1. Introduction

Ti:Sapphire lasers and optical parametric oscillators (OPOs) based on χ⁽²⁾ crystals are the current state-of-the-art for generating wavelength-agile short-pulsed laser radiation [1]. These sources are useful for pump-probe measurements of the carrier lifetimes in semiconductors or for spectroscopically resolving fast chemical or biological reactions [2–4]. Although χ⁽²⁾ OPOs are becoming more compact and user friendly, there has been a trend towards using fiber-based optical parametric oscillators (FOPOs) that operate through four-wave mixing (FWM) mediated by the χ⁽³⁾ nonlinearity of glass. They are an attractive alternative to their χ⁽²⁾ counterparts for a number of key reasons: (i) the FWM phase-matching bandwidth can be continuous and hundreds of nanometers wide; (ii) signal gain occurs at wavelengths near to, as well as far from, that of the pump; (iii) the transverse mode quality of fiber-based oscillators is exceptionally good; and (iv) a fiber-based gain medium lends itself to integration with fiber components.

The use of microstructure fiber (MF) in parametric devices such as amplifiers [5–7], generators [8], and wavelength converters [9,10] has been the subject of much recent work. A number of FOPOs have been demonstrated using standard and highly-nonlinear dispersion-shifted optical fibers [11–14]. Microstructure fibers offer the promise of dramatically extending the wavelengths of operation and efficiency of FOPOs [15–17]. Indeed, MF-OPOs have been demonstrated with as much as 200 nm of wavelength tunability, pulse durations ranging from 400 fs up to several ps, and output powers of a few hundred μW. The potential for wide-band tuning and short pulse durations is clear from previous work, but the principal drawback of virtually all of these fiber-based systems is that they do not generate sufficient power for widespread commercial appeal.

In this paper, we report on an FOPO design that utilizes short pieces of MF. The advantages of using short fibers are explored theoretically using the standard theoretical description for parametric processes in optical fibers. The results of three experimental embodiments are then described that employ various pump-laser wavelengths, pump-pulse durations, and microstructure fibers. One of these systems features signal and conjugate fields that span an octave of optical spectrum. The MF-OPOs reported can generate pulses that can be tuned over 200 nm, and the output pulses in the near IR output are measured to be 570 fs with 1.6-ps pump pulses. We demonstrate the highest average power (50 mW maximum), peak power (1.2 kW maximum), and total conversion efficiency (11 % maximum) of any tunable pulsed FOPO reported to date. These results represent two critical achievements: (i) the efficient generation of wavelength-tunable short-pulsed visible light from a Ti:Sapphire laser using only a single stage of frequency conversion; and (ii) the first tunable FOPO that produces sufficient output peak power (100 times greater than that of previously reported FOPOs) to serve as a source for nonlinear optical studies such as multi-photon microscopy. This approach is particularly interesting for introducing broad tunability to mode-locked ytterbium and erbium fiber lasers. The device demonstrated here is a bulk device that incorporates an optical fiber as the gain medium; nevertheless, it illustrates numerous desirable features. Since all the fields are collinear, the system is extremely robust and easy to align, as compared to most χ⁽²⁾-based OPOs. Furthermore, the fiber fixes the spatial mode of the cavity so that each half of the cavity can be aligned independently. Additionally, the parametric amplification process results in very high gain so that a large percentage of output coupling and other cavity losses can be tolerated. Wavelength tunability is achieved by translating a single stage.

2. Theory

Parametric amplification in optical fibers is described in a number of review articles [18,19] and texts [20,21]. Parametric amplification in MFs is similar to that of standard optical fibers, but differences arise from the large effective refractive index contrast between the core and cladding in MFs as compared to that in standard optical fibers. This large contrast provides additional control of the optical field confinement, transverse modal behavior, and waveguide dispersion [22,23]. Firstly, confinement of light to the core’s small effective area, A _eff, increases the effective nonlinearity, γ = (n ₂ Ω)/(c A _eff), where n ₂ is the nonlinear refractive index, Ω is the angular frequency of the field, and c is the speed of light. Secondly, these fibers exhibit excellent spatial overlap between propagating modes even at widely different wavelengths [22]. Finally, there is a large contribution to the total dispersion arising from the waveguide design, which can be used to phase match wave-mixing phenomena such as FWM.

The FWM process in optical fibers can be described by the coupled-amplitude equations [19] for electric fields with a slowly-varying envelope propagating through a dielectric medium of length L in the z-direction. For an undepleted pump wave, the small-signal gain of the signal field can be expressed as,

where P _S is the signal power, P _P is the pump power, and g = [-Δβ(Δβ/4 + γP _P)]^1/2 is the parametric gain coefficient. The propagation constants for the pump, signal, and conjugate (idler) fields are denoted as β _P, β _S, and β _C, respectively, and Δβ = β _S + β _C - 2β _P. In order to observe efficient gain, phase matching must be achieved, which implies that the propagation constants of the pump, signal, and conjugate fields, including any intensity-dependent phase shifts ϕ _nl, satisfy the relation Δβ + ϕ _nl = 0. For the FWM parametric process the energy conservation relation 2Ω _p = Ω _s + Ω _c must also hold.

 

Fig. 1. Plots of Eq. (1) showing the device performance as the fiber length is reduced. (a) The gain is plotted versus wavelength for fiber lengths ranging from 3 mm to 2.1 m. Calculation parameters are: λ ₀ = 730 nm, λ _p = 737 nm, γ= 94 (W km)^-1, β ₂ = -6.8 × 10^-28 s₂/m, β ₄ = -4.2 × 10^-56 s⁴/m. (b) The expected output pulse energy (squares, left axis) and gain bandwidth (solid line, right axis) are plotted versus fiber length.

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Plots of Eq. 1 reveal that decreasing the length of the fiber dramatically increases the phase-matching bandwidth. Figure 1(a) shows a comparison of the single-pass, small-signal gain as a function of wavelength for different lengths of fiber where γP _P L = π. The negative-exponential relationship between the gain bandwidth and fiber length is plotted on the right axis of Fig. 1(b). The overall output power also improves with decreasing fiber length because the system saturates at a higher pump power when the fiber length is shortened. The nonlinearity γ, pump power P _P, and fiber length L should be chosen so that the system operates slightly below the saturation power, and we have found experimentally that the maximum amount of power that can be converted from the pump into either signal or conjugate is about 10-20%. This condition occurs when γP _P L = π ≈ π. Plotted on the left axis of Fig. 1(b) is the expected output pulse energy as a function of fiber length for optimal operation where it has been assumed that 10% of the pump energy is converted to useful output.

A second strategy for extracting more power from the system is to couple out the conjugate field rather than the oscillating signal field. One can extract 100% of the optical power in the conjugate field without changing the threshold for oscillation, which is determined by the gain and loss in the signal field. For example, a MF with a zero-GVD wavelength λ _o of 790 nm will have γ ≈ 75 (W ∙ km)^-1. A commercial Ti:Sapphire oscillator can deliver about 2.5 kW of pump peak power into the fiber (i.e., 500 mW average power at a repetition rate of 75 MHz for 2.7 ps pump pulses). For γP _P L = π the optimal fiber length is approximately 2 cm, and under these conditions one can expect 10-20% of the pump energy to be converted to either the signal or conjugate waves. Under these assumptions, Fig. 1(b) shows the expected output energy as a function of fiber length.

 

Fig. 2. Left: Schematic of the experimental apparatus. Right: Typical output spectrum where the FWM orders are labeled, and the system is configured to oscillate in the +1 order. See Table 1 for NL-1.8-730 test parameters.

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3. Experiment

We implement these ideas in the experimental setup depicted in Fig. 2 using three different MFs whose properties are described in Table 1. Pulses from a Ti:sapphire laser (740 nm - 820 nm in wavelength, 200 fs or 1.6 ps in pulse duration, 76-MHz repetition rate, and 700-mW average power) are coupled into the MF via a dichroic mirror (DM1) and a short focal-length aspheric lens or microscope objective (L1). A second lens (L2) is placed at the output of the MF such that the pump light is nearly collimated. The oscillator is a Fabry-Perot cavity formed between a broadband high reflector (M4) and DM1. The output is captured using a second dichroic mirror (DM2). The dichroic mirrors DM1 and DM2 are both coated such that they pass the pump wavelength, but DM1 reflects wavelengths longer than the pump (i.e., it is a short-pass dichroic), while DM2 reflects wavelengths shorter than the pump (i.e., it is a long-pass dichroic). Inclusion of the 5-cm piece of glass allows the wavelength of operation to be dispersion-tuned by translating DM1. Cavity folding mirrors M1-M3 allow the system to fit conveniently onto an 18-by-24-inch breadboard.

Table 1. Comparison of FOPO devices

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With the cavity length adjusted for synchronous operation, the system as described above oscillates at wavelengths longer than the pump wavelength and which fall within the gain bandwidth of the FWM process. The conjugate field, which corresponds to shorter wavelengths than that of the pump, is coupled out. A typical output optical spectrum for the 1.8-μm-core MF system is shown in Fig. 2, where the oscillating mode is labeled +1. This FOPO is pumped at a fixed wavelength of 740 nm. It can be reconfigured to oscillate at wavelengths shorter than the pump by swapping DM1 and DM2. Figure 2 also shows that the output energy is divided between three modes (labeled -1, -2, and -3). The output wavelength is tuned by translating DM1, and a composite of several output spectra for different positions is shown in Fig. 3(a). The set of short-wavelength curves on the left-hand side corresponds to the case in which the long-wavelength (+1) mode is oscillating, whereas the curves on the long-wavelength side of center correspond to the case where the short-wavelength (-1) mode is oscillating. In both cases, it is the conjugate, non-oscillating field that is output coupled. Figure 3(b) shows the variation in average output power measured for the -1, -2, and -3 modes as a function of wavelength.

 

Fig. 3. (a) A composite of optical spectra (with the central pump peak removed) of the output of the FOPO. (b) The measured output powers versus wavelength for the -1, -2, and -3 output modes. See Table 1 for NL-1.8-730 test parameters.

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The 740-nm-pumped system is designed to achieve tunability at wavelengths shorter than those available directly from a Ti:Sapphire laser. We are able to obtain 200 nm of tunability ranging from 590 nm up to 710 nm in the short-wavelength range and at long wavelengths from 790 nm up to 870 nm. For this system we use custom-coated long-wavelength-pass and short-wavelength-pass dichroic mirrors as DM1 and DM2. In this system the output power is limited by that delivered by our Ti:Sapphire pump laser.

In order to demonstrate ability of this scheme to scale to higher powers, we use a 2.3-μm-core MF pumped at 795 nm. A cold mirror (ThorLabs part no. FM03) is used as DM1 and a hot mirror (Edmund Scientific part no. U43-955) as DM2. The system oscillates in the -1 mode (see Fig. 2), and the long wavelength (+1) mode is output coupled. Figure 4(a) shows the threshold behavior of the output power as a function of pump power, and the measured average output power is as high as 50 mW for an average pump power of 480 mW. An autocorrelation of the output with the system tuned to 915 nm is shown in the inset of Fig. 4(a). The output pulses are measured to be 570 fs, which is narrower in duration than that of the pump (1.6 ps) due to the fact that the coupling between the pump, signal, and conjugate fields is largest at the peak of the pulses. Experimentally, we observe a pulse narrowing factor of about three throughout the range of tuning.

 

Fig. 4. (a) A plot of output average power as a function of pump power where the oscillation threshold is 390 mW, and the slope efficiency is 58 %. Inset in (a) is an intensity autocorrelation (AC) of the output where τ _ac = 810 fs. (b) The spectral tuning capability of the system for which oscillation is in the -1 (short-wavelength) mode. See Table 1 for NL-2.3-790 test parameters.

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Figure 4(b) illustrates the spectral tunability of the 795-nm pumped system in which the output wavelength is tuned from 850 nm up to 960 nm. This tunable range is 30 nm larger than the corresponding portion of the tuning range obtained using the 745-nm pump, implying that with customized dichroic mirrors the total wavelength tunability of the 795-nm-pumped system can exceed 200 nm.

The data in Fig. 5 is obtained from a third FOPO embodiment, which uses a 5-mm-long fiber pumped by 200-fs pulses. This configuration is optimized for wide spectral tunability, where we expect the gain-bandwidth to increase by about a factor of two when the length of the MF is reduced from a few cm to a few mm. The data in Fig. 5 shows that one can achieve signal and conjugate fields that are detuned from each other by a full octave in frequency.

 

Fig. 5. A composite of optical spectra showing the broad phase matching capability afforded by using a very short fiber. See Table 1 for Low Air-Fill test parameters.

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4. Conclusions

In summary, we have reported on the development of FOPOs featuring hundreds of nm of tunability and tens of mW average output powers (∼1 kW of peak power), making it an ideal system for applications such as multiphoton microscopy and time-resolved spectroscopy applications.