] was demonstrated in the past. Here we employ widely available 750-nm LED as a pump source to an Nd:YAG slab crystal and demonstrate efficient laser output with a pulsed current just 4 times higher than in the CW operation.
2. LED pump configuration
Our pump source is one of those off-the-shelf mass-produced infrared planar-array LED widely available from market (eBay), as shown in Fig. 1(a). The 20 mm × 20 mm emission plane of the LED contains a square array of 10 × 10 = 100 dies. Specifically 10 LED dies are connected in series to form a linear array and 10 linear arrays are connected in parallel to form the square array. Each die has an emission area of 1 mm × 1 mm. The center-to-center distance between two adjacent dies is 2 mm. The LED is specified with a maximum CW current of 3.5 A with 0.35 A flowing down a linear array of 10 serially connected dies. By masking some area of this planar-array LED, we are able to study in the following the minimum pump requirements for different laser configurations. Figure 1(b) shows a cut-away view of the LED pump chamber. The right half of the chamber is symmetric about the cut plane. The two LED planar emitters pump a 2-mm thick 1%-doped Nd:YAG slab crystal sandwiched between two uncoated sapphire plates. The sapphire plates, each having a thickness of 3 mm, help conduct the heat away from the laser crystal to a water-cooled aluminum (Al) housing. The pump chamber was maintained at 20° C by water cooling. The 20 mm × 20 mm surface of the Nd:YAG crystal was polished and uncoated, and its area is matched to the emission area of the LED. The two 2 mm × 20 mm laser surfaces of the crystal are anti-reflection (AR) coated at 1064 nm. The slab configuration of the laser crystal provides better heat dissipation and permits multiple gain paths in the crystal.
Fig. 1 (a) The LED plannar emitter used in our laser experiment: the 20 mm × 20 mm emission area contains a square array of 100 dies. (b) The cut-away view of the LED pump chamber: an Nd:YAG crystal is sandwiched between two 3-mm thick sapphire plates and two LED planar emitters. The sapphire plates dissipate the heat to the side walls of a water cooled aluminum housing.
Figure 2 shows the measured emission spectrum of the LED and the absorption spectrum of our Nd:YAG crystal in the pump direction, indicating good overlap between the two spectra near the 750-nm absorption band of the Nd3+ ions. To determine the optical power available from the pump LED, we first measured the emission power of each die as a function of the LED driving current. This measurement was accomplished by transmitting the light from a single die through a 2-mm diameter aperture in a metal foil immediately followed by a calibrated large-area photodiode. In the experiment, our diode-laser power supply (ILX Lightwave LDX-36125-24) could only deliver a current 4 times the maximum CW current or 28 A to the two LED planar emitters connected in parallel. As 10 linear arrays of the LED dies are connected in parallel for each planar emitter, a maximum current of 1.4 A flows through a linear array of 10 serially connected LED dies. For the following small-signal-gain measurements, we found that each die emits a peak optical intensity of 17 W/cm2 at 10 Hz when driven by the maximum current to the LED over a 1-ms duration. The LED emission spectrum in Fig. 2 was recorded under such a condition.
Fig. 2 The measured emission spectrum of the pump LED (blue curve) and transmission spectrum of our 2-mm thick, 1%-doped Nd:YAG crystal (black dots) along the pump direction. When measuring the LED emission spectrum, we drove the two LED planar emitters with a 28-A current pulse in a 1-ms duration repeating at 10 Hz. The emission spectrum of the LED overlaps well with the absorption band of the Nd:YAG crystal near 750 nm.
3. Small-signal gain
In the following, we first report the performance of a linear-cavity laser and then a V-cavity laser. The small-signal-gain measurement in this section helps the design of the high-efficiency, high-power Z-cavity laser in the next section. Figure 3 shows the schematic of the linear-cavity laser in our experiment. The laser cavity consists of a curved high reflector at 1064 nm with a radius of curvature (ROC) = 50 cm and a flat output coupler with 1% output coupling (OC). The laser cavity has a length of 10.5 cm. In practice, with custom-made LED bars, this laser can be pumped by just two face-to-face linear arrays of 10 dies aligned along the laser axis. To simulate such a configuration, the 20 mm × 20 mm surfaces of the laser crystal are covered by aluminum foils with 2-mm opening slits along the laser direction. With uniform illumination, equivalently only the power from a linear array of 10 dies on each LED transmits the slit and pumps the Nd:YAG crystal. The two LED planar emitters were connected in parallel by a pulsed current power supply, which drives the LED emitters with 1-ms electric pulses repeating at 10 Hz. We drove the two LEDs up to a peak current of 28 A or 4 times the specified maximum CW current and operated it over hours without noticing any damage or degradation to the LED. At the peak driving current of 28 A, the two 10-die LED arrays illuminate the Nd:YAG crystal with 2.73-mJ pulse energy in a 1-ms pulse duration.
Fig. 3 Our linear laser cavity consists of a curved high reflector at 1064 nm and flat output coupler with 1% output coupler. To pump the crystal with power equivalent to that from just one linear array of dies, the laser crystal is covered by aluminum foils with 2-mm opening slits along the laser direction.
Figure 4 shows the output laser energy versus input pump energy for the linear-cavity laser, indicating a laser output energy of 37.5 μJ at the maximum LED pump energy of 2.73 mJ. At the maximum pump, the optical and the slope efficiencies are 1.36 and 9%, respectively. When calculating the input optical energy, we have taken into account the 8.45% Fresnel reflection of the LED light from the YAG crystal surface. As shown in Fig. 2, not all the optical pump power is absorbed by the crystal for laser generation. The integration from the multiplication of the two curves in Fig. 2 gives an absorbed optical energy of 30 μJ per optical pump pulse from an LED die at 4 times the maximum CW current. With 10 dies pumping from two sides of the crystal, the optical efficiency of the laser based on the absorbed optical power is 6.9%. In the range of our pump energy, the laser shows no sign of saturation. This implies that, with a more powerful LED driver, the output energy of the laser could be scaled up quickly with the 9% slope of the laser buildup curve in Fig. 4.
Fig. 4 Output laser pulse energy versus input LED pulse energy. At 2.73-mJ pump energy, the laser generates 37.5 μJ laser energy with an optical efficiency of 1.36% and slope efficiency of 9%. The inset shows typical waveforms of the input LED (blue curve) and output laser (red curve) pulses at 2.43 mJ pump energy. The 250-μs delay of the laser waveform with respect to the LED one is the laser buildup time, which varies with the pump power. The laser waveform also shows some relaxation oscillation.
The inset of Fig. 4 shows typical waveforms of the input LED and output laser pulses. For this measurement, the LED pump energy was 2.43 mJ. The onset of the laser pulse is delayed by ~250 μs with respect to the optical pump pulse. The amount of time delay corresponds to the laser buildup time in the cavity and varies with the LED pump power. The output laser waveform also shows relaxation oscillation and a little bit gain switching due to the sharp rise time of the pump pulse. The output waveform settles to a quasi-CW value after a few hundred microseconds.
To obtain a single-transverse-mode output, we inserted a 2-mm diameter aperture into the laser cavity, as shown in Fig. 3. Figure 5 shows the measured laser beam diameter in the horizontal and vertical directions nearby a focused laser waist outside the laser cavity. The measurement was performed at the maximum output energy of 37.5 μJ from the linear cavity laser. The theoretical curves (continuous lines), calculated from the TEM00 mode theory, agree very well with the measured data points. By using the technique described in [11], we deduced M2 = 1.1 for the output laser in both the horizontal and vertical directions. The inset of Fig. 5 shows the intensity profile of the laser beam at the laser waist, indicating a nearly perfect TEM00 output mode.
Fig. 5 Measured beam diameter in the horizontal (square) and vertical (circle) directions nearby by a focused laser waist outside the laser cavity. The measurement was performed at the maximum output energy of 37.5 μJ from the linear cavity laser. The continuous lines are fitting curves from the TEM00 mode theory. The deduced M2 in both directions is 1.1.
The slab Nd:YAG crystal allows us to carry out laser generation with multiple passes in the crystal. Figure 6(a) illustrates a near-confocal V-cavity laser in our experiment. In this setup, the two cavity mirrors remained the same as those used in the linear cavity, but were installed to the same side of the laser crystal. On the other side of the crystal, a flat high reflector sends the laser beam back into the crystal with a small angle. For this V-cavity configuration, the laser gain length is effectively doubled. However, the overall passive loss associated with the laser crystal is also doubled. The passive loss associated with the crystal includes the some small reflections from the AR coated crystal surfaces, the optical scattering, and absorption in the crystal. The overall passive loss of the laser includes those associated with the crystal and the transmission loss of the output coupler. In this experiment, we removed the Al foils from the LED pump chamber, so that the LED pump area covers the whole laser crystal. When the pump current just exceeded the threshold value, the transverse laser profile was a fundamental Gaussian mode. As the pump current continued to increase, high-order transverse modes showed up at the output. By inserting a 2-mm diameter iris at 1.5 cm from the curved cavity mirror, we were able to ensure a fundamental-mode output throughout the whole pump range of our experiment. Figure 6(b) shows the laser output energy versus peak LED current for the single-mode and multi-mode operations. Both curves for the V-cavity laser show the same pump threshold, because near the oscillation threshold the laser always generates an output with the fundamental Gaussian mode regardless of the presence of the intra-cavity iris. This result also indicates that the 2-mm diameter iris does not introduce appreciable loss to the fundamental cavity mode. For comparison, shown in the same figure is a plot for the output energy of the linear-cavity laser. It is seen that the single- and multi-mode output energies of the V-cavity laser are 4.3 and 10.6 times the linear-cavity one, respectively.
Fig. 6 (a) Schematic of the V-cavity laser: the intra-cavity iris ensures a fundamental Gaussian mode at the output. (b) Output laser energy versus peak LED pump current for the V-cavity laser with multi-mode (blue triangle), single-mode (red dot) outputs, and linear-cavity laser with a single-mode output (black dot). The V-cavity design reduces the threshold current by 1.2 times. Insets are the single- (left) and multi-mode (right) profiles from the V-cavity laser.
The gain coefficient of the laser is proportional to the optical pump intensity, which is proportional to the pump current to the LED in our setup. Therefore, the measured laser data from the two cavities in Fig. 6(b) allow us to estimate the small signal gain of the lasers. For the linear-cavity laser, the threshold condition holds
where gth,1 is the threshold gain coefficient, L is the crystal length, T is the transmittance of the crystal surface S1 or S2, and R is the reflectance of the output mirror.We have assumed the losses at the AR coated S1 and S2 surfaces are the same. To be precise, the value of 1−T2 also includes all the other one-way losses in addition to the reflection loss at the crystal surfaces. The other losses, to name a few, include scattering and absorption in the crystal. For the V-cavity laser, the threshold condition satisfies
From the threshold currents in Fig. 6(b), the ratio gth,2/gth,1 is found to be approximately 18/15 = 1.2. The T value calculated from Eqs. (1),2) is 99.5%. We independently verified this T value by measuring the transmittance of the crystal by using a CW Nd:YVO4 laser. With known T in Eqs. (1),2), the net threshold gains or total cavity losses for the linear- and V-cavity lasers are = 3.1% and = 5.1%, respectively. Before laser saturation, the small signal gain is linearly proportional to the pump current. Given a known threshold gain at a pump current, the small signal gain at an arbitrary pump current can be calculated by using the proportionality. At the maximum LED pump current of 28 A, the round-trip small signal gains for the linear- and V-cavity lasers are therefore 4.8 and 9.8%, respectively.It is possible to increase laser efficiency and output power by optimizing, for instance, the output coupling, gain path length, and the pump current. From the small-signal-gain measured in this section, the linear-cavity laser cannot achieve lasing with output coupling larger than 4.8% and yet a multi-pass cavity is promising to generate more output power with the limited pump power from our power supply. We therefore in the following section report a Z-cavity laser for high-power operation.
4. Z-cavity laser
As an attempt to generate more laser power within the capability of our power supply, we acquired additional 6 pieces of the 750-nm LEDs from different vendors and identified two with the highest output power. For the chosen LED (produced by Epileds), each die emits a power density of 25 W/cm2 at 10 Hz when driven by a peak current of 14 A to the 100 LED dies over a 1-ms duration. We further constructed a Z-cavity laser with 1 and 5% output couplers, as shown in Fig. 7. The roundtrip gain path now consists of 6 passes through the crystal. We inserted two 2-mm-diameter apertures in the Z-cavity to suppress the high-order laser modes during high-power operation. To well define the pump energy, this time, we widened the 2-mm opening slit between the Al foils to 4.5 mm and limit the pump energy from only two rows of the LED dies from each pumping side.
Fig. 7 Configuration of the Z cavity for the 750-nm LED pumped Nd:YAG laser with 1 or 5% output coupling. In this setup, a round-trip gain path consists of 6 laser passes through the crystal. The slit in the Al foil allows 20 LED dies from each side of the crystal to pump the laser.
Figure 8 shows the measured output laser energy versus LED pump energy from the Z-cavity laser with 1 (square) and 5% (circle) output couplings. The LED pump current has a 1-ms pulse width, repeating at 10 Hz. With 1% output coupling, the maximum output laser energy, optical efficiency, and slope efficiency are 346 μJ, 3.4%, and 6.6%, respectively. The laser mode profiles at 200 and 346 μJ output energies are also shown in the plot, indicating a good circular shape over the range of our measurement. At the highest output energy, we measured an M2 value of 3.6, which is considerably smaller than the M2 = 19 reported in [8] for an LED pumped Nd:YVO4 laser and ~10 reported in [12] for typical diode-side-pumped solid-state lasers. It is evident from the power-dependent mode profile that the high laser gain of the Z-cavity laser facilitates the buildup of some high-order laser modes, resulting in a larger M2 value than that measured from the linear-cavity laser. The inset illustrates the waveforms of the input LED (blue curve) and output laser (red curve) pulses at the highest laser output. The laser buildup time is about 175 μs for this particular pump level and cavity design.
Fig. 8 Mresued laser output energy versus LED input energy for 1 (black squares) and 5% (red dots) output coupling from the Z-cavity laser. At the maximum LED pump current, the optical efficiencies are 3.4 and 2.8% for the cavity with 1 and 5% output couplings, respectively. The 12.6% slope efficiency of the 5% out-coupled laser promises high-efficiency and high-power laser operations upon availability of a more powerful LED power supply. The laser mode profiles at 200 and 346 μJ output energies are also shown in the plot, indicating power-dependent circular modes at the output. The inset illustrates the waveforms of the input LED (blue curve) and output laser (red curve) pulses at the highest laser output.
With 5% output coupling, the maximum output laser energy and optical efficiency are 288 μJ and 2.8%, respectively. The 14% slope efficiency of the 5% out-coupled laser promises high-efficiency and high-power laser operations upon availability of a more powerful LED power supply.
Thermal management is usually difficult for an LED pumped laser, because a proximity pumping scheme could block heat dissipation from the laser crystal or add LED heat to the laser crystal. With the configuration in Fig. 1(b), a sapphire plate with high thermal conductivity (35 W/(m⋅K) at 300 K, parallel) [13] is inserted between the LED and the laser crystal to dissipate crystal heat to the aluminum holder through the LED. Alternatively, one might insert a quartz plate with poor thermal conductivity (33-6.2 W/(m⋅K) at 323 K, perpendicular) [13] to insulate the LED heat from the laser crystal and rely on the water-cooled aluminum side walls to cool the laser crystal. As a comparison, we plot in Fig. 9 the output laser energy of the 1% out-coupled Z-cavity laser versus repetition rate at the highest pump energy (10.2 mJ over 1 ms) for both configurations. It is seen that the thermal property of the sapphire design (blue dots) is evidently superior to that of the quartz design (green dots) for high repetition-rate operation of the laser.
Fig. 9 Output laser energy of the 1% out-coupled Z-cavity laser versus repetition rate at the maximum LED pump energy (10.2 mJ over 1 ms) for the laser fixture in Fig. 1(b) containing sapphire heat-conducting plates (blue dots) and quartz heat-insulating plates (green dots). At a high pulse rate, using sapphire to conduct the crystal heat through the LED gives a larger laser output than using quartz to insulate the crystal from the LED heat.
As mentioned previously, a diode-pumped laser can be highly efficiency by pumping a laser crystal at a narrow absorption line, but its output power could be sensitive to temperature or current variation of the pump diode. For example, the absorption linewidth of a Nd:YAG crystal near 808 nm is 0.8 nm [14], whereas typical temperature tuning of a diode laser at 808 nm is about 0.2-0.3 nm/°C. This means that a temperature variation of 5°C for the pump diode can move the pump wavelength completely outside the gain bandwidth of a diode-pumped Nd:YAG laser. However, an LED-pumped laser can be insensitive to temperature or current variations, because LED is a broadband emitter. Figure 10 shows the output energy of the 1% out-coupled Z-cavity laser versus LED-holder temperature, measured at 9.2-mJ pump energy over a 1-ms time duration and a 10-Hz pump rate. It is seen from the plot that the output laser energy varies only ± 4.3% about the average value (red dashed line) over a 5°C range for the LED temperature. This stability performance can never be matched by a diode-pumped Nd:YAG laser for the same range of temperature variation. In the inset, the nearly identical LED emission spectra over the Nd:YAG absorption spectrum (dotted line) at 15, 20, 25°C explain the output stability of the laser.
Fig. 10 Output energy of the 1% out-coupled Z-cavity laser versus LED-holder temperature, measured at 9.2-mJ pump energy over a 1-ms time duration and a 10-Hz pump rate. The energy variation is within ± 4.3% of the average value (red dashed line) over a 5°C range for the LED temperature. The inset shows that the overlap between the LED emission spectrum and Nd:YAG absorption spectrum is relatively insensitive to the LED temperature.
5. Conclusion
In summary, we have demonstrated a 750-nm LED pumped Nd:YAG laser with superior efficiency and stability. The strong and broadband absorption between 4I9/2 and [4S3/2, 4F7/2] energy levels of Nd3+ ions is well suited for moderately broadband LED pumping. When pumped by 2.73-mJ, 1-ms LED pulses at a 10Hz rate, our linear-cavity laser generated 37.5 μJ pulse energy with 1.36% optical efficiency and 9% slope efficiency. When the LED pump was driven by a 1-ms pulsed current 4 times higher than in the CW operation, our V-cavity laser generates 0.15-mJ pulse energy with a fundamental Gaussian mode profile. The V-cavity laser experiment indicates a promising multi-pass configuration to achieve a high-power, high-efficiency output from a laser pumped by low-optical-intensity LEDs.
With 1% output coupling, our LED-pumped Z-cavity laser generated a maximum laser pulse energy of 346 μJ with optical and slope efficiencies of 3.4 and 6.6%, respectively, when pumped by 10.2-mJ LED energy in a 1-ms pulse width. With 5% output coupling, we measured 288-μJ output pulse energy from the Z-cavity laser with 2.8 and 14% optical and slope efficiencies at the same pump condition.
The measured 1.36 and 3.4% optical efficiencies for the 1% out-coupled linear and Z-cavity lasers with M2 = 1.1 and 3.6, respectively, are compared favorably with the demonstrated 0.5% efficiency for the 850-nm LED pumped Nd:YVO4 laser with M2 = 19 in [8] and 0.8% efficiency for the 810-nm LED pumped Nd:YAG laser with a single-order-mode output in [9]. Our measured 9% slope efficiency for the linear-cavity laser is superior to the 0.3~0.6% slope efficiencies demonstrated for the 850-nm LED pumped Nd:YVO4 laser of the same cavity configuration in [8] and the 1.3% slope efficiency for the 810-nm LED pumped single-mode Nd:YAG laser in [9]. The best measured 14% slope efficiency of our 5%-out-coupled Z-cavity laser is comparable to the best measured 12.8% slope efficiency of the 460-nm LED pumped cesium-doped multi-mode Nd:YAG laser reported in [9].
There are a number of ways to further improve the output power and pump efficiency of the LED pumped laser. First of all, the maximum optical intensity of 25 W/cm2 per die from our best LED could be greatly increased with a much higher driving current. Currently, the 28-A maximum driving current, which is only 4 times higher than in the CW operation of our LED, was limited by our diode-laser power supply. Similar experiments in [8,9] have powered an LED with a ~ms pulsed current ~10 times higher than in the CW operation. Although the slab configuration of our laser crystal is well matched to the square array of the LED dies and permits performance comparison among linear, V-, and Z-cavity lasers, a long crystal rod geometrically matched to a custom-fabricated linear-array LED is certainly desirable to maximize the laser gain and pump efficiency without introducing interface losses. An interesting next effort is to Q-switch the LED-pumped laser and investigate its performance under a high peak power.
Acknowledgment
This work is supported by the Ministry of Science and Technology under Contract MOST 103-2221-E-007-062-MY2. Kuan-Yan Huang acknowledges receiving a scholarship from Epistar Corporation. The authors thank Ming-Hsiung Wu of National Tsing Hua University, Taiwan, and Fredrik Laurell of Royal Institute of Technology, Sweden, for their helpful advices.
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