Supercontinuum laser sources are useful for applications requiring ultra-broadband radiation. Well-established techniques for generating a laser supercontinuum often employ the peak power from an ultrafast laser to induce self-phase modulation, cross-phase modulation, Raman scattering, and four-wave mixing in 3rd-order nonlinear optical materials. Useful materials serving this purpose include zero dispersion fibers, micro-resonators, and even air. Multiple Stokes scatterings are sometimes useful to generate broadband laser radiation [1,2]. Although the 2nd-order nonlinearity is relatively higher than the 3rd-order one, broadband phase matching is usually necessary to support cascading nonlinear frequency mixing to generate a supercontinuum. Recently, with combined 2nd-order and 3rd-order optical nonlinearities, a supercontinuum between 400 and 600 nm has been demonstrated from orientation-patterned gallium phosphide pumped by a mode-locked Yb:fiber laser with ${\sim}{20}\;{{\rm GW/cm}^2}$ pump intensity [3]. Although cavity resonance could further enhance a nonlinear process, a resonator could also limit the radiation bandwidth. In this Letter, we combine 2nd-order and 3rd-order nonlinearities in a monolithic KTP crystal oscillator pumped by a ${Q}$-switched Nd:YAG with a ${\sim}{1}\;{{\rm GW/cm}^2}$ intensity to generate supercontinuum radiation covering the visible and infrared spectra between 540–750 and 1095–1800 nm. The oscillator bandwidth is extremely broadband due to optical feedback from total internal reflection.

The supercontinuum source demonstrated in this Letter is compact, monolithic, and low in cost. Lasers are generally quite sensitive to mirror alignment, and small changes will lead to loss of power and change of the spectrum. In addition, a cavity mirror often limits the laser bandwidth. A mirrorless laser oscillator can be monolithic, robust, and free from mirror misalignment. Commonly seen mirrorless oscillators, for instance, are micro-disks or microsphere oscillators [4,5], distributed-feedback lasers [6,7], and backward parametric oscillators [8,9]

In this Letter, we employ a rarely developed mirrorless laser cavity, called the off-axis oscillator [10], as shown in Fig. 1, with a KTP crystal in air as a Raman gain crystal. In the crystal, the resonant wave bounces back and forth between the transverse crystal surfaces via total internal reflections, while circulating along the longitudinal axis of the crystal. The phenomenon of total internal reflection is intrinsically broadband. The distance between the two transverse surfaces is much larger than the radiation wavelength, so that the wave appears to propagate in a bulk material. As the off-axis oscillation is locked in the device, a prism, a grating, or a dielectric wedge at the end of the crystal can be added to frustrate the total internal reflection and couple out the laser radiation. To maximize the gain, it is desirable for the pump wave to fill up the gain volume for the zigzag propagating waves. To trap the resonant waves in the crystal, the incident angle of the wave at the crystal boundaries ${\theta}$ has to be larger than the critical angle of total internal reflection ${\theta _c}$. In Fig. 1, this means $\theta \; \ge \;{\theta _c}$ on the $y$ surfaces (side surfaces) and $\bar \theta=90^{\circ}-\theta \ge \theta_c$ on the $x$ surfaces (end surfaces). The two conditions set the incident angle $\theta$ in a range, given by

 

Fig. 1. Off-axis laser oscillator, wherein the resonant waves propagate with zigzag paths via total internal reflections between the crystal surfaces. A wedged dielectric can be installed on the side surface to frustrate the total internal reflection and couple out the laser radiation. In the plot, $\bar \theta=90^{\circ}-\theta$, where $\theta$ is the incident angle on the side surface.

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Equation (1) also sets a constraint on the critical angle and the refractive index of the crystal, given by

On the side surfaces of the crystal, when the bouncing angle is smaller than the critical angle $\theta \; \lt \;{\theta _c}$, the oscillating wave suffers from transmission loss at the surface boundaries, and its oscillation threshold increases. On the other hand, if $\theta \; \gt \;{\theta _c}$, the total gain length of the oscillating wave in one roundtrip is smaller than the wave propagating with $\theta = {\theta _c}$, because the large-angle ray of the wave has fewer bounces and thus a shorter gain length in a crystal of a fixed length along $x$. Since laser radiation builds from the mode with the lowest roundtrip loss at a steady state, the angle $\theta = {\theta _c}$ is the preferred propagation angle of the lasing mode inside an off-axis oscillator. Under the condition $\theta = {\theta _c}$, the roundtrip length of the traveling-wave mode in a crystal of length $L$ is simply

The effective roundtrip length of the traveling-wave mode ${L_{{\rm tw}}}$ is therefore a value between (3) and (4), expressed by

Equation (5) defines a free-spectral range of the traveling-wave modes between two boundary values:

In the transverse direction along $y$, self-consistency of a standing-wave mode requires the roundtrip phase difference along $y$ be equal to an integer multiple of ${2}\pi$, or

For $n = {1.83}$ and $d = {1}\;{\rm mm}$, the transverse free-spectral range is between 98 and 150 GHz. The angular acceptance in Eq. (1) supports a broad oscillation bandwidth manifested with the longitudinal and transverse modes in Eqs. (5) and (8). Therefore, an off-axis oscillator is well suited for broadband supercontinuum generation with dense axial and off-axial cavity modes. In KTP, the Raman cross section associated with the $A_{1}$ symmetry optic phonon mode has a strong Stokes shift of ${267}\;{{\rm cm}^{- 1}}$ [12]. This radiation mode has its dipole moment aligned in the crystallographic $z$ direction when pumped by a $z$-polarized laser [13]. To maximize the laser gain, we have previously studied the so-called anisotropic off-axis laser oscillator [14], in which the gain dipole axis is aligned transverse to the plane of the reflection feedback. Figure 2 shows the orientation of the KTP crystal in our experiment. The side surfaces of the crystal are cut along $y$. The pump laser is polarized along $z$ and propagates along $x$. In the same figure, we show an antenna pattern of the induced Raman dipole polarized along $z$. Since the radiation intensity of the gain dipole is strongest in the $x - y$ plane, the $y$ surfaces of the crystal therefore provide the strongest optical feedback to the laser oscillation. In Fig. 2, we also show a glass rod polished with a wedge on a $y$ surface to couple out the trapped resonance waves.

 

Fig. 2. Three-dimensional illustration of the preferred configuration of a KTP off-axis laser oscillator containing a radiating gain dipole. The gain dipole is excited by a pump source so that its dipole axis is transverse to the plane of incidence. A glass rod polished with a wedge is attached to a $y$ surface to couple out the laser.

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In our experiment, we first pumped the KTP crystal with 24 mJ pulse energy at 1064 nm in an 11 ns pulse length. The crystal dimensions are ${30}\;{\rm mm}\;(x) \times \;{1}\;{\rm mm}\;(y) \times \;{6}\;{\rm mm}\;(z)$. The $x$ and $y$ surfaces were optically polished without any anti-reflection coating. According to Eq. (5), the 11 ns pulse duration corresponds to the time duration of 25–30 axial or $x$-direction roundtrips of the Stokes wave in the crystal. The pump beam has a radius of 0.55 mm at the center of the crystal. Without the output coupler, the combined axial and off-axial oscillations of the Stokes waves in the high-${Q}$ crystal cavity energizes the whole crystal with their second-harmonic generation (SHG) and sum-frequency generation (SFG) [15], as shown in Fig. 3(a). Some light emits from the edges of the crystal. On one side of the crystal, we used a cylindrical lens and a 1200-groove/mm grating to resolve a rainbow-like spectrum from the SHG and SFG of the Stokes waves. The downstream screen shows a circular pattern of rainbow lines generated from the angular phase matching of the SHG and SFG processes in the crystal. As Fig. 3(b) shows, the output light consists of two spectral groups between 540 and 1800 nm. The first group contains multiple Stokes lines in the infrared spectrum, and the second group contains their SHG and SFG lines in the visible spectrum. Figure 3(c) shows the observed 2.2 GHz quasi-mode-locked pulse train of the output Stokes wave in the pump envelope. The measured pulse separation or the resonator roundtrip time is 451 ps, which is close to the 437 ps calculated from Eq. (4) with an incident angle $\bar \theta \sim \theta_c$ on the $x$ surface. This means that the preferred oscillations are $\theta \; \gt \;{\theta _c}$ modes in the crystal. Since stimulated Raman scattering is a nonlinear process, it is not a surprise that the Stokes modes with phase coherence build into high-intensity mode-locked pulses to extract the Raman gain in the crystal [16,17]. Working as a positive feedback, those high-power mode-locked pulses in turn expand the bandwidth of the supercontinuum.

 

Fig. 3. (a) Photograph of the anisotropic off-axis Raman oscillator when pumped by an 11 ns pulse at 1064 nm. A 1200-groove/mm grating resolves the scattered light into a rainbow. (b) Output light consists of two spectral groups. The one in the visible spectrum is the SHG and SFG of the Stokes waves in the infrared spectrum. (c) Measured quasi-mode-locked Stokes pulse train (red curve) in the pump pulse envelope (black curve). The inset shows the Fourier spectrum of the pulse train. The 2.2 GHz mode spacing is the inverse of the roundtrip time of the oscillating modes in the resonator.

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To couple out the supercontinuum for potential applications, we prepared another uncoated KTP crystal with the dimensions of ${22}\;{\rm mm}\;({x})\; \times {1}\;{\rm mm}\;({y}) \times {30}\;{\rm mm}\;({ z})$. Again, its $x$ and $y$ surfaces are optically polished. Given the 11 ns pump pulse width, the shortened length in $x$ allows more longitudinal roundtrip oscillations for the resonant waves. The increased height in $z$ is convenient to inject more pump energy by using an elliptical pump beam. In the crystal, the pump beam has 2 and 0.5 mm radii along the major and minor axes along $z$ and $y$, respectively.

Figure 4(a) is the experimental setup. The pump beam provides a forward pulse and is reflected back into the same crystal by a mirror located 75 mm from the downstream end of the crystal. We devised two schemes to couple out the supercontinuum from the off-axis resonator. In the first scheme, we installed a fiber bundle (Spectra-physics 0129-4350) with a linear array of fibers aligned along the crystal edge in $z$ to guide the edge emitted supercontinuum to a circular array of fibers at the other end of the fiber bundle. Figure 4(b) shows a typical beam profile with a circular intensity distribution obtained from this scheme. With 350 mJ pump energy, we measured 0.1 mJ at the output of the fiber bundle. If all the emitted light at the four crystal edges were collected into the fiber bundle, we could expect a four-fold increase in output energy, or ${\sim}{0.4}\;{\rm mJ}$.

 

Fig. 4. (a) Experimental setup with two schemes to couple out the supercontinuum. The first scheme used a linear-array fiber bundle to collect the laser light emitted from the crystal edge along $z$, and the 2nd scheme was used to attach a wedge-polished glass rod to frustrate the total internal reflection and couple out the resonant wave. (b) Output end of the fiber bundle arranged with a circular array of fibers, which produced a circular beam profile for the out-coupled supercontinuum laser. (c) Zoomed-in view of the glass-rod coupler, which behaves like a “straw” to “drain” the resonant waves toward its output end.

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Fig. 5. Measured supercontinuum output energy from the glass-rod coupler versus pump pulse energy. At 350 mJ pump energy, the measured supercontinuum output is 0.6 mJ.

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In conclusion, we have reported generation of an octave-spanning supercontinuum from a ${Q}$-switched laser pumped off-axis Raman oscillator in a monolithic KTP crystal. An off-axis oscillator resonates waves with zigzag paths between two planar boundaries in a gain crystal, supporting an ultrabroad bandwidth for waves satisfying total internal reflection conditions. Given the ${z}$-polarized pump, the induced nonlinear polarization of the Raman scattering is also along $z$. Such a scattering configuration satisfies the design of the so-called anisotropic off-axis laser oscillator for maximizing the laser gain [14]. With 24 mJ energy in an 11 ns pump pulse width in one pump transit, we measured a supercontinuum output with two spectral groups between 540–750 and 1095–1800 nm. The infrared group is primarily a result of cascading Raman Stokes filled with many oscillation modes. The visible group is mostly the SHG and SFG of the infrared group.

We demonstrated two schemes to couple out the supercontinuum trapped in the monolithic off-axis KTP oscillator. The first scheme is to adopt a linear-to-circular fiber bundle commonly designed to work for a diode laser array. The second scheme is to attach a glass rod to the $y$ surface of the crystal to frustrate the total internal reflection of the trapped resonant waves and guide the waves along the rod axis toward the output end of the rod. By pumping a 22 mm long and 1 mm thick $y$-cut KTP with a double-pass cylindrical pump beam, we coupled out 0.1 and 0.6 mJ supercontinuum energy from the 1st and 2nd schemes, respectively, when injecting 350 mJ pump energy into the crystal. For the fiber-bundle coupler, the measured output mode profile was nicely circular, and it was possible to extend the linear-array fibers to more crystal edges to collect more output power. For the glass-rod coupler, the mode profile is not an ideal circle, but depends on the coupling angle and the rod diameter versus the pump beam area. Although the pump depletion and thus the internal conversion efficiency is a few tens of percent [14], further optimization to reduce the air gap between the rod and the crystal could greatly increase the output coupling. The demonstrated resonator-enhanced octave-spanning supercontinuum from a monolithic crystal oscillator can be an ultra-compact and low-cost light source for useful applications.