We demonstrate a scheme for efficient generation of a 5.9 eV coherent light source with an average power of 23 mW, 0.34 meV linewidth, and 73 MHz repetition rate from a Ti: sapphire picosecond mode-locked laser with an output power of 1 W. Second-harmonic light is generated in a passive optical cavity by a BiB3O6 crystal with a conversion efficiency as high as 67%. By focusing the second-harmonic light transmitted from the cavity into a β–BaB2O4 crystal, we obtain fourth-harmonic light at 5.9 eV. This light source offers stable operation for at least a week. We discuss the suitability of the laser light source for high-resolution angle-resolved photoelectron spectroscopy by comparing it with other sources (synchrotron radiation facilities and gas discharge lamp).
©2012 Optical Society of America
Recent developments in light source technologies using lasers and synchrotron radiation facilities have realized advanced spectroscopy in the ultraviolet (UV) to extreme ultraviolet (XUV) regions, such as UV-frequency-comb-based high-resolution spectroscopy, X-ray absorption spectroscopy, and photoemission spectroscopy. A major advance in the spectroscopic technique is angle-resolved photoelectron spectroscopy (ARPES), which can provide direct information on the electronic structures of bulk materials and surfaces in energy–momentum space, contributing to the development of solid-state physics . In particular, progressive efforts toward high-resolution ARPES have been made for observation of fine structures near the Fermi surface, helping us to elucidate the mechanism of exotic phenomena such as anisotropic superconductivity in strongly correlated systems (cuprate and iron pnictide superconductors) [2–7]. Exploring the underlying physics of these phenomena is important for both fundamental and applied physics. Owing to tremendous improvements in instrumental and cryogenic techniques, the highest instrumental resolution is currently 0.25 meV , and the lowest sample temperature is currently 1 K . To use these capabilities of high-resolution ARPES, we should develop vacuum UV (VUV) light sources with sub-meV linewidths. The linewidth of a helium discharge lamp, which is the most conventional light source, is limited to around 1 meV by Doppler broadening. In synchrotron radiation facilities, the spectrum of synchrotron radiation is a continuum extending from the infrared to beyond the XUV; thus, to achieve a linewidth narrower than 1 meV, we have to consider the balance between the linewidth and the photon flux. Therefore, it is necessary to produce a high photon flux and a small beam divergence by installing large-scale undulators [7, 9, 10]. As an alternative light source, lasers have attracted attention owing to rapid progress in wavelength conversion techniques [4, 11]. The advantages of a laser light source for high-resolution ARPES are its high photon flux per wavelength, easy polarization control, wavelength stability, high spatial coherence, expandability to ultrafast time-resolved spectroscopy [12, 13], and compactness. Actually, a 7 eV pulsed light source produced by the sixth-harmonic generation of a Nd:YVO4 laser is used for high-resolution ARPES; its linewidth of 0.26 meV is assumed to be a transform-limited Gaussian pulse with the 10 ps pulse duration of the frequency-tripled Nd:YVO4 laser . Recent high-resolution ARPES data using this light source [2–5] suggest that it is a very promising probe for this application; however, it cannot be widely used because the KBe2BO3F2 nonlinear crystal is not commercially available. To use advanced detection technology for ARPES, it is necessary to develop a light source based on a commercially available laser system and optical components.
Light sources for high-resolution ARPES must meet the following requirements: narrow width, photon energy higher than the work function of the materials, and high photon flux. Moreover, we have to make the pulse energy low and the repetition rate high in order to acquire photoelectron spectra with a high signal-to-noise ratio because the space charge effect is a problem when pulsed light sources are used . However, because of the low peak intensity of the electric field, the wavelength conversion efficiency of high-repetition-rate, picosecond pulses is low in single-pass configurations . In addition, the effective interaction length in a nonlinear crystal is limited by the dispersion and walk-off effects, especially in the UV .
Our aim in this study is to realize the generation of UV fourth-harmonic (FH) light with a narrow linewidth, high repetition rate, and high power by a simple configuration using a conventional laser source. To achieve this, we use a recently developed technique for efficient wavelength conversion using a passive optical cavity  so that we can generate a strong second-harmonic (SH) light. When we make the cavity round-trip time for a passive optical cavity equal to the inverse of the repetition rate of the laser, we can store pulses inside the cavity and enhance the intracavity power. Then, by installing a nonlinear crystal in the enhancement cavity and choosing an appropriate input coupler for impedance matching, as discussed in section 3.1, we can perform efficient SH conversion.
We developed a 5.9 eV coherent pulsed light source with a 73 MHz repetition rate, 23 mW average power, and 0.34 meV linewidth using a commercially available Ti: sapphire 1 W picosecond mode-locked laser. Using an enhancement cavity with a BiB3O6 (BIBO) crystal, we obtained SH light with a power of 612 mW at 420 nm against an injection power of 918 mW at 840 nm. Then, with a single-pass configuration using a β–BaB2O4 (BBO) crystal, we obtained FH light with a power of 23 mW at 210 nm (5.9 eV). Moreover, we confirmed the stable operation of this light source for at least a week. Therefore, we believe that our developed light source is suitable for high-resolution laser-based ARPES.
In this paper, we explain the technical details of the scheme for generating this light source so that non-specialists can reproduce the system. In section 2, we describe the optical system for wavelength conversion using a passive optical cavity. In section 3.1, we show the experimental results of efficient SH generation using the cavity and discuss the conditions necessary to obtain the maximum SH conversion efficiency using a cavity with an intensity-dependent loss. Then, we show the results of FH generation and the stability of the FH light. In section 3.2, we describe a scheme to measure the spectrum of the FH light using a Fourier- transform spectrometer. In section 3.3, we discuss the advantages of the laser light source by comparing it with synchrotron radiation and gas discharge lamp sources.
The experimental setup is shown in Fig. 1(a) . It consists of a standard 1 W picosecond mode-locked Ti: sapphire laser (Coherent, MIRA), an enhancement cavity for SH generation, a feedback control system to lock the cavity to the laser, and a single-pass configuration for FH generation. The repetition rate and pulse duration of the mode-locked laser are 73 MHz and 10 ps, respectively. This laser is tunable from 660 nm to 1050 nm. We set the central wavelength to 840 nm in order to obtain the shortest FH wavelength by the second stage of the frequency doubling with a BBO crystal. A pair of concave and convex lenses was used for spatial mode matching, as explained later. A half-wave plate was placed so as to produce horizontal polarization of the laser beam after a Faraday isolator (BB9-5I, EOT). The input power of the cavity was 918 mW.
The enhancement cavity consists of six dielectric mirrors. All the mirrors except an input coupler [M1 in Fig. 1 (a)] are highly reflective (R840 nm > 99.9%) around 840 nm, and a pair of concave mirrors (M4, M5) with a radii of curvature of 100 mm are highly transmissive (T420 nm > 99%) around 420 nm. We prepared input couplers with different reflectances from 30% to 90% at 840 nm. An appropriate reflectance for the maximum SH power is discussed in section 3.1.
To store many pulses inside the cavity and enhance the intracavity power, we need to match both the longitudinal modes and the transverse modes of the incoming laser light beam and the cavity.
For longitudinal mode matching, we need to match the longitudinal mode of the cavity to that of the incoming beam of the pulsed laser. We tuned the cavity length to match the round trip time to the interval of the pulses. The repetition rate was 73 MHz, and we set the cavity length to 4.1 m. We actively stabilized the cavity length using a piezoelectric actuator attached to cavity mirror M2. The feedback control system is described later.
To describe the transverse mode and propagation of the Gaussian beam, the q parameter and ABCD matrices are useful. The q parameter, which characterize the minimum spot size and beam divergence of the Gaussian beam, is given by where is the spot size, and R(z) is the radius of wavefronts of the Gaussian beam with a propagation direction of z, λ is the wavelength, and n is the refractive index . When the minimum spot size and beam divergence are unknown, we can specify the q parameter by measuring the spot size at two different positions. The stable mode of the cavity is uniquely determined by the mirror configuration on the basis of the requirement that the mode of the resonator reproduces itself after one round trip . For example, when the cavity length is 4.1 m and we use concave mirrors with a radii of curvature of 100 mm, the distance between the concave mirrors [M4, M5 in Fig. 1(a)] has to range from 100 to 102.5 mm. When we set the distance between M4 and M5 to 101 mm, there are two beam waist positions: the midpoint between M1 and M2 [depicted in Fig. 1(a)], where ω0M1-M2 = 771 µm, and the midpoint between M4 and M5, where ω0M4-M5 = 13 µm. To match the transverse mode of the incoming laser beam to this cavity mode, we installed a lens pair consisting of a concave lens (f = −75 mm) and a convex lens (f = 100 mm). A schematic image of transverse mode matching of the laser output to our cavity is shown in Fig. 1(b).
Then, to generate SH light in the enhancement cavity, we placed the nonlinear crystal at the beam waist of the cavity at the midpoint between M4 and M5, as shown in Fig. 1(a). For efficient SH generation, nonlinear crystals should have a large effective nonlinear coefficient deff and a small walk-off angle. We chose a 5-mm-long, type-I BIBO crystal with antireflection coatings at 840 nm and 420 nm (R840 nm < 0.05% and R420 nm < 0.25%), because the BIBO crystal has a larger deff and smaller walk-off angle than the BBO crystal .
To enhance the intracavity power, we stabilized the cavity length with the piezoelectric actuator attached to M2 using the Hänsch–Couillaud scheme . In this scheme, the resonance mode is detected using the relative change in the polarized state of the reflecting light on the input coupler, M1 in Fig. 1(a). A Brewster plate (T840 nm = 99.5% for horizontal linear polarization) inserted in the cavity selects horizontal polarization for the eigenpolarization of the cavity resonance mode. As a result, the polarized state of the reflecting light depends on the cavity conditions. The light reflected from M1 is elliptically polarized off-resonance but linearly polarized on-resonance because the relative phase change in the cavity is an integral multiple of 2π. Therefore, we can stabilize the cavity length using an error signal produced by the polarization-sensitive detection of the reflecting light from the input coupler . We used a servo controller (LB1005, New Focus) with high-speed proportional-integral (P-I) control, and a feedback signal was sent to a piezoelectric transducer. The P-I corner frequency was set to 3 kHz, which is the higher limit below the piezoelectric resonance frequency.
For FH generation, we created a single-pass configuration with a BBO crystal. Before focusing the SH light beam onto the BBO crystal, we corrected the SH beam profile by two cylindrical lenses (focus lengths are 80 mm for the vertical axis and 1000 mm for the horizontal axis) because the SH light at 420 nm transmitted from mirror M5 was vertically elongated by the walk-off effect. We focused it with a concave lens (f = 150 mm) into a 10-mm-long, type-I BBO crystal, whose surfaces are antireflection-coated for 420 nm and 210 nm (R420 nm < 0.02% and R210 nm < 0.15%). The FH light is separated from the SH light by a Pellin–Broca prism.
The Fourier-transform spectrometer used to measure the spectrum of the FH light is described in section 3.2.
3. Results and Discussion
3.1. Efficient second-harmonic generation and subsequent generation of fourth-harmonic light
Efficient SH generation in an enhancement cavity is achieved when we match the reflectance of the input coupler to the cavity loss to achieve impedance matching. The cavity loss in this enhancement cavity corresponds to the intensity-dependent conversion efficiency of SH light: As the SH conversion efficiency increases, the enhancement factor decreases. We tested various input couplers of the reflectance from 30% to 90% at 840 nm, and we evaluated the enhancement factor as follows. The enhancement factor is defined as the intracavity power divided by the incident power. The intracavity power was estimated from the signal level of the photodetector behind M4, as shown in Fig. 1(a). The correspondence between the signal level and the actual intracavity power was calibrated in a single-pass (non-circulating power) configuration.
The circles plotted in Fig. 2(a) represent the enhancement factor of the fundamental light as a function of the reflectance of the input couplers. The maximum enhancement factor is around 2.8 when the reflectance of the input couplers is 50% to 70%. The results are matched to theoretical results [solid curve in Fig. 2(a)], as explained below. Following the notation given in , let P1 be the incident power, Pc the circulating power, r1 the reflectivity of the input coupler, and r2 the total reflectivity of this cavity excluding the input coupler. With a low-loss cavity and a SH crystal, the loss is determined by the nonlinear conversion of the fundamental to the SH. The crystal transmission term tSH associated with the nonlinear conversion factor γSH of the fundamental to the SH is described byFig. 2(a) shows the calculated enhancement factor as a function of the reflectance of the input couplers using Eq. (2) with the nonlinear conversion factor of calculated from the measured single-pass conversion and a total reflectivity inside the cavity, excluding the input coupler, of r2 = 0.988. The measured values are consistent with Eq. (2) without adjustable parameters.
Then, the SH light power is expected to be described byFigure 2(b) shows the measured power of the SH light versus the expected power calculated by Eq. (3). The maximum power of the SH light is 612 mW immediately after the crystal with a 50% input coupler; the maximum power was deduced considering the transmittance of mirror M5. Without the cavity, power of the SH is 132 mW, which is less than one-quarter of the maximum power obtained by using the resonator.
We see that the measured power of the SH light [circles in Fig. 2(b)] is lower than the value calculated by Eq. (3). Because the absorption edge of the BIBO crystal is at 280 nm , it is possible that nonlinear absorption at 420 nm is occurring. Assuming that two-photon absorption exists while the linear absorption is zero, the transmitted peak-power density of the crystal Itrans., which is the outgoing intensity of the SH light divided by the repetition rate, the pulse width, and the beam area, is given byEq. (4), which is a reasonable value compared with the reported value of two-photon absorption at 355 nm .
For FH generation, we focused the SH light at 420 nm transmitted from mirror M5 of the cavity having the input coupler with R = 50% onto the BBO crystal, resulting in a maximum power of the FH of 23 mW at 210 nm. The FH light intensity corresponds to a photon flux of 2 × 1016 photons/s, which is a sufficient photon number for ARPES. Furthermore, we investigated the long-term stability of this source. The cavity locking lasted for at least a week, until the laser was turned off, which proved that this light source is suitable for long-term data accumulation in photoelectron spectroscopy measurements. The power stability is 2% in 2 h and 4% in 12 h, as is typical for acquisition time. The long-term power stability is limited by the wavelength stability of the mode-locked laser output, because the phase-matching condition of the frequency conversion is very sensitive to wavelength. For example, the shift of the center wavelength of the fundamental pulses from 839.86 nm to 839.78 nm changes the FH light power from 9 mW to 6 mW. For high-resolution ARPES experiments, it is crucial to stabilize the wavelength of the laser within the linewidth. In this condition, we can stabilize the FH power within 2%. We emphasize that because of the low-Q cavity, this system requires no enclosure or vacuum chamber for the cavity, which are normally required for a high-Q cavity to avoid external perturbations.
3.2 Spectral measurement of fourth-harmonic light by Fourier-transform spectrometer
Assuming a 10 ps pulse is Fourier-transform-limited, the linewidth is of the order of 1010 Hz against a central frequency of 1.5 × 1015 Hz. For a grating-based spectrometer, the resolution is limited by the number of grooves and the length of the spectrometer. If the number of grooves is 1200 /mm and the slit width is 100 μm, we need a focal length of as long as 3 m for the required resolution of 1010 Hz. On the other hand, if we use a Fourier-transform spectrometer based on the Wiener–Khinchin theorem, which states that the Fourier transform of the field auto-correlation is the power spectrum, its spectral resolution is determined by the inverse of the total delay time of the interferometer. The required scan length is only 3 cm for the required resolution of 1010 Hz.
Our setup for the Fourier-transform spectrometer using a Michelson interferometer is shown in Fig. 3(a) . The FH beam was separated into two beams by a beam splitter; one beam went to a fixed mirror, and the other went to a moving mirror on a delay stage. The two reflected beams overlapped again on the beam splitter and interfered with each other. We used a flat substrate of fused silica 3 mm thick as the beam-splitter (BS in Fig. 3) and UV-enhanced aluminum flat mirrors. To measure the relative delay precisely, we used a frequency-stabilized helium–neon laser (HRS015, Tholabs). The He–Ne laser beam was made to overlap the beam of FH light on a dichroic mirror (DM in Fig. 3) before they were sent into the Michelson interferometer. The beam combiner (DM in Fig. 3) is highly reflective for the FH light and transmissive for light from the He–Ne laser. The laser beam was carefully aligned to be the same as the path of the FH light in the Michelson interferometer. The two outgoing beams were split by a dichroic mirror (DM in Fig. 3) and detected by amplified silicon photodetectors. The interferograms were simultaneously acquired by an oscilloscope (GDS-1072A-U, GwInstek) having one MB of memory per channel while the delay stage was moved.
The obtained interferograms are functions of the relative delay which, however, is affected by fluctuations in the scanning velocity. To retrieve the interferogram as a function of the true relative time delay, we used the interferogram of the frequency-stabilized single-mode He–Ne laser. The oscillating frequency of this laser is 473.612 THz in air with a stability of ± 2 MHz in 8 h. The interferogram of a single-frequency laser is described by a single sinusoid with maximum and minimum intensities of Imax. and Imin., respectively,
When we obtained the interferogram of the FH light, we corrected the horizontal axis of the interferogram to reflect the relative time delay by using the interferogram of the He–Ne laser, as described above. A typical interferogram is shown in Fig. 3(b); it shows a mixture of the FH light and the light of the He–Ne laser. To execute the discrete Fourier transform, we interpolated the interferograms at evenly spaced points. The power spectra of the FH light and the He–Ne laser were obtained by use of the fast Fourier transform algorithm. The full width at half-maximum of the laser’s power spectrum indicates the resolution of the present spectrometer.
The power spectrum of the FH light is shown in Fig. 4 . The spectral resolution of this measurement is 8.6 × 109 Hz, corresponding to the inverse of the total scan length on the delay stage of 3.6 cm divided by the speed of light. Finally, we determined that the linewidth of the FH spectrum is 0.34 meV versus a linewidth of 0.28 meV for the fundamental light at 840 nm. This value is comparable to the linewidth of the sixth-harmonic light of a Nd:YVO4 laser (0.26 meV), which is assumed to be a transform-limited Gaussian pulse with the 10 ps pulse duration of a frequency-tripled Nd:YVO4 laser . The waveform of the fundamental pulse is Gaussian; in contrast, that of the FH light is Lorentzian rather than Gaussian, implying saturation of the conversion efficiency around the peak frequency of the fundamental light, which can act to broaden the spectrum of the FH light.
3.3. Comparison of light sources for ARPES
Table 1 compares the linewidths and photon fluxes of the laser light source for high-resolution ARPES. We note that the light source presented here offers the narrowest linewidth and highest photon flux. We defined the photon flux as the number of photons per second in the field of view of a photoelectron analyzer. We set the size of the field of view on a sample to 0.1 × 4 mm2 by using an electrostatic hemispherical analyzer (R4000, VG-Scienta), with a 0.1-mm slit width for high-resolution ARPES. As a typical VUV light source provided by synchrotron radiation facilities, we used data from UVSOR-II, BL7U . The minimum spot size is 0.2 × 0.2 mm2 . The linewidth of synchrotron radiation sources is limited to a few meV in order to obtain a reasonable photoelectron count rate. As a typical example of a gas discharge lamp, we used data from a Baltzer-type VUV 5000 helium discharge lamp (VG-Scienta) . The diameter of the spot on a sample is reportedly 3 mm . The effective photon flux of this gas discharge lamp decreases because the spot size is larger than field of view. The beam profile of the laser light source is close to that of the Gaussian beam. The collimated beam has a beam diameter of 2 mm. Focused by a 400-mm focal length convex lens, the spot size on the sample was approximately 100 μm. Also, we can easily match the shape of the illuminated region to the field of view by using cylindrical lenses. Elongated focusing is helpful in reducing the space charge effect when using a pulsed laser. The high photon flux of the laser light source enables us to achieve a high signal-to-noise ratio in a shorter acquisition time than with the other light sources.
In addition to the high photon flux and narrow linewidth, the laser-based light sources have strong potential for polarization-sensitive measurements. However, the narrow-linewidth laser-based light source restricts the accessible range of the Brillouin zone owing to the low photon energy. Recently, a laser-based extreme ultraviolet light source with a narrow linewidth and high repetition rate has been reported . With further improvement of the photon flux, this could be a potential light source to cover the whole Brillouin zone for ARPES experiments.
In summary, we demonstrated efficient generation of a 5.9 eV coherent light source from a Ti: sapphire mode-locked laser with a 10 ps pulse duration and a 73 MHz repetition rate by efficiently converting the fundamental to the SH by using a passive enhancement cavity. The power of the SH light at 420 nm is 612 mW versus an incident power of the fundamental light of 918 mW, for a maximum conversion efficiency of 67% for SH generation. The saturation of the conversion efficiency at 420 nm implies two-photon absorption of the SH light in a BIBO crystal. The maximum power of the FH light, 23 mW at 210 nm, is obtained by single-pass frequency-doubling of the 420 nm light with a BBO crystal, indicating a total conversion efficiency from the fundamental to the FH of 2.5%. In addition, we measured the spectrum of the FH light using a Fourier-transform spectrometer and a frequency-stabilized He–Ne laser to calibrate the interferometer. The linewidth of this light source is 0.34 meV. By comparing the laser light source with synchrotron radiation and gas discharge lamp sources, we clarified that the laser light source offers the narrowest linewidth and highest photon flux. Therefore, it meets the requirements for state-of-the-art laser-based ARPES.
We note some consequences of these results. If we use a pair of concave mirrors (M4, M5 in Fig. 1) in the cavity with longer radii of curvature, we can prevent two-photon absorption in the BIBO crystal and obtain a higher conversion efficiency for SH generation. Because the power of this light source is sufficient for photoelectron spectroscopy, we could achieve a narrower linewidth by using an etalon. Pump–probe spectroscopy with a pump source of 840 nm and a probe source of 210 nm is possible by using a 1 W output-mode-locked Ti: sapphire laser. By using the sum frequency technique, it is possible to acquire even shorter wavelengths using a LBO (LiB3O5) crystal .
We would like to thank M. Sakano, D. Hirano, and N. Kanda for their cooperation in our experiment, and T. Shimojima and K. Ishizaka for very fruitful discussions of the light source for photoelectron spectroscopy. This work was supported by Grant-in-Aid for Scientific Research on Innovative Area “Optical science of dynamically correlated electrons (DYCE)” (20104002) of the Ministry of Education, Culture, Sports, Science, and Technology (MEXT), Japan, and the Photon Frontier Network Program of MEXT, Japan.
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