1. Emission regimes of random lasers with spatially localized feedback
A. Consoli and C. López
Inst. de Ciencia de Materiales de Madrid (CSIC)

2. Experimental set-up
Aim of the experiments: measure the spectral emission as afunction of the device geometry.
Sample pumped with W = 780 (a) with outlined in white the geometries with minimum and maximum widths. Experimental set-up (b)

3. Typical spectra for small and large widths

4. Pump dependent spectrum for different widths
For W < 250 µm, multi mode narrow linewidth emission, so called “resonant” random lasing spectrum
More modes as W is increased
Modes lasing at small widths are still present at larger W, but with different threshold and slopes
For W = 250 µm, modes start collapsing around the peak gain
For W > 250 µm, single peaked spectrum, so called “non-resonant” random lasing spectrum

5. Pump dependent spectrum for different widths
Comparison between ASE and single peaked spectrum
Animated sequence
Spectra obtained for lasing device with L = 3.5 mm and W = 780 µm (solid line) and ASE experiment (no TiO2 walls) with same geometry (dashed line). Pump flux is 50 pJ/µm2.

6. Modelling Single device
A. Consoli and C. López “Decoupling gain and feedback in coherent random lasers: experiments and simulations” Scientific Reports 5, (2015)

7. Modelling
Each “reflector ” is modeled with R(n)·exp(if(n)), where R(n) and f(n) are the amplitude and phase spectral profiles, n the frequency variable and i the imaginary unit.
In devices which share a portion of the backscattering reflectors allowed frequencies for Wn-1 will be available for Wn = Wn-1 + DW, with DW an arbitrary increment, but with a different balance of gain and losses.
We construct the amplitude responses of left and right reflectors of the nth device as Rn(n) = 0.5(Rn-1(n) + RRAND(n)) where Rn-1(n) refers to the device with W = Wn-1 and RRAND(n) is a reflection profile arbitrarily shaped at each n.
N different phase profiles are constructed as f1(n), f2(n) .. fN(n), corresponding to N nested devices of increasing width; then, for the n-th device, the available phase values at a given frequency ν0 are given by the ensemble of all previously constructed phases evaluated at that frequency.

8. Modelling. Intuitive picture
Active area
Right scatterer
Figurative example for amplitude change with width.
Small width W1 : frequency f1 is poorly back-scattered into the gain area.
Large width W2 : frequency f1 is efficiently back-scttered into the gain area.
Reflection coeff. at large width is the average of the one seen at small width and the one due to width increment. W1 W2
Active area
Right scatterer
Figurative example for phase change with width.
Small width W1: frequency f1 (red) is back-scattered into the gain area. Frequency f2 (blue) is back-scattered outside the active area.
Large width W2 : frequency f1 (red) and frequency f2 (blue) are both back-scattered into the gain area. W1 W2

9. Losses and allowed modes in simulations
Total losses (black lines, left axis) and allowed modes (red lines, right axis) calculated for n = 1 (a), 5 (b), 10 (c) and 20 (d).

10. Simulations results with pump
Increasing number of lasing modes as the width is increased 
Modes lasing at small widths are still present at larger W, but with different threshold and slopes 
For maximum width modes occupy all the gain window, no spectral narrowing as in experiments 

11. Introducing coupled mode theory (CMT) in simulations
coupling : FWHM 7 times narower
no coupling : full gain window
M. Leonetti, C. Conti and C. López Nature Photonics 5, 615–617 (2011).
M. Leonetti, C. Conti and C. López, Phys. Rev. A 88(4), , (2013).
H.A. Haus, Waves and fields in optoelectronics (Prentice Hall, 1984), Chap. 7.

12. Results including the CMT
Simulation results obtained after solving CMT model, for different devices with 5 (a), 10 (b), 20 (c) and 40 (d) modes.

13. Conclusions
Experimental observation of “resonant” and “non-resonant” random lasing spectra in RLs with spatially localized feedback
Emission regimes dependent on illuminated area of back-scattering “walls”
Theoretical model based on arbitrary shaped amplitude and phase profiles which vary with the illuminated area of back-scattering “walls”
Coupling between modes accounting for “non-resonant” spectral signature
Good qualitative agreement between experiments and simulations
More details in A. Consoli and C. López “Emission regimes of random lasers with spatially localized feedback” Opt. Express, to be published (Abril 2016)