Transcending the gain bandwidth limitation in semiconductors for full-colour-tunable lasers

Yi Jiang Hong Kong Baptist University Qi Wei University of Macau https://orcid.org/0000-0002-5322-3692 King Fai Li Hong Kong Baptist University Mingke Jin Southern University of Science and Technology Hoi Lam Tam Hong Kong Baptist University Guixin Li Southern University of Science and Technology https://orcid.org/0000-0001-9689-8705 Guichuan Xing University of Macau Kok Wai Cheah (  kwcheah@hkbu.edu.hk ) Hong Kong Baptist University https://orcid.org/0000-0002-5226-2040


Introduction
Semiconductor laser opens the gate to laser miniaturization, and yields more compact and higher integrated optoelectronic devices. It enables the maturation of a wide range of new technologies, such as, optical fiber communications, image scanning, compact disc players, barcode scanners, laser printers, and compact LIDAR systems, with the development of gain materials, optics, and electronics [1][2][3][4] . Tunable lasing wavelength region, arising from specific application requirements, is a key parameter of semiconductor laser. However, the fundamental gain bandwidth of a single semiconductor itself limits the range of discrete lasing wavelengths that a semiconductor can produce.
Although engineered bandgaps have been demonstrated in traditional Ⅱ-Ⅳ and Ⅲ-Ⅴ inorganic semiconductor alloys [5][6][7] , and inorganic and hybrid perovskite alloys [8][9][10] , the inevitable lattice mismatch issue, sophisticated fabrication technology, and imprecise composition control severely restrict the range of achievable bandgaps from the semiconductor alloys 11 . In fact, semiconductors with wide tunable gain bandwidth would make revolutionary advances in optoelectronics.
Unlike inorganic semiconductors and perovskites, organic semiconductors have the abundant energy levels and thus can form multiple radiative channels arising from electronic-vibrational coupling [12][13][14][15] . This enables them theoretically ideal materials with wide gain bandwidth for continuously tunable laser application. With quasi-four level laser system for population inversion, the amplification generally occurs in the emission region with high Franck-Condon activity. In most cases, the gain bandwidth of organic gain medium is from 0-1 vibronic transition 16-19 , corresponding to an optimum and stable quasi-four level laser system. The distinct gain bandwidth has enabled lasing in a relatively wide range of discrete wavelengths but has not led to continuous tuning in the entire emission spectrum [20][21][22] . A novel approach that utilize the abundant energy levels of organic semiconductors to overcome the gain bandwidth limitation is an attractive alternative, especially 4 considering its enormous potential in integrating into optoelectronic circuits 23,24 .
Here, we present a new strategy to tune the effective gain region across the emission spectrum by constructing Förster resonance energy transfer (FRET)-assisted guest-host gain system. FRET mechanism describes the energy from the host compound by light absorption, initially in its electronic excited state, could be resonantly and non-radiatively transferred to the guest compound. Taking the advantages of efficient excitation, suppressed concentration quenching, and reduced self-absorption, ultralow amplified spontaneous emission (ASE)/lasing thresholds have been demonstrated in guesthost gain systems with efficient and completed energy transfer [25][26][27][28][29] . Here we show the feasibility of continuously tunable light amplification across the optical range from polymeric guest-host gain systems. The key to successfully tune the gain bandwidth across the optical range is manipulating the energy transfer efficiency. Different host/guest ratio produces a shift in the energy transfer preference of the blended compound, and therefore the energy transfer efficiency would change with respect to the blending ratio. These changes create different meta-stable energy environments for light amplification and thus novel effective gain regions, leading to the wavelength tunability in light amplification. We assume that the individual host or guest compound holds a typical quasi-four level laser system with optical gain region at its 0-1 vibronic transition. With FRET taking place in the process, at least five different energy environments for light amplification can be created with possible stimulated emission channels in both guest and host (Fig. 1a). Combining with distributed feedback (DFB) resonating modulation, the full-colour range of continuously tunable lasing is achievable in these guest-host blends.
There is a good overlap between PFO (or BEHP-PPV) emission spectrum and BEHP-PPV (or MEH-PPV) absorption spectrum, indicating efficient energy transfer between PFO and BEHP-PPV, and between BEHP-PPV and MEH-PPV. Two blend systems, PFO:BEHP-PPV and BEHP-PPV:MEH-PPV, were investigated as guest-host gain systems.  6). This is accompanied by nonlinear increase in emission intensity with well-defined thresholds of 48.4 and 40.1 μJ/cm 2 for the green and yellow ASE features, respectively (Fig. 2c). Similar dualwavelengths ASE phenomenon with gain bandwidths in both yellow and red is observed by adjusting the host/guest ratio to 98:2 ( Fig. 2c and Supplementary Fig. 7). These tunable gain bandwidths originate from the competing stimulated emission at several vibronic transition channels in both guest and host, which is created from the variation of energy environments for light amplification. By tuning the blending ratio, the single-wavelength amplification in yellow or red region is also observed   Table 3). BEHP-PPV:MEH-PPV blend system is used as the main example for further discussion on energy transfer process and stimulated emission cross-section simulations.  19). The corresponding PIA bands are assigned to weakly coupled polaron-pair charge states of host, similar to other polymers 36-38 , with the dominated wavelength region in 650-750 nm. The PIA signals in these blended samples are formed rapidly (<200 fs) before decaying with average time constants of ~1 ns (Fig. 3e, Supplementary Fig. 20 and Table 5). As a result of the increased MEH-PPV stimulated emission from FRET competing with host PIA, the isosbestic points at 1 ps delay are redshifted from 615 nm to 670 nm with increasing dopant concentrations to 10% in BEHP-PPV:MEH-PPV blend system (Fig. 3d) pumped under an excitation density of 38.2 μJ/cm 2 (with yellow ASE output; Supplementary Fig. 21), the promptly formed PB signals at sky-blue and green regions with rise time of 0.70 ps and 0.85 ps exhibit excited-state decay that is kinetically correlated with the formation of PB signal at yellow region (Fig. 3f). Complementary kinetics under a higher excitation density (56.0 μJ/cm 2 ) with dualwavelengths ASE in green and yellow regions present shorter rise time and similar lag in the formation of PB signals between host regions (sky-blue and green) and yellow region (Fig. 3g). The  Table 6). These experiments illustrate that yellow ASE readily proceeds from guest 0-0 radiative channel, exhibiting behavior characteristics of guest in guest-host gain system. Note that the short laser pulse width (100 fs), which is even shorter than FRET time, is    representing the typical green, green and yellow (dual-wavelengths), yellow, yellow and red (dualwavelengths), and red ASE under nanosecond pulse excitation, respectively (Fig. 2a). The change of energy environments for light amplification, i.e., the change of contribution ratios of effective stimulated emission cross-sections at different radiative channels, could be clearly observed in these blended samples. It is easy to decide that the contributions for effective stimulated emission crosssections at yellow and red regions are dominated by guest 0-0 and 0-1 radiative channels. As an example, with MEH-PPV concentration at 0.8%, the contribution ratio from guest 0-0 vibronic band is 0.381, which is 6-fold higher than that from host 0-2 vibronic band. When MEH-PPV concentration is up to 2%, the contributions from host radiative channels at yellow and red regions are almost negligible. These results reveal that the construction of guest-host gain system is an effective strategy to achieve the tunable light amplification, beyond the limits of the fundamental gain bandwidths of guest and host themselves.

Full-colour range tuning lasing
Distributed feedback (DFB) lasers were then conducted and fabricated by spin-coating PFO:BEHP-PPV or BEHP-PPV:MEH-PPV blends on top of patterned silica gratings, to further demonstrate the wide range of continuously tunable lasing from our guest-host gain systems. The grating periods of 270 nm, 300 nm, 340 nm, 370 nm and 410 nm are selected for blue, sky-blue, green, yellow, and red DFB lasing outputs, respectively. Thus three second-order DFB gratings (Grating-1/2/3) and four mixed second-order DFB gratings (Grating-4/5/6/7) were prepared by electron beam lithography (Supplementary Section 6, Figs. 28-35). The latter are designed for one or more wavelength lasing.
The details of DFB grating fabrication and the selection of gain media are presented in Supplementary Section 6. The summary of grating parameters and gain media are also listed in Table 1. Under optical excitation, continuously tunable lasing, that span the full visible region of the electromagnetic spectrum (from 450 nm to 619 nm), are achieved (Fig. 5a). Fig. 5b shows the derived chromaticity for these lasing spectra on a CIE colour diagram. The full-colour range tuning organic lasing cover 78% of CIE colour gamut, which is 120% more perceptible colours specified by CIE LAB colour space (standard Red Green Blue, sRGB) 40 .
The lasing wavelength range could be further extended. For example, for RGB lasers, the lasing wavelengths are 450 nm, 523 nm, and 619 nm (Fig. 5a), with the corresponding lasing thresholds of 5.7 nJ/pulse, 5.1 nJ/pulse, 32.2 nJ/pulse (Fig. 5c) nm, 500-541 nm, and 600-644 nm (Fig. 5d). The extended trajectory of tunable lasing colours in the CIE coordinate diagram through the variation of polymer film thicknesses shows that the colours cover approximately 170% more perceptible colours than sRGB (94% of CIE colour gamut; Supplementary Fig. 36). Although further studies will be needed to further fine characterize these blend systems and optimize feedback resonators, this is to the best of our knowledge the widest tunable semiconductor laser system from three materials. Overall, these data demonstrate that our concept and realization of guest-host gain systems with wide tuning of gain bandwidth yield unprecedented wavelength tunability in semiconductor lasers.

Conclusion
In conclusion, we have presented a fundamental strategy to design organic semiconductor materials with wide tuning of gain bandwidth. The strategy, which involves the construction of FRET-assisted guest-host gain systems, provides convenient access to full-colour-tunable semiconductor lasers. The key to our achieved results lies in the manipulation of energy transfer efficiency that changes the energy environments for light amplification, which is elucidated by our experimental and theoretical investigations. These results will accelerate the development of next generation semiconductor materials with wide tuning of gain bandwidth that may revolutionize the fields of full-colour displays, multi-colour security tag/sensing, visible colour communications, and solid-state lighting, taking advantage of the flexibility and processability of organic electronics.

Data availability
The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. TA experiments. The broadband femtosecond TA spectra of the blended films were taken by using 25 the Ultrafast System HELIOS TA spectrometer. The laser source for TA experiments was the same source in TRPL measurements. The broadband probe pulses (420-800 nm) were generated by focusing a small portion (around 10 mJ) of the fundamental 800 nm laser pulses into a 2 mm sapphire plate. The 400 nm pump pulses were obtained through doubling the fundamental 800 nm pulses with a BBO crystal. We fitted the TA kinetics according to a multi-exponential decay function,

Methods
where t is the probe time delay, Hi (t) = [1+erf(-t/r-r/2τi)] (erf: error function) is the rising function, r (~ 0.1 ps) is the Gaussian laser pulse width, Ai is the amplitude or pre-exponential function, and τi is the decay time.
Simulations. The stimulated emission cross-section (σem(λ)) is deduced from the Einstein A and B coefficients. It can be determined as 41 , where Ef(λ) is the PL quantum distribution (at different emission where σabs is absorption cross-section of the ground-state species, σS-S is absorption cross-section of the singlet-singlet excited-state species, σcharge is charge absorption cross-section, and σT-T is triplet-26 triplet excited-state absorption cross-section. Due to the negligible overlap between host PIA and effective gain regions from TA measurements, σS-S, σcharge and σT-T at each selected emission wavelength are almost zero in BEHP-PPV:MEH-PPV blend system. The calculations of σabs are using the method reported by W. Holzer, et al. 43 The results of σem, eff (λ) are shown in Supplementary Fig.   26. As a result, the contribution ratios of σem, eff (λ) at different colours, i.e., sky-blue, green, yellow, and red, from possible radiative channels in both guest and host are shown in Supplementary Fig. 27. pulse energy on the sample was adjusted by the continuously variable neutral density filter into the beam path, which was detected by Power meter PM100D (Thorlabs). The sample was normal to the incident pump laser beam. The transmitted pump laser was cut off by placing filter BG38 behind the sample. The laser spectra were collected by the fiber spectrometer (Ocean Optics USB4000-US-VIS).