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1 Supplementary Information Speckle-free laser imaging using random laser illumination Brandon Redding 1*, Michael A. Choma 2,3*, Hui Cao 1,4* 1 Department of Applied Physics, Yale University, New Haven, CT 06520, USA 2 Departments of Diagnostic Radiology and of Pediatrics, Yale School of Medicine, New Haven, CT 06520, USA 3 Department of Biomedical Engineering, Yale University, New Haven, CT 06520, USA 4 Department of Physics, Yale University, New Haven, CT 06520, USA * brandon.redding@yale.edu; michael.choma@yale.edu; hui.cao@yale.edu These authors contributed equally to the work. 1. Light source characterization In this work, we compared the imaging performance of five illumination sources: a narrow band laser, a broadband laser, a light emitting diode (LED), a dye-based random laser and a dye-based amplified spontaneous emission (ASE) source. Kӧhler illumination was used in all cases. We collected images of the different sources on the object plane in the absence of an imaging object (Fig. S1a). In Fig. S1b-f, interference fringes are visible in the images of the narrowband laser and broadband laser, but the other source produced relatively uniform illumination. We also collected the emission spectra of the five sources using a fiber bundle and a spectrometer, shown in Fig. S1g. The spatial coherence of the sources was measured by placing a double slit of width 150 μm and center-to-center spacing 500 μm on the object plane and measuring the interference pattern in the far-field 3. We found that the narrowband laser and broadband laser produced interference fringes with visibilities higher than 0.8, while the ASE source produced fringes with a visibility of The random laser and LED did not produce interference fringes, confirming that they are effectively spatially incoherent at a distance on the object plane of 500 μm. NATURE PHOTONICS 1

2 Figure S1 Light source characterization. a, Schematic of the experimental setup. To characterize the uniformity of illumination on the object, we positioned a CCD camera directly on the object plane to take images. Obj: microscope objective, OP: object plane. b-f, Images taken with the five sources used in this work: a light emitting diode (LED), a random laser (RL), an amplified spontaneous emission (ASE) source, a broadband laser (BBL), and a narrowband laser (NBL). The scale bar is 500 μm. g, Emission spectra of the five sources. 2. Effect of numerical aperture on speckle contrast We investigated the effect of the numerical aperture (NA) of our imaging system on the speckle contrast. We repeated the study presented in Fig. 2 in which we illuminated a scattering medium and imaged the transmitted light to the charge coupled device (CCD) camera. In this case, we varied the NA by closing an iris positioned near the back focal plane of the imaging objective, as shown in Fig. S2a. The imaging objective used in this experiment was a Newport M-Series 40 objective with NA=0.65. This allowed us to vary the NA over a wider range than would have been possible using the 10 objective (NA=0.25) used in Fig. 2. The speckle contrast was extracted from images collected with each source at three values of NA, as shown in Fig. S2. For the narrowband and broadband lasers as well as the ASE source, the speckle contrast increased at 2 NATURE PHOTONICS

3 smaller values of NA, as expected 21,22. However, even at the relatively high NA of 0.65, the speckle contrast remained above 0.8 for the narrowband laser and above 0.4 for the broadband laser. The images taken with the random laser and the LED exhibited very low contrast for all values of NA studied. Figure S2 Effect of numerical aperture on speckle contrast. a, Schematic of the experimental setup. S: scattering medium, O1: collimating microscope objective, O2: imaging microscope objective, OP: object plane, IP: image plane. The NA of the imaging objective (O2) was varied by closing the iris at its back focal plane. The speckle contrast was recorded at three values of NA for five sources described in Fig. S1. b, Speckle contrast versus the NA of the imaging objective (O2). For the spatially coherent sources (NBL, BBL) and the partially coherent source (ASE), the speckle contrast increased with decreasing NA. For the sources with low spatial coherence (RL, LED), the contrast remains very low for all values of NAs studied. 3. Random laser pumped by closely spaced pulses As discussed in the main text, the average power produced by the random laser solution is primarily limited by the low repetition rate of our Nd:YAG pump laser (10 Hz). Due to the fast (~ns) radiative decay lifetime of the Rhodamine 640 dye, we expect that repetition rates of ~MHz are possible, allowing the random laser to produce high enough average power so that the degeneracy parameters become comparable to the existing broadband spatially coherent sources such as SLDs. To support our expectation that the random laser can operate at ~MHz, we split a single Nd:YAG laser pulse into two pulses of equal energy and delayed one of them by 5 ns (corresponding to the pulse spacing at a repetition rate of 200 MHz). This was accomplished using a beamsplitter and two mirrors, as shown schematically in Fig. S3a. The beamsplitter divided the pump beam into two arms, one of which was ~150 cm longer than the other. When the beams recombined, the pulse from the longer arm was delayed by ~5 ns relative to that from the shorter arm. We then used these pulses to excite random lasing in the dye solution. We collected the time-integrated emission spectrum excited by pulses from the two arms separately (by blocking the beam in one of the arms) and by the combined two pulses. We found similar random lasing emission from the two separate pulses and the integrated emission intensity doubled when both pulses were used to pump the random laser [Fig. S3b]. Furthermore, the normalized emission spectrum in all three cases exhibited the same shape [inset of Fig S3b]. NATURE PHOTONICS 3

4 These results indicated that the random laser behavior was not affected by a previous pulse separated by 5 ns. We therefore expect that pumping at a repetition rate of ~MHz (submicrosecond pulse spacing) would not affect the random laser performance and the average emission power would scale linearly with the pump rate. Figure S3 Random laser excitation with closely spaced pulses. a, Schematic of the experimental setup. The Nd:YAG laser pulses are split by a beamsplitter into two arms, one of which is 150 cm longer than the other. The recombined pulses are separated by 5 ns and used to pump the random laser. The random laser emission is subsequently measured by a spectrometer. b, Time-integrated random laser emission spectra when pumped by pulses from either of the two arms alone, and from both arms simultaneously. The emission intensity doubled when the random laser was pumped by pulses from both arms. The inset shows the normalized emission spectra in all three cases, indicating that the spectral shape is unaffected by a previous pulse separated by 5 ns. 4. Emission at high average pump power Increasing the repetition rate of the random laser excitation will dramatically increase the total average power delivered to the random laser sample. At the ~uj energy per pulse required to achieve lasing, a repetition rate of 1 MHz would require pumping the random laser with an average power of ~1 W. To confirm that pumping the random laser with this level of average power did not introduce heating or bleaching effects, we excited the dye solution with scattering particles using a 1 W CW laser (Coherent Verdi) at λ=532 nm. While the conventional dye lasers have routinely operated at ~100 MHz repetition rates with high average pump powers 16-19, these systems relied on a dye jet to circulate the solution to avoid heating and bleaching issues. In our experiment, we enclosed our dye solution in a cylindrical capsule and attached it to a spinning apparatus which rotated the solution at ~10 revolutions per second. While the dye solution was spinning, we excited it with the CW laser and measured the emission spectrum with a spectrometer. Since the pump intensity was much lower than the peak intensity of the 30ps Nd:YAG pump pulses used to excite the random laser, the lasing threshold could not be reached, and we instead measured the spontaneous emission intensity as a function of pump power. We found that the spontaneous emission intensity increased linearly with the pump power across a range of pump powers from 20 mw to 1 W. When the pump power was doubled, for instance from 500 mw to 1 W, the integrated emission intensity was also doubled (Fig. S4b). The normalized emission spectrum, shown in the inset of Fig. S4b, was unchanged over this wide range of pump powers. These results confirmed that sample heating or dye bleaching would not be an issue when ~1W of average pump power is delivered to the random laser sample. 4 NATURE PHOTONICS

5 Figure S4 Exciting the random laser sample at high average power. a, Schematic of the experimental setup. To confirm that the random laser performance was not affected by dye bleaching or sample heating under an average pump power of ~1W, we collected emission from the dye solution sealed in a spinning capsule and pumped by a high power CW laser (λ=532 nm). b, Measured emission spectra at the pump powers of 0.5 W and 1 W. When the pump power was doubled, the emission intensity was also doubled, thus the emission intensity scaled linearly with the pump power. Inset: normalized emission spectra at the pump powers of 20 mw, 500 mw and 1 W. The spectral shape remained unchanged at a range of pump powers from 20 mw to 1 W. NATURE PHOTONICS 5