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We have experimentally demonstrated the feasibility of direct compression, or stretching and recompression of laser pulses in a very wide temporal time scale spanning 10’s fs to ~1 ps time with sub-mm thick cholesteric liquid crystal (CLC) cells. The mechanisms at work here are the strong dispersion at the photonic band-edges and nonlinear phase modulation associated with the non-resonant ultrafast molecular electronic optical nonlinearity. The observed pulse compression limit, spectral characteristics and intensity dependence of the compression are in good agreement with theoretical expectations and simulations based on a coupled-mode propagation model. Owing to the large degree of freedom to engineer the wavelength locations of CLC photonic bandgap and band-edges, these self-action all-optical processes can be realized with ultrafast lasers pulses in a very wide spectral region from the visible to near infrared, with potential applications in compact ultrafast photonic modulation devices/platforms.
© 2016 Optical Society of America
1. Introduction
Many applications involving ultrafast (femtoseconds–picoseconds) time scale laser pulses require modulating the temporal characteristics of fixed output pulses from an oscillator. Engineering the temporal profile and propagation characteristics of sub-picosecond laser pulses in the form of solitons, slow light, compressed or broadened pulses are usually achieved by delicate balance and control of dispersion and nonlinear processes with specialized optical materials [1–15]. Besides being physically cumbersome in most cases, the reliance on the interplay and mutual actions between dispersion and nonlinear optical effects often place restrictions on the range of pulse intensity and duration that these schemes can operate; what works for compressing picosecond laser pulses of specific wavelength generally does not work for femtosecond pulses, and vice versa. For example, direct self-compression using fiber and Bragg grating structures [5–11] tend to work only with picoseconds lasers whereas thin cholesteric liquid crystal cells that could compress 100fs laser pulse to 10’s fs [15] will not work for longer ~ps laser pulses. It is therefore highly desirable to develop compact and easily reconfigured compression device that could work with a large dynamic range of laser pulse durations and wavelengths.
In this paper, we show how group velocity dispersion and enhanced nonlinear phase modulations at the band edges of sub-mm thick, transparent but highly dispersive cholesteric liquid crystals (CLC) can work in concert to compress picoseconds - femtosecond laser pulses; additionally, we have employed linear dispersion caused chirping at two opposite band-edges of two CLC cells to first stretch and then re-compress femtoseconds laser pulses c.f. Fig. 1. In this ordered phase of liquid crystals, the constituent molecules self-organize to form a 1-D photonic crystal structure (Bragg grating) with a photonic bandgap that can be tuned (electrically or optically) to cover a wide spectrum spanning the visible to near-infrared [16–21], resulting in tunable filters, lasers and other photonic devices Liquid crystals in general are known to possess extraordinarily large optical nonlinearities [22]; depending on the originating mechanisms (macroscopic crystalline rotation or order parameter change, and individual molecular electronic response), the response times of the laser induced nonlinear index change can range over 13 decades. For the present purposes of modulating ultrafast laser pulses, we employ the corresponding ultrafast molecular electronic optical nonlinearity which typical of organic materials, is characterized by a non-resonant nonlinear index coefficient n2 on the order of 10−14–10−13 cm2/W [22–24]. Owing to enhancement by group velocity dispersion at the photonic band edges, n2 of CLC’s can be as large 10−12–10−10 cm2/W [15, 25–27]. This nonlinearity is several orders of magnitude larger than other nonlinear optical materials, e.g. silicon fiber used for ultrafast pulse compressions, and enables direct compression of femtosecond laser pulse with a 6-micron thick CLC as reported in a previous study [15].
Fig. 1 (a) Schematic depiction of a cholesteric liquid crystal cell (CLC) for femtoseconds laser pulse compression or stretching, caused by nonlinear phase modulation and dispersion at the band edge (b) Plots of the propagation wave vector k (normalized to the cholesteric spiral wave vector q = 2π/P) and group velocity as a function of the frequency (normalized to c/q) in the vicinity of the CLC photonic bandgap), using a representative values for the optical dielectric anisotropy Δε = 3, and ne = 1.585; note the dramatic changes in group velocity for laser wavelength located near the band edges (red dotted lines).
It is important to note here that large and ultrafast optical nonlinearity is but one of several material and optical properties required for balancing nonlinear phase modulation and dispersion dynamics in such self-compression operations, as reflected in the so-called nonlinear length LNL and the dispersion length LD [6, 7]. In the case 100 fs pulse compression [15], these lengths are on the order of ~10 microns and so standard microns-thin cell would suffice; for longer (~1 ps) laser pulses with narrower spectra bandwidth and weaker dispersion, these lengths are much longer (~100’s μm) and so a prerequisite for extending the time scale of self-compression operation is fabricating CLC’s of record-setting thicknesses (~100 times thicker than conventional ones). This calls for special attention to the mechanisms underlying CLC molecular self-assembly and pushing the limit of crystalline order in a largely fluidic material like liquid crystal. For this study, we have succeeded in fabricating well aligned CLC cells with thicknesses as large as 500 μm by an appropriate choice of the starting mixture materials and most importantly, the use of a bias field to enforce the desired CLC texture during preparation.
2. Fabrication of unconventionally thick cholesteric liquid crystals
The major component used in the fabrication of the CLC cells is a dielectrically negative nematic substance (procured from Tsinghua University) with the following properties: S→N transition < –40°C; Clearing point 100°C; optical index anisotropy Δn = 0.096 with ne = 1.585; Δε (1kHz, 25°C) = –4.7; ε⊥ (1kHz, 25°C) = 8.6. The CLC mixture comprises 82.5 wt% of TH-Neg-3 and 17.5 wt% chiral smectic, S811 (Jiangsu Hecheng Display Technology Co., Ltd). The samples are made by filling a room-temperature CLC into glass sandwich cells made with two indium-tin-oxide (ITO)-coated glass slices separated by non-ITO-coated glass spacers with a thickness of ~500 μm. The ITO coated glass slides are treated with a planar alignment layer. With such a large thickness (d)-to-pitch(P) ratio (d/P ~1000), however, the influence of surface-alignment layers on the bulk alignment of LC molecules is weak as opposed to conventional thin [low-d/P (~10)] samples; therefore, thick CLC samples tend to form highly scattering focal conic texture upon filling even if the cell surfaces are treated with alignment agents The key to our successful fabrication of nearly planar state CLC is to enforce the planar alignment of the negative dielectric Th-Neg-3 by a strong field (AC voltage (1 kHz; 2500V) applied across the cell windows. on the negative dielectric CLC sample while it slowly cools down from the isotropic liquid phase to the CLC phase; the applied electric field is kept on until the samples has been situated at room-temperature (~25°C) for at least 12 hours. The fabricated cell is highly transparent with almost negligible scattering loss (< 5%), and exhibits well defined photonic bandgap for circularly polarized light, c.f. later section on characterization. The CLC planar texture remain intact till present, i.e. over a year.
3. Experiments on pulse compression and analysis
Figure 2 depicts the complete experimental set-up. The fundamental oscillator output is derived from a mode-Micra-5 (Coherent) Ti:Sapphire mode-locked laser system that delivers nearly transform-limited 40 fs pulses at a repetition rate of 1000 Hz, with an average power of < 1 mW. The source is tunable from 575 to 1300 nm. It is important to note here that when the average intensity of the pulse train is high, cumulative heating by the laser pulse train is appreciable. To eliminate the thermal accumulation associated with high rep. rate (high average power) pulse train, we also introduce a chopper to further reduce the repetition rate, thereby decreasing the average intensity without changing the peak intensity of individual pulse. The laser output is then sent to a home-built 4f-line system to modulate the pulse width. The home-made 4f-line system consists of a grating to first spatially disperse the laser, and a spherical lens to re-collimate the light; a tunable slit is used to narrow the spectrum of the pulse, which is retro-reflected through the spherical lens and the grating to generate an output pulse with a lengthened duration. Owing to the narrower spectra, the output pulse duration is lengthened to the desired value for specific experiments described in this paper.
Fig. 2 Schematic of experimental setup comprising a fundamental oscillator that emits pulse train of 40 fs laser pulses, a laser pulse width modulator, input/output optics surrounding CLC sample, and diagnostic instruments. M: Mirror; BS: Beam splitter; G: grating; λ/4: quarter wave plate to convert laser polarization from linear to circular, and vice versa; S: spectrometer; F: filter to remove the fundamental input lasers: D: ultrafast detector. Note the bulkiness of the (meter size) conventional pulse width modulator compared to the 0.5 mm thick CLC cell.
The pulsed laser output [847 fs; λ = 777nm] is then lightly focused to a spot size of 0.56 mm (measured by Ophir-Spiricon SP620U laser beam diagnostics) onto the CLC sample. After traversing the CLC sample, the transmission, pulse duration and spectrum are measured by various means commonly used in fs-ps pulsed laser studies. We measure the pulse duration and the spectrum (by a Zolix Omni-λ-500 monochromator with resolution limit of 0.1 nm) before and after CLC sample and obtain the corresponding time-band width products (product of pulse duration and spectra width). Pulse width measurement is performed by non collinear second harmonic autocorrelation scheme with a BBO crystal for second-harmonic generation. This procedure requires linearly polarized light which is accomplished by a pair of λ/4 wave-plates – the first one to transfer the linear polarized output from the Ti:Sapphire laser to circular polarization for propagating through the CLC sample, and the second one to convert the transmitted circular to linear polarization for correlation measurement; the signal is measured by a Zolix RMTH-S1-CR131 photomultiplier.
Experimental data are simulated by a coupled-mode model described previously [7, 15]. Briefly, in this model, the refractive index of the CLC is written as:
where and are the slowly varying amplitude of the circularly polarized forward and backward propagating waves respectively. The dynamical interactions between and are described by the coupled-mode equations [7, 15, 16]:where nav is the average unperturbed refractive index; Δn = ne – no = 0.096 the CLC birefringence; Λ is the period (½ pitch P); n2 is the nonlinear index coefficient; vg = c/nav is the pulse group velocity; δ is the wave-number detuning, κ = πΔn/λ is the coupling coefficient between forward and backward waves, γ = kn2 = 2πn2/λ is the nonlinear parameter associated with the nonlinear index coefficient n2. These coupled-mode equations are solved by the Split-step Fourier method to analyze experimental results.We begin with characterization of the ultrafast optical nonlinearity of the newly minted CLC by examining its intensity dependent transmission spectrum. As depicted in Fig. 3(a), for a laser wavelength located at the band edges with steep slopes, the transmission would experience a pronounced change for any shifting of the bandgap. Since the mechanism causing the shift is the intensity dependent index change induced by the laser pulse, a shift towards the red/blue region would cause a corresponding increase/decrease in the pulse transmission from which one can deduce the sign of the index change. For the laser wavelength of 777 nm located on the short wavelength edge, the observed transmission depicts an increasing function, c.f. Fig. 3(b), signifying a positive index change. Using a standard CLC theory to simulate the bandgap shift and the transmission (and index) change as a function of laser intensity, we obtain an n2 value of 10−13 cm2/Watt. Although this is smaller than the n2 value (–10−11 cm2/Watt) of the 6-μm thick CLC used in [15], the extended interaction length provided by the 500-μm thick sample more than makes up for the shortfall, and enables various self-action modulation of the temporal and spectral characteristics of picoseconds–femtoseconds laser pulses, c.f. Fig. 4(a)–4(c).
Fig. 3 (a) The Transmission spectra of the 500-μm thick CLC sample at low light level illumination showing a typical photonic transmission bandgap centered at ~800nm; dotted line indicates the location of the laser wavelength. (b) The transmission spectrum as a function of input laser Intensity (laser wavelength: 777 nm, pulse duration 847 fs) depicting an increasing function corresponding to the shift of the photonic bandgap towards the long-wavelength region.
Fig. 4 (a) Pulse duration measurements for an input 847 fs pulse (open circles) showing compression to 286 fs (open squares). Theoretical simulations using the measured n2 value of 10−13 cm2/W and the birefringence Δn = 0.096 for the CLC are shown in dotted and continuous lines. Laser intensity: 125 MW/cm2.; wavelength: 777 nm. (b) Measured and simulated intensity dependence of the pulse compression. (c) Experimental and simulation results of the spectrum of the input and compressed laser pulses at an input laser intensity of 100 MW/cm2.
In particular, Fig. 4(a) shows how an input 847-fs pulse duration is compressed to 286 fs, closely resembling theoretical simulations. The compression rate, defined by the ratio of input vs. output pulse duration, continues to increase with the input laser intensity, reaching an ultimate single-cell compression limit of ~3 at an intensity of ~130 MW∕cm2 before pulse splitting ensues, c.f. Fig. 4(b). From the experimental data of peak power, wavelength and pulse duration, we can estimate the nonlinear length LNL and the dispersion length LD to be 115 μm and 96 μm, respectively. That these two lengths are similar means nonlinear effect and dispersion can compensate each another and maintain the transform-limited nature of the pulse. This is borne out in the experimental observations of the spectra, c.f. Fig. 4(c); a nearly transform-limited 847 fs laser pulse with a FWHM linewidth of 1.07 THz is compressed to a 286 fs pulse with a broadened spectral width of 2.87 THz. The calculated time-bandwidth products in both cases are in agreement to within 10%.
Based on such direct all-optical action of a single cell, one can envision several possibilities. An obvious one is cascaded operation with tandem cells of appropriate thicknesses and CLC make-ups (e.g. thick CLC used in the present study, and a conventional thin CLC cell used in previous study [15]) to perform successive compressions and attain higher compression ratio. In this manner, nearly ps laser pulses can be compressed to a few 10’s fs.
Another possibility is to have two CLC cells that are individually tailored-made to have their respective blue/red band edges matching the operating laser wavelength, and utilize the opposite linear dispersions (i.e. without involving the optical nonlinearity) from these band edges to impart opposite chirping effect on these pulses, and consequently stretch and then recompress the laser pulses. Such pulse stretching and recompressing abilities by tandem CLC cells, noted also for their high laser damage threshold [28], may find a niche in chirped pulse amplification (CPA) systems [29] that requires an intermediate pulse stretching process to prevent amplification saturation. To demonstrate this, the laser system is adjusted to put out 100 fs laser pulses. The laser wavelength is 780 nm and coincides with the blue/red band edge of the first/second CLC cell. Since the laser wavelength is at the blue band edge of the first CLC [the one used in the compression studies described in previous section], the initial non-chirped 100 fs acquires a positive chirp after traversing the first call and is broadened to > 2 ps, c.f. Fig. 5 middle trace. Upon traversing the second CLC cell [made with a different concentration of chiral agent so that the laser wavelength is located at the red band-edge], it experiences a negative chirp since the laser wavelength is at the low frequency band edge, and consequently it is recompressed to almost its original pulse duration, c.f. Fig. 5 bottom trace. It is important to note here that the compression by the second cell is by means of negative chirp through the linear dispersion effect, in contrast to the nonlinear index change caused compression discussed in previous section.
Fig. 5 Pulse stretching and re-compression of a 100 fs laser pulse (wavelength: 780 nm) with two tandem 550-μm thick CLC cells. Upper trace: Input laser pulse. Middle trace: Temporal profile of laser pulse after the 1st cell. Bottom trace: Temporal profile of laser pulse after the 2nd cell. Small side lobes noise is likely due to high order dispersion from the thick CLC cells.
4. Conclusion
In summary, we have demonstrated the uncanny ability of transparent sub-mm thick CLC cells for direct compression, or stretching & recompression of ultrafast (picosecond-femtoseconds) laser pulses. Such self-actions operations with non-absorptive liquid crystals do not rely on specific electronic resonances or externally applied fields (i.e. electrodeless operations), and could naturally be used in a wide spectral region covering the entire visible to near-infrared. The success is brought about by synergistic combination and interplay of a multitude of material and optical parameters including optical nonlinearity, band edge dispersion, laser intensity and the interaction length. The results reported here will open up many avenues for fundamental research into the promising field of ultrafast nonlinear photonics of liquid crystals, as well as practical integration of CLC in compact ultrafast modulation devices/platforms.
Acknowledgment
This work is supported in part by the Chinese National Natural Science Foundation (61505265, 11374067, 11534017) and the National Key Basic Research Special Foundation (G2010CB923204), the Ministry of Science and Technology of Taiwan (MOST 104-2628-E-110-003-MY2). I. C. Khoo’s work is supported by the US Air Force Office of Scientific Research (FA9550-14-1-0297). We also acknowledge J. Wen technical contribution in building the 4f pulse-width modulator.
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