August 15, 2012 / Vol. 37, No. 16 / OPTICS LETTERS
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Higher-order-mode fiber optimized for energetic soliton propagation Martin E.V. Pedersen,1,†,* Ji Cheng,2,† Kriti Charan,2 Ke Wang,2 Chris Xu,2 Lars Grüner-Nielsen,1 and Dan Jakobsen1 1 2
OFS Fitel Denmark ApS, Priorparken 680, DK-2605 Brøndby, Denmark
School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14853, USA *Corresponding author:
[email protected] Received May 21, 2012; revised July 6, 2012; accepted July 10, 2012; posted July 11, 2012 (Doc. ID 169075); published August 15, 2012
We describe the design optimization of a higher-order-mode (HOM) fiber for energetic soliton propagation at wavelengths below 1300 nm. A new HOM fiber is fabricated according to our design criteria. The HOM fiber is pumped at 1045 nm by an energetic femtosecond fiber laser. The soliton self-frequency shift process shifts the center wavelength of the soliton to 1085 nm. The soliton has a temporal duration of 216 fs and a pulse energy of 6.3 nJ. The demonstrated pulse energy is approximately six times higher than the previous record in a solid core fiber at wavelengths below 1300 nm. © 2012 Optical Society of America OCIS codes: 060.2280, 060.4370, 060.5530.
For many applications in optics, dispersion control is very important, and the ability to control and design the dispersion properties of an optical fiber continues to be a crucial skill within the optical fiber community. The majority of the optical fibers are made from silica and, depending on the intended application of the fiber, either the core or cladding is doped with dopants to achieve the desired properties of the fiber within the wavelength region of interest. Silica glass has a zero dispersion wavelength around 1.3 μm. Therefore, a standard solid fiber operated in the single mode regime will always have normal dispersion below 1.3 μm because the waveguide dispersion is normal in this case. To achieve anomalous dispersion below 1.3 μm in an optical fiber, the use of more elaborate fibers is necessary. Anomalous dispersion can be accomplished by photonic crystal fibers (PCFs) [1] and HOM fibers [2], and soliton self-frequency shift (SSFS) has been demonstrated in both fiber types for generating femtosecond, wavelength tunable sources [3–6]. Soliton formation and SSFS require an optical fiber with anomalous dispersion to counteract the phase change from the optical nonlinearity of the fiber. The energy of the soliton pulse is then given by E sol
N 2 λ3 DAeff ∝ DAeff ; 2π 2 cnI2 T 0
(1)
where N is the soliton order, λ is the wavelength, D is the group velocity dispersion in the wavelength domain, Aeff is the effective mode area, c is the speed of light in vacuum, nI2 is the intensity dependent refractive index, and T 0 is related to the pulse duration. From a design perspective using silica glass, the significant parameters related to the energy of the soliton are D and Aeff because these are direct attributes of the waveguide design. The waveguide design also influences the nI2 value; however, the change in value is relatively small [7] when compared to the possible changes in the values of D and Aeff . To generate a femtosecond, wavelength tunable source for practical applications, energetic pulses are desirable. For example, in in vivo deep tissue multiphoton microscopy [8,9], significant pulse energy (e.g., greater than 0146-9592/12/163459-03$15.00/0
1 nJ at the sample) is required to achieve an adequate signal-to-noise ratio and fast frame rate. Such applications require output pulse energies greater than 5 nJ from the source. Microstructured PCFs normally have a small Aeff ; hence the energy of the soliton also is small (e.g., a small fraction of nJ). For a hollow core photonic bandgap fiber, the non-linearity is extremely low; hence, the energy of the soliton is very large (100 s of nJ) [10]. In between these two energy regions are the HOM fibers, where the soliton energy is potentially well matched to practical applications (e.g., multiphoton microscopy). However, previous reports, the soliton energy in HOM fibers have been limited to around 1 nJ [5]. In this work, we describe the design optimization of a HOM fiber for energetic soliton propagation. A new HOM fiber is fabricated according to our design criteria, and the resulting soliton has a temporal duration of 216 fs and a pulse energy of 6.3 nJ at a wavelength of 1085 nm. The demonstrated pulse energy is approximately six times higher than the previous record in a solid silica fiber at wavelengths below 1300 nm [5]. The HOM fiber also provides better pulse energy for the considered tuning range with fs operation than current Yb fiber-laser systems. The soliton energy is directly proportional to the DAeff product [Eq. (1)]. Thus, to increase the soliton energy, it is a matter of designing a fiber with a very large anomalous dispersion and/or a large effective mode area for the mode where the soliton propagates. We focus on the LP02 mode in the HOM fiber. To enhance the waveguide dispersion of the LP02 mode, the fiber has a triple clad design. The parameter space of the design of the HOM fiber has been thoroughly investigated by running numerous computations of different configurations to find the optimum design for the highest soliton energy. The optimized design is a compromise of soliton energy and the wavelength range for SSFS. An intuitive explanation is offering in [11] regarding the scaling of the group velocity dispersion for the LP01 mode in a triple clad design, which also applies for the LP02 mode. The triple clad design can be viewed as a superposition of two waveguides, a core waveguide and a ring waveguide, as shown in Fig. 1. © 2012 Optical Society of America
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Fig. 1. Schematic refractive index profile of the core and the ring waveguides that make up the triple clad waveguide structure.
The area under the D curve between the two zerodispersion wavelengths can be regarded as a constant given by the difference in group index of the core waveguide and the ring waveguide [11]. Therefore, a larger peak D leads to a narrower wavelength region where the dispersion is anomalous. It is fairly easy to optimize the D value while ensuring a relatively large Aeff . However, as the peak of the D curve is increased, the effective index for the the LP02 mode and LP11 mode crosses at a wavelength closer to the peak of the D curve. In Fig. 2, this mode-crossing wavelength as a function of the DAeff product at the wavelength of 1060 nm is shown for a number of different waveguide perturbations. Figure 2 shows that the mode-crossing wavelength moves closer to the input wavelength (i.e., ∼1060 nm) as the DAeff product increases, which is undesirable for a stable operation. Any imperfection in the fabrication process will result in a fiber without perfect cylindrical symmetry; therefore, any mode-crossing could create a strong coupling between the two modes. The mode-crossing limits the wavelength range in which the soliton can be formed and shifted without any significant loss. As a compromise between soliton energy and stability, our optimized design has a mode-crossing between the LP02 and LP11 modes at around 1120 nm. Figure 3 shows the effective indices as a function of wavelength for the first four LP modes of the chosen design for the HOM fiber. To show the decomposition of the triple clad design into a core and a ring waveguide, the effective indices as a function of wavelength are shown for the core and the ring waveguides in Fig. 4. The effective indices for the individual LP01 modes in the core and ring waveguides cross at around 1120 nm. Because the core and ring waveguides are coupled waveguides in the triple clad design and they have the same angular symmetry, the two LP01 modes are forced to make an avoided crossing to satisfy the orthogonality requirement. This can be seen by comparing Fig. 3 to Fig. 4. The LP02 mode starts out as the LP01 mode of the isolated ring waveguide at the shorter wavelengths and ends up as the LP01 mode of the isolated core waveguide at the longer wavelengths.
Fig. 2. (Color online) Mode-crossing wavelength as a function of the DAeff product at wavelength of 1060 nm for a number of different waveguide perturbations.
Fig. 3. (Color online) Effective indices of the lowest four propagating modes in the HOM fiber, with respect to pure silica.
Therefore, the mode-crossing between the LP02 and LP11 modes comes as an effect of the avoided crossing between the LP01 and LP02 modes. The closer the intersect angle between the two LP01 modes in the isolated core and ring waveguides are to 90°, the larger the curvature the avoided crossing will experience. The curvature in the effective index is directly related to the 2 dispersion value as D − λc ddλn2eff . However, from Fig. 4, the closer the intersect angle is to 90°, the closer the mode-crossing between the core LP01 mode and the ring LP11 mode is to the mode-crossing between the core LP01 mode and the ring LP01 mode. Thus, with the triple clad design there is a natural trade-off between a high anomalous dispersion value for the LP02 mode and the position of the mode-crossing wavelength between the LP02 and LP11 modes. Figure 5 shows the group velocity dispersion and effective area of the LP02 mode as well as the DAeff product. Figures 3 and 5 show that the mode-crossing wavelength is very close to the wavelength at the peak of the D curve. For the Yb-based fiber laser system we used as the pump, it is only possible to use the left hand side of D curve for the SSFS. In this optimization process, we have focused on the LP02 mode; however, other HOMs also could be used. In general, the process would become more complex because more mode-crossings will be involved. We have fabricated a HOM fiber according to the design shown in Fig. 5. Figure 6 shows the measured output spectrum after 25 cm of the optimized HOM fiber, where the input source is an IMRA FCPA μJewel system at a wavelength of 1045 nm. The FWHM pulse duration of the input pulse is approximately 600 fs, and the input pulse energy into the fiber is 23 nJ. Because the fiber is a HOM fiber and the pulse is coupled in from free space, only a fraction of the pulse energy is coupled into
Fig. 4. (Color online) Effective index for the LP01 mode in the core waveguide and the effective indices for the LP01 and LP11 in the ring waveguide. All the effective indices are shown with respect to pure silica.
August 15, 2012 / Vol. 37, No. 16 / OPTICS LETTERS
Fig. 5. (Color online) Dispersion, effective area, and DAeff product curves of the LP02 mode.
the LP02 mode. The fraction is estimated to be 48% from the simulated pulse propagation in the LP02 mode shown in Fig. 6. For future applications, the excitation of the LP02 mode can be more efficiently accomplished by using long period gratings. Nonetheless, the LP02 mode is the only propagating mode with anomalous dispersion and therefore the only mode that can support a soliton pulse and the subsequent SSFS. Figure 6 shows the soliton has red-shifted to a center wavelength of 1085 nm. The energy of the soliton is measured by recording the total power out of the fiber and the power through a long pass filter with the band edge at 1064 nm. This results in a soliton energy of 6.3 nJ, which is approximately six times higher than the previous record in a solid core fiber at wavelengths below 1300 nm. The pulse duration of the soliton pulse is measured by using second order intensity autocorrelation, and the FWHM is 216 fs, assuming a sech2 pulse profile (Fig. 6). The autocorrelation measurement is done with the long pass filter in place. The theoretical DAeff product at 1085 nm is 29 fs, which together with the measured pulse duration yields a fundamental soliton2 pulse energy of 6.3 nJ, assuming nI2 2.55 × 10−20 mW , which is in excellent agreement with our experiments. The HOM fiber also provides better pulse energy for the considered tuning range with fs operation than current Yb fiber-laser systems [12,13] and, with the possibility to engineer both the wavelength and bandwidth of the anomalous region, the HOM fiber provides a more flexible design platform. In conclusion, we have optimized the HOM fiber design to achieve an energetic soliton pulse. A new HOM fiber is fabricated according to our design criteria, which enabled an energetic soliton that has a temporal FWHM of 216 fs and a record pulse energy of 6.3 nJ in a solid core fiber at wavelengths below 1300 nm.
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Fig. 6. (Color online) (a) Measured spectrum with the shifted soliton pulse together with a simulation corresponding to the pulse propagation in the LP02 mode. (b) Corresponding measured intensity autocorrelation of the soliton pulse.
The research is supported in part by the National Institutes of Health (NIH) R01CA133148 and R21RR024415. The authors thank Chris Schaffer for sharing equipment. †These authors contributed equally to this work. References 1. J. Knight, J. Arriaga, T. Birks, A. Ortigosa-Blanch, W. Wadsworth, and P. Russell, IEEE Photon. Technol. Lett. 12, 807 (2000). 2. S. Ramachandran, S. Ghalmi, J. W. Nicholson, M. F. Yan, P. Wisk, E. Monberg, and F. V. Dimarcello, Opt. Lett. 31, 2532 (2006). 3. X. Liu, C. Xu, W. H. Knox, J. K. Chandalia, B. J. Eggleton, S. G. Kosinski, and R. S. Windeler, Opt. Lett. 26, 358 (2001). 4. I. Cormack, D. Reid, W. Wadsworth, J. Knight, and P. Russell, Electron. Lett. 38, 167 (2002). 5. J. V. Howe, J. H. Lee, S. Zhou, F. Wise, C. Xu, S. Ramachandran, S. Ghalmi, and M. F. Yan, Opt. Lett. 32, 340 (2007). 6. J. Lee, J. V. Howe, C. Xu, and X. Liu, JSTQE 14, 713 (2008). 7. M. Pedersen, T. Palsson, K. Jespersen, D. Jakobsen, B. Palsdottir, and K. Rottwitt, in 2011 IEEE Photonics Conference (IEEE, 2011), pp. 571–572. 8. D. Kobat, M. E. Durst, N. Nishimura, A. W. Wong, C. B. Schaffer, and C. Xu, Opt. Express 17, 13354 (2009). 9. D. Kobat, N. G. Horton, and C. Xu, J. Biomed. Opt. 16, 106014 (2011). 10. D. G. Ouzounov, F. R. Ahmad, D. Mu ̈ ller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, Science 301, 1702 (2003). 11. S. Ramachandran, ed., Fiber Based Dispersion Compensation (Springer, 2007). 12. M. Schultz, H. Karow, D. Wandt, U. Morgner, and D. Kracht, Opt. Commun. 282, 2567 (2009). 13. L. Kong, X. Xiao, and C. Yang, Laser Phys. 20, 834 (2010).
