5-1 Band-edge modes in dispersion curves
In this section, we will simulate the dispersion curves of photonic crystal nanostructure by plane wave expansion method (PWEM). From the dispersion curves, there are two axis including normalized frequencies (ratio of photonic crystal lattices and wavelength) and in-plane k vector directions (K0sinθ) showing different PhC band-edge modes such as Г, K, and M. According to the position of normalized frequencies of the dispersion curves, we can distinguish the relation between lasing wavelengths and what the PhC laser modes are.
The angle-resolved μ-PL (AR μ-PL) system is designed for multiple choices. As shown in
Optical pumping system (Angle-resolved μ-PL)
Figure 5. 1, we have two optical pump sources, two optical pump incidence paths, two collecting PL method and two way to collect sample surface image. The two optical pump sources are: one is frequency tripled Nd:YVO4 355 nm pulsed laser with a pulse width of ~0.5ns at a repetition rate of 1KHz; the other is 325 nm He-Cd continuous wavelength laser. The samples are optically pumped by laser beam with an incident angle of 0 degree or 60 degree to the sample. The laser spot size is about 50 μm in diameter so that covering the whole PhCs pattern area. The PL is collected by a 15 X objective lens and straightly collected by spectrometer with a charge-coupled device (Jobin-Yvon iHR320 Spectrometer) or collected by a fiber with a 600 μm core, which rotating in the normal plane of the sample, and also coupled into spectrometer. The spectral resolution is about 0.07 nm for spectral output measurement. Figure 5. 1 shows the setup of our AR μ-PL system. The GaN-based PCSELs were placed in a cryogenics controlled chamber for performing PL experiment under low temperature (in order to prevent damage caused by heat). The temperature of the chamber can be controlled from room temperature (300 K) down to 77 K via the liquid nitrogen. We can also monitor the image and spatial
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distribution on the sample surface by charge-coupled device (CCD) and beam view, respectively.
(resolution ~ 0.7A) Spectrograph
Objective 15X
mirrorflip
dichroic mirror CCD
Beam View
mirrorflip
Nd:YVO4 355nm pulse laser Pulse duration:500 ps frequency:1000 Hz
He-Cd 325nm Continuous Wave laser
Cooling Chamber 10cm
Convex lens
Figure 5. 1 The angular-resolved μ-PL (AR μ-PL) system
The typical photoluminescence (PL) spectrum of as-grown samples, as shown in Photoluminescence of the PCSEL structure
Figure 5. 2, had a peak centered at a wavelength of 425 nm with a linewidth of 25 nm. At normal incidence at room temperature, the DBR showed the highest reflectivity of 99 % at the center wavelength of 430 nm, with a stopband width of about 30 nm, measured by an n&k ultraviolet-visible spectrometer as shown in Figure 5. 3. Here, we used the circular hole diameter r chosen such that r/a is about 0.28. After the PMMA layer was removed by acetone, we used ICP-RIE to etch down the as-grown sample to about 400 nm deep. The etching penetrated the MQWs active regions and created the PC patterns in the nitride layers. Finally, the SiNx hard mask was removed by buffered oxide etch dipping. The structure of GaN-based 2-D photonic crystal surface emitting lasers (PCSEL) with bottom AlN/GaN distributed Bragg reflectors (DBR) are as shown in section 4.4.
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360 390 420 450 480 510
0 20 40 60 80 100
R ef lec tan c e( % )
Wavelength(nm)
Figure 5. 2 Reflectivity spectrum of the half structure with 35 pairs of GaN/AlN DBRs measured by N&K ultraviolet-visible spectrometer with normal incident at room temperature.
380 400 420 440 460 480 0.0
0.5 1.0 1.5 2.0 2.5 3.0
@~425nm
Int e ns it y (a rb. uni t)
Wavelength(nm) 25nm
Figure 5. 3 The u-PL spectrum of as-grown sample
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In our PCSEL devices, the lasing action was clearly observed in several different devices with different lasing wavelength from 395 nm to 425 nm. Take the PC lattice constant 254 nm for example.
Threshold characteristics
Figure 5. 4 shows the output emission intensity as a function of the pumping energy density. The clear threshold characteristic is observed at the threshold pumping energy density of 2.8 mJ/cm2, with a peak power density of 5.6 MW/cm2. Then the laser output intensity increases abruptly and linearly with the pumping energy above the threshold energy. Figure 5. 5 shows the excitation energy dependent emission spectrums from 0.8 Eth to 1.3 Eth. These spectrums clearly show the transition behavior from spontaneous emission to stimulated emission. Above the threshold, we can observe only one dominant peak wavelength of 419.7 nm with a linewidth of 0.19 nm.
2 3 4 5
0 2 4 6 8
Int e nsi ty( a rb. uni t)
Pumping energy density(mJ/cm
2)
Figure 5. 4 Laser intensity as a function of pumping energy density
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414 417 420 423
0 10 20 30 40 50
0.8Eth 1Eth 1.2Eth 1.3Eth
Int e ns it y (a rb. uni t)
Wavelength(nm)
FWHM~0.19nm
~419.7nm
Figure 5. 5 The lasing spectrums under different pumping energy densities
It’s worth noting that the single mode lasing phenomenon only occurs in the area with PC patterns. On the other hand, multiple lasing peaks were occurred when the area without PC patterns was pumped at the threshold energy density two-order of magnitude higher. The normalized frequency (lattice constant over wavelength, a/λ ) for the lasing wavelength emitted from our PC lasers with different lattice constants were plotted as shown in Figure 5. 6(a). All the PhC lasers have lasing peaks in a range from 401 nm to 425 nm. It can be seen that the normalized lasing frequency (dotted points in the figure) increased with the lattice constant in a discontinues and step-like fashion. To calculate the band diagram of the hexagonal PhC patterns in this structure, we employ the plane-wave expansion method in two-dimensions with an effective index approach that took into account the effects of partial modal overlap of electromagnetic fields with the PhC structures [1]. As a starting point, the ratio of light confined within the 2-D PhC structure to light extended in the entire device, Γg, and the effective refractive index of the entire device neff were first estimated by the transfer matrix method. The calculation shows that the lowest order guided mode has the highest confinement factor for both PC and MQW
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regions and the Γg, and neff are estimated to be 0.563 and 2.495, respectively. Then, we determine the effective dielectric constants of the two materials in the unit cell, εa and εb,
using neff2= fεa +(1− f)εb and ∆ε =εb −εa =Γg(εmat −εair), where, the calculation of the band diagram for the 2-D hexagonal-lattice structure with r/a = 0.28.
Figure 5. 6(b) shows the calculated dispersion curve of the 2-D hexagonal-lattice structure for transverse-electric mode. It can be expected that the lasing occurs at special points such as at Brillouin-zone boundary near the band edges, because the Bragg condition is satisfied and the density of states is higher in these points [1]. At these lasing points, wave can propagate in different directions and couple with each other. The dotted lines are guides for band edges calculated in Figure 5. 6(b) and extended horizontally to Figure 5. 6(a) with the same normalized frequency. It can be seen that different groups of the normalized frequency observed in the PC samples with different lattice constants occur exactly at band edges such as Γ, M, and K points, indicating that the laser operation was provided by multidirectional distributed feedback in the 2-D PC nanostructure [2]. The characteristics of Γ, M, and K points lasing can be further identified by the polarization angle of the output emission shown in the following section [3]. Note that the output intensity is higher when some of the lasing frequencies are in the stopband of DBR, which could be due to that the bottom DBR here could be treated as a high reflectivity reflector, facilitating top-emission efficiency.
The lasing area of the GaN-based 2-D PCSEL, obtained by a CCD camera is relatively large which covers almost whole area of PhC pattern with only one dominant lasing wavelength as shown in Figure 5. 7. It’s interesting to note that the threshold power density of GaN-based 2-D PCSEL is in the same order of or even better than the threshold for GaN-based VCSEL we demonstrated recently [4]. Unlike the small emission spots observed in the GaN-based VCSELs, the large-area emission in 2-D PCSEL has great potential in applications required high power output operation.
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180 200 220 240 260 280 0.0
0.2 0.4 0.6 0.8
Normalized frequencyω (a/λ)
Lattice constant (nm)
0.0 0.2 0.4 0.6 0.8
Normalized frequency ω(α/λ)
Γ K M Γ
Γ1
K2
M3
(a) (b)
Figure 5. 6 (a) Normalized frequency as a function of the lattice constant.
The solid circle points are the lasing wavelengths from the different PhC structures. (b) Calculated band diagram of the 2-D hexagonal-lattice structure. The dotted lines are guides for band edges.
Figure 5. 7 The lasing CCD image is at 1.3 Eth and the dash circle is the PhC nanostructure region of about 50μm
In order to understand the β of this PhC cavity, we plotted the L-I curve in a logarithm scale as shown in
The coupling efficiency of spontaneous emission (β)
Figure 5. 8. The spontaneous emission coupling efficiency β value is about 5*10-3.
This value of the PCSEL is similar to the value of VCSEL but one order of magnitude higher than that of the typical edge emitting semiconductor lasers (normally
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about 10-5) [5], , indicating the enhancement of the spontaneous emission into a lasing mode by the high quality factor microcavity effect in the PCSEL structure.