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The unique structure of SLDs makes them ideal for many applications. For example, the high spatial coherence simplifies coupling the light into optical fibers in FOGs, which also benefits from the lower temporal coherence and short coherence length since it lowers the level of noise. In addition, SLDs can support higher modulation speeds as compared to LEDs due to the increased stimulated emission in the case of SLDs. This makes SLDs an excellent source of light to be used for communication as well as low-coherence applications (e.g., illumination). Furthermore, the narrower spectral width of visible-light SLDs can potentially be exploited to develop red-green-blue (RGB) projectors with a wider color gamut.

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where 2d is the round-trip distance difference for beams traveling from the sample and from the mirror. As can be seen from the expression, it introduces ambiguity in determining absolute distances since they are only contained in the cosine term, limiting the precision of the measurements given the multiple possible solutions.

All of these techniques lower the reflectivity in order to prevent longitudinal modes from forming in the device. Simply adding an anti-reflection (AR) coating is theoretically possible, but in practice, it is difficult to achieve the needed low reflectivity (in the order of 10−5)80. One or more of the above designs (shown in Fig. 4a) can be used to get the best performance from the SLD, which results in a beam having high spatial coherence due to the standing waves in the transverse plane within a ridge waveguide structure, but substantially low temporal coherence due to breaking the cavity in the direction of propagation. By allowing the photons to exit the active region after only a single pass (or two passes if one facet has high reflectivity), the phase information of these photons is lost, and any newly generated photon is spontaneously emitted with a random phase. In addition to implementing various feedback suppression strategies, SLDs with diverse active region structures are under active development. While two-dimensional quantum well (QW) structures dominated the research on SLDs before the 21st century, zero-dimensional QD and wire-like Q-dash SLD structures have witnessed investigation in the last twenty years, which broaden the width of spectra by taking advantage of the size fluctuations of the QDs and Q-dashes32,67,68,81,82. Particularly, GaAs based QD SLDs have gained great interest due to their superior application potential in on-chip light sources for silicon photonics83. Table 1 provides an overview of SLDs along with their wavelengths, materials, active region structures, AR designs, and spectral widths.

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a Integrated RGB SLD light source143. Reproduced with permission from Primerov, N. et al. Copyright 2019 SPIE Digital Library. b The reconstructed hologram from a laser diode (LD), an SLD and an LED, with their zoomed-in c speckle and d sharpness properties142. Reproduced with permission from Deng, Y. et al. Copyright 2017 Springer Nature.

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where \(\gamma (2d)\) is the complex degree of coherence of the light field which modulates the oscillating part of the interferometric signal. As illustrated in Fig. 8b, this envelope provides a clear and unambiguous determination of the absolute distance, effectively overcoming the limitations of coherent light sources. The position of the coherence signal peak immediately reveals the sample surface location, while the intensity of the signal depends on the reflectivity of the sample.

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As highlighted in this article, the increasing demand for compact and efficient devices providing partially coherent light has spurred the development of various low-coherence semiconductor light emitters. These devices, with their promising potential, are positioned to play crucial roles in emerging technologies such as VR/AR, Lidar, and quantum communication, shaping an intelligent and secure future. The demand for partially coherent light is expected to grow as conventional incoherent light sources become the bottleneck in many systems. For example, high-brightness and high-resolution displays needed for VR/AR headsets require a combination of high directionality of high optical power emission (high brightness) from a small size (high resolution). SLDs can be a potential solution for this challenge given their high spatial coherence (high directionality) and low temporal coherence (low speckle density). Moreover, the narrower spectral width of SLD light allows for a wider color gamut as compared to LEDs. However, the future implementation of SLDs in displays would require improvements in the efficiency of the three needed types of SLDs, red, green, and blue (especially green SLDs, given their low efficiency as a result of the high indium composition in the InGaN active region). Moreover, surface-emission SLDs are needed if they are to replace 2D LED arrays used in displays. This poses new challenges in developing novel types of visible-light semiconductor ASE sources that can meet these requirements.

To gain insight into the photon scattering process in RLs, several relevant length scales were introduced, including the scattering mean free path (MFP) ls (i.e., the average distance that the light travels between successive scattering occurrences), the transport MFP lt (i.e., the average distance that the light travels before the final scattering direction loses memory of the initial direction), and the gain length lg (i.e., the distance over which the intensity of light is amplified by a factor e). The scattering MFP and the transport MFP are determined by the following equations:

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a The temporal coherence of an incoherent light source, like LEDs, exhibits noise-like intensity due to multiple frequencies and the random phase noise. b Light sources with high temporal coherence, like single-mode DFB lasers, exhibit low phase noise and narrow spectrum. c Light sources with low temporal coherence, like SLDs, exhibit moderately wide spectra with lower phase noise than LEDs and a lower number of frequencies, m, than that of LEDs, n. Right: Spatial coherence demonstration in Young’s double-slit interference experiment. d A spatially incoherent source yields no intensity fringes on the screen. e A high-spatial-coherence light source generates intensity fringes with a high contrast. f In a low-coherence light source, the contrast of fringes is in between those two extreme cases.

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By having either low spatial coherence or low temporal coherence, or a combination of both, these light sources enable a wide range of applications. On one hand, low spatial coherence serves as an effective tool for artifact reduction, particularly in scenarios involving rough samples or multiple reflective surfaces. It improves the precision and reliability in measurements and imaging. On the other hand, low temporal coherence manifests as waves spanning a wide range of frequencies, with phase correlations extending over a short period of time, which makes them suitable for use in interferometric measuring tools while significantly improving the resolution.

Low-coherence light sources, e.g., SLDs, introduce unique advantages in the quest for random numbers. Compared to conventional lasers, SLDs exhibit broadband ASE noise which is important for RNG38,199,200,201,202. Additionally, this solid entropy source simplifies the system compared to other broadband sources, like chaotic signals from cascaded lasers or external feedbacks203,204,205,206. The distinctive low temporal coherence property of SLDs results in a broad optical spectrum. This rich spectrum can be sliced into multiple independent segments using optical filters, giving a chance to form parallel wavelength-division channels. Each of these channels can generate random numbers concurrently, drastically increasing the overall generation rate. The first demonstration of RNG using wavelength demultiplexing was performed in 201138, as shown in Fig. 10a, b, in which a pair of optical filters were used to get two nonoverlapping spectral slices from a single broadband optical signal. In this work, the original broadband optical noise was from the output of a fiber-coupled SLD, and a 20-Gb/s RNG rate was obtained by these two statistically independent channels, each having a 10-Gb/s RNG rate. It is worth noting that this entropy source does not need external feedback, in contrast to other broadband sources, which represents an important step toward a chip-based ultrafast parallel quantum random number generator. Furthermore, a real-time random number generator using a latch comparator was proposed with a data rate of 3 Gb/s, which involved exclusive or (XOR) operations from two spectrally sliced channels from a broadband SLD207. Recently, a higher data rate was achieved by 10 random bit stream channels using a commercial 100-GHz dense wavelength division multiplexing (DWDM) module [see Fig. 10c]199. In this work, the entropy source is also from the broadband ASE noise produced from an SLD into different wavelength parts, and each part is used for generating random bit streams separately. Ten independent sliced spectra having a narrow bandwidth of 0.3 nm were used for RNG. 25 Gb/s was obtained from these 10 channels with independent random binary bit streams with a speed of 2.5 Gb/s each. So far, such spectral-domain parallel random bit generation (RBG) has been demonstrated with no more than 10 channels due to the limitation of optical filters and the width of the useful bandwidth.

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RD Sigler · 1982 · 6 — A well-corrected telescope with a large spherical primary mirror can be realized by using three or four small, widely spaced, corrector lenses. An interesting ...

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Almost twenty years ago, Tattile began a successful collaboration with Fideltus, a company primarily focused on offering high-tech vehicle tracking and license plate recognition systems. Turkey recently started a major operation to better its roadway system,

More advanced designs that feature electrical controllability of the degree of coherence would also allow the development of multifunctional semiconductor light sources. These devices would find use in a wide range of applications in which switching between high and low coherence would be desired. For example, such devices can be used for speckle imaging in the high-coherence mode and for OCT in the low-coherence mode. Although such systems have been achieved with external optics, an integrated solution is of great interest given the faster response and compact design, which would make it more suitable in many applications.

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One way to achieve the above is to replace the conventional ordered laser cavities with chaotic cavities, in which the light experiences chaotic ray dynamics. Generally, cavities with asymmetric shapes can result in chaotic behavior90. In such cavities, there are no modes with exceptionally high Q factors (low lasing thresholds). Moreover, it was shown numerically using steady-state ab initio laser theory (SALT) that the chaotic cavity does indeed have a larger number of modes with similar thresholds as compared to conventional cavities even after taking mode competition into account34.

As a result, opticians commonly refer to lens width as the glasses 'Size'. With 49 mm sitting as an average lens width, frames in sizes 40mm to 48mm will look ...

a RF spectrum of the optical noise from the SLED and from the background noise with the SLED off. b Optical spectrum of the SLED with its two spectrally sliced channels measured with a resolution bandwidth of 0.1 nm38. Reproduced with permission from Li, X. et al. Copyright 2011 OPTICA. c Experimental setup of multi-channel QRNG scheme, which includes an SLED as the low-coherence light source, a dense wavelength division multiplexing (DWDM) module used to slice the spectrum; optical attenuators (ATTs) used to adjust the intensity; photodetectors (PDs) used to receive the signal; and 12-bit analog-to-digital converters (ADCs). d The broad-area violin-cavity designed to accommodate a large number of modes. e The lasing emission at one facet of the 600-μm-long cavity captured using a streak camera. f The correlation function of the measured lasing emission intensity exhibits spatial and temporal correlation widths of 1.5 μm and 2.8 ps, respectively242. Reproduced with permission from Kim, K. et al., 2021 IEEE Photonics Conference (IPC). Copyright © 2021, IEEE.

In the early 19th century, the initial indications of coherence within light waves emerged through Thomas Young’s groundbreaking double-slit experiment. This finding demonstrated that light waves could interfere constructively and destructively, implying an inherent degree of coherence in the beam profile. Over the subsequent 130 years, the pursuit of a more precise definition of optical field coherence gradually materialized. In 1938, Nobel laureate Frits Zernike made seminal contributions to the definition of coherence by proposing the use of interference fringes to characterize it, emphasizing the intrinsic link between the coherence of an optical field and the visibility of these fringes1. After over ten years, another luminary in optics, Emil Wolf, introduced the concept of the mutual coherence function and power spectral density function to quantitative assessment of the degree of correlation in both spatial and frequency domains2. Concurrently, advancements in the field of quantum optics also contributed to understanding the quantum coherence of light, unveiling its particle-like characteristics and correlations between photons3. This exploration laid the foundation for progress in quantum information and quantum computing. Furthermore, the enhanced comprehension of coherence based on these studies opened the door for its practical utilization in everyday life by enabling the control of the degree of coherence to fulfill specific application requirements.

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To increase the number of lasing modes from a semiconductor laser, two conditions must be satisfied. First, the threshold gain for these modes must be similar. Assuming uniform pumping, this entails that the different modes must experience similar losses inside the cavity. Therefore, the quality factors (Q factors) of the lasing modes, which are inversely proportional to the lasing threshold, should be similar. A high Q factor indicates a long photon lifetime (narrower spectral linewidth) and a small amount of loss experienced by the mode. The second condition for multimode lasing is limiting the mode competition. This is needed since the number of carriers in the active region is limited, and high mode competition causes the carriers to be depleted by the few modes that reach the threshold gain34,89.

Low-coherence light, characterized by its moderate temporal and/or spatial correlations, presents a potent tool in various applications. The research on low-coherence light sources attracted significant attention from the 1970s. At this initial stage of investigation, low-coherence light was commonly referred to as partially coherent light, with the Gaussian Schell-model (GSM) beam serving as a fundamental model this type of light8. In contrast to conventional lasers with Gaussian distribution for intensity, the GSM beam conforms to Gaussian distributions also in their coherence function, defining a distinctively partially coherent light source9. Since the introduction of the GSM, extensive research has ensued, covering its generation, transmission, and application10,11,12,13,14,15. It has been shown that this kind of low-coherence light offers unique advantages compared to conventional high-coherence laser beams across numerous domains. For instance, the GSM beam proves effective in reducing the bit error ratio (BER) while enhancing the signal-to-noise ratio (SNR) in free-space communication scenarios10,16,17. Furthermore, GSM beams have been studied in advanced applications like ghost imaging, optical trapping, and inertial confinement fusion11,18,19,20,21. Their versatility extends to the domains of nonlinear optics, remote detection, and quantum optics.

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One issue with some chaotic-cavity designs, including the D-shaped cavity, is the challenge of collecting the light emitted from them, given that light escapes from all sides of the cavity90,95. Another approach was used to increase the number of lasing modes with directional emission. This was done by using a stable, near-concentric resonator with two concave circular mirrors that support a large number of axial modes95. This device was also shown to result in a low speckle contrast with a larger degree of directionality as compared to the D-shaped laser.

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a The different designs of SLDs based on typical edge-emitting lasers with ridge-waveguide structures. In many cases, a combination of these techniques is used to achieve the required feedback suppression. b A comparison of their optical power versus current characteristics. c A comparison between the typical optical spectra from a laser diode, a superluminescent diode (SLD) and a light-emitting diode (LED).

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Right: photon degeneracy of various light sources241. a Low-temporal coherence and high-spatial coherence light, which can be generated from SLDs, or from an LED passing through a pinhole. b High-temporal coherence and high-spatial coherence light, which is typically emitted from conventional single-mode lasers, such as single-mode vertical-cavity surface-emitting lasers (VCSELs) and distributed-feedback (DFB) lasers. c Low-temporal coherence and low-spatial coherence light, which is which is typically emitted from LEDs and conventional thermal light sources, like tungsten light bulbs and stars. d High-temporal coherence and low-spatial coherence light which can be generated by chaotic-cavity lasers, degenerate-cavity lasers, VCSEL arrays and random lasers.

Photonics Laboratory, Electrical and Computer Engineering Program, Division of Computer, Electrical, and Mathematical Sciences and Engineering (CEMSE), King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Kingdom of Saudi Arabia

This publication is partially based upon work supported by King Abdullah University of Science and Technology Research Funding (KRF) under Award No. ORFS-2022-CRG11-5079 and ORA-2022-5313. The authors further acknowledge the support of KAUST baseline funding BAS/1/1614-01-01.

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To suppress random speckles, the most straightforward way is to average the optical intensity either from a temporal or spatial aspect using time-averaging or spatial-averaging technologies. These techniques often involve moving parts, such as moving grating153, rotational micro-optic diffuse154, dynamic light scattering liquid crystal or moving diffuser device155,156 in which the careful control of the illumination angle, scatter size, and the rotational speed is also necessary. While they can reduce speckle contrast, these approaches complicate system configurations and decrease time resolution. Post-processing methods are another avenue to suppress speckles, relying on offline data manipulation. While these methods can yield practical results, they often sacrifice detailed information within the image157,158. Moreover, reducing the coherence by external means is at the cost of reduced intensity or extra energy consumption. Thus, the quest for an optimal light source veers towards finding a light source with reduced coherence. Such a light source would aim to strike a balance, offering sufficient brightness and resolution while minimizing speckle formation and potential eye hazards.

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Based on the feedback mechanisms, RLs with distinct size of random media (L) and lt can be categorized into coherent RLs and low-coherent RLs. If \({l}_{t} \,<\, \lambda \,<\, L\), the feedback provided by recurrent light scattering in a closed loop path [as illustrated in Fig. 6a, c] can result in localized modes and a coherent and resonant random lasing behavior, which is close to that of the conventional lasers108. These coherent RLs are under extensive research including systematic and comprehensive summaries109,110,111. More relevant to this review is the non-resonant, delocalized RL [as illustrated in Fig. 6b, d] characterized by its lack of temporal coherence when \(\lambda \,<\, {l}_{t} \,<\, L\). These systems operate based on diffusive feedback, where only a portion of the energy or photons can return to the gain medium109. Consequently, such systems generally exhibit broadband, less-directional emissions with less well-defined modes. This can result in emission spectra characterized by wide and weak spikes108. These low coherent RL sources can be particularly advantageous for speckle-free laser imaging49,112, white-light illumination113, and biomedical optical sensing114,115. For now, RLs have been realized with diverse gain media and scatterers in a variety of dimensionalities. The coherence can be adjusted by pumping power, cavity design, scattering strength116,117,118, and excited lasing modes89,119. For incoherent or low-coherent random lasing, it can be induced using scattering reflectors, photonic comb, powder, and laser paint109.

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Coherence serves as the foundational concept for characterizing light fields. Within the context of coherence, two distinct properties are studied—spatial coherence and temporal coherence. They describe correlations observed between optical fields at separate spatial locations and at distinct moments in time, respectively. To quantitatively assess the degree of coherence across both time and space, the first-order correlation function is used39,40, which is expressed as:

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a Schematic of TD-OCT. b By adjusting the distance of x or y, the light reflecting from sample interferes with the reference beam based on the optical path difference (OPD), hence causing the intensity changes.

Temporal coherence is a fundamental property of optical waves. This property characterizes the extent to which the phases of light waves within a beam remain correlated or coherent over time. It defines the regularity and predictability of fluctuations in the optical field. Temporal coherence is crucial in contexts involving interference phenomena and the dynamic behavior of light waves. To quantitatively assess temporal coherence, the concept of coherence time τc was introduced, which measures the duration for which the phase of a light wave retains correlation. Coherence time is also closely related to the spectral width (Δν) of coherent light sources through the relation40:

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Monochromaticlight

The application of low temporal coherence light sources improves the performance of TD-OCT by modifying the detected intensity, introducing a complex degree of coherence parameter that acts as an envelope of the interferogram40:

The discussions surrounding temporal and spatial coherence, as described above, are firmly rooted in the principles of geometric and wave optics. In laser physics, coherence is frequently examined through a comprehensive combination of temporal and spatial coherence, both of which are encapsulated within what is termed as “coherence volume”3,39,46. This perspective is exemplified in the coherent properties of laser light generated through the stimulated emission process within the gain medium39,47,48. In this process, every emitted photon shares identical attributes of propagation direction, frequency, polarization, and phase. This uniformity contributes to the high temporal and spatial coherence. Furthermore, the high temporal coherence of laser light is also attributed to the presence of resonator modes which are formed by the optical cavity. For instance, when only a single mode possesses the requisite laser gain for sustained oscillation, this mode yields a single-frequency operation characterized by its exceptionally high temporal coherence. The concept of the coherent volume \({V}_{c}={A}_{c}\times {l}_{c}\) emerges as a comprehensive indicator of overall coherence. This volume is defined as the product of the coherence, area Ac, which pertains to spatial coherence, and the coherence length, lc, representing temporal coherence. This description of the coherent volume accommodates a parallel interpretation linked to the optical standing wave formed in three directions x, y, and z39:

Coherencelength

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where \(\left\langle \cos \theta \right\rangle\) represents the average cosine value for the scattering angle, ρ denotes the number density of scatterers and σs is the scattering cross section. There are three regimes for light transport in a 3D random medium: (i) the localization regime is defined for \({l}_{t}\le \lambda\), where λ is the light wavelength; (ii) the diffusive regime is defined as \(L\gg {l}_{t}\gg \lambda\), where L is the size of the random medium; and (iii) the ballistic regime is defined as L ≤ lt107.

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Unpolarizedlight

To achieve interference in FOGs, the two light beams must exhibit similar wavelengths but different phases. Low-coherence light sources are preferred in this regard. They emit light waves with a short coherence length, characterized by a broader range of wavelengths and resulting in varied phases. As a consequence, when the light beams recombine after traversing the fiber coil, interference occurs due to the phase variations, ultimately enabling the measurement of rotation-induced phase differences. Moreover, long-term wavelength stability is needed for broadband sources in FOGs. Changes in the phase of Rayleigh backscattering due to small vibrations and temperature variations are significant sources of noise in fiber-optic Sagnac interferometers181,182. Low-coherence light sources can address these demands by minimizing phase noise and artifacts while ensuring high SNRs183,184. Companies like Exalos AG in Zurich, Switzerland, have made significant strides in this regard by developing SLDs that exhibit reduced susceptibility to wavelength shifts due to temperature or aging. Also, FOG products equipped with broadband SLDs are under popular investigation185. These SLDs are ideal optical sources in FOGs due to their low cost, small size, reliability, stability, and low power consumption184,186.

SLDs are found to significantly improve the speckle characteristics of the resulting holograms compared to coherent lasers and incoherent LEDs due to the broadband output optical spectrum and high-power level142. As illustrated in Fig. 7b, the reconstructed holographic image of the SLD is sharp with reduced speckle noise at an acceptable brightness, which exhibits visibility of 0.67 and coherence length of 22 µm. In contrast, the holograms captured with the laser show high sharpness but are accompanied by significant speckles due to the long coherence length of 113 µm, while LED introduces blur and low contrast with the visibility of 0.02 caused by its low optical power per mode (see Fig. 7c, d). In projection applications, the spatial coherence typical of SLDs translates into a small beam divergence, corresponding to a directional light beam output, which is conveniently collimated into parallel beams or focused to µm-scale spot sizes, allowing for a reduced complexity of collimation optics required in the optical subsystems. Given that the SLD light is bright, eye-safe, and produces a lower speckle contrast, they have potential use in display, illumination, projection, and holography applications. For even lower speckle contrasts, it was shown that low-spatial-coherence chaotic-cavity lasers can be used for illumination and imaging with speckle contrasts below human perception34.

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103 Benefit St, Pawtucket, RI 02861 is currently not for sale. The 2016 Square Feet single family home is a 4 beds, 4 baths property.

Similar to the edge-emitting lasers discussed above, it was shown that VCSELs with chaotic transverse shapes can experience chaotic dynamics96,97,98. Therefore, they were proposed as a tool to study wave chaos96. More recently, we showed that chaotic-cavity VCSELs with a D-shaped transverse profile can support a larger number of modes as compared to conventional circular VCSELs99,100. Moreover, we showed that these devices allow for high-speed communication with low-speckle illumination, especially when driven by a strong alternating current (AC) signal that is inserted between the communication symbols33,37. This opens the door for many applications that would benefit from the surface emission configuration and the emission direction of VCSELs.

Since the advent of lasers in 1960, their extraordinary attributes—high power, efficiency, directionality, and monochromaticity—have propelled them to the forefront of scientific and technological innovation4. Many of these unique features attributed to high coherence. Nevertheless, these significant characteristics that make lasers exceptional can sometimes present challenges in various applications, which act as a double-edged sword, manifesting as artifacts in imaging, unintended interference patterns in optical configurations, and noise in measurements. For example, in display technology, the high coherence of lasers can give rise to discernible artifacts that impact the visual fidelity of projected images5. Furthermore, applications like interferometry and metrology face challenges as the interference of waves originating from high-coherence light sources introduces unwanted noise, thereby complicating precision measurements6. This challenge arises from the fixed phase relationship among constituent waves in high-coherence beam profiles. When these waves interact with multiple interfaces or optical components, the multiple reflections of high-coherence light can make the extraction of precise depth information difficult, rendering the interpretation of images challenging, thereby limiting the depth of information in applications like optical coherence tomography (OCT)7. These challenges highlight the need for alternative light sources that can provide high power while mitigating coherence-related artifacts. In many instances, the transition to lower-coherence light sources is a practical solution to alleviate the inherent shortcomings of high-coherent sources, and thus the low-coherence light sources have carved their niche by offering several unique advantages.

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Since the invention of the laser, there have been countless applications that were made possible or improved through exploiting its multitude of unique advantages. Most of these advantages are mainly due to the high degree of coherence of the laser light, which makes it directional and spectrally pure. Nevertheless, many fields require a moderate degree of temporal or spatial coherence, making conventional lasers unsuitable for these applications. This has brought about a great interest in partially coherent light sources, especially those based on semiconductor devices, given their efficiency, compactness, and high-speed operation. Here, we review the development of low-coherence semiconductor light sources, including superluminescent diodes, highly multimode lasers, and random lasers, and the wide range of applications in which they have been deployed. We highlight how each of these applications benefsits from a lower degree of coherence in space and/or time. We then discuss future potential applications that can be enabled using new types of low-coherence light.

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coherence中文

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Reproduced with permission from Zheng, G. et al.145. Copyright 2015 Springer Nature; Wang, Z. et al.240. Copyright 2017 Springer Nature; Regimanu, B. et al.239. Copyright 2019 Springer Nature; Alatawi, A. A. et al.57. Copyright 2018 OPTICA; Alkhazragi, O. et al.196. Copyright 2023 Wiley Online Library.

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Low coherence light source plays an important role in optical communication which typically includes telecommunication using fibers and optical wireless communication (OWC). Although low-coherence light sources are not usually used as the light source in telecommunication systems, the semiconductor optical amplifier (SOA) is a significant component in these systems that has a similar mechanism as SLDs, which can be used to increase the laser power from the transmitter; compensate the fiber loss, especially in the long-distance link; and improve the sensitivity of the receiver187,188. They are also investigated in wavelength-division multiplexing (WDM) systems to improve communication performance189,190. While SOAs help with telecommunication systems by amplifying coherent light, low-coherence light sources found their importance in OWC, which is often seen as a complementary technology to Wi-Fi, and in indoor scenarios, visible light serves a dual role for both illumination and communication. In visible-light communication (VLC), incoherent light sources like LEDs encounter limitations in offering high data transmission rates due to their low efficiency and varying angles. On the other hand, while conventional lasers can provide high-speed data transmission, they suffer from the formation of speckles, which degrades their illumination performance. In addition, concerns surrounding eye safety have limited their application in this context. Therefore, the quest for an ideal light source that balances high power output with high illumination quality has led to the consideration of low-coherence light sources for high-brightness and high-speed visible-light communication systems.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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where \(U({{\bf{r}}}_{i},t)\) represents the complex wavefunction at the measurement point, and \(U({{\bf{r}}}_{i}{\boldsymbol{,}}t+\tau )\) denotes the wavefunction after the time delay τ. When the time delay \(\tau =0\), it provides information about the spatial coherence existing between optical field fluctuations at two different locations, r1 and r2. In the scenario where \({{\bf{r}}}_{1}{\boldsymbol{=}}{{\bf{r}}}_{2}\), it describes the temporal coherence, \({g}^{(1)}\left(t,\tau \right)\), representing the fluctuation behavior over the time interval from the measurement moment t to \(t+\tau\) at a certain location. For stationary light, it depends only on the time difference, τ, and it can be expressed as \({g}^{(1)}\left(\tau \right)\). It is noteworthy that, for most light sources, \(\left|{g}^{(1)}\left(\tau \right)\right|\) exhibits a gradual decline from a maximum value of 1 (when τ = 0) to infinitesimal levels as the delay τ becomes sufficiently longer than the coherence time, signifying a transition to full loss of correlation.

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Coherencetime

Spatial coherence describes the extent of correlation or coherence observed among the phases of individual light waves at various spatial points on the same wavefront within a light beam. Considering a cross-section of a laser beam characterized by diffraction-limited beam quality, the optical fields at distinct positions oscillate in a perfectly correlated manner. Crucially, spatial coherence exhibits a direct relationship with the formation of interference patterns. When coherent light waves intersect, they create well-defined and stable interference fringes, as vividly exemplified in Young’s double-slit experiment, as shown in Fig. 2d–f. In the case of spatial incoherence (Fig. 2d), the emitted light has random phase relationships across different spatial points, resulting in a broader and smoother profile. These sources can be represented by natural light sources, such as LEDs, incandescent bulbs, and the sun. Conversely, single-mode laser-emitted waves exhibit high correlation in space (Fig. 2e). The individual wavefronts emanating from diverse spatial points maintain consistent phase relationships as they propagate, giving rise to distinct and sharply defined interference fringes on a screen after passing through the two slits. In scenarios characterized by low spatial coherence (Fig. 2f), wavefronts emerging from distinct points fail to maintain stable phase relationships. This results in the appearance of washed-out or less distinct fringe patterns on the screen.

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As represented by the GSM beam, low-coherence light sources constitute a fascinating category of light sources that emit optical waves with a distinctive blend of attributes, setting them apart from their high-coherence and incoherent counterparts. The development of low-coherence light sources has attracted extensive research into related technologies about their generation. For instance, the development of superluminescent diodes (SLDs)22,23,24, random lasers (RLs)25,26,27, broad-area lasers28,29,30 and inhomogeneous quantum dot (QD) and quantum dash (Q-dash) broadband lasers31,32 has drawn increasing interest in the last twenty years. Their applications have also expanded in many scenarios; for example, chaotic-cavity lasers serve as a special type of broad-area lasers, have shown their promise in reducing coherence artifacts33,34, which benefits the display industries. Other potential applications in diverse fields are being explored, including instability suppression35, illumination36, communication37, and random number generation38. Collectively, these innovations play a pivotal role in driving breakthroughs across diverse scientific and technological fields.

The above lasers are based on edge-emitting configurations. However, in many applications, surface emission is preferred, and in some, it is required. Vertical-cavity surface-emitting lasers (VCSELs) have been used in a wide range of applications ranging from optical communication, sensing, to imaging. Nevertheless, their high degree of coherence limits them in applications that would suffer from speckles and a long coherence length. Due to the short cavity length of VCSELs in the longitudinal direction (λ or λ/2 in many cases), they only support a single longitudinal mode because of the wide free spectral range. However, broad-area VCSELs feature a high Fresnel number, which is proportional to the cavity’s transverse area and inversely proportional to the length of the cavity and the wavelength, and therefore, the higher order mode experiences lower diffraction loss. This allows the lasing of multiple transverse modes.

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Furthermore, the true potential of semiconductor RLs is yet to be realized, mainly due to difficulties in achieving random lasing based on electrical pumping. This would open the door to a wide range of applications that would greatly benefit from the reduced spatial coherence of RLs while maintaining high-speed operation and relatively high temporal coherence. The challenges in achieving electrical pumping are primarily due to issues related to low conductivity, high-intensity stability, and significant scattering losses stemming from the spatial noncontinuity of the scattering elements, which impede their steps toward large-scale manufacturing and commercialization. The development of electrically pumped RLs with high efficiency, flexibility, multiple functionalities, low power consumption and large-scale on-chip integration, will pave the way towards harnessing the full potential of low-coherence RLs in fields such as telecommunications, sensing, and portable devices. In the meantime, deep physics investigations of such complex laser systems are also essential.

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To lower the speckle contrast even further, chaotic-cavity lasers with low spatial coherence can be used instead of SLDs. We recently showed that the careful design of chaotic cavity VCSELs and their injected signals can effectively lower the speckle contrast while maintaining higher speeds as compared to SLDs. These low-coherence chaotic-cavity VCSELs supported high-speed communication with a modulation bandwidth of up to 5 GHz and a net data rate of 12.6 Gb s–1 using orthogonal frequency-division multiplexing (OFDM)76.

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The light from SLDs is generated through amplified spontaneous emission (ASE). When current is injected below the population inversion condition, the SLD operates as an LED and light is generated mainly through spontaneous emission. As the current increases beyond the population inversion threshold, the spontaneously emitted light experiences more stimulated emission than absorption, and the light output power starts to increase exponentially as the current increases. This can be clearly observed in the superlinear relationship between the optical power and the injected current when the SLD is operated above the threshold, as shown in Fig. 4b. However, unlike in lasers and as can be seen in the same figure, there is no sharp increase at the threshold for the SLD. The exponential increase in power is one of two main characteristics of SLDs. The other one is the SLD’s smooth emission spectrum, which is similar to that of LEDs, but with a narrower spectral width due to stimulated emission. This is illustrated in Fig. 4c. In addition, the spectral width of SLDs decreases substantially as the current increases above the threshold, but not to the same degree as laser diodes.

It is important to note that while high temporal coherence and spatial coherence often coexist, they are not inherently interdependent. This diversity in coherence attributes gives rise to four distinct combinations, as visually represented in Fig. 3. The first case shown in Fig. 3a represents light marked by high spatial coherence but accompanied by low temporal coherence. While the beam quality remains high, variations in phase occur along its propagation path. Such beams find applications in scenarios like time-domain OCT, where imaging relies on a broadband light source and concentrated energy distribution. In this context, high resolution necessitates low temporal coherence. Suitable light sources for such applications encompass amplified spontaneous emission (ASE) from a laser amplifier or SLDs. Figure 3b depicts a scenario featuring a monochromatic Gaussian beam characterized by high spatial and high temporal coherence. Such a source is ideal for applications like optical fiber communication, precision laser cutting, and photolithograph. Figure 3c shows light sources exhibiting both low temporal and low spatial coherence. This category, which includes LEDs and thermal light sources, serves as an ideal illumination source and has been employed in diverse applications in indoor lighting, screens of consumer electronics, and agricultural production. Figure 3d illustrates a light beam exhibiting low spatial coherence yet retaining high temporal coherence. In this case, the wavefronts may exhibit deformation, leading to higher beam divergence and reduced contrast. This configuration can arise from random lasers which can find numerous applications in display and projection49, providing speckle-free imaging. Here, we focus our exploration on the low-coherence semiconductor light sources, mainly encompassing scenarios depicted in Fig. 3a, d.

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Partially coherent

Conventional pseudorandom number generators, while widely used, are based on deterministic algorithms and initial seeds. Their output is deterministic and predictable once the initial conditions are known, making them susceptible to exploitation by malicious actors. As the demand for secure data transmission and cryptographic operations continues to rise, the inadequacy of pseudorandom numbers becomes increasingly apparent. This deficiency has propelled the quest for true random numbers. Photons, as fundamental particles of light, can possess inherent randomness in their generation and behavior. This intrinsic randomness has made photons a prime candidate for generating true random numbers, and their utilization has been a cornerstone of quantum random number generation (QRNG)196,197,198. While lasers have historically dominated this domain, low-coherence light sources are emerging as a promising alternative, offering new avenues to harness the inherent unpredictability of photons.

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There have been significant advancements in the development of visible-light low-coherence light sources based on Group-III-Nitride SLDs. These SLDs boast a broad spectral emission range attributed to ASE, characterized by the coexistence of spontaneous and stimulated emission processes. These unique properties position SLDs as promising alternatives for applications in solid-state lighting (SSL) and communication. These devices produce highly directional beams with limited etendue, providing high power output while minimizing speckle noise, which is essential for both illumination and communication applications. Furthermore, they feature higher speeds compared to LEDs due to the reliance on stimulated emission.

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For example, OCT has been extensively used in medical diagnostics, particularly in ophthalmology, cardiology, and dermatology161,162,163. OCT is a non-invasive medical imaging technique that delivers high-resolution cross-sectional images, facilitating the visualization and analysis of biological tissues, and enabling the precise measurement of tissue thickness and the determination of key properties of biological samples164. This technology can be carried out in either a frequency-domain OCT (FD-OCT) or time-domain OCT (TD-OCT) configuration. More specifically, the FD-OCT can be classified into spectrometer-based OCT (SB-OCT), which requires high-resolution spectrophotometer, and swept source OCT (SS-OCT) which relies on wavelength-tunable narrowband laser sources. While high-coherence wavelength-tuning VCSELs are crucial for SS-OCTs, both SB-OCT and TD-OCT benefit from low-coherence light sources163,165,166. For example, TD-OCT employs temporal low-coherent light sources in an interferometer setup, as shown in Fig. 8a167. In this general setup, light emitted from the source, Is, is split into two beams: one serving as the reference light, while the other interacts with the sample and reflects back to the photodetector with a reflectivity of R. Both reflected beams are recombined at the beam splitter, and 50% of each beam intensity is directed toward the photodetector, ID. For coherent light sources with monochromatic properties, the interference at the photodetector is described by the following expression168:

SLDs are the preferred low-coherence light source for TD-OCT and SB-OCT applications. These solid-state semiconductor devices offer broadband optical spectra with high power levels. SLDs provide excellent depth resolution, enabling the imaging of thin layers and fine structures within samples. This is because for light with high temporal coherence, the signal reflected from multiple layers in the sample across its coherence length can interfere with the reference beam, lowering the axial resolution.

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Besides displays, holography plays an increasingly significant role in applications like virtual reality (VR) and AR displays145,146,147,148. Unlike traditional photography, holography records both the amplitude and phase of light waves, resulting in comprehensive 3D object reproduction. In this context, coherent light sources are required, as the interference of scattered light with a reference beam records the hologram. However, this process can introduce unwanted speckles into the holograms if highly coherent light is used, degrading image quality149,150. Lasers have been widely adopted for these applications due to their spatial coherence, enabling the generation of collimated beams with high brightness. Especially for pico-projectors, lasers are focus-free and can deliver a wider color gamut55. However, the high degree of coherence characteristic of lasers results in speckle formation within the projected images, significantly degrading the viewing experience. Moreover, the localized high energy emanating from the lasers could potentially pose hazards to the retina if not properly managed and became a matter of concern for eye safety for humans151,152.

Coherenceanalysis

Schematic diagrams of (a) coherent random lasing with multiple scattering in closed-loop paths formed by disordered particles confining the light in the gain medium, and (b) incoherent random lasing with opened-loop photon scattering paths. Typical emission spectrum of (c) coherent RLs and (d) incoherent RLs.

The spatial coherence of light can be quantitatively assessed by examining the brightness and darkness of interference fringes formed in a double-slit experiment, employing a parameter known as the fringe visibility or fringe contrast, C, which is defined as39,40:

Given the critical role that the cavity of a semiconductor laser plays in the degree of coherence of the emitted light, changing the shape of the cavity can be a powerful technique to control the temporal and spatial coherence. Instead of effectively eliminating the presence of cavity effects in the case of SLDs, it is also possible to achieve low coherence by using carefully designed optical cavities that can support a large number of modes which are mutually incoherent. This results in an output that has low spatial coherence. Moreover, since different modes are mutually incoherent which do not share the same phase, and since they can lase at slightly different wavelengths, the temporal coherence is also lowered.

The degree of second-order and higher-order coherence are also important factors to be considered. Unlike in lasers where the saturation of optical gain results in low fluctuations in the emitted intensity, other light sources that lack this saturation exhibit what is known as photon bunching. This is true for thermal light as well as LEDs and SLDs. Photon bunching of these sources has been utilized in mimicking entangled photons in ghost imaging41. It has also been used in ranging42 and two-photon excited fluorescence43. Nevertheless, our focus in this article is on applications that rely on the low degree of first-order coherence.

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Despite their usefulness in many applications, the edge-emitting configuration of SLDs limits their practicality in scenarios in which two-dimensional arrays are required. While surface emission has been achieved in LEDs and in laser diodes, in the form of vertical-cavity surface-emitting lasers (VCSELs), it still remains a challenge in SLDs. This is mainly due to the small thickness of the active region of semiconductor light sources, which does not provide enough gain for photons traveling vertically through the gain medium, preventing ASE from taking place. While this issue is commonly circumvented in VCSELs by the formation of the optical cavity with high reflectivity to ensure multiple passes through the active region, optical feedback cannot be used to design SLDs as it would allow only certain modes to lase. Nevertheless, several studies have reported SLDs with apparent vertical emission. For example, grating out-couplers have been proposed to redirect the light toward the surface of the device84. Moreover, micromirrors can also be used to serve the same function85,86. Similarly, a sloped waveguide whose facets act as total internal reflectors was shown to achieve surface-emission through a transparent substrate87. However, these techniques rely on long horizontal waveguides and asymmetric apertures. Therefore, they lack the symmetric beam profiles of LEDs and VCSELs and are not suitable for forming two-dimensional arrays of light sources. A theoretical study proposed the use of a circular grating to overcome some of these issues88.

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Low-coherence light sources find a significant application in the field of navigation systems, particularly in the context of fiber optic gyroscopes (FOGs), which are extensively utilized in avionics and aerospace173,174. These FOGs present several distinct advantages when compared to traditional mechanical gyroscopes. They are characterized by their compactness, lightweight nature, and the absence of moving parts, making them less prone to wear and tear. Additionally, FOGs offer high levels of accuracy, stability, and reliability, making them ideal for various applications in navigation systems175,176. These applications span across aircraft, spacecraft, submarines, autonomous vehicles, and precision instruments that demand precise angular rate measurements177. At the core of these precision rotation measurement systems lies the concept of the Sagnac effect, as shown in Fig. 9a177. FOGs are built around the determination of the phase shift of radiation as it propagates along a fiber optic coil while being rotated around the winding axis178. The fundamental components of FOGs include a light source, a single-mode polarization-maintaining fiber coil, a coupler, and a detector. This system operates by splitting a light beam into two paths and subsequently recombining the beams.

Figure 5 shows the near-field profiles (NFPs), far-field profiles (FFPs), the sum of the intensity values of the pixels with the same distance from the center of the FFPs, and the spectra recorded from a chaotic-cavity VCSEL at different injection currents. The NFPs clearly show a speckled pattern indicating the chaotic ray dynamics in the cavity. The optical field can also be observed over most of the cavity, unlike in circular cavities that feature high-Q-factor whispering gallery modes (WGMs), which are concentrated around the edges of the cavity. This has been shown to increase the power and efficiency of VCSELs with asymmetric cavities33,101. Moreover, the FFPs show a mostly circularly symmetrical beam, which is useful in coupling the light into fibers. In addition, since VCSELs emit light in a single longitudinal mode, modes at higher frequencies (longer angular wave vectors and shorter wavelengths) are emitted at larger angles than those at lower frequencies. Therefore, there is a correlation between the shape of the FFPs and the spectra recorded from the VCSEL. This is shown in the bottom two rows of Fig. 5. Despite the limited resolution of the imaging system and the camera, the resemblance can still be observed.

Lens Width: The length of the lens from left to right; for best fit your eye should be nearly centered in the frame. How do I know what size glasses I have?

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Low-coherence light sources have the potential to revolutionize the fields of displays, illumination, projection, and holography. The balance they strike between high brightness and reduced artifacts sets them apart from traditional high-coherence laser sources and incoherent light sources such as LEDs. Displays are found everywhere in modern society, encompassing traditional screens and emerging technologies like head-up displays (HUDs), pico-projection, mixed-reality (MR), and augmented reality (AR) displays. Creating full-color displays requires a combination of RGB light sources. LEDs are the predominant choice due to their incoherence as well as vibrant color reproduction. However, LEDs have limitations in terms of power per mode141. The low brightness and resolution could negatively affect the display quality, making the images less vivid or discernible, especially in well-lit or outdoor environments. This is mainly due to the fact that the smaller LEDs that are needed for higher resolutions emit lower optical powers. Facing this challenge, different low-coherence light sources have been investigated for displays and imaging applications. For example, engineered RLs could provide low spatial coherence, in which the intense optical scattering results in speckle-free full-field imaging49. However, most RLs rely on optical pumping which impedes the practical use in consumer electronics. Therefore, compact semiconductor low-coherence light sources are ideal for more application scenarios, providing high-quality images with high sharpness and minimum speckle contrast142. For displays, visible-light SLDs are much more powerful than LEDs with their high-power densities which can provide high efficiency and high color saturation with low speckle noise, focus-free operation, and a wider color gamut compared to LEDs (provided by the narrower optical spectrum). Additionally, they are commercially available in RGB wavelength regions (635 nm, 510 nm, and 450 nm) needed for full-color displays143,144. As shown in Fig. 7a, the first integrated RGB SLD module has been demonstrated, opening a new door for micro-display architectures.

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where n represents the refractive index of the medium, λ denotes the central wavelength, and Δλ signifies the full width at half maximum (FWHM) of the emission spectrum.

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Compared to conventional lasers, the gain medium of RLs contains many scatterers and lasing can occur without a conventional cavity. In this case, the spontaneously emitted photons will be scattered multiple times and undergo a “random walk.” The increase in the path length of photons in the gain medium enhances light amplification via stimulated emission of photons. Furthermore, the scattered waves may return to spatial positions that they have visited before, providing feedback for lasing oscillation. This unique process gives RLs some appealing features including complex and dynamic modes.

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In addition to the advantages of low temporal coherence in RNG, low-spatial-coherence light sources are also studied for this application. Although parallel generation of physical random numbers was started in the 1980s208, the first proposed systems were cumbersome because they relied on laser speckle patterns created by a moving diffuser or a vibrating multimode fiber, which is also inherently slow due to the long mechanical moving time. Another way is to rely on the intrinsic instability of the sources. For example, chaotic broad-area semiconductor lasers have been investigated for high-speed parallel RBG209, but correlations of intensity fluctuations at different spatial locations impede independent parallel bitstream generation. Thus, a low-spatial coherence light source is an effective way to form parallel spatial channels. In 2021, a violin-cavity broad-area laser, shown in Fig. 10d, was introduced to generate ultrafast random number sequences with a generation rate of more than 250 Tb/s using 127 spatial channels210. In this cavity, the number of transverse lasing modes is enhanced and they are well-confined inside the cavity, which prevents the long-term correlated lensing and self-focusing effects. The dynamics of such intensity fluctuations are inversely proportional to the spectral width of the total emission and are on the order of pico-second [see Fig. 10e]. As shown in Fig. 10f, this designed laser exhibits both low temporal coherence and low spatial coherence. Short temporal correlation improves the quality of random bits generated at one spatial location, and short spatial correlation means that the random bit streams generated at different locations are independent, thus allowing massively parallel RNG. This attribute opens the door to creating parallel channels based on spatial variations in the light source. However, the detection of this ultrafast signal relies on a streak camera, which greatly increases the cost and reduces the flexibility of the overall system, therefore, it severely hinders practical application. Very recently, we demonstrated an ultrafast physical random number generator with a data rate of 200 Gb/s using the chaotic dynamic of a free-running VCSEL, which promises a compact and low-cost way for parallel chip-integrated high-speed physical random number generator211.

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From coherence time, τc, and the speed of light, c, the coherence length, lc, can be introduced to obtain the distance that a wave can traverse while maintaining coherence. The coherence length is defined by the product of the coherence time, τc, and the speed of light, c. For light sources featuring a Gaussian emission spectrum, the coherence length takes on the following expression40:

Low-coherence light sources are essential components in low-coherence interferometry techniques, with widespread applications in various fields. These interferometers harness the unique properties of low-coherence light to make non-invasive and highly precise measurements for distances, thicknesses, and refractive indices, particularly in the domain of biomedical imaging159,160. Low-temporal coherence light can be used to obtain clear signals in these applications with low background noise. When high-temporal coherence light sources are used, complex interference patterns can emerge from multiple reflections, leading to artifacts in imaging. Low-temporal coherence light sources, on the other hand, minimize these artifacts, simplifying the interpretation of results. In various interferometric applications, including surface profiling, displacement measurements, and optical testing, low-coherence light sources strike the ideal balance between high brightness and minimal interference patterns. This balance ensures that precise measurements can be made with reduced interference noise.

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Random lasers (RLs) have sparked considerable scientific investigations and discussions over the past several decades with their low coherence due to photon random amplification path that does not rely on conventional cavities. The early stage of random lasing started in 1966 with the first reported non-resonant feedback using a “scatterer-mirror”102. After that, the classical model103,104 and experimental demonstration105 of photon diffusion and amplification through disordered gain media appeared in 1967 and 1986, followed by the discovery of laser-like behavior based on the optically pumped colloidal suspension of TiO2 particles in 1994106. These pioneering dedications paved the way for the future development of RLs.

In reciprocal space (the space of wave vectors), the optical wave mode can be represented by coordinate axes consisting of three wave vectors \({k}_{x}\), \({k}_{y}\) and \({k}_{z}\), and \(\varDelta {k}_{x},\varDelta {k}_{y},\) and \(\varDelta {k}_{z}\) are the intervals between each mode with its nearest neighboring modes. The photon degeneracy denotes the number of photons within one coherent volume, with higher photon degeneracy indicative of higher coherence. The microscopic perspective on coherence is described in terms of photon degeneracy, while the macroscopic view is characterized by fringe contrast.

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Perhaps the most commonly used low-coherence semiconductor light source is the SLD (sometimes referred to as superluminescent LED, or SLED), which is characterized by its low temporal coherence. SLDs were first developed in the near-infrared (NIR) region of the electromagnetic spectrum based on GaAs in the 1970s50,51. Since then, SLDs have been proposed to be used in time-domain optical coherence tomography (TD-OCT), fiber-optic gyroscopes (FOGs), displays and projectors, and simultaneous illumination and communication systems. Given the wide range of applications in which they are needed, various types of SLDs have been developed. This includes near-ultraviolet and short-wavelength visible light based on GaN52,53,54,55,56,57,58,59,60,61,62,63, to red and NIR wavelengths based on GaAs and InP24,50,64,65,66,67,68,69,70,71, to short-wavelength infrared (SWIR) based on InP and GaSb72,73,74,75.

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The commonly used gain media are semiconductors (e.g., III–V, II–VI, perovskites, etc.)120,121, polymers122, liquid crystals123, laser dyes, rare-earth doped materials, or their combinations115,124,125. The scatterers can be biological tissues126, photonic crystals127, metallic/dielectric nanoparticles128, random fiber Bragg gratings129, and 2D layered structures130. Especially, semiconductor nanostructures or quantum dots can serve as both gain medium and scatterers simultaneously due to the specific structures and configuration. For the pumping methods, most random lasing was predominantly achieved through optical pumping. However, recent efforts by researchers aim to reduce the optical pumping threshold and gradually transition towards electrical pumping131. Most electrically pumped RLs rely on ZnO films or nanowires to form homo-/hetero-junctions or ZnO-based metal oxide semiconductor devices132,133,134,135,136,137. This choice is attributed to the large exciton binding energy (~60 meV at room temperature) and naturally formed disordered polycrystalline, which supports strong optical scattering. Besides, electrically pumped RLs using other semiconductors and structures have also been reported including AlGaInP multiple quantum well structures138, CdSe quantum dots139, and GaAs-based quantum cascade lasers140. Despite the advantages offered by electrical pumping, such as enhanced energy efficiency, compactness, and precise control, achieving low threshold electrically pumped random lasing remains challenging.

In this expression, \({I}_{\min }\) and \({I}_{\max }\) denote the minimum and maximum intensities of the interference fringes at a certain position, respectively. The fringe contrast serves as a measure of the distinguishability of the fringes, yielding the following insights: when interference fringes are nearly indistinguishable, the maximum and minimum values are nearly equal, leading to C ≈ 0. In cases where the stripes exhibit a marked and clear contrast, the maximum value can be significantly greater than the minimum value, yielding C ≈ 1. The fringe contrast thus encapsulates the degree of distinguishability among the interference fringes, providing a quantitative criterion for evaluating the degree of spatial coherence.

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The near-field patterns (NFPs), far-field patterns (FFPs), the intensity of the FFPs summed over all pixels with the same distance from the center, and the spectra of a D-shaped VCSEL at different injection currents.

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a Schematic of the Sagnac effect. b Schematic of the fiber optic gyroscope (FOG). Light emitted from a broadband light source passes through the fiber optic coupler 1 and enters the polarizer. The linearly polarized light propagates along the polarization-maintaining fiber, and then through the fiber optic coupler 2, forming two beams of light propagation along the clockwise and counterclockwise directions. These two optical signals interfere with each other when they return to fiber coupler 2, and this interference signal is then detected by the photodetector (PD) through coupler 1.

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Several studies have been carried out on the coherence of chaotic-cavity laser diodes. For example, an edge-emitting laser with a chaotic D-shaped cavity was shown to support a significantly larger number of modes as compared to conventional rectangular and circular cavities of similar sizes34. The D-shaped cavity is defined as a circular cavity with a flat cut made at a distance d from the center. It was shown that for a value of d close to half the radius, a D-shaped laser can achieve high imaging quality with a speckle contrast close to human perception34. This type of laser was also shown to exhibit small spatiotemporal instabilities compared to rectangular, Fabry-Perot lasers, which suffer from self-focusing, which results in an output that is unstable in time and space35. The number of emitted modes from lasers having other cavity shapes with chaotic behavior have also been studied, including elliptical and stadium-shaped cavities91,92,93. However, it is important to mention that not all chaotic cavities are suitable for highly multimodal emission since some can feature scar modes with high Q factors89,94.

Various light sources with different degrees of temporal coherence can be evaluated by the coherence length. Thermal light sources, including incandescent bulbs and natural sunlight, typically exhibit coherence lengths at the nanometer scale. On the other hand, LEDs typically possess coherence lengths of less than 20 μm40,44,45. Generally, these light sources exemplify the incoherent sources, exhibiting no discernible phase relationships within their constituent optical fields over time. As shown in Fig. 2a, when a light beam lacks temporal coherence, the phases of individual monochromatic waves assume random and uncorrelated values throughout their temporal evolution due to the phase noise, and the light appears as a blend of waves of various frequencies and random phases. In stark contrast, temporal coherence length in a conventional high-coherence gas laser reaches up to cm or meter scale, and semiconductor laser diodes typically maintain coherence lengths in the hundreds of micrometers40, signifying the preservation of highly correlated phases among individual light waves throughout their propagation. As represented in Fig. 2b, the peaks and troughs of high-temporal-coherence light maintain a consistent relationship as they traverse over time. This results in a narrow spectrum. Low-coherence light sources, shown in Fig. 2c, bridge the gap between high-coherence light and incoherent light, which typically exhibit a coherence length in the tens of micrometers, corresponding to spectral bandwidths of tens of nanometers and sometimes above 100 nm. Not only do they provide a solution to the challenges associated with high-coherence and its resulting interference patterns, but also offers high power and high efficiency for illumination44,45. By deliberately reducing the temporal coherence, these light sources introduce randomness into the phases of individual light waves. This lack of phase correlation over time leads to a lower and broader interference pattern, which effectively mitigates the issues of low energy and high-level noise observed in incoherence and high-coherence light sources.

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As shown in Fig. 9b, a FOG involves the splitting of a laser beam and sending the resulting beams in opposite directions through a coiled fiber-optic cable. This system is designed to ensure that the light beams traveling in opposing directions travel the same distance179. Under stationary conditions, the light waves interfere constructively at the detector, producing a maximum signal. However, during the rotation of the fiber coil, the two optical waves undergo different optical paths that depend on the rotation rate. The resulting phase difference between these fields induces variations in the intensity detected by the photodiode, effectively providing information on the rotation rate. The sensitivity of the pattern to angular velocity dictates that faster rotations will lead to a more pronounced interference pattern180. The faster the rotation, the greater the phase difference and the more pronounced the interference pattern becomes.

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Here, the spectral width signifies the span of frequencies or colors that constitute the light. A light source with high temporal coherence exhibits a narrow spectral width (characterized by a single, well-defined frequency or color), but the narrow spectral band does not necessarily guarantee the high temporal coherence because the phase correlation cannot be indicated only from the spectrum. In high temporal coherence light sources, the phase relationship among different segments of the wave remains constant, leading to a long coherence time. Conversely, a light source that has a broad spectral width (encompassing a wide range of frequencies and colors) exhibits random phase relationships among distinct spectral components, which leads to a shorter coherence time and reduced temporal coherence.

This paper covers the principles and technologies of low-coherence semiconductor light sources and explores their potential in the advancements of a wide variety of optical applications, as summarized in Fig. 1. First, we give a brief background introduction to temporal and spatial coherence with the methodologies for their characterization. We also discuss various types of semiconductor low-coherence light sources with their designs, characteristics, and unique advantages. We then explore how these devices facilitated and revolutionized different fields, including displays, holography, interferometry, optical gyroscopes, optical wireless communication, and random number generation. By unraveling the mechanisms and techniques behind the creation of these sources and their applications, we aim to provide a comprehensive understanding of their unique attributes and their pivotal role in advancing the field of optics, optoelectronics, quantum technology.

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2023712 — Uniform Illumination: Uniformity in illumination helps create a visually comfortable environment. By ensuring consistent lighting levels across ...

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Notable research efforts have explored the use of low-coherence light sources for data transmission across various scenarios61,191,192. In 2016, Shen et al., investigated for the first time the implementation of low coherent light using semipolar GaN SLDs in communication systems61. The semipolar crystal orientation allows for higher speeds due to the increased overlap between the wavefunctions of electrons and holes in the active region, resulting in faster radiative recombination. Using on-off keying (OOK), a data rate of 1.3 Gb s–1 with a BER below the forward error correction (FEC) limit. In 2018, Alatawi et al. tested SLDs for high-speed VLC and speckle-free lighting by using a color-converting material to generate white light57. The SLD also demonstrated a data rate of 1.45 Gb s–1 is achieved with a 300-MHz modulation bandwidth. Shen et al. demonstrated the generation of white light using an SLD with a high color rendering index (CRI) of 88.2 at a correlated color temperature (CCT) of 3522 K, and it was used in a VLC system with a high data rate of 1.2 Gb s–1 using the OOK modulation technique and up to 3.4 Gb s–1 using the discrete multitone (DMT) modulation technique53. More recently, the highest communication data rate using an SLD was demonstrated (up to 4.6 Gb s–1 using DMT)192. The application of SLDs in communication systems has yielded promising results and has the potential to revolutionize high-speed data transmission, offering a balance between power, safety, and efficiency. Some of the reported results are summarized in Table 2.

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SLDs have similar device structures to that of edge-emitting laser diodes based on ridge waveguide designs. The main difference between them is the careful suppression of feedback needed in SLDs to prevent resonance inside the gain medium, which would otherwise result in high coherence. This is done by breaking the optical cavity by using a tilted output facet57, a bent76,77, tilted24,78, or tapered waveguide design71, an active absorbing section (reverse biased)51, a passive absorbing section50,79, or by intentionally making one of the facets rough63.

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OCT technology can be further enhanced by incorporating fluorescence, absorbance, or Raman spectroscopy/imaging systems, which allow for precisely identifying biochemical composition169. Both excitations for OCT and spectroscopy are usually coupled in the same optical path to illuminate the specimen and the OCT and spectral signals will be detected for analysis170,171. However, laser-induced fluorescence is opted to cause photodamage for biological tissue during diagnosis. Therefore, low-coherent semiconductor light sources can be used for enhanced imaging and microscopy. Jechow et al. measured two-photon excited fluorescence (TPEF) from fluorescent markers excited by SLD thermal light43, which only requires 30-μW power to trigger the TPEF. Other than that, with broadband emission, SLDs are also widely used in ghost spectroscopy172 and absorption spectroscopy for multiple gas sensing173,174.

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