A Miniaturized Wide-stopband Wide-passband Cavity Filter with Two Asymmetric Stepped Probes

Introduction Higher-order modes of optical beams have been the subject of many studies over the past 20 years [1, 2]. Because laser resonators deliver in principle quite complex spatial patterns, spatial modes of beams were studied intensively when lasers were first developed [3]. Beams in higher-order spatial modes are solutions of the paraxial wave equation, with Hermite-Gauss and Laguerre-Gauss beams being the most important families of beams. These are solutions of the wave equation in Cartesian and cylindrical coordinates, respectively. The latter beams have been at the heart of a revival of research on higher-order modes due to the orbital angular momentum that they carry [4]. They have also received much attention due to the phase singularities present in their transverse amplitude [5]. Higher-order modes have stimulated much research in the application of forces and torques to objects in optical tweezers [1, 2]. Their usefulness has carried higher-order spatial modes further into new paths, in studies with non-classical sources of light and applications in quantum information [6]. The beams mentioned above are scalar solutions of the wave equation and thus independent of the polarization of the light. Vector beams are formed by the non-separable combinations of spatial and polarization modes. This enhanced modal space produces an interesting set of beams that offer new effects and applications. The origin of these beams is not recent either, as the possibility of combining higher-order spatial modes and polarization started with those early studies of modes as well.

In order to suppress the higher order modes and improve beam quality in high power waveguide laser, based on gainguided index-antiguided theory, a new symmetric layered waveguide structure is designed, and an interval layer is proposed to be sandwiched between waveguide layer and cladding layer in traditional symmetric GG-IAG waveguide structure. As a result, while reducing the leakage loss of fundamental mode, the threshold gain coefficient differences between fundamental mode and higher order modes will be further increased. When the gain in waveguide layer is between threshold gain coefficient of fundamental mode and that of higher order mode, the fundamental mode will have a greater advantage in mode competition than others, so higher order modes can be suppressed and the laser can obtain a single mode output. In the meantime, the guided-mode principle of this waveguide structure is explained with the theory of wave optics in this paper, the eigen equation of each mode is derived from the wave equation, and the field distributions of fundamental mode and higher order mode are also given. Additionally, in this paper we give the solution process of the threshold gain coefficient of each mode in this waveguide structure. The mode leakage losses of fundamental mode and higher order mode, after adding the interval layer, are numerically calculated, and the parameter optimization process of the interval layer is also given in this paper. In addition, the field distributions of fundamental mode and higher order mode are numerically simulated. The calculation results show that comparing with the traditional symmetric GG-IAG planar waveguide, after adding the interval layer, the loss of fundamental mode can be greatly reduced, while ensuring that the leakage loss of higher order mode reaches a maximum value by reasonably controlling the parameters of interval layer. In this way, we can suppress higher order modes and improve laser efficiency. This paper provides a new idea for improving the beam quality of high power waveguide laser with a large mode area.

Suppression of higher-order modes in a large-optical-cavity waveguide structure for high-power high-efficiency 976-nm diode lasers

A complete theoretical model on the stimulated Brillouin scattering (SBS) for multi-mode fibers (MMF) is developed by solving the optical-acoustic coupling wave equations. It shows that all optical modes of the signal and of SBS are coupling each other through proper acoustic waves. The Brillouin gain spectrum of each optical mode pair is obtained by certain three-wave couplings (optical-acoustic-optical). The model is further coupled with an optical amplification model on the fiber lasers to take the mode competition into account. By applying the model to a large mode-area double cladding fiber, it is found that the multi-acoustic mode combination plays an important role in the SBS coupling between optical higher order modes (HOM). While for double-mode (fundamental mode +HOM) performance, the SBS threshold increases gradually along with the increase of HOM content. It is also found that the SBS process in the fiber amplifiers can be completely different comparing with that of the passive fiber, because the mode competition not only changes the mode contents of the signal power but also influences the initial growth rate of SBS noise. The Al/Ge co-doped MMF is investigated theoretically as well, and is shown to be able to suppress SBS significantly. Finally we compare our model with a SBS experiment for a MMF, main theoretical predictions agree with the experiment well.

A theoretical investigation of the static and dynamic behaviour of an optically injected multitransverse mode vertical-cavity surface-emitting laser is performed. Selection of the fundamental transverse mode is induced by injecting light with a polarization that is parallel to the one of the fundamental mode. We analyze two different situations. The first one corresponds to operation in the fundamental and first higher-order transverse modes. Selection of the fundamental mode is achieved when the polarization of both transverse modes is parallel or orthogonal. The second situation corresponds to operation in more than two transverse modes. Selection of the fundamental mode is obtained when the higher order modes are orthogonally polarized to the fundamental mode. The injected power required for that selection is much higher than in the two-mode operation. That selection is not obtained when the higher order modes are parallel to the fundamental mode. A rich variety of nonlinear dynamics have been found out of the stable locking operation. A regime where the fundamental and first higher order mode evolve in a chaotic way is found for small positive detunings and small injection powers.

Random fiber lasers are of tremendous interest to diverse applications for optical fiber sensing, speckle-free imaging. To date, random fiber lasers with fundamental mode oscillation have been well developed. However, controllable oscillating spatial mode in random fiber lasers have not been reported yet. Here, we propose and demonstrate a few-mode random fiber laser with a switchable oscillating spatial mode based on mode injection locking. An external signal light is injected to realize the locking of transverse mode in this random fiber laser and the direct oscillations of the fundamental mode, hybrid mode, and high order mode can be realized, respectively. This random fiber laser operates in the high-order LP11 mode stably with a threshold of as low as 88 mW. High efficiency and high purity cylindrical vector beams can be obtained by removing the degeneracy of the LP11 mode. This work may pave a path towards random fiber lasers with controllable spatial modes for specific applications in mode division multiplexing, imaging, and laser material processing.

A discussion of the transverse electromagnetic modes in single and double heterojunction lasers is presented. Three basic structures are analyzed: a laser with single heterojunction and optical cavity defined by the (p+-p) heterojunction and p-n junction; a double heterojunction laser with the second heterojunction at the p-n junction; and another double heterojunction unit which can have a large range of optical cavities because the second heterojunction is in the n region spaced a controlled distance from the p-n junction. Since the dielectric discontinuity at a heterojunction is an order of magnitude larger than at a p-n junction, these double heterojunction lasers can have high-order transverse modes. To model the observed radiation fields and, in particular, the preference for high-order modes, the optical properties of the junction region are treated as a five-layer dielectric slab. The two outer regions are bulk p+ and n+ (AlGa)As in the double heterojunction structures and p+(AlGa)As and n+ GaAs in the single heterojunction structures. The section between the p+ heterojunction and the p-n junction, which is customarily treated as the active section of the laser, has here been partitioned into two regions: a gain region adjacent to the p-n junction where recombination occurs and a lower gain region adjacent to the p-p+ heterojunction. In fact the latter region may be absorbing. The width of the first gain region is associated with the electron diffusion length in heavily doped p-type GaAs. For a suitable partition the modal gain of the high-order modes becomes larger than for the low-order modes, resulting in the highest mode reaching threshold first. In contrast, were the region between the n-p junction and the p-p+ heterojunction uniformly inverted, the laser would operate in the fundamental mode, contrary to experimental observation. Machine calculations indicate that structures radiating high-order modes have a gain region narrower than 1 μm.

Replica symmetry breaking (RSB), as a distinctive phase transition occurring between the paramagnetic and spin glass states in magnetic systems, has been anticipated and validated in diverse complex systems. Random fiber lasers with intrinsic disorder feedback have proved to exhibit diverse RSB behaviors. To date, significant attention has been mainly focused on RSB phenomena in random fiber lasers that involve only the fundamental optical mode in optical fibers. In this paper, we propose and demonstrate the RSB observation and its transient dynamics of a high-order mode (HOM) random fiber laser based on Brillouin scattering and distributed Rayleigh scattering in a few-mode fibers, for the first time, to the best of our knowledge. In this photonic system, the disorderness is not only provided by randomly distributed Rayleigh scattering and the active interplays among multiple orders of Stokes components but also by additional inter-modal couplings. Ultimately, diverse laser mode landscapes featured by unique random mode densities of the first-order Stokes emission can be aroused, accompanied by optically controlled RSB dynamics. The statistics evidentially show that Parisi’s order parameter q of the first-order HOM Stokes laser beam presents distinct distributions as per specific observation windows. Moreover, RSB dynamics in the proposed disorder system show a prominent dependence on the occurrence of multiple-order Stokes components and the mode purity of the HOM laser beams. It is believed that this approach offers new insight into exploring the underlying physical mechanisms behind the occurrence of the RSB phenomenon in photonic complex systems.

Mirror thermal noise will be a main limitation for the sensitivities of the next-generation ground-based gravitational-wave detectors (Einstein Telescope and Cosmic Explorer) at signal frequencies around 100Hz. Using a higher-order spatial laser mode instead of the fundamental mode is one proposed method to further mitigate mirror thermal noise. In the current detectors, quantum noise is successfully reduced by the injection of squeezed vacuum states. The operation in a higher-order mode would then require the efficient generation of squeezed vacuum states in this mode to maintain a high quantum noise reduction. In our setup, we generate continuous-wave squeezed states at a wavelength of 1064nm in the fundamental and three higher-order Hermite-Gaussian modes up to a mode order of 6 using a type-I optical parametric amplifier. We present a significant milestone with a quantum noise reduction of up to 10dB at a measurement frequency of 4MHz in the higher-order modes and pave the way for their usage in future gravitational-wave detectors as well as in other quantum noise limited experiments.

We investigate chirality of light in the quasicircularly polarized fundamental HE11 mode and thequasicircularly polarized higher-order hybrid modes of vacuum-clad ultrathin optical fibers. Weshow that, for a given fiber with the parameters in the range of experimental interest, the higherorder modes have smaller optical chirality per unit energy than the fundamental mode. The sign ofthe chirality per unit energy of a HE or EH mode is the same as or opposite to, respectively, thesign of the phase circulation direction. Outside the fiber, the fields in the quasicircularly polarizedHE11 mode and the quasicircularly polarized higher-order HE21 and HE31 modes are superchiral.

In continuous-wave cavity ring-down spectroscopy (CW-CRDS), the measurement sensitivity is seriously affected by the multimode excitations in the ring-down cavity. The using of an intracavity aperture is a common way to restrain the excitation of high-order modes, thus leading the laser power to additionally lose and the signal-to-noise ratio to degrade. In this paper, two numerical methods, named “trigger threshold method” and “curve fitness method”, are proposed for selecting the mode in which the decays excited by the high-order modes can be removed. The laser coupling efficiency between the incident laser and the oscillating fundamental or high-order modes is studied in a misadjusted ring-down cavity. It is found that with a misadjusted ring-down cavity, the laser energy is partially coupled into the high-order modes, and the coupling energy increases with the extent of the cavity misadjustment increasing. In this case, the ring-down decaying traces excited by these high-order modes are different from and much shorter than those excited by the fundamental mode, which are respectively called “bad decays” and “good decays” in this paper. Both the fundamental mode and the high-order modes can reach the threshold in the case of low triggering threshold selection and result in the components of both good and bad decays in the output ring-down curves. When the trigger threshold rises, the bad decays are effectively restrained by the deficient coupling into the high-order modes. Thus raising the trigger threshold is an effective method to restrain bad decays for the mode selection. Another approach is to consider the time spent on turning off the laser injection since the fitting goodness of good decays is better than that of bad decays. In this paper this characteristic is also used to separate the good decays from the bad ones. These two methods are demonstrated in the CW-CRDS experiments. The results show that the sensitivity of the CW-CRDS instrument can be greatly improved by one order of magnitude in the trigger threshold method with the minimum of Allan deviations gradually approaching to a constant, while the acquisition rate of the ring-down decays slows down with the increase of the trigger threshold. The results also explain the relationship between single sampling and averaged sampling, which presents an answer to the question about the sequence choice between averaging and fitting. A numerical model is proposed to estimate the probability of good decays versus the trigger threshold, which can be used to choose appropriate trigger threshold for CW-CRDS experiment. The applicable conditions and the limitations of these two methods in CW-CRDS for trace gas detection are also discussed in the paper.

Transverse mode characteristics of a laser are related to a variety of interesting applications. An on-demand mode solid laser in the 1064 nm band was proposed previously. In this paper, we provide a fiber laser for on-demand modes in the 1550 nm band to prescribe the pure and high-quality emission of a higher-order transverse laser mode, based on a simple construction with one spatial light modulator (SLM) and a single-mode erbium-doped fiber (SM-EDF). The SLM is designated to generate the desired higher-order mode and separate the higher-order mode and the fundamental mode. The fundamental mode oscillates in the fiber ring laser, and therefore the SM-EDF can be pumped with a single-mode 980 nm laser, no matter what higher-order mode is prescribed. In this proof-of-principle experiment, high-quality higher-order modes are observed from LP01 to LP105. Stable emission and real-time switching between modes can be easily realized by altering the phase on the SLM. In addition, the propagation of the LP01, LP11, LP21, and LP02 modes from the fiber laser is also demonstrated in a four-mode few-mode fiber.

This Letter derives explicit factors linking mode-mismatch-induced power losses in Hermite-Gauss optical modes to the losses of the fundamental spatial mode. Higher-order modes are found to be more sensitive to beam parameter mismatches. This is particularly relevant for gravitational-wave detectors, where lasers employing higher-order optical modes have been proposed to mitigate thermal noise, and quantum-enhanced detectors are very susceptible to losses. This work should inform mode matching and squeezing requirements for Advanced+ and third generation detectors.

As a new multiplexing dimension, spatial modes are catching increasing attentions nowadays. It is a fundamental task to establish an appropriate theoretical model to describe these spatial modes, especially higher-order spatial modes. However, existing theoretical models are only able to explain some special higher-order spatial states in fiber. The basic problem in these models is that their discussed dimensions are not enough. Indeed, to describe a higher-order spatial state, at least four dimensions are needed. In this paper, we present an expanded Jones complex space model, which is four-dimensional when a single higher-order state is discussed. The expanded Jones model is based on the discussion of an arbitrary combination of four degenerated higher-order modes. As a result, arbitrary spatial states are described. Because the number of used dimensions matches that of the problem, the descriptions of higher-order modes are more complete than other models. Also, we have verified the reliability of the expanded Jones model in our experiment. This model has the potential to simplify many analyses related to spatial modes in fiber.

The paper study on the effect of index distribution on the mode field and calculated the mode distribution in various index profiles. A single mode gaussian hybrid multicore fiber with 19 hexagonally arranged high index quartz rods is designed and investigated. Theoretical and simulative results are presented and compared to the conventional large mode area double clad fiber, the fundamental mode (FM) area can be reached 694.28 μm 2 , the confinement loss of FM and high order modes (HOMs) are 0.186 dB/m and 1.48 dB/m respectively with the bending radius of 20 cm at 1.064 μm wavelength, moreover, the index distribution can resistant the mode field distortion, which caused by fiber bending. So the FM delivery can be formed and the beam quality can be improved.