Contenedor ISO

As mentioned in Section2.4, the deposition system for AR coatings contains a (quasi) in-situ measurement setup for the P-I characteristic of the laser. In that sense, the analysis of the optical coating is performed while the coating is deposited, and the setup of the setup of the coating process already contains the expected behavior of the finished result.

The in-situ evaluation of the layer thickness, i.e. coating quality during deposition is best done in two stages. In the first stage, the residual reflectivity of the deposited layer can easily be determined from the rising threshold current of the QCL, as long as there is a clearly defined threshold current. This works as follows. Eq. (2.32) states that the threshold current density of a QCL is

Jth=

αw+ αm1+ αm2

Γg , (2.75)

where αmi = _2l1 ln_R1_i are the mirror losses of facet i, Γ is the confinement factor, i.e. the

overlap of the laser mode with the active region, and g is the gain coefficient defined by gJ = γ. Inserting the mirror losses and cross sectional area of the current flow, l × b, where b is the width of the laser stripe, Eq. (2.75) reads

Ith = lb · Jth= lb · αw+ αm gΓ = lb gΓ(αw− ln R1 2l − ln R2 2l ). (2.76)

If αw is known, gΓ can be extracted from a P-I curve measured for the uncoated laser. R2

of Eq. (2.76) is now to be understood as the residual reflectivity of the coated facet.

Eq. 2.23, giving the reflectivity of a layer of some material of thickness d and refractive index n deposited on a substrate with refractive index ns for a given wavelength λ at normal

incidence in ambient vacuum or air, can be rewritten to

R= 1 − 4 2 + 1 ns + ns 1 + (ns− n2 ns)( 1 n2 −1) sin2 2πnd_λ . (2.77)

For the case of n2 _{= n}

s and d = _4nλ , R reduces to 0. This is the ideal case. If n2 ≈ ns,

then R ≈ 0 but finite at the same thickness d. Next, Eq. (2.77) is substituted for R2 of Eq.

(2.76) to give the threshold current as a function of layer thickness d. This is plotted as the resonance curve in Fig. 2.16, together with actual measurement results during a coating run marked as dots.

The second term on the right-hand side of Eq. 2.77 has the shape of a resonance curve in d. This plus the fact that R2 of Eq. (2.76) is log-transformed, lead to the fact that this

measurement is very sensitive to R2 as R2 approaches 0.

However, as discussed in Section 2.5.3, at some point during deposition, the picture of a clearly defined threshold current loses validity. But instead of seizing emission entirely, as would be expected for an ideal laser below threshold, a considerable amount of emission

Figure 2.16 Protocol of the threshold current measurements during the deposition of a quarter-wave

Y2O3 AR coating on a QCL facet. The curve is calculated with Eqs. (2.76) and (2.77) with a design

wavelength of 4.44 µm and index of 1.843. The dots mark the measured values of the threshold current after intervals of deposition.

remains. The response just misses the characteristic “kink”. This is because, as also discussed in previous sections, the former laser turns into a superluminescent diode (SLD), which, due to the long stripes of often around 6mm, causes considerable emitted powers. This makes interpretation of the in-situ results rather hard, and the best way around it is the following. It is clear from Eq. (2.39) and Fig. 2.8, that the “slope” of the uncoated facet’s P-I curve, even if the picture of a laser is not strictly valid, decreases with decreasing reflectivity of the other facet. Consequently, the best way to reach the lowest possible reflection is to follow carefully the decrease of emitted power at the highest allowable pump current value during deposition. Since this does not translate in any simple way to the residual reflectivity, the only way to find the optimal value is to measure in gradually decreasing intervals and to observe when the emission minimum is passed. The final reflectivity can then only be determined ex- situ by perfoming P-I measurements on both facets and fitting the results using the photon flux density model.

The first stage of the in-situ evaluation can also be performed when depositing two-layer coatings. Instead of Eq. (2.77) it is necessary to use Eqs. (2.25), (2.26), and (2.27) from Section 2.3. The challenge with this is that the threshold current is very insensitive to changes of the overall reflectivity R2 as long as R2 is not very small. Therefore, the actual

layer thickness of the first layer is strongly prone to error. Extracting the thickness from the reading on the quartz oscillator is also completely futile, since the tiny facets are directly on the edge of the substrate and edge effects dominate the deposition of the coating material onto it. These in turn dependent strongly on exact facet size, whether the structure is overgrown, and the thicknesses of the insulating layer and gold overcoat. From this it follows, that the

best way to make two-layer anti-reflection coatings is by using two materials that are both as close as possible from two sides to the ideal one-layer value. The more this is the case, the more tolerant the process is to thickness errors of the first layer, since the error of the first layer can be balanced out by the second. The final stage of the deposition can then also be monitored by the maximum-power method, which once overall reflectivity is small becomes very sensitive.

3

Versatile Littrow External Cavity

QCL with Reflective optics

(V-ECQCL)