Laser threshold

Now it s time to apply our mathematics to a scientific example. We analyze an extremely simplified model for a 1 aser, following the treatment given by Haken (1983). 

Each atom can be thought of as a little antenna radiating energy. When the pumping is relatively weak, the laser acts just like an ordinary lamp the excited atoms oscillate independently of one another and emit randomly phased light waves. 

Now suppose we increase the strength of the pumping. At first nothing different happens, but then suddenly, when the pump strength exceeds a certain threshold, the atoms begin to oscillate in phase—the lamp has turned into a laser. Now the trillions of little antennas act like one giant antenna and produce a beam of radiation that is much more coherent and intense than that produced below the laser threshold. 

This sudden onset of coherence is amazing, considering that the atoms are being excited completely at random by the pump Hence the process is self-organizing the coherence develops because of a cooperative interaction among the atoms themselves. 

A proper explanation of the laser phenomenon would require us to delve into quantum mechanics. See Milonni and Eberly (1988) for an intuitive discussion. 

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Figure 10-15. Output vs. input energy characteristic of our laser device. The horizontal dashed curve indicates the zero line. A clear laser threshold behavior at an excitation pulse energy ol 1.5 nJ is observed. Below the lasing threshold only isotropic phololuminesccncc is entitled. Above threshold the device emits low divergence single mode laser emission perpendicular to the surface, as schematically shown in the inset. The laser light is polarized parallel to the grating lines.

Fig. 12.8 (a) The experimental setup, (b) Optical spectra emitted from a CBNL under different pump levels. Inset Integrated emitted power vs. pump power, showing laser threshold at 800 mW. Inset 2 Lasing pattern. Reprinted from Ref. 21 with permission. 2008 Institute of Electrical and Electronics Engineers... 

Figure 31. (a) The concentration dependence of the fluorescent lifetime of Nd in CaW04. (b) The concentration dependence of the laser thresholds [from Ref. (HO)]. 

Figure 32. Concentration variation of laser thresholds of Nd in the series Na .5Gdo.5, xNd W04 [from Ref. (111)1...

Johnson et al. (55) observed energy transfer from erbium to thulium and from erbium to holmium ions in crystals. They were able to obtain substantial decreases in laser thresholds because of this energy migration. The fluorescent lifetime of the 3//4 state of thulium in CaMo04 containing 0.75 atomic per cent erbium and 0.5 atomic per cent thulium as inferred from the time delay before the onset of laser oscillation is 900 /xsec at both IT and 20°K. 

A neodymium-ytterbium-coupled rare-earth ion system was given extensive study by Peterson and Bridenbaugh (109, 166) Peterson et al. (167) and Pearson and Porto (168). The simultaneous doping of Nao.5Gdo.5-W04, or Calibo (168) glass with neodymium and ytterbium results in a resonance-coupled system in which energy pumped into the neodymium appears as fluorescence from the ytterbium. The fact that the energy absorbed by the neodymium is rather efficiently transferred to the ytterbium results in a substantial reduction in laser threshold for ytterbium. 

Although a considerable number of optical detectors and waveguide structures have been created from Si-based materials5 8 123 124 there is still a paucity of LEDs constructed from Si and, most importantly for many all-Si optoelectronic applications, no lasers. The requirements for an acceptable semiconductor laser for optical fiber applications are rather stringent 5-10 mW of laser facet power at 1.3 pm, maximum laser threshold less than 70 mA, spectral width less than 10 nm, operation over the temperature range -40°C to +85°C, average lifetime of 106 hr, and low cost.123... 

To put the experimental sections in perspective the maximum power in a GaN Er LED and Er-doping density to achieve laser threshold are calculated as follows ... 

A variety of lasers based on tetrakis p-diketonates of have been developed over the last few years. A summary of the chemistry and energy transfer in these laser systems is presented, with particular attention to the salts of tetrakis benzoyltrifluoroacetone chelates of europium. Chemical effects attributed to solvents, benzene ring substitutions in the ligand, differing cations, and deuteration are considered. These effects manifest themselves most markedly in the variability of laser thresholds from compound to compound and solvent to solvent. The thresholds reflect association-dissociation equilibria, as well as energy transfer processes in the ligand and throughout the manifold of Eu " states. 

We prepared a number of derivatives of benzoyltrifluoroacetone bearing substituents on the meta and para positions of the benzene ring and converted these to the corresponding europium tetrakis chelates. Schimitschek (33) has studied the nine BTFA derivatives obtained by substituting fluorine, chlorine, or bromine at the ortho, meta, or para position of the ring. Table I shows that substituents can have a considerable effect on the laser threshold of these compounds although the... 

The thermodynamic stability of could clearly influence the position of this equilibrium. The importance of this effect is shown by the work of Reidel and Charles (23) who prepared salts of [(BTFA)4Eu] with 15 different substituted ammonium cations and observed a more than threefold change in laser threshold at 0°C. on going from piperi-dinium through quinolinium. The increase in threshold roughly parallels an increase in the pKb of the amine from which the cation is derived for those compounds with other than quaternary ammonium ions, and for the quinolinium salt these workers showed that the extent of dissociation to tris chelate is about 40%, as compared with 10% or less for the piperidinium compound. 

It was shown that for semiconductor lasers based on InGaN/GaN heterostructures, at optical excitation by the laser pulses of the femtosecond duration ( 150fs) the laser threshold exceed 2 0 GW/cm. It is caused most probably by non-steady excitation conditions. FWHM of the laser spectra alters from 13 to 25 nm. Amplification occurs in a wide interval of 60-80 nm and the gain at maximum reaches 85-153 cm . 

When Nq < k/G, the fixed point at n = 0 is stable. This means that there is no stimulated emission and the laser acts like a lamp. As the pump strength is increased, the system undergoes a transcritical bifurcation when - k/G. For Ag > k/G, the origin loses stability and a stable fixed point appears at n = (GNq -k)laG > 0, corresponding to spontaneous laser action. Thus Ng = k/G can be interpreted as the laser threshold in this model. Figure 3.3.3 summarizes our results. 

The laser threshold g depends on the length of grating section L and the coupling between the electromagnetic wave and the grating, expressed by the DFB coupling coefficient k [108]... 

Fig. 12.9 PL and second-order DFB laser spectra for different grating periods for neat thin films of Spiro-60T (a) Spiro-DPVBi (b). The laser threshold energy densities of the neat guest, neat host and an optimized G-H system are compared (c).

When comparing the laser threshold energy values it is apparent that the most promising candidates for low-threshold operation are guest-host systems. Here, the self-absorption of the material matrix is effectively separated from the spectral region of the emission. The doped systems containing DCM2 or the stilbene... 

A technological approach to decrease the threshold of DFB lasers is the use of first-order grating structures instead of second-order DFB lasers. As can be seen in Table 12.1, this experiment was performed with three material systems, two low molecular weight based G-H systems and with the conjugated polymer MeLPPP. In all cases the laser threshold was reduced significantly - on average by a decade. 

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