7 Waveguide Experiments
7.5 Gain in Channel Waveguides
7.5.3 Gain Measurements
7 Waveguide Experiments
In order to estimate if such large inversions can be obtained in the waveguide channels of the Nd:(Gd, Lu)2O3 film, the saturation intensity atλp= 820 nm and the attainable pump intensity were compared. For the calculation of Isat, the lifetime τu= 230µs measured in section 6.2.2 for the 4F3/2 level was used and the absorption-cross section of the film was roughly estimated to be 2×10−20cm2, which is approximately half the value given in [For99] for a Nd:Y2O3 bulk crystal.37 The calculation results in a saturation intensity of 50 kW/cm2. Considering the maximum incident pump power Pmax of approximately 400 mW attainable with the Ti:Al2O3 laser used for the Nd3+ laser experiments and assuming a homogeneous distribution of the pump power in the approximated channel area of 5µm×2µm, intensities of up to 4×103kW/cm2 can be obtained. Since this intensity is significantly higher than the saturation intensity, a high inversion is possible in the waveguide, even if the pump intensity is considerably reduced due to high coupling and propagation losses.
The attainable small-signal gain is thus most likely comparable to the one determined in section 7.5.1. Therefore, a doping concentration of 0.5 % is expected to be sufficiently high to compensate the waveguide losses. This concentration corresponds to a Nd3+ density similar to that of the Nd(1 %):YAG amplifier investigated in [Guy98] and is comparable to the optimum doping concentration given in [Dan73] for Nd:YAG. Hence, a Nd3+ con-centration of 0.5 % was chosen for first waveguide laser experiments. However, due to the reduced impact of fluorescence quenching, which is expected for the small waveguide dimensions, higher doping concentrations may be beneficial and should be investigated in future experiments.
7.5 Gain in Channel Waveguides A tunable diode laser38(λ= 1501−1583 nm) was used as signal source and a laser diode39 at λp= 1480 nm as pump. The light from both fiber-coupled sources was combined40 in one single-mode fiber,41 collimated and then coupled into the waveguide channel by use of a microscope objective with a NA of 0.35. Using another objective with a NA of 0.7, the outcoupled light was collected. Signal and pump light were separated with a dichroic mirror and a monochromator. The outcoupled signal light was detected with a germanium photodiode and its intensity Is,out(Pp) (in arbitrary units) was measured in dependance of the incident pump power42 Pp for values up to Pmax≈200 mW. In order to distinguish between the signal and spontaneous fluorescence light, the former was modulated and the lock-in technique was applied.
λ (nm) IsatkW
cm2
Gsp (%) G (dB/cm)
1535.5 0.54 257 5.9
1542.0 3.51 122 1.2
1547.6 1.31 135 1.9
1555.1 1.51 140 2.1
1577.0 4.67 112 0.72
Table 7.5: Single-pass signal enhancement Gsp measured for the 3.1µm thick Er:(Gd, Lu)2O3 waveguide as well as the signal enhancement G in dB/cm. Isatis the calculated saturation intensity at the corresponding signal wavelength λ.
By use of Eq. (7.30), the single-pass signal enhancementGspwas determined (see Tab. 7.5).
Gsp = Is,out(Pmax)
Is,out(Pp= 0) (7.30)
Considering the waveguide length l of 0.7 cm, the signal enhancement G in dB/cm is obtained as follows:
G = 10·logGsp
l dB (7.31)
The signal enhancement corresponds to the gain if the absorption of the signal in the unpumped case can be neglected. Otherwise aG higher than the gain would be measured, as pumping reduces the signal absorption.
38Lion Series of theSacher Lasertechnik Group, Littman design
393400 Series fromJDS Uniphase
40A wavelength division multiplexer (WDM) was used for that purpose.
41SM15 polarization maintainingFujikura Panda fibers with NA of 0.11 were used.
42Ppwas measured between the waveguide and the coupling optics.
7 Waveguide Experiments
In order to estimate the effect of signal absorption in the unpumped case, the intensity dependent absorption coefficient αabs(Is) at the signal wavelength λ=c0/ν is determined.
As in section 7.5.1, solely the 4I15/2 and 4I13/2 manifolds with populations Nl and Nu are considered. Neglecting reabsorption of spontaneously emitted photons leads to the following rate equations:
dNu
dt =−Nu τu + Is
hν σabsNl− Is
hν σemNu (7.32)
Nt = Nl + Nu (7.33)
Here, τu is the lifetime of the metastable 4I13/2 level. By solving the rate equations for the steady-state, αabs(Is) can be derived from Eq. (2.48):
αabs(Is) = αabs(0) 1 + Is
Isat
(7.34) Isat = h ν
τu(σabs+σem) (7.35)
At the saturation intensity Isat, the absorption coefficientαabs(Is) equals half the value of the small-signal absorption coefficient αabs(0). The saturation intensities for the investi-gated signal wavelengths were calculated with the spectroscopic parameters determined in section 6.2.1. The results are summarized in Tab. 7.5.
Incident signal powers Ps of at least 1.2 mW were used for the gain measurements of the 3.1µm thick waveguide.43 The signal intensities which would be obtained if all this power was coupled into a 5µm wide channel of the investigated waveguide and no propa-gation losses occurred,44 were simulated for the wavelengths with the highest and lowest saturation intensity.
Figure 7.20a shows the resulting intensity distribution for λ= 1535.5 nm. At this wave-length, most of the waveguide channel is significantly saturated. Less than 1.3 % of the signal power is propagating in regions where the saturation intensity is not reached, and 91.2 % is confined to areas with an intensity more than eight times higher than Isat. How-ever, the small-signal absorption coefficient at this wavelength is 2.91 cm−1 (12.5 dB/cm) and thus very high. Therefore, even at high intensities, absorption is not entirely negligi-ble.
In order to estimate the signal absorption in the unpumped case, the average absorption coefficient ¯αabs is calculated as follows:
¯
αabs = modeD(x, y)αabs(Is(x, y))Is(x, y)dx dy
modeIs(x, y)dx dy (7.36)
D(x, y) is the function introduced in section 7.3.2 in order to describes the dopant dis-tribution. By substituting Eq. (7.34) and integrating numerically over the entire mode
43Ps was measured between the waveguide and the coupling optics.
44
7.5 Gain in Channel Waveguides
-5 0 5
-4 -2 0 2
0 0.1000 1.0000 2.0000 4.0000 8.0000 16.0000 32.0000 64.0000 118.5185
y( m)m
x(m)m
Is/Isat
0 0.1 1 2 4 8 16 32 64 128 (a)
-5 0 5
-4 -2 0 2
0 0.1000 1.0000 2.0000 4.0000 8.0000 10.4497
x(m)m
Is/Isat
0 0.1 1 2 4 8 16
y( m)m (b)
Figure 7.20: Simulated distribution of the signal intensity Is in a 5µm wide channel of the 3.1µm thick Er:(Gd, Lu)2O3 waveguide. The simu-lation was performed for a signal power of 1.2 mW, TE polarization, and two wavelengths with different saturation intensities: (a) λ= 1535.5 nm, Isat= 0.54 kW/cm2 and (b) λ= 1577 nm,Isat= 4.67 kW/cm2
7 Waveguide Experiments
profile, an ¯αabs of 0.11 cm−1 (0.47 dB/cm) is obtained. This value corresponds to ap-proximately 8 % of the measured signal enhancement G. The actual gain G is therefore expected to be at least 8 % smaller than G. Considering the high waveguide losses and thus reduced signal intensities, a lesser degree of saturation is obtained in most waveguide regions and G deviates more than 8 % from the actual gain.
At λ= 1577 nm, the saturation intensity is significantly higher. Therefore, the waveguide channel is much less saturated at this wavelength (see Fig 7.20b). Nevertheless, 90.2 % of the signal propagates in regions where the saturation intensity is reached. While the chan-nel is less saturated at λ= 1577 nm, the small-signal absorption coefficient of 0.202 cm−1 (0.87 dB/cm) is significantly smaller at this wavelength. By use of Eq. (7.36), an average absorption of 0.040 cm−1 (0.17 dB/cm) is obtained, which is 24 % of the measured signal enhancement. The actual gain at this wavelength is thus expected to be at least 24 % smaller than G.
In the previous paragraphs, a rough estimation of the measurement error associated with signal absorption in the unpumped case was made. A more precise treatment requires the simulation of the signal-intensity evolution during propagation. However, several required parameters, such as the coupling and propagation losses, could not be determined precisely. Hence, such a simulation has not been performed.
For a qualitative comparison of the measured signal enhancement and the theoretically calculated gain, the measured values are plotted in the theoretical gain spectrum illus-trated in Fig. 7.12. Since the pump power is two orders of magnitude higher than the signal power, an almost complete bleaching of the waveguide channel on the pump tran-sition is expected. As detailed above, the signal enhancement is merely an upper limit for the actual gain. However, the measured values are still lower than the calculated ones.
This is most probably due to a lesser confinement of the propagating light to the doped regions; as indicated by the comparison of the measured and simulated mode profiles in section 7.3.2, the actual confinement is most likely lower than the simulated one. Since the signal linewidth of 0.3 nm (FWHM) is smaller than the smallest linewidth in the film spectra, effects caused by the signal line shape and its overlap with the absorption and emission peaks are negligible. However, the deteriorative processes mentioned in section 7.5.2 may be responsible for the deviations from the simplified theoretical model. Nev-ertheless, the measurement results reproduce qualitatively the curve calculated from the spectroscopic data.
A signal enhancement of 4.8 dB/cm at λ= 1535 nm has been determined in a similar way for a rib channel of the 1.0µm thick Er(0.6 %):(Gd, Lu)2O3 film. The smaller signal enhancement measured for this waveguide is mostly due to a lower confinement of the signal light to the doped regions. However, the measured signal enhancement for both samples is significantly higher than the value of 2.6 dB/cm measured at the same pump and signal wavelengths in a sputtered Er(0.34 %):Y2O3 channel waveguide [Hoe93].
The extreme losses in the channels of the 3.1µm thick Er:(Gd, Lu)2O3 sample are most probably higher than the achievable gain. In the 1.0µm thick Er:(Gd, Lu)2O3 waveguide, however, the losses are significantly lower. Hence, the 1.0µm thick waveguide is more promising for first Er3+ waveguide laser experiments, although a lower gain is expected to be obtainable in this waveguide.