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This study demonstrates for the first time a continuously tunable photonic bandgap (PBG) of wide spectral range based on a blue phase (BP) wedge cell. A continuously shifting PBG of the BP wedge cell occurs due to the thickness gradient of the wedge cell at a fixed temperature. The wedge cell provides a gradient of boundary force on the LCs and thus forms a distribution of BP crystal structure with a gradient lattice. Additionally, a spatially tunable lasing emission based on a dye-doped BP (DDBP) wedge cell is also demonstrated. The tunable band of the PBG and lasing emission is about 130 nm and 70 nm, respectively, which tuning spectral ranges are significantly wider than those of CLC and DDCLC wedge cells, respectively. Such a BP device has a significant potential in applications of tunable photonic devices and displays.
© 2014 Optical Society of America
1. Introduction
Manipulation of light emission and propagation by utilizing periodic structures of dielectric materials is a fascinating area in science research. They exhibit a high potential for considerable use in applications of photonic engineering. Such periodic structures exhibit specific photonic bandgaps (PBGs), in which the photons are prohibited from propagating, analogous to electrons in solid crystal [1]. PBG materials, the so-called photonic crystals (PCs), have attracted wide interest because of their wide applicability in optoelectronic and microwave devices [2]. In particular, emission tuning and lasing action in optically active PCs can provide new applications for ultra-small low-threshold lasers [3–5]. Liquid crystals (LCs) with chirality, such as cholesteric liquid crystal (CLC) [6–8], chiral smectic liquid crystal (Sm*LC) [9–11], and blue phase (BP) [12–20] are novel materials used in the development of PCs because of their inherently self-assemble periodic structure and high flexibility in external tunability in the PBG structure.
Blue phase, a mesophase between isotropic and CLC phases, has attracted significant attention in the fields of optoelectronics and photonics because of their advantages, such as fast electrooptic response, no need of surface alignment, viewing-angle independence, and a high potential for use in display and photonics [12–15]. BPs generally have self-assembly 3D periodic structures composed of double-twisted cylinders (DTCs) and disclinations between adjacent DTCs. By virtue of the crystal periodicity on the scale of several hundred nanometers and specific charity for a BP structure, the BP has a PBG for the visible light of a circular polarization with a handedness that is the same as that of the helix of the DTCs [12, 13]. Since the PBG of the BP PC is sensitive to external stimuli, such as change in temperature [14, 15] and exertion of an electric [15–17] or optical field [18–20], BPs are promising for the fabrication of tunable reflectors or filters [14–20] and tunable lasers [21–25].
Etchegoin first proposed the concept of thermally tunable PBG based on a BP [14]. Heppke et al. investigated the electrically tunable lattice constant and thus the PBG of BP [16, 17]. In addition to temperature and electric field, optical field is also employed to control the PBG of BP with doping photosensitive materials [18–20]. Despite of the wide tunable range, the stability and the response time of the doped photosensitive materials still need to be improved for the further applications. The investigations for the tuning of PBG in BP systems have been further exploited in applications of tunable BP lasers. In 2012, Mazzulla et al. demonstrated an electrically and thermally tunable dye-doped BP (DDBP) laser for the first time. The tuning range of the lasing wavelength, however, is only around 20 nm because of the inherent limitation in the property of the employed BP material [23]. A thermally tunable DDBP laser composed of two DDBP cells with a wide tunable composited band (about 115 nm) was developed by Hur et al [24]. But the laser takes a long response time (tens of seconds to several minutes) in tuning lasing wavelength because the tuning rate of the temperature is as slow as 1 °C/min. Spatial tuning method is superior to the above-mentioned methods because of its multiple advantages, such as a high stability due to the invariance of the resonant structure during spatial tuning, time-saving and wide spectral tunability, simultaneous multi-wavelength lasing output, and prevention of irreversibility probably occurred using other tuning methods. Past studies in spatially tunable laser primarily exploited DDCLC samples by creating a pitch gradient formed with a gradient of temperature [26], of concentration of chiral dopant [27–29] or an azo-chiral dopant under an intensity-gradient UV irradiation [30], and based on a wedge cell [31]. Considering issues of reliability, fabrication cost, and time, and practicability, the use of a wedge cell with a thickness gradient is most advantageous in such tuning applications. However, the spatially tunable spectral range in the PBG and lasing wavelength for a traditional DDCLC wedge cell are as narrow as only about 15 nm and 9 nm, respectively, because of the restriction caused by the surface-pinning-effect-induced quantization of the half-pitch [31].
This work demonstrates for the first time a spatially-tunable PBG of wide spectral range and lasing emission based on a BP and DDBP wedge cell, respectively. Experimental results show that the peak wavelength (λp) of the PBG and the lasing peak of the laser may be continuously tuned at best from 491.33 nm to 624.62 nm and 554.62 nm to 622.39 nm by continuously changing the pumped position of the wedge cell, respectively. Both the tunable bands of PBG and lasing peak (~133 nm and ~68 nm, respectively) are significantly broader than those based on the traditional CLC and DDCLC wedge cells, respectively (~15 nm and ~9 nm, respectively). The relatively wide tunability of the PBG and lasing emission of the DDBP device is attributable to the continuously varying gradient of the boundary force on the LCs from the gradient influence of the boundary during the formation of the BPI crystal, resulting in the gradient of the crystal lattice and thus of the PBG and the lasing wavelength.
2. Sample preparation and experimental setups
The materials exploited in this work include two kinds of nematic liquid crystal (NLC), MDA-98-1602 and LCT-09-1475 (both from Merck), a left handed chiral dopant, S811 (from Merck), and a laser dye, Pyrromethene 597 (P597, from Exciton). The helical twisting power (HTP) values of S811 in MDA-98-1602 and LCT-09-1475 are 10.8 and 11.3 μm−1, respectively. As displayed in Table 1, two prescriptions for preparations of BP and DDBP mixtures are used to fabricate BP and DDBP wedge cells, which are used in the investigations of spatial tunability in PBG and lasing peak, respectively. The BP (DDBP) mixture includes 60 wt% mixed NLC and 40 wt% S811 (61.875 wt% mixed NLC, 37.125 wt% S811, and 1.0 wt% P597). The weight ratio of MDA-98-1602 and LCT-09-1475 in the mixed NLC for either BP or DDBP mixture is 1:1. The homogeneously mixed BP (DDBP) mixture is injected into an empty wedge cell at isotropic state, and then diffused uniformly via capillary effect to form the BP (DDBP) wedge cell. The empty wedge cell is pre-fabricated by combining two cleaning glass slides with no surface alignment, separated by two narrow pieces of plastic spacers with various thicknesses of 12 and 250 μm on two sides of the cell. Both the cell temperature and cooling rate are controllable with a hot stage (TS-102V, from INSTEC). A slow cooling rate of 0.03 °C/min is used in the present experiment to obtain large BP frustrated platelets in the cell, when the cell cools down from isotropic to BP.
Table 1. Prescriptions for preparing BP and DDBP mixtures.
Figure 1 displays the experimental setup for measuring the reflection and lasing emission spectra of the BP and DDBP wedge cells at various positions. The BP or DDBP wedge cell is installed on the hot stage, which is fixed on a XYZ translation stage, and the thickness gradient of the cell is set along Y-axis. The positions on the two sides of the wedge cell with thicknesses of t = 12 and 250 μm are set as y = 0 and 30 mm, respectively. A white light is coupled into a reflective fiber (R200-7-SR, from Ocean Optics) and then illuminates normally on the wedge cell. The reflective fiber can receive the reflected light from the cell at the direction along the cell normal and a spectrometer (Jaz-Combo-2, from Ocean Optics) can record the corresponding reflection spectrum, which result reveals the PBG feature of the cell. On the other hand, one Nd-YAG pulse laser (wavelength: 532 nm, repetition rate: 1 Hz, pulse duration: 8 ns, Spectra-Physics) is used to excite the DDBP wedge cell in lasing experiment. The pumped energy (E) of the incident pulses is adjustable through the combination of a half-wave plate and a polarizer. The incident pumped pulse beam is divided into two beams with identical energy through a nonpolarizing beam splitter. One beam is focused by a lens (focal length f = 20 cm) on the cell at an included angle of 15° from the cell normal, while the other is detected by an energy meter (1916C, Newport) that measures the incident pumped energy. The spot size of the pumped beam focused on the cell is about 250 μm. The lasing output from the DDBP wedge cell can also be received with the above-mentioned fiber-based spectrometer in the direction of the cell normal. The continuous spatial-tunabilities for the PBG and lasing emission may be examined by continuously moving the detected position of the BP or the DDBP wedge cell. The continuous spatial-tunabilities for the PBG and lasing emission may be examined by continuously moving the position of the cell from y = 2.5 mm to y = 28.5 mm, in which the corresponding cell thickness continuously changes from t = 20 μm to t = 238 μm. The reflective BP images at various positions of the wedge cell can be observed under the R-POM with crossed polarizers (IX-71, Olympus).
Fig. 1 Experimental setup used in measuring the reflection and lasing emission spectra of the BP and DDBP wedge cells. Each cell is fixed on the hot stage which is pre-fixed on a XYZ translation stage. The hot stage can be moved along Y-axis to change the detected position of the wedge cell.
3. Results and discussion
The BP wedge cell is initially heated to 60 °C, which is confirmed to be higher than all transition temperatures between isotropic phase and BP (TI-BP ≅ 45 °C to 57 °C) measured at y = 2.5 mm to y = 28.5 mm of the wedge cell. At 60 °C, the entire cell appears uniformly dark when rotating under the reflection-type polarizing optical microscope (R-POM). Afterwards, the wedge cell is gradually cooled down with a cooling rate of 0.03 °C/min from isotropic state in the entire cell to a state in which a stable color-gradient BP structure with large frustrated platelets (> 100 μm) can be obtained. Figures 2(a)-2(d) show the measured reflection spectra at regions of the wedge cell with various thicknesses and corresponding R-POM images of formed BP at these regions after the cell is cooled down to 57, 56, 55, and 54 °C, respectively. After cooling to 57 °C, the wedge cell exhibits a color gradient BP structure [Fig. 2(a)], primarily in green light region from λp = 527.6 nm to λp = 568.2 nm (measured at thicker regions of t = 166 ~238 μm) while the isotropic phase retains at thinner positions of the wedge cell (t <166 μm). With decreasing the temperature from 57 °C to 54 °C, the self-formed BP structure extends gradually from thick to thin positions of the cell. As displayed in Fig. 2(b)-2(d), the wavelength in the color-gradients of the reflection band in the wedge cell distributes increasingly from λp = 522.7 nm to λp = 594.4 nm, from λp = 512.9 nm to λp = 610.4 nm, and from λp = 506.5 nm to λp = 622.6 nm (measured at regions of t = 129 ~238 μm, t = 93 ~238 μm, and t = 57 ~238 μm, respectively) after the cell is cooled to 56 °C, 55 °C, and 54 °C, respectively. Once the cell is cooled down to 53 °C, an optimum color gradient forms in the entire wedge cell, which distributes in spectrum from λp = 491.3 nm to λp = 624.6 nm measured at regions of t = 20 ~238 μm. Figures 3(a)-3(c) show the R-POM images, the images of Kossel diagrams, and the theoretical Kossel diagrams for the BP wedge cell measured at positions of t = 20 to 238 μm, respectively, at 53 °C. To identify the crystal plane of the formed BP in the wedge cell, the Kossel measurement is examined. The Kossel diagram is the reflected image of the observed BP crystal on the back focal plane of the objective lens of a reflection microscopy equipped with a monochromatic source [32]. In this work, an oil immersion lens with NA of 1.25 is employed to converge the incident light and collect the reflected light from the crystal planes. A band-pass filter with central wavelength of 488 nm is attached to the lamp of the microscope for providing monochromatic incident light. A CCD camera is equipped on the microscope to capture the reflected image of the BP crystal on the back focal plane of the oil immersion lens. Figure 3(c) further shows the theoretical Kossel diagrams from left to right observed along the viewing direction of [011] and obtained when the fitting lattice constants of the BP are 224, 230, 242, 252, 266, 274, and 282 nm in order at t = 20 μm to 238 μm. The average refractive index and the crystal plane of BPI used in the simulation are around 1.56 and (011), respectively. These lattice constants are obtained by substituting the measured wavelength of the reflection peak at various positions into the Bragg condition of normal incidence for the reflection of BP lattice planes. Each Kossel diagram shown in Fig. 3(c) is composed of one circle, four ellipses, and two straight lines. As shown in the simulated results, the central circle is the Kossel lines associated with reciprocal lattice vector (011). The four ellipses correspond to the Kossel lines of (110), (101), (–110), and (–101), and the two straight lines are obtained by (01–1) and (0–11). Apparently, the diameter of the circle increases and the four ellipses move toward the center of the circle when the lattice constant of the BP increases. The similarity between the Kossel diagrams obtained experimentally and theoretically, shown in Figs. 3(b) and 3(c), respectively, indicates that the reflection spectra measured at positions of t = 20 to 238 μm in this work resulted from the crystal plane (011) of BPI. The four ellipses and the two straight lines in the Kossel diagram images are mostly or totally not observed in our experiment because they are mostly or totally out of the viewing range of the objective employed. Figures 3(d) shows the reflection spectra of the BP wedge cell measured at positions of t = 20 to 238 μm at 53 °C. Figure 3(e) shows a linear variation of the peak wavelength of the PBG with the position of the wedge cell at 53 °C obtained based on the data shown in Fig. 3(d), and clearly indicates that the spatially tunable spectral range for the BP wedge cell can encompass almost the entire visible region (from λp = 491.33 to λp = 624.62 nm). The spatial tunability in spectral ranges for the PBG based on a BP wedge cell (about 133 nm) is significantly wider than that based on a traditional CLC wedge cell (about 15 nm) [31]. After the temperature decreases below 53 °C, the phases of the wedge cell at thicker regions begin to transit into CLC (focal conic texture) and in turn the spatially tunable spectral range of the PBG decreases. Once the temperature is lower than 45 °C, no BPG can be measured at any position of the wedge cell since the LC has became CLC phase in the entire cell.
Fig. 2 The thickness-dependent PBG features of the BP wedge cell with corresponding R-POM BP images at (a) 57 °C, (b) 56 °C, (c) 55 °C, and (d) 54 °C measured at the positions with various thicknesses in the wedge cell.
Fig. 3 The thickness-dependent PBG of the BP wedge cell at 53 °C. (a) R-POM images, Kossel diagrams obtained (b) experimentally and (c) theoretically, and (d) the corresponding reflection spectra of the BP at the positions with thickness of 20, 57, 93, 129, 166, 202, and 238 μm in the wedge cell. (e) The variations of the central reflective wavelength of the BP with the cell thickness.
Figure 4 shows the complete relations of the peak wavelength of the BP PBG with the thickness in the entire cell and temperature, which results are summarized into Table 2 for a further discussion. Apparently, some properties of the BP wedge cell such as the peak wavelength of the PBG appearing as the LC just phase-transits from isotropic phase to BP (λI-BP), the transition temperature from isotropic to BP (TI-BP), and the temperature range for the appearance of BP (ΔTBP) in the cooling process are thickness-dependent. That is, the λI-BP and TI-BP both decrease and the ΔTBP increases if the thickness decreases. The presentation of the thickness-dependent PBG gradient corresponds to the formation of a thickness-dependent lattice gradient in the self-assembly process of the BP texture in the wedge cell. The thickness-dependences in the features of λI-BP, TI-BP, and ΔTBP must be related to the boundary force originated from the boundary surfaces acting on the LC molecules during the formation of the BP crystals in the cooling process. Because the substrates of the wedge cell used herein are non-alignedly treated, this boundary force is mainly originated from the interaction (adhesion force) between the hetero-molecules of boundary surfaces and the LC molecules near the boundary. As reported in a previous literature [33], the reflection bands of the BP cell with a uniform cell gap of 12 μm and pre-coated with and with no a rubbed polyimide (PI) alignment layer have very small and large shifts in spectral position if the temperature of the BP changes, respectively. The very small variation in the reflection band of the BP with changing the temperature in the surface-aligned BP cell is attributable to the strong pinning effect, which states that the anisotropic boundary force (anchoring force) provided by the surface alignment layer is strong enough to pin the BP platelets significantly such that the lattice constant of the BP cannot change and the reflection band cannot shift with varying the temperature of the BP. On the contrary, the lattice and the reflection band of the BP of the surface-nonaligned cell cannot be pinned and, thus, changeable with varying temperature because this cell just offers a weak boundary force on the LC molecules of the BP. The results in the previous work show that the lattice feature of the formed BP crystal is strongly relevant to the boundary force. This further implies that the boundary force must play a significant factor in influencing the lattice feature during the self-assembling process of LCs from isotropic to BPI phase in the present work. Because the wedge cell has no surface alignment, the boundary force due to the hetero-interaction between the LC and the boundary molecules must be isotropic. Considering the stability of the LC system, the isotropic force from the boundary provides a global tendency for stability towards the defect-free isotropic state, while the twisting force in the LCs gives a local tendency for stability towards the double-twisting state. If the latter tendency is higher than the former, the BP can occur [13]. In the present experiment, the boundary force effectively acting on the LC molecules at thicker regions of the wedge cell is relatively weaker than those at thinner regions. The relatively weaker twisting force in the LCs at thicker regions can provide a sufficiently large local tendency to exceed the global tendency given by the weaker boundary force. Therefore, the lattice constant (or the pitch) of the BP crystal appearing once the LC just phase-transits from isotropic phase to BPI is larger and thus the λI-BP is longer at thicker regions. After transiting from isotropic state to BP, the lattice (or the pitch) of the formed crystal and, thus, the corresponding peak wavelength of the PBG decreases with decreasing temperature at all regions of the wedge cell. This may lead to the reflective color-gradient of the wedge cell displayed at any temperature of BP state, e.g., the optimum color-gradient of the cell appearing at 53 °C [Fig. 3(a)]. Based on the above-mentioned analysis, the twisting force of the LCs at thicker regions is easier to overcome the competition of the weaker boundary force at those regions at the phase transition of isotropic to BP, resulting in the TI-BP is higher at the thicker regions. In addition, the stability of BP at the thinner regions is higher than that at the thicker regions because the twisting force of the BP at the thinner regions is stronger than that at the thicker regions. This causes the increase of ΔTBP with decreasing the thickness.
Fig. 4 Variations of the peak wavelength of the BP reflection band with the thickness of the wedge cell and temperature.
Table 2. Variations of the peak wavelength of the BP PBG with thickness and temperature. These variations are summarized from the experimental results in Fig. 4. The peak wavelengths of the BP PBG appearing as just transiting from isotropic to blue phase [λI-BP (nm)], transition temperatures from isotropic to BP [TI-BP (°C)], and the temperature range of BP [ΔTBP (°C)] in cooling process are all dependent on the thickness of the BP wedge cell.
Referring to previous studies [34, 35], two kinds of nucleation process can simultaneously occur in the crystal growth of BP: homogeneous and heterogeneous nucleations. They take place in the bulk region of materials and on the interface of LCs and glass substrates, respectively. The homogeneous nucleation results in crystals of random orientation while the heterogeneous nucleation results in crystals with ordered orientation. In the thinner regions of the BP wedge cell, the ratio of BP crystals from heterogeneous nucleation is high. Thus, the orientation of the BP crystals is highly ordered. The amount of BP crystals from homogeneous nucleation rises with increasing sample thickness. Therefore, the orientated directions of the BP crystals in the thicker regions of the wedge cell are in a lower order. The variation of the orientated directions of the BP crystals between the bulk and surface regions in the thicker regions gives rise to the coexistence of platelets with various colors in the sample. For example, in the case of the red and green platelets shown in Fig. 2(c), they could be both from the reflection of the (110) plane of the BP crystal. However, the crystal plane of the red region is parallel to the glass substrate, whereas that of the green region is tilted at a certain angle relative to the glass substrate. The whole textures in the sample exhibit no obvious variation after remaining at the same temperature for at least two days. Although a few of the platelets are green, red platelets dominate the reflection color of the BP.
Suppose a temperature gradient is non-negligible along the direction of cell thickness. Then, the corresponding temperature gradient along the thickness direction at the position with 20 μm thickness to the position with 238 μm thickness must be apparently increased; that is, the temperature on the other side (indirectly heating side) of the wedge cell must be apparently increased with increasing thickness. To clarify if there is a non-negligible temperature gradient in the depth direction, we use a thermal imager (Ti10, from Fluke) to measure the temperatures on the indirectly heating side of the wedge cell at various temperatures measured on the directly heating side. As shown in Fig. 5, when the temperatures on the directly heating side are 56 °C, 55 °C, and 54 °C, the measured temperatures on the indirectly heating side are homogeneously 55.8 °C, 54.8 °C, and 53.8 °C through the entire wedge cell, respectively. The experimental result of the homogeneous distribution of the temperature on the indirectly heating side of the entire wedge cell indicates that no non-negligible temperature gradient along the direction of the thickness can be obtained. In Fig. 5, the same temperature difference between the top and bottom of the wedge cell (0.2 °C) can be obtained. This finding is probably attributed to the separation of the two glass substrates (1.4 mm) between the directly and indirectly heating sides. The cell gap of the whole wedge cell (whether at thin or thick region) is significantly thinner than this separation, so the temperature in the space between the substrates of the wedge cell from 20 μm to 238 μm must be uniform. This experimental result has ruled out the effect of a temperature gradient along the direction of thickness.
The spatial tunability of the PBG in the BP wedge cell can be applied to develop a spatially tunable BP laser using a DDBP wedge cell. This work adopts the fluorescence dye P597 as the gain medium in the lasing experiment. Figure 6 presents both the absorption and fluorescence emission spectra (black and blue curves, respectively) of the DDBP cell in isotropic phase. The peaks of the absorption and fluorescence emission spectra of the cell are located at around 530 and 570 nm, respectively. When the wavelength is higher than 575 (680) nm, the absorption (fluorescence emission) almost vanishes and can be neglected. Since the wavelength of the pumped pulse, 532 nm, is very close to 530 nm, the laser dye can be efficiently stimulated.
Fig. 6 Measured absorption and fluorescence emission spectra (blue and red curves, respectively) of 1.0 wt% P597 doped in BP at isotropic state.
For lasing emission, we adjust the recipe of the DDBP, as shown in Table 1, to tune the reflection band of the DDBP resonant cavity to locate at wavelength region exceeding 532 nm. Figure 7(a) display the measured reflection spectra of the wedge cell at 54.5 °C measured at y = 2.5 mm to y = 28.5 mm, with recorded R-POM BP images at corresponding positions. Obviously, the chiral and LC molecules in the wedge cell can self-organize a stable color-gradient BP structure with large frustrated platelets (> 100 μm) in the entire cell. A stable thickness-dependent PBG gradient at a central wavelength from 541.23 nm to 646.92 nm measured at y = 2.5 mm to y = 28.5 mm (t = 20 μm to t = 238 μm) can form in the cooling process from isotropic phase to 54.5 °C. The spatially tunable spectral range (~106 nm) for the central wavelength of the PBG of the BP in the entire wedge cell is included in the fluorescence emission region of the laser dye. This result is expected to induce a wide spatial tunability in lasing emission occurring at the bandedge(s) of the PBGs in the DDPB wedge cell. The solid (dotted) violet, deep blue, blue, green, yellow, orange, and red peaks (curves) in Fig. 7(b) show the measured lasing emissions (corresponding reflection band) of the DDBP wedge cell at y = 2.5 mm to y = 28.5 mm at E = 30 μJ/pulse. Experimental results shown below confirm that 30 μJ/pulse is higher than all energy thresholds measured at various pumped positions of y = 2.5 mm to y = 28.5 mm in the entire wedge cell. Apparently, the lasing peak can be spatially tuned from 554.62 nm to 622.39 nm at y = 2.5 mm to y = 28.5 mm of the DDBP wedge cell. All these lasing peaks occur roughly at the LWEs or SWEs of the PBG at various pumped positions along the direction of cell normal, which direction is matched with the reflection from the crystal plane (110) of BPI. The position of y = 15.5 mm (t = 129 μm) can be regarded as a tuning point, at which the lasing peak can occur at the LWE at positions of y < 15.5 mm (t < 129 μm) and at the SWE at positions of y > 15.5 mm (t > 129 μm). This result can be explained by considering the effect of the two main factors that influence the spectral position of the lasing occurrence: the strength of the fluorescence emission of the laser dye and the reabsorption of the fluorescence photons within the absorption region. As displayed in Fig. 7(b), the corresponding strength of the fluorescence emission at the SWE is significantly stronger than that at the LWE at positions of y > 15.5 mm (t > 129 μm), resulting in the occurrence of the lasing peaks at the SWEs. In contrast, the reabsorption effect at the SWE is significantly stronger than that at the LWE at positions of y < 15.5 mm (t < 129 μm), resulting in the occurrence of the lasing peaks at the LWEs. The above-mentioned spatial tunability in spectral ranges for the PBG and associated lasing emission (about 106 and 68 nm, respectively) based on a DDBP wedge cell are significantly wider than those based on a traditional DDCLC wedge cell (about 15 and 9 nm, respectively) [31]. This result is mainly attributable to the inherent difference between the two systems: the surface-treatment-free merit in the former and the limitation of the surface-pinning-effect-induced quantization of the half-pitch in the latter. The inherent advantage makes the BP wedge cell effective for use in applications of wide-band spatially tunable filter (reflector) and laser.
Fig. 7 (a) Measured reflection spectra and corresponding R-POM BP images for the DDBP wedge cell at y = 2.5 mm to 28.5 mm (t = 20 μm to 238 μm) at 54.5 °C. (b) Measured lasing spectra (solid curves with sharp peaks) and corresponding reflection spectra (dotted curves, same as those shown in (a)) for the DDBP wedge cell measured at y = 2.5 mm to 28.5 mm (t = 20 μm to 238 μm) at 54.5 °C. The black solid curve is the fluorescence emission spectrum of the laser dye.
Figures 8(a)-8(g) display the variations of the measured peak intensity of the fluorescence emission and its corresponding full-width at the half-maximum (FWHM) for the DDBP wedge cell at various thicknesses of t = 20, 57, 93, 129, 166, 202, and 238 μm, respectively. At each position, the measured peak intensity and FWHM of the fluorescence output rises and drops abruptly, respectively, once the pumped energy exceeds a certain threshold. The existence of the lasing threshold is standard evidence for the lasing occurrence in the DDBP material. The measured FWHMs of the lasing peak at various positions of the wedge cell can be as narrow as 1.1 nm to 1.3 nm, which value is close to the spectral resolution of the spectrometer (~1.0 nm).
Fig. 8 Variations of the measured peak intensity of the fluorescence output and its corresponding full-width at half-maximum (FWHM) with pumped energy for the DDBP wedge cell at various thicknesses of t = (a) 20, (b) 57, (c) 93, (d) 129, (e) 166, (f) 202, and (g) 238 μm.
Figure 9(a) summarizes the experimental data presented in Fig. 7(b) into the variation of the lasing wavelength of the DDBP wedge laser with the thickness (also, the pumped position) of the wedge cell. A straight line with a fitting equation of λ = 0.3076t + 548.71 just matches the experimental data of the lasing wavelength versus thickness. The linear relation between the lasing wavelength and thickness (also, the pumped position) is quiet convenient in applications. Figure 9(b) further describes the experimental results shown in Fig. 7 related to the thickness-dependent (also, the position-dependent) lasing threshold for the spatially tunable DDBP wedge laser. The lasing threshold concaves upward as thickness, and consequently the lasing wavelength, increases. The dominative factors that determine the lasing threshold mainly include the strength of the fluorescence emission and the reabsorption of the fluorescence photons within the absorption region. At t ≥ 93 μm, the lasing threshold increases with increasing the thickness and thus the lasing wavelength. This is attributable to the decrease of the corresponding strength of the fluorescence emission with increasing the thickness and zero reabsorption effect [26]. However, at t ≤ 93 μm, the lasing emissions occur near and within the absorption region. The increasing reabsorption of the fluorescence photons by the laser dyes may increase the lasing threshold through a decrease in the thickness and thus the lasing wavelength.
Fig. 9 (a) Linear variation of the lasing wavelength with the thickness of the DDBP wedge laser. (b) Variation of the lasing threshold with the thickness and thus the lasing wavelength of the DDBP wedge cell. The corresponding thicknesses of the wedge cell are indicated under the solid black dots. The blue solid curve is the fluorescence emission spectrum of the laser dye (same as that shown in Fig. 7).
4. Conclusion
In summary, a spatially tunable PBG of wide spectral range and lasing emission based on BP and DDBP wedge cells, respectively, is demonstrated for the first time. The gradient thickness in the wedge cell provides different boundary forces to the LC molecules, hence achieving the continuously spatial shifting reflections of BP in the wedge cell. The continuously shifting reflection is even more than 130 nm nearly covering the range of blue, green, and red regions. Base on the tunable PBG of the wedge cell, a spatially tunable laser based on a DDBP wedge cell is demonstrated as well. The lasing wavelength is continuously tunable within a spectral range of about 68 nm. Both the tuning ranges of PBG and lasing emission are extremely larger than those of CLC and DDCLC wedge cells. The spatially tunable reflection and lasing emission of BP can have a potential in applications of photonic device and display.
Acknowledgments
The authors thank the National Science Council of Taiwan (Contract number: MOST 103-2112-M-006-012-MY3) and the Advanced Optoelectronic Technology Center, National Cheng Kung University, under the Top University Project from the Ministry of Education, for financially supporting this research.
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