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1 Lasing and anti-lasing in a single cavity Zi Jing Wong, Ye-Long Xu, Jeongmin Kim, Kevin O Brien, Yuan Wang, Liang Feng, Xiang Zhang s: xiang@berkeley.edu; fengl@buffalo.edu I. Derivation of the lasing and anti-lasing condition II. Sample fabrication III. Measurement setup IV. Theoretical estimation of coherent amplification and absorption A. Ideal theoretical plot B. Operation away from CPA-laser point C. Realistic theoretical plot D. Operation above lasing threshold V. The role of PT symmetry VI. Reliability of the measurement VII. Power scaling of the measured signals VIII. Output phase difference versus wavelength NATURE PHOTONICS 1

2 I. Derivation of the lasing and anti-lasing condition For a waveguide system with balanced PT gain/loss modulation along the propagation direction of z, the coupled mode equations can be written as da( z) = iκ Bz ( ) dz db( z) = iκ Az ( ) dz where the coupling coefficient between the forward amplitude Az ( ) and backward amplitude 2n Bz ( ) is κ = k 0. The amplitudes of the forward and backward propagating waves at both ends π of the optical system ( z = 0 and z = L) are related through the 2 2 transfer matrix M as follows, AL ( ) M11 M12 A(0) = BL ( ) M21 M. 22 B(0) Solving the coupled mode equations will lead to M11 = M22 = cos( κ L), and M12 = M21 = isin( κ L). Therefore, in this unique PT-symmetric system, both the lasing ( M 22 = 0 ) and anti-lasing ( M 11 = 0 ) conditions can be satisfied by equating cos( κ L) = 0. This is in stark contrast with conventional non-pt optical systems where M 11 and M 22 cannot both become 0 at the same frequency. For the design in this experiment, we use the device length of π L =. 2κ II. Sample fabrication A 500-nm-thick InGaAsP multiple-quantum-well (MQW) is first grown on an InP substrate by metal organic chemical vapor deposition (MOCVD). The CPA-laser pattern and the alignment marks are then defined in a PMMA A2 resist by electron beam lithography (EBL), followed by electron beam evaporation of Chromium (Cr) and Germanium (Ge), 8.5 nm and 8.6 nm respectively, to form the PT symmetric periodic structures. We then use a shadow mask to block the structures area such that only the alignment mark regions are exposed where a 2 nm of 2 NATURE PHOTONICS

3 Chromium (as adhesion layer) and a 35 nm of gold (Au) are deposited. Gold is used to make the alignment marks for its better image contrast under the scanning electron microscope (SEM) during the subsequent EBL alignment steps. Upon the lift-off process, the grating coupler patterns are defined in a PMMA C4 resist by a second EBL exposure. Electron beam evaporation of 200-nm-thick Germanium is then carried out followed by another lift-off process. To define the multimode interference (MMI) coupler and the waveguide patterns, we use a thick HSQ (FOX-15) as the negative resist for the third EBL exposure. Upon development, the HSQ structures serve as the etch mask for the 1.5-µm-deep inductively coupled plasma (ICP) etching using Cl 2 /CH 4 /H 2 gases. Finally, the mask layer is removed by soaking the sample in hydrofluoric (HF) acid solution for 30 seconds. The key steps of the fabrication process are illustrated in Fig. S1. Figure S1 Schematic of the fabrication process. a, EBL patterning of the PT nanostructures and the alignment marks with a PMMA resist on a InGaAsP MQW grown on an InP substrate. b, Electron beam evaporation of Cr/Ge layers to form the PT nanostructures. c, Selective electron beam evaporation of a thick Au layer at the alignment mark positions using a shadow mask. d, EBL patterning and lift-off process to form the thick Ge grating couplers. e, EBL patterning on a NATURE PHOTONICS 3

4 FOX-15 negative resist to define the waveguides and MMI couplers. f, Deep ICP etching followed by the removal of the masking layer. III. Measurement setup To demonstrate coherent optical amplification and absorption, we built a single-pump doubleprobe measurement setup with precise phase control at telecommunication wavelengths. We utilized pulsed laser beams to perform single-shot broad spectrum measurement, and more importantly to minimize the heat generation, which can potentially reduce the gain and perturb the PT symmetry condition. As our probe beam is set at around 1,556 nm wavelength, with an estimated transform-limited pulse width on the order of ~10 ps, it can be treated as quasi continuous-wave (CW) due to the many (~2000) optical cycles contained within the slowlyvarying pulse envelope. The detailed layout of the setup is shown in Fig. S2. Figure S2 Schematic of the measurement setup. OPO: optical parametric oscillator; ND: variable neutral density filter; GTH: Gaussian-to-Top-Hat beam shaping lens; CL: cylindrical lens; VS: variable slit; DM: dichroic mirror; FM: flipping mirror; BPF: band pass filter; BS: beam splitter; HWP: half-wave plate; PZT: piezoelectric actuator; OBJ: objective lens; LPF: long pass filter; SF: spatial filter. 4 NATURE PHOTONICS

5 To attain uniform pumping over the entire length of the PT structures, the pump beam from a mode-locked Ti:Sapphire laser (Chameleon Ultra II, Coherent) at 840 nm is carefully shaped into a slit beam as follows. We employ a Gaussian-to-Top-Hat beam shaping lens (GTH) which converts a Gaussian intensity profile into a square intensity profile. The Ti:Sapphire output is 2.2X expanded to make a Gaussian beam diameter (1/e 2 ) of 5 mm as an input requirement of GTH (GTH IR, Eksma Optics). The GTH forms a square intensity distribution (4 mm x 4 mm) at 250 mm distance away. By using a cylindrical lens (f = 100 mm), the square beam at the GTH focus is reduced to a slit beam, of which length is fine-tuned by a variable slit. The tailored slit beam is 15x demagnified by the tube lens (f = 150 mm) and the objective lens (f = 10 mm, M Plan Apo NIR 20X, 0.40 NA, Mitutoyo) to uniformly pump only the CPA-laser region. To demonstrate the coherent amplification and absorption effects, two probe beams with precise phase control are required. The probe beams in our experiment are supplied from an OPO signal tuned to the desired wavelength. The beam is collimated by 1.2X expansion optics and is passed through a band-pass filter to confine its spectral width to the range of interest. Then the light is split into two, forming the two probe beams which couple to the CPA-laser via input grating couplers at a designed angle of incidence (AOI) of 7. The positions of the two mirrors sitting on one-dimensional (1D) stages (i.e. the AOI adjusters) are tuned to laterally shift the probe beams from the optical axis, thereby adjusting the AOIs of the probe beams onto the grating couplers as desired. Also, the tip/tilt of two mirrors (i.e. the Field angle adjusters), of which positions are conjugate to the back focal plane (BFP) of the objective lens through 3:1 reduced relay optics, is adjusted to induce field angles of the probe beams at the BFP, so that each of the focused probe spots illuminates the correct location of the gratings while keeping their AOIs unchanged. The Delay 1, which consists of a retroreflector on a 1D motorized stage, is used to adjust the temporal overlap between the pump and probe pulses. The Delay 2, another retroreflector on a 1D motorized stage, is utilized to further tune the delay between probe 1 and probe 2, so that the two probes meet at the centre of the device. A PZT is incorporated along the path of probe 1 to fine control the relative phase between the two probes and allow for precise phase scanning during the measurement. The HWP and linear polarizer provide the right polarization direction for the grating couplers, while the LPF and analyzer selectively capture the output probe signals. NATURE PHOTONICS 5

6 An iris on a XZ motorized stage, as a spatial filter, is placed at the intermediate image plane of the sample for selective signal collection from each output gratings sequentially. The position and the diameter of the iris are visually adjusted from images by an IR camera placed at the conjugate image plane via 2f-2f optics. The spatially filtered probe signals are 30x demagnified and coupled to the core of a multimode fibre connected to a spectrometer (SP-2300i, Princeton Instruments). Note that the intensities of two probe beams shall be of tiny difference in theory due to the anti-symmetrically distributed gain and loss. However, such a subtle difference becomes negligible in experiment as we can dynamically fine-tune the intensities of two probe beams to reach the best performance when switching between the lasing and anti-lasing states. The off-axis illumination of a by-passed probe beam is intermittently used to find the device on the sample and to adjust the imaging focus of the device as seen by the IR camera. The mounted device is aligned to the pump beam and then the two probe beams are independently aligned to the corresponding input gratings. For higher stability in our interferometric measurements, we enclosed the two probe beam paths for minimal environmental perturbations such as air flows and temperature changes. The picture of the built setup (with the top cover of the optical enclosure removed) is shown in Fig. S3 below. Figure S3 Real measurement setup. A picture of the measurement setup built. 6 NATURE PHOTONICS

7 IV. Theoretical estimation of coherent amplification and absorption A. Ideal theoretical plot The amplification-absorption contrast depends on how close the introduced gain and loss approaches the CPA-laser point 9,16. Ideally when the CPA-laser point is reached, the contrast would to go to infinity. At the Bragg wavelength (without detuning), the singular CPA-laser point π πλ0 occurs when the condition L = = 2κ 8n is met precisely (where both M 11 and M 22 go to zero, as discussed in Section I of the Supplementary Information). Therefore, for our target device length L of about 200 µm, the ideal imaginary index modulation (i.e. the introduced gain and loss) that corresponds to the CPA-laser point is approximately n = Fig. S4 shows the ideal theoretical plot of the output coefficient Θ for such a condition, where the magnitude of max(θ) amplification peak and min(θ) absorption dip both reach more than 100 db (they are in fact approaching towards infinity and the values in the plot are limited only by the number of digits used after the decimal point of n ). NATURE PHOTONICS 7

8 Figure S4 Ideal theoretical plot. The ideal theoretical estimation of the lasing and anti-lasing modes shows coherent amplification and absorption both approaching positive and negative infinity ( ). No waveguide loss and dispersion are considered here. B. Operation away from CPA-laser point In experiment, the ideal infinite amplification-absorption contrast is hard to attain. The biggest factor limiting the contrast is the deviation of the introduced gain and loss from the ideal n = ± required to hit the singular CPA-laser point for maximum contrast. This is mostly due to fabrication imperfections and the slight discrepancy between the actual material parameters and those used in our design. Figs. S5a and S5b below show respectively the colour map of max(θ) (amplification) and min(θ) (absorption) for different gain-loss values ( n ) at a fixed device length of 200 µm within the wavelength range of interest. Here we only plot up to a maximum of ±40 db to better observe the magnitude change of the amplification and absorption modes. As n approaches the CPA-laser point, min(θ) will decrease rapidly for the anti-lasing mode, while max(θ) will increase sharply for the lasing mode, and together they give rise to an extremely large modulation contrast. For comparison, when the device is operated well below the CPA-laser point, say n = 0.001, the magnitude of max(θ) and min(θ) will drop significantly to about 5 db each, as shown in Fig. S5c. Similarly, when the system is working well above the CPA-laser point ( n = 0.005, Fig. S5d), the modulation depth will reduce substantially, accompanied by the shrinking of the wavelength separation between the central out-of-phase points. The measured contrast of 30 db in our experiment therefore indicates that the device is operating close to the CPA-laser point already. 8 NATURE PHOTONICS

9 Figure S5 Operation away from the CPA-laser point. a, Max(Θ) amplification and b, Min(Θ) absorption as a function of wavelength and imaginary part of index ( n ). The CPA-laser point is marked with a star, corresponding to n = c, When the operation is well below the CPA-laser point ( n = 0.001), the magnitude of coherent amplification and absorption will be reduced substantially as compared to those operating near the CPA-laser point. d, Similarly, when the design is well above the CPA-laser point ( n = ), the contrast diminishes significantly. C. Realistic theoretical plot Fig. S6 shows the theoretical amplification and absorption plots best fitted with our experiment results (Fig. 3c), taking into account the realistic deviation from the singular CPA-laser point. In addition, waveguide loss and the associated frequency dispersion will cause slight background attenuation to the signals. This mainly occurs when the signals propagate through the NATURE PHOTONICS 9

10 waveguides connecting the CPA-laser device and the output grating couplers. The dotted lines in Fig. S6 show the theoretical amplification and absorption plots when there is no waveguide loss, yielding zero background attenuation. Solid lines in Fig. S6 show the same plot except the waveguide loss dispersion (measured separately with a control sample) is now incorporated, and thus an average background attenuation of less than 2 db is observed. Larger waveguide absorption typically occurs at lower wavelength range, which explains why our overall measured result is a little tilted, as shown experimentally in Fig. 3c, and theoretically in Fig. S6. However, since the CPA and lasing operate at a particular frequency with narrow linewidths, the effect of waveguide loss and dispersion on the amplification-absorption contrast is small. Figure S6 Realistic theoretical plot. Theoretical estimation of the lasing and anti-lasing modes shows coherent amplification and absorption behaviour similar to those obtained in experiment (Fig. 3c). The dotted lines represent the ideal lossless waveguide (WG) case, while the solid lines include the effect of waveguide loss and dispersion. 10 NATURE PHOTONICS

11 Other imperfections like amplified spontaneous emission (ASE) and optical nonlinearity have negligible effects on the measured contrast between the lasing and anti-lasing modes: 1. ASE is mainly acting as a constant background noise in the measurement. In our linear system, the coherent probe beams and the interferometric phase tuning are insensitive to the ASE noise (see Section VI of the Supplementary Information for more detailed discussion). Therefore ASE will not limit the maximum contrast attainable, as far as the probe beam is concerned. 2. Optical nonlinearity can cause a mismatch in either the real or imaginary part of the index and perturb the PT symmetry condition. As shown in Section V of the Supplementary Information, this can potentially result in wavelength offset and contrast reduction between the lasing and anti-lasing modes. However, in our experiment, a linear response of the signals is measured (Fig. S11), thereby ruling out any nonlinearity contribution. In summary, the biggest factor limiting the amplification-absorption contrast in the present experiment is the deviation of the imaginary part of index from the singularity CPA-laser point due to fabrication imperfections. In comparison, other factors like waveguide dispersion, ASE and nonlinearity play a much smaller role in limiting our device performance. D. Operation above lasing threshold While the measurement of the lasing and anti-lasing modes is carried out at the lasing threshold, it is interesting to discuss what might happen to the amplification and absorption spectrum when the pump is increased beyond the lasing threshold. The measured light-light curve (Fig. 3b) and the extracted spontaneous emission coupling factor (β) of 0.01 indicate that beyond the laser threshold the gain is well-clamped, albeit not a perfect clamping. In other words, when the device is brought deeper into the lasing regime, the gain can increase marginally. Similarly, in the loss regions (with the lossy Cr/Ge structures on top of the InGaAsP gain medium), there will be a small increase of gain due to carrier diffusion, and thus the effective loss can be reduced slightly. As an example, in Fig. S7 (below), we plot the amplification and absorption spectrum when there is a mismatch in the imaginary part of the index of n = and n = , respectively. In both cases, the gain is assumed to increase and the loss is assumed to decrease by the same amount. While the system still preserves the amplification and absorption resonances, NATURE PHOTONICS 11

12 the entire spectrum is shifted upwards, and their magnitudes are no longer balanced, with the lasing mode more dominant than the anti-lasing mode. Figure S7 Operation above lasing threshold. The dotted lines show the balanced PT symmetry case best fitted to our measurement result, while the dash lines and solid lines contain mismatch in the imaginary part of the index of n = and n = , respectively. In both cases, the gain is assumed to increase while the loss is assumed to decrease by the same amount. Such a deviation can potentially occur when the pump exceeds the lasing threshold, which leads to asymmetric lineshape and much stronger amplification than absorption. The effect of waveguide loss and dispersion is already included in the plot. On the other hand, when the pump is too strong, the nonlinear Kerr effect can also occur to alter the real part of the refractive index and thus cause a wavelength shift to the measured amplification and absorption spectrum. In brief, when operating beyond the laser threshold, nonlinear effects can in principle kick in to change both the real and imaginary part of the index, 12 NATURE PHOTONICS

13 which then perturbs the exact PT symmetry condition and distorts the lasing and anti-lasing features measured at the lasing threshold. V. The role of PT symmetry In principle, if one is to confine light either in gain or loss regions within a single device for lasing or anti-lasing [coherent perfect absorption (CPA)], respectively, no PT symmetry is needed. However, to achieve CPA-lasing, i.e. lasing and anti-lasing occurring at the same frequency with symmetric responses, PT symmetry must be satisfied, as proven in the theoretical papers 9,16. Consider the optical transfer matrix of a two-port system as used in our experiment, where lasing and anti-lasing are associated with M 22 = 0 and M 11 = 0, respectively. In general, M 11 and M 22 do not concurrently reach zero at the same frequency. For a PT symmetric system, however, a stringent requirement 9 M * * ( ω) = M ( ω ), which leads to M22 ( ω) M11 ( ω ) * 1 * frequency 0 is that =. Assuming lasing occurs at a particular ω such that M ( ω ) =, the above condition indicates that ( ) [ ; ] M = M M M M M ω = must be valid as well, meaning CPA must coexist with lasing at the same frequency within the same device. To elucidate this point, we plot in Fig. S8a the max(θ) (amplification) and min(θ) (absorption) curves for two different cases: the perfectly balanced case ( n = 0 ) and the slightly unbalanced case assuming there is a mismatch in the real part of refractive index ( n = ). It is clear that the lasing and anti-lasing will no longer occur at the same frequency (even with a small wavelength offset of about 1 nm) in the unbalanced case since the PT symmetry condition is not strictly satisfied. Similarly, the effect of imaginary part of the refractive index deviating from the PT symmetry requirement, e.g., n = 0.001, with loss larger than gain, is presented in Fig. S8b. The consequences are clear: 1. Both the amplification and absorption curves will be shifted downwards for all wavelengths due to the effectively larger background loss; 2. The amplification and absorption resonances become asymmetric and unbalanced in magnitude; 3. The amplification-absorption contrast will be significantly reduced. NATURE PHOTONICS 13

14 Figure S8 The role of PT symmetry. a, A real part index mismatch will result in wavelength offset between the lasing and anti-lasing modes. b, An imaginary part index mismatch will lead to asymmetric and unbalanced amplification and absorption magnitude with respect to the shifted background, and significantly reduced contrast. Above all, PT symmetry is the unique condition that guarantees lasing and anti-lasing modes to both occur at the same wavelength with balanced amplification and absorption magnitude and considerably large modulation contrast, all within a single device. VI. Reliability of the measurement To more precisely validate the measurement accuracy, we performed multiple measurements on the same sample to obtain the error bars rigorously, as shown in Fig. S9. The error bars are negligibly small for most of the data points, except when they are close to the CPA dip (around - 15 db). This is expected, for the output signals are now almost completely terminated, with signal counts approaching the noise level of our measurement system. Even at the extreme boundary of the error bars, a clear coherent absorption dip is still clearly visible, with wavelength matching the amplification peak, thereby proving the coexistence of both lasing and anti-lasing modes. 14 NATURE PHOTONICS

15 Figure S9 Repeated measurements. Experimental plot of the coherent amplification and absorption data together with the error bars (one standard deviation). Due to the high data density, we plot the error bars for every other data points for viewing clarity. As the pump light is constantly illuminating the CPA-laser device during the measurement, there is an associated background emission which contains the amplified spontaneous emission (ASE). This pump-induced background emission will always be there regardless of the probe beams and thus contribute noise to the measured signals. Fig. S10 shows the raw data for both the (a) amplification mode and the (b) absorption mode. With the pump on, the background emission noise is measured by blocking the probe beams, while the scattered noise is referring to the weak scattered stray lights whenever the probe beams are turned on. Since our device is operating in the linear regime (as proven in Fig. S11, and therefore eliminating any signal-ase coupling and other nonlinear effects like four-wave mixing etc.), and the fact that our coherent probe beams NATURE PHOTONICS 15

16 are insensitive to both the ASE and scattered noise, we can subtract these noise contributions to obtain our true signals with respect to the input probe beams. In other words, the output intensities O 1 and O 2 terms used in the output coefficient Θ already exclude the photon counts from the ASE. For practical applications, this ASE noise can be eliminated by using a narrow bandpass filter, a four-level gain media or a lock-in detection scheme, where the probe beam is modulated at a different frequency. Figure S10 Raw data for both the (a) amplification (b) absorption modes. The final signal is obtained upon subtracting the background emission noise and scattered noise coming from the stray lights. VII. Power scaling of the measured signals High-intensity probe beams can lead to nonlinear frequency mixing and undesired saturation effects. To prove that the measured sharp amplification and absorption peaks are not caused by nonlinear interactions, we investigated the power scaling of the collected signals. The average probe power was tuned from 10 mw to 45 mw by the variable neutral density (ND) filter wheel located between the band pass filter (BPF) and the half-wave plate (HWP) (see Fig. S2), while the Output 1 signal was measured at the coherent amplification resonance wavelength (1,555.8 nm). It is apparent from Fig. S11 that the signals scale linearly with the input probe power. Since we performed the amplification and absorption measurements at 30 mw probe power, this confirmed that our CPA-laser operated in the linear scattering regime and thus excluded any 16 NATURE PHOTONICS

17 contribution from nonlinear effects. In fact, no nonlinearity is observed within the maximum probe beam power available in our optical setup. Figure S11 Absence of nonlinearity. Linear scaling of output signals to the input probe beam power. The Output 1 signal intensity at the lasing/amplification mode was found to linearly scale with the averaged input probe power. VIII. Output phase difference versus wavelength To understand the phase relationship between the two outgoing waves, we plot in Fig. S12 the measured output phase difference ( ϕout = ϕout,1 ϕ ) as a function of wavelength. When out,2 the two outgoing waves are at off-resonance wavelengths such as 1,554.2 nm, they are completely out-of-phase. However, the output phase difference gradually diminishes as it approaches the coherent amplification and absorption resonance wavelengths of 1,555.8 nm. This closely in-phase behaviour is to be expected due to the constructive interference in the gain/loss regions, which leads to concurrent build-up/termination of the outgoing waves at both ports of the CPA-laser. This further confirms the same phase dependence of the coexisting lasing and anti-lasing modes in the CPA-laser. NATURE PHOTONICS 17

18 Figure S12 Measured output phase difference versus wavelength. The relative phase difference between the two outgoing waves gradually diminishes as the wavelength approaches the point of lasing and anti-lasing modes at 1,555.8 nm. 18 NATURE PHOTONICS