1. Introduction

The unique photonic band gap of photonic crystals prevents the propagation of light at certain wavelengths within the crystal and allows the confinement of photons through the near-zero velocity of the band edge group or through the design of defects. Due to their distinct optical properties related to the photonic bandgap and band edge, photonic crystals have been widely employed in micro-laser systems. Photonic crystal lasers are typically fabricated using semiconductor materials [1–5]; however, the manufacturing process often involves complex and time-consuming procedures. Cholesteric liquid crystals (CLCs) are self-assembling photonic crystals [6] that can be easily formed by incorporating chiral dopants into nematic liquid crystals and injecting them into a properly confined space. Compared to photonic crystal lasers fabricated from semiconductor materials, the fabrication process of CLC lasers is relatively simple, and they exhibit greater tunability, allowing control of the photonic bandgap position by electrical [7,8], thermal [9–12], mechanical [13,14], or photoinduced [15,16] methods, thereby controlling the emission wavelength of the laser. Moreover, CLC is a selective photonic crystal that exhibits photonic band gaps only for specific circular polarization states. This unique property causes the laser emission from CLC-based lasers to be circularly polarized, which is difficult to achieve with semiconductor-based lasers.

Unlike band-edge lasers, which confine photons to the edges of the photonic bandgap to produce laser emission, defect mode lasers [17–25] introduce defects by perturbing the continuity of CLCs. This creates resonant modes that allow certain frequencies of light to propagate, even within the photonic bandgap, forming one or more localized leaky modes. There are three main types of methods to create discontinuous defects in CLC: Layer defects [17–20]: Adding a layer of another material inside the CLC to break the continuity of the LC; Pitch jumping [21,22]: Changing the pitch of specific regions of the CLC to create discontinuities; and Phase jumping [23,24]: Creating dislocation angles of the liquid crystal molecules at specific locations to break the continuity of the CLC.

Bandedge lasers exhibit a higher laser threshold and only emits circular polarized light with the same chirality as its structure. In contrast, defect mode lasers have a lower threshold [18] and exhibit unique polarization characteristics. Schmidtke et al. have observed that a defect mode laser emits circularly polarized light opposite to the CLC structure [24]. Kopp et al. published calculations on the correlation between the polarization states of defect mode resonance peaks and CLC thickness [26]. Their calculations employed phase-jump CLC defect structures and showed that the thickness of the CLC strongly affects the polarization state of the defect mode resonance peaks. As the thickness increases, the defect resonance peak changes from a transmission peak with the same circular polarization as the CLC structure to a reflection peak with the opposite circular polarization. This calculation result offers the possibility of chirality control for defect mode lasers by adjusting the CLC thickness to change the polarization state of the light coupled into the defect resonance peaks.

The purpose of this study is to investigate the feasibility of controlling the chirality of emitted lasers in defect-mode lasers fabricated with layered defects, which are different from the phase-jump defect structures presented in Refs. [24,26]. We compare and analyze the discrepancies between layered defects and phase jump defects from the experimental and calculated results. We also discuss the effect of the thickness and refractive index of the defect layer in a defect mode laser on the emission wavelength and mode number [27]. Based on the combined control of emission chirality, wavelength, and mode number, it can contribute to a wider range of possibilities in the field of multifunctional laser light sources.

2. Experimental and computational methods

2.1 Fabrication of a CLC polymer film on a single substrate for use as a chiral mirror

First, two glass substrates are coated with 0.2 wt% of the photoalignment material Brilliant Yellow (BY, purchased from Acros Organics B.V.B.A.) dissolved in N-methylpyrrolidone (NMP) solvent using spin coating, followed by hard baking at 125°C for 30 minutes. Next, the two glass substrates are assembled with their photoalignment layers facing each other to form an empty cell, with the cell gap controlled by spherical spacers in between. The empty cell is then exposed to a 457 nm linearly polarized laser for photoalignment, making the alignment layer's director axis perpendicular to the linear polarization direction. Subsequently, a CLC mixture with a reflection center wavelength of approximately 590 nm is prepared by mixing polymer liquid crystal HRM1001-002 (purchased from HCCH), chiral dopant R5011/S5011 (purchased from HCCH), and 0.1 wt% photoinitiator Irg 651 (purchased from Acros Organics B.V.B.A.), and is injected into the empty cell via capillary action. By heating and annealing the substrate, the CLCs are arranged into an ordered planar state and then exposed to UV light to polymerize into a CLC polymer film. Finally, the liquid crystal cell is immersed in water and the substrate can be peeled off relatively easily due to the hydrolytic nature of the BY layer. Careful peeling of one side of the substrate yields a CLC polymer film on a single substrate, which can be used as a chiral mirror required for the fabrication of chiral DBR lasers with defect modes.

2.2 Fabrication of a defect-mode chiral DBR laser with a dye-doped defect layer

The schematic diagram of the defect-mode chiral DBR laser structure is shown in Fig. 1(a). First, we measured the transmission spectrum of the single-substrate CLC polymer film fabricated in Section 2.1, as shown in Fig. 1(b), to confirm the photonic band gap in the spectrum. Next, two CLC polymer films with matching bandgaps were stacked, with 12 µm spherical spacers placed between the films. Due to the elasticity and uneven surface of the CLC polymer films, the spacers could only ensure the separation of the polymer films, but not an accurate gap distance. Therefore, we did not precisely control the thickness of the intermediate layer in this study.

 

Fig. 1. (a) Schematic diagram of chiral DBR laser composed of two layers of CLC chiral mirrors and a middle dye layer. The pitch of CLC is P, the thickness of the chiral reflective mirror is D, and the number of chiral mirror layers in the entire device is N. Therefore, the thickness of a single layer of chiral mirror film is D = N × P/2. (b) Transmittance spectrum of the prepared CLC chiral reflective mirror film, with the yellow region indicating the photonic bandgap (PBG). Insert: POM image of the chiral reflective mirror. (c) The gray line represents the transmittance spectrum of the two reflective mirrors stacked together, and the orange line represents the transmittance spectrum after the injection of isotropic material containing laser dye.

Download Full Size | PDF

We mixed 0.1 wt% of laser dye Pyrromethene597 (PM597, purchased from Toagosei Co., Ltd.) with CB15 (purchased from HCCH), an isotropic material in liquid state at room temperature to create an isotropic medium. The refractive index of CB15 (n = 1.59) closely matches the average refractive index of the liquid crystal used in our study ((n_e + n_o) / 2), which helps to reduce interface reflections between the middle layer and the CLC film. Using capillary action, we injected the medium into the gap between the CLC films in the liquid crystal cell to form a defect-mode chiral DBR laser with a dye-doped defect layer. The transmission spectra before and after injecting the isotropic material are shown in Fig. 1(c). We carefully examined the reflection bandgap state after completion to ensure the quality of the chiral DBR laser.

2.3 Experimental setup for measurements

The experimental setup for laser measurements is shown in Fig. 2. A 532 nm, 20 ns pulsed laser (Surelite, Continuum Electro-Optics, Inc.) with a repetition rate of 5 Hz was used as the pump light source. The intensity of the pump light was controlled using a half-wave plate (HWP) and a high-power polarizer (P). The pump beam was focused to a 50-µm-diameter spot on the sample. A filter behind the sample was used to filter out the 532 nm pump light. Finally, a spectrometer was used to measure the intensity and spectrum of the emitted laser. A left or right circular polarization plate (CPL) was placed in front of the spectrometer to detect different circular polarization ratios of the emitted laser.

 

Fig. 2. Experimental setup for measuring the threshold and output polarization state of the chiral DBR laser.

Download Full Size | PDF

2.4 Calculation method and parameters

We employed the Berreman 4 × 4 matrix method [28] to calculate defect-mode chiral DBR lasers with dye-doped defect layers. We separately calculated R-CLC and L-CLC structures with different pitch numbers N . The parameters used for the calculations were liquid crystal n_e = 1.65, n_o = 1.51, and P = 373.4 nm, which positioned the center of the bandgap at 590 nm. The refractive index of the defect layer was n = 1.59, and its thickness d_dye was 12 µm. We calculated the transmission and reflection rates of the right-circular and left-circular polarizations at the peak of the defect mode resonance. The effects of different defect layer thicknesses were also calculated with the same parameters as above, except that N was fixed at 20 and the calculated thicknesses were d_dye = 2 µm, 4 µm, and 12 µm, respectively. In addition, to verify that the circular polarization of the emitted laser is determined by the number of layers N or the thickness of the CLC layer, we calculated the results for R-CLC with a pitch of P = 873.4 nm and N = 20 for comparison.

3. Results and discussions

3.1 Chirality control of the emitted chiral DBR laser

First, we fabricated both left- and right-handed single substrate CLC polymer films with various numbers of periods (defined as half of the pitch), N = 26, 40, and 64, corresponding to different thicknesses of 5 µm, 7.5 µm, and 12 µm, respectively. We then fabricated chiral DBR lasers with these different conditions of chiral mirrors and measured the different circular polarization ratios of the emitted lasers as shown in Fig. 3. The blue line represents the right circular polarization intensity, while the red line represents the left circular polarization intensity. At N = 26, the emitted laser is almost the same chirality as the CLC structure. The right and left circularly polarized laser emission can be observed in right and left handed CLC, respectively. On the other hand, for N = 64, the emitted laser is almost entirely opposite to the chirality of CLC structure. The left and right circularly polarized laser emission can be observed in right and left handed CLC, respectively. For N = 40, the left and right circularly polarized laser emissions have almost the same intensity in the two samples with different chirality. From these results, we found that when the N value is small, the circular polarization of the emitted laser is the same as the helicity of the CLC structure. The mode numbers and wavelengths of the emitted lasers vary slightly between different samples due to differences in the thickness of the defect layer which will be discussed later.

 

Fig. 3. (a) The polarization-resolved spectra of the laser emission at N = 26. (b) The polarization-resolved spectra of the laser emission at N = 40. (c) The polarization-resolved spectra of the laser emission at N = 64.

Download Full Size | PDF

The polarization inversion of the laser emission above a certain number of periods (N) can be understood as follows. Since the chiral Bragg mirrors only reflect the light of the same handedness as its structure, only the same-handedness light is confined and amplified in the defect, which determines the lasing polarization in the defect. However, once light departs from the defect propagating in the mirror, the polarization is subject to change depending on N. When N is much lower than the so-called crossover number (N_co), the lasing polarization is nearly unchanged throughout the mirror thickness. As N increases, a transformation of the laser polarization during light propagation in the mirror gradually becomes noticeable, from circular to elliptical, for N < N_co. The output polarization becomes linear at N = N_co. Beyond N_co, the handedness of the output polarization is inversed.

3.2 Calculations

We have calculated the transmittance and reflectance of RCP and LCP for a stacked sample consisting of two CLC polymer film layers of different periods separated by a defect layer, as shown in Fig. 4(a). The calculations were performed for N = 26, 40, and 64, which correspond to the thicknesses of the individual CLC film layers of 5 µm, 7.5 µm, and 12 µm, respectively. The thickness of the defect layer is set to 12 µm, and the corresponding calculated defect mode wavelengths are as shown in Fig. 4(b). The calculated results were compared with experimental data obtained from chiral DBR laser in R-CLC structure. Here we define the g-factor as (I_LCP – I_RCP)/(I_LCP+ I_RCP) to represent the circular polarization tendency of the emitted laser. A g-factor close to 1 indicates a preference for LCP, while a g-factor close to –1 indicates a preference for RCP. The relationship between N and the g-factor for R-CLC and L-CLC is also shown in Fig. 4(a). When N < 20, the transmittance of RCP (red dashed line) is close to 1, while the reflectance of LCP (black dashed line) is close to 0. As N increases, the transmittance of RCP gradually decreases to 0, and the reflectance of LCP gradually increases to 1. This represents the transition from RCP transmittance to LCP reflectance in the proportion coupled to the resonance peak. During this gradual transition, there is a pitch number N where the transmittance of RCP and the reflectance of LCP are both 0.5, called the crossover number (N_co), which is calculated to be 42. A crossover number can correspond to a crossover thickness (L_co) of the CLC. From the experimental results, when N = 26, g = –0.97; when N = 40, g = –0.01; and when N = 64, g = 0.90 which agrees well with the theoretical calculations. The error in the g-factor is due to the uniformity of the sample thickness control. For L-CLC structures, the relationship between g-factor and N is almost opposite.

 

Fig. 4. (a)The transmittance/reflectance ratios of chiral DBR lasers and g-factor at different pitch numbers N. (b) The calculated transmission spectra with different intermediate layer thicknesses of d_dye = 2 µm, 4 µm and 12 µm. (c) The measured laser threshold with N values of 26, 40, and 64.

Download Full Size | PDF

This result shows a similar trend to the phase jump defect mode CLC calculations by Kopp et al. [26]. They use scattering and transfer matrix methods [29,30] to calculate the energy density inside a R-CLC structure and to decompose that density into components of different circular polarization and propagation direction. The analysis reveals that when the thickness is much smaller than the crossover thickness (L << L_co), the circularly polarized wave with the same handedness as the structure (RCP in this case) excites the localized mode, while the orthogonal wave (LCP) cannot excite it. At the crossover thickness (L = L_co), the localized mode is most efficiently excited by a linearly polarized wave, while the perpendicularly polarized wave cannot excite it. When the thickness is much larger than the crossover thickness (L >> L_co), the wave coupling to the localized state has the circular polarization opposite to the handedness of the structure (LCP in this case), while the orthogonal wave (RCP) cannot excite the localized mode. Furthermore, the transmittance of RCP waves and the reflectance of LCP waves can only be formed through the excitation of localized states. Therefore, the transmittance of RCP waves is the coupling coefficient between RCP waves and localized states, and the reflectance of LCP waves is the same. Thus, the sum of the corresponding coupling coefficients for energy is equal to 1 at any CLC thickness. In Fig. 4(a), it can also be seen that the sum of RCP transmittance and LCP reflectance is equal to 1. The same calculation was applied to the L-CLC structure, and the result is the exact opposite: as N increases, the dominance of the resonance peak gradually transitions from the LCP transmittance to the RCP reflectance.

We calculated the effects of different intermediate layer thicknesses for d_dye = 2 µm, 4 µm, and 12 µm, with a pitch number of N = 20, as shown in Fig. 4(b). The results show that the intermediate layer thickness directly affects the number and wavelength of high-transmittance defect modes, similar to the effect of a Fabry-Pérot resonator. Therefore, the actual thickness of the intermediate defect layer can be inferred from the wavelength of the emitted laser and the spacing between adjacent laser wavelengths. In addition, to investigate whether the circular polarization of the emitted laser is determined by the pitch number N or the CLC layer thickness, we calculated the results for R-CLC with a pitch P = 873 nm and N = 20. Under these conditions, the CLCs thickness is 17.46 µm, which is approximately the same as the calculated thickness for P = 373 nm and N = 46. The calculation results show that the transmitted light in the defect mode is almost completely right-circularly polarized, with no left-circularly polarized component. This confirms that the polarization characteristics of the emitted light are affected by the CLC pitch number N rather than the CLC layer thickness.

3.3 Threshold

We measured the laser threshold of the defect mode chiral DBR laser as shown in Fig. 4(c). The laser threshold is determined by monitoring the output intensity as a function of the pump intensity. In the case of multiple peaks, the output intensity of the highest peak is used. The laser threshold is identified when the slope of the graph shows a significant increase, indicating the occurrence of lasing. It can be seen that the laser threshold increases with increasing N. Since the pitch of the CLC is fixed, the increase in N is proportional to the increase in CLC thickness. The threshold properties of dye-doped CLC lasers have been extensively studied by Cao et al. [31]. They reported that below 15 µm, an increase in thickness causes the threshold to decrease. But for thickness above 15 µm, the threshold increases with increasing thickness due to absorption loss and cavity loss. In our study, the threshold did not decrease with increasing thickness in the range of N from 26 to 40 (thickness of the CLC bilayer is approximately 15 µm). This could be attributed to the difference between our system and the dye-doped CLC system, as our CLC serves only as a reflector, with N = 26 providing sufficient reflectivity. If the N were to be further reduced, resulting in a decrease in reflectance, the threshold would be expected to increase accordingly. In addition, the intermediate layer that serves as a gain medium (at least 10 µm thick) contributes to the overall thickness difference, which may also affect the relationship between threshold and thickness. The thickness and concentration of the laser dye can also affect the laser threshold due to different gain coefficients. These effects can be explored in further research and applications.

3.4 Cone-shaped emission

During the measurement of the chiral DBR laser, we discovered that in addition to the central laser emission along the direction of the helical axis of the CLC, there is also a concentric circular pattern of cone-shaped emission, as shown in Fig. 5(a). The transmission spectrum of the sample, the central laser emission spectrum, and the cone-shaped emission spectra at different angles are recorded in Fig. 5(b). Folcia et al. have investigated the physical mechanisms of various cone-shaped laser emissions [32]. The concentric circular pattern of cone-shaped emission in our research should be caused by the energy leakage of the central laser emission. The physical mechanism is light scattering, and its angular dependence is due to the photonic crystal structure, which results in significant differences in transmittance at different angles. CLC is an arrangement of liquid crystal molecules in a helical structure, so its refractive index distribution is also similar to a one-dimensional photonic crystal structure. The band gap of CLC changes with the incident angle θ, and as θ increases, the band gap exhibits a blue shift. As θ increases to 18 degrees, the long wavelength edge of the CLC bandgap (614 nm) multiplied by cos18° equals the wavelength of the center laser emission (585 nm). At this point, the scattering of the center laser emission can leak out at this angle, resulting in an annular light spot, cone 1, emitted at 18°. Cone 2 and cone 3 should also correspond to the sideband oscillations outside the photonic bandgap.

 

Fig. 5. (a) Photograph of the cone-shaped beam laser. (b) Transmittance spectra of the sample and cone-shaped beam laser spectra at different angles.

Download Full Size | PDF

3.5 Implications and potential applications

We have verified that the chirality and pitch number N of the CLC structure can control the ratio of different circularly polarized emissions in the chiral DBR laser. We have also observed the effect of the defect layer thickness on the laser mode number and wavelength. In terms of next-step applications, spatially gradient chiral mirrors can be fabricated using methods such as wedge cells [20], enabling the creation of defect mode chiral DBR lasers in which the polarization state of the emission can be spatially selected. In addition to the adjustable ratio of circular polarizations, if the phase difference between the two circularly polarized laser emissions can be altered by designing chiral mirrors or defect layers, a greater variety of output laser polarizations can be achieved (such as linear polarizations at different angles or elliptical polarizations). With the addition of wavelength control or the realization of multi-wavelength lasers, there is a promising outlook for the development of versatile micro-laser sources.

4. Conclusions

In summary, this study demonstrates the ability to control the polarization states of layered defect chiral DBR lasers through the selection of different pitch numbers of the chiral mirror. In the computational simulations, we employed Berreman matrix numerical methods to calculate the left and right circular polarization components resonating in the defect mode under different CLC layer numbers, as well as the influence of the intermediate defect layer thickness on the emitted mode numbers and wavelengths. In the experiments, we fabricated chiral reflectors with different period numbers N and measured the left and right circular polarization ratios emitted in chiral DBR lasers. We successfully produced defect-mode laser devices with circular polarizations identical, opposite, and equal in amount to the CLC structure. Furthermore, we confirmed that N not only influenced the emitted light's polarization but also increased the laser threshold as the thickness increased. Additionally, we observed and validated conical emission leaking at an oblique angle from the long wavelength edge of the defect mode's forward laser. Apart from realizing tunable polarization states in layered defect chiral DBR lasers, future potential applications may involve fabricating chiral reflectors with gradient thickness using wedge cells or chiral reflectors with different N values on two surfaces, enabling spatially selectable emitted light polarization states or bidirectional asymmetric laser components. This research offers immense potential for the development of diverse micro-laser device components.