Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group

Frequency doubling of a broadband Raman fiber laser to 655 nm

Open Access Open Access

Abstract

655 nm laser radiation with power of >60 mW is generated by frequency doubling of a broadband randomly-polarized 1.31-μm Raman fiber laser (RFL). The red power appears to grow linearly with increasing RFL power up to 7 W at efficiency comparable with that for single-frequency lasers. It has been shown that multiple sum-frequency mixing processes involving different RFL modes provide the main contribution to the output, which is enhanced by 2 times due to the modes stochasticity.

©2009 Optical Society of America

1. Introduction

CW Raman fiber lasers (RFLs) are known as stable robust high-power fiber light sources providing almost any wavelength in the near-IR range (1.1-1.7 μm), see e.g. [1]. Recently, lasing at 2.1 μm has been demonstrated in GeO2 fiber [2]. Moreover, RFLs are able to emit multiple wavelengths simultaneously [3], and its output radiation can be tuned over a wide frequency range in an all-fiber configuration [4,5]. All these features turn the RFLs into useful tools which are already being applied in telecommunications as well as other fields such as supercontinuum generation [6] and optical coherence tomography [7].

A possibility to generate visible radiation by frequency doubling and thus to extend the range of RFLs applications is very attractive. A fiber-based yellow laser was proposed in [8]. The first experiment was performed in [9]. The bulk LBO crystal was placed inside the cavity of the RFL in order to increase efficiency. However, only ~10 mW of yellow power was obtained because of low conversion efficiency for the broadband unpolarized fundamental wave in this scheme. An impressive result has been obtained in [10]: 3 W at 589 nm was generated from a 23 W narrow-line linearly-polarized RFL with 8-mm long MgO-doped PPLN crystal. Recently, the yellow power of 14.5 W has been obtained with 20.7 W Raman amplifier [11]. A conversion of RFLs to red with tuning and power scaling capabilities is also possible [9] but not studied in spite of importance for bio-medical applications.

In the present paper, we report on the development of a robust CW red laser source based on the 1.31-μm phosphosilicate RFL. The obtained output power of >60 mW at 655 nm is the highest to our knowledge for frequency-doubled fiber lasers in the red range. The second harmonic generation (SHG) efficiency of ~1% obtained for the broadband fundamental wave appears comparable with that for single-frequency radiation at studied powers. A model taking into consideration sum-frequency mixing (SFM) processes inside the broad RFL spectrum has been developed. Computations show that SFM of multiple RFL modes with different frequencies provide significant changes in SH output power and spectral characteristics. A good qualitative and quantitative agreement of the model with the experimental data has been demonstrated.

2. Experiment

The experimental setup is shown in Fig. 1. We have utilized linear all-fiber scheme for the phosphosilicate RFL pumped by the Yb-doped fiber laser (YDFL), see e.g. [1, 12]. The YDFL is pumped by 3 laser diodes (LDs) and delivers up to 13.8 W at ~1.115 μm. Its cavity consists of fiber Bragg gratings (FBGs) with high reflection (HR1.1) and high transmission (HT1.1) at 1.11 μm. The RFL cavity is formed by FBGs HR1.3 and HT1.3 with reflection coefficients 99% and 23% at 1.31 μm, correspondingly, placed at the ends of 350-m long fiber produced by FORC (Moscow) having the Raman gain of 6.5 dB/km·W, the loss of ~1.1 dB/km and MFD of 5.9 μm at 1.31 μm. The second Stokes shift (~1330 cm-1) associated with phosphorus secures conversion from 1.11 to 1.31 μm in one stage. Additional FBG HR1.1 (highly-reflective at 1.11 μm) is installed at the RFL output to implement a double pass pumping, see e.g. [12]. The RFL generates up to 7 W with PRFL/PYDFL~50% efficiency. Its output spectrum broadens significantly with increasing power, see Fig. 2(a), in spite of a narrowband (~0.2 nm) output FBG (HT1.3). At high powers the spectrum acquires wide exponential tails with a central dip corresponding to the output FBG reflection. Mechanisms of the spectral broadening in RFLs have been clarified recently: multiple four-wave mixing processes involving numerous longitudinal modes (~106 in ~1-km cavity) induce stochastic evolution of their amplitudes and phases [13, 14]. The weak wave turbulence model [14] is applicable to RFLs having high-Q cavity with broadband HR Gaussian FBGs and describes their spectra well, i.e. exponential shape and square-root growth of the width with power. However, this analytical model is not applicable directly to our RFL with narrowband low-reflection FBG which behavior deviates from [14]: its linewidth grows almost linearly, see Fig. 2(c) (similar result has been obtained numerically [15]), while the power density tends to saturation at 3.5 W/nm level, see Fig. 2(a), that is important for frequency doubling.

 figure: Fig. 1.

Fig. 1. Experimental setup.

Download Full Size | PPT Slide | PDF

 figure: Fig. 2.

Fig. 2. Fundamental wave (a) and SH (b) output spectra measured at different RFL powers. (c) Fundamental wave (boxes) and SH (circles) spectral widths together with SH width calculated from Eqs. (4),(5) (line).

Download Full Size | PPT Slide | PDF

Frequency doubling is performed in a simple and robust single-pass scheme with the 5% MgO-doped periodically poled LiNbO3 (PPLN) crystal with poling length L≈8 mm and specified poling period ≈12.73 μm that provides quasi-phase matching (QPM) at ~49°C for 1.31-μm operation. Corresponding QPM bandwidth amounts to ~0.6 nm. The crystal has anti-reflection coatings for the fundamental and SH waves at both facets. RFL output radiation is collimated (see Fig. 1), then cleaned from 1.1 μm radiation by dichroic mirror DM and focused by lens L to beam waist radius w0=22 μm into the PPLN crystal placed in the oven. The generated red spectrum has typical sidelobes, Fig. 2(b). The main SH peak is narrow, its width (FWHM) approaches ~0.3 nm at high powers, Fig. 2(c), in accordance with the QPM bandwidth. Although the RFL spectral width reaches ~1.6 nm (3 times broader than QPM bandwidth), the SH power (selected by filter F) grows linearly up to > 60mW at ~7 W RFL power, see Fig. 3.

 figure: Fig. 3.

Fig. 3. Experimental data (points) and calculated SHG power P versus Pω =PRFL for single frequency (dashed line) and multiple frequency (solid line) fundamental wave. Inset: corresponding SHG efficiency P/Pω.

Download Full Size | PPT Slide | PDF

The obtained ~1% efficiency is comparable with that for a single-frequency fundamental wave (results of calculations are shown by dashed line in Fig. 3). Moreover, in the low-power domain (PRFL<2.5 W) the obtained efficiency is higher than that in the single-frequency model, while at PRFL>2.5 W it becomes lower. Thus we can conclude that not only direct frequency doubling contributes to the SH of the broadband RFL.

3. Theoretical model

To explain the observed behavior, let us take into account sum frequency mixing (SFM) processes. In our description we follow methods of [16]. If the fundamental wave spectrum consists of N equidistant modes with frequencies ω1j (N~106 in the RFL), the second harmonic (SH) spectrum should consist of 2N-1 modes with frequencies ω2j. Even SH modes are generated only due to SFM, but odd modes have also direct SH contribution. Inset in Fig. 4 shows a SHG example for N=4. The power conversion is described by 2N-1 equations:

A2nz+1uA2nt=iσ2(A1m2ξn+j+k=n+1jkA1jA1k)m=(n+1)2ξn=[(1)n+1+1]2,

where Ain is the complex amplitude of n-th spectral mode of i-th harmonics, u is the group velocity, σ 2 is the nonlinear coefficient. The first term in the brackets describes the direct frequency doubling, the second one corresponds to the SFM. From Eq. (1) one can find an intensity of n-th spectral component of the SH:

 figure: Fig. 4.

Fig. 4. Second harmonic spectrum: experiment at Pω≈7.1 W (dots), calculation from Eqs. 4, 5 for direct frequency doubling (dashed line) and the same with sum-frequency mixing (solid line). Inset: an example of SHG for N=4.

Download Full Size | PPT Slide | PDF

I2n=(σ2z)2[(a1m4+2a1m2j+k=n+1jka1ja1k×cos(2φ1mφ1jφ1k))ξn+
+2jk(a1ja1k)2+2jkpqa1ja1ka1pa1q×cos(φ1j+φ1kφ1pφ1q)]

where aij and ϕij are the real amplitudes and phases of corresponding modes, respectively. The equation can be simplified for free-running modes, when all the phases ϕij are random:

I2n=(σ2z)2[a1m4ξn+2jk(a1ja1k)2]

Eqs. (1–3) are valid in the case of exact phase matching for all interacting waves. One can modify Eqs. (1–3) taking into account finite width of the phase matching (PM):

I2n=(σ2z)2[a1m4ξnsinc2(Δkmmz/2)+2jk(a1ja1ksinc(Δkjkz/2))2],

where Δkjk = k(ωj + ωk)— k(ωj)- k(ωk) is the wave vector mismatch.

It is also necessary to take into account specifics of the periodically-poled crystals (with period ∧). It is known, see e.g. [17], that the transition from PM to QPM can be done by:

z2πz,Δk(Δk2πΛ)π2,

One also needs to take into account Gaussian beam profile [18], which leads to modification of conversion coefficient (2σ2 L/π)2 at single frequency and polarization to

η=P2ω(Pω)2=16π2deff2Lλω3nωn2ωε0ch,

where deff =2d 33/π is the effective nonlinear coefficient, nj is the corresponding refractive index, ε0 is the permittivity of vacuum, c is the speed of light, and h~1 is the Boyd-Kleinman focusing factor. For d 33 = 27 pm/V and L=8 mm η = 1.24%/W at optimal focusing.

4. Comparison of the model with the experiment

Using Eqs. (4–6) we have calculated an expected SH spectrum using the measured RFL spectra (Fig. 2(a)). To obtain results at a reasonable computational time, we have reduced number of modes taking the effective mode spacing of 0.025 nm and checked that a further increase in number of modes does not lead to significant changes in SH power values (≤1%). Two cases have been compared: direct frequency doubling (first term in Eq. (4)) and frequency doubling assisted by SFM (both terms in Eq. (4)). The SH spectrum calculated for direct frequency doubling has a very low amplitude. It is normalized to 1 at maximum for a comparison (Fig. 4, dashed line). This spectrum “copies” the dip in the fundamental wave spectrum (Fig. 2(a)), that is absent in the measured SH spectrum. At the same time, calculations considering SFM (Fig. 4, solid line) provide a good coincidence with the experimental shape. Calculated second harmonic spectral width (FWHM) is also in a good agreement with the measured one, see Fig. 2(c). Thus, in presence of multiple frequencies in the fundamental wave the SFM makes the main contribution to the SH power.

For a quantitative comparison of the calculated and measured power values, we take into account that for the randomly polarized RFL laser a half of the power corresponds to one linear polarization component. We have also found a more exact value of the poling period (∧=12.54 μm) by fitting positions of the two first minima in the SH spectra. Slight difference with the specified period may be associated with temperature dependence and MgO doping while we use the refraction index data for pure lithium niobate [19]. Under these conditions, the SH power values calculated by summing up the power of individual modes (Eq. (4)) in frames of the SFM model (solid line in Fig. 3) are in very good agreement with the experimental points in low-power domain (≤2.5 W), confirming the fact that the multimode SH power is higher than single-frequency one. At higher powers one can see a significant deviation of the experimental points from the theory, which can be attributed to the poorer beam quality (M2≈1.3) and non-uniform crystal heating induced by the SH light absorption (see [20] and references therein). Nevertheless, the SFM model describes the experimental data quite well, especially a character of the dependence both for the SH power and efficiency (see inset in Fig. 3), that is quite different from that for the single-frequency model.

The obtained results can be easily understood taking into account that the RFL modes are stochastic, i.e. they have random phases and amplitudes. Summing up the power of N random modes within QPM bandwidth results in factors N and N 2 for the first and the second terms in Eq. (4), correspondingly, both proportional to squared RFL mode power (Pω/N)2. So the relative contribution of the direct doubling 1/N is vanishingly small at N≫1. Moreover, the second term in Eqs. (3,4) describing SFM takes factor 2 after transition from Eq. (2) to the stochastic case (with gaussian statistics). The enhancement coefficient is (2–1/N) and tends to 2 at N≫1. Let’s focus our attention on this fact, which means that the conversion efficiency for the multi-frequency radiation is higher than that for single-frequency one. This interesting effect is discussed in theory starting from classical paper [21] (see also [16] and citation therein), here it is convincingly confirmed in the experiment with the RFL at low powers. At high powers the input spectrum becomes broader than QPM bandwidth, so an additional factor proportional to the ratio of the mode number within QPM and total mode number leads to relative reduction of the resulting SH power below the single-frequency curve. At linear growth of the RFL modes number with power, the SH power should grow nearly linearly.

Note that frequency doubling of fiber lasers generating multiple frequencies was studied in experimental works [10, 20] and was compared with calculations, but not accurately. In [10] a single-frequency model has been used with a correction of the input power according to the QPM bandwidth. In [20] the multi-frequency nature of Yb fiber lasers was taken into account, but without mode phases “randomization,” as a result factor 2 could not be obtained.

5. Conclusion

We proved that SHG with radiation comprising multiple modes, the sum-frequency mixing gives the main contribution to the SH power, while the direct frequency doubling gives a vanishing value at large number of modes. Thus, efficient SH generation is possible for broadband fiber lasers, which spectral width is sufficiently larger than QPM bandwidth of the crystal. The developed SFM model describes quite well the SH spectrum and power measured at frequency doubling of 1.31-μm Raman fiber laser. Laser radiation of >60 mW at 655 nm has been generated that corresponds to the ~1% SHG efficiency. To increase the efficiency further, one can use a linearly polarized RFL like in [10]. Another parameter is the crystal length, but calculations in frames of the SFM model have shown that there is no significant enhancement owing to a QPM bandwidth reduction at the lengthening.

The authors acknowledge financial support by the grants of the Presidium and the Department of Physical Sciences of the Russian Academy of Sciences, Russian Ministry of Education and Science and CRDF (RUP1-1509-NO-05). We also thank A. A. Vlasov for FBGs fabrication and E. V. Podivilov for fruitful discussions.

References and links

1. E. M. Dianov, I. A. Bufetov, M. M. Bubnov, M. V. Grekov, S. A. Vasiliev, and O. I. Medvedkov, “Three-cascaded 1407-nm Raman laser based on phosphorus-doped silica fiber”, Opt. Lett. 25, 402–404 (2000). [CrossRef]  

2. B. A. Cumberland, S. V. Popov, J. R. Taylor, O. I. Medvedkov, S. A. Vasiliev, and E. M. Dianov, “2.1 μm continuous-wave Raman laser in GeO2 fiber”, Opt. Lett. 32, 1848–1850 (2007). [CrossRef]   [PubMed]  

3. Y.-G. Han, C.-S. Kim, J. U. Kang, U.-C. Paek, and Y. Chung, “Multiwavelength Raman fiber-ring laser based on tunable cascaded long-period fiber gratings”, IEEE Photon. Technol. Lett. 15, 383–385 (2003). [CrossRef]  

4. P. C. Reeves-Hall and J. R. Taylor, “Wavelength tunable CW Raman fibre ring laser operating at 1486-1551 nm”, Electron. Lett. 37, 491–492 (2001). [CrossRef]  

5. S. A. Babin, D. V. Churkin, S. I. Kablukov, M. A. Rybakov, and A. A. Vlasov, “All-fiber widely tunable Raman fiber laser with controlled output spectrum”, Opt. Express 15, 8438–8443 (2007). [CrossRef]   [PubMed]  

6. N. S. Kim, M. Prabhu, C. Li, J. Song, and K. Ueda, “1239/1484 nm cascaded phosphosilicate Raman fiber laser with CW output power of 1.36 W at 1484 nm pumped by CW Yb-doped double-clad fiber laser at 1064 nm and spectral continuum generation”, Opt. Commun. 176, 219–222 (2000). [CrossRef]  

7. M. Higashihata, K. Tochigi, Y. Nakata, and T. Okada “Application to the optical coherent tomography of fiber Raman laser”, 5th CLEO/Pacific Rim 2003 (15-19 Dec. 2003), 1, 183 (2003).

8. W. Hackenberg, D. Bonaccini, and D. Werner, “Fiber Raman laser development for multiple sodium laser guide star adaptive optics”, Proc. SPIE 4839, 421–428 (2003). [CrossRef]  

9. Y. Feng, S. Huang, A. Shirakawa, and K.-I. Ueda, “Multiple-color cw visible lasers by frequency sum-mixing in a cascading Raman fiber laser,” Opt. Express 12, 1843–1847 (2004). [CrossRef]   [PubMed]  

10. D. Georgiev, V. P. Gapontsev, A. G. Dronov, M. Y. Vyatkin, A. B. Rulkov, S. V. Popov, and J. R. Taylor, “Watts-level frequency doubling of a narrow line linearly polarized Raman fiber laser to 589 nm”, Opt. Express 13, 6772–6776 (2005). [CrossRef]   [PubMed]  

11. Y. Feng, L. Taylor, and D. Bonaccini Calia, “20W CW, 4 MHz linewidth Raman fiber amplifier with SHG to 589 nm”, Photonics West 2009, San Jose (postdeadline paper 7195–101).

12. V. I. Karpov, W. R. L. Clements, E. M. Dianov, and S. B. Parenyi “High-power 1.24 μm phosphosilicate-fiber-based laser pumped by laser diodes”, Can. J. Phys. 78, 407–413 (2000). [CrossRef]  

13. S. A. Babin, D. V. Churkin, A. E. Ismagulov, S. I. Kablukov, and E. V. Podivilov, “Spectral broadening in Raman fiber lasers”, Opt. Lett. 31, 3007–3009 (2006). [CrossRef]   [PubMed]  

14. S. A. Babin, D. V. Churkin, A. E. Ismagulov, S. I. Kablukov, and E. V. Podivilov, “Four-wave-mixing-induced turbulent spectral broadening in a long Raman fiber laser”, J. Opt. Soc. Am. B 24, 1729–1738 (2007). [CrossRef]  

15. J. Hagen, R. Engelbrecht, O. Welzel, A. Siekiera, and B. Schmauss, “Numerical modeling of intracavity spectral broadening of Raman fiber lasers”, IEEE Photon. Technol. Lett. 19, 1759–1761 (2007). [CrossRef]  

16. V. G. Dmitriev and L. V. Tarasov, Applied nonlinear optics (M., Radio i svyaz’, 1982) [in Russian].

17. V. G. Dmitriev and Yu.V. Yur’ev, “Equations for second-harmonic generation under quasi-phase-matched interaction conditions in nonlinear crystals with a regular domain structure,” Quantum Electron. 28, 1007–1010 (1998). [CrossRef]  

18. G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams”, J. Appl. Phys. 39, 3597 (1968). [CrossRef]  

19. S. D. Smith, H. D. Riccius, and R. P. Edwin, “Refractive indices of lithium niobate,” Opt. Commun. 17, 332(1976) and 20, 188 (1977) (errata). [CrossRef]  

20. F. J. Kontur, I. Dajani, Y. Lu, and R. J. Knize, “Frequency-doubling of a CW fiber laser using PPKTP, PMgSLT, and PPMgLN,” Opt. Express 15, 12882–12889 (2007). [CrossRef]   [PubMed]  

21. J. Ducuing and N. Bloembergen, “Static fluctuations in nonlinear optical processes,” Phys. Rev. 133, A1493–1502 (1964). [CrossRef]  

References

  • View by:

  1. E. M. Dianov, I. A. Bufetov, M. M. Bubnov, M. V. Grekov, S. A. Vasiliev, and O. I. Medvedkov, “Three-cascaded 1407-nm Raman laser based on phosphorus-doped silica fiber”, Opt. Lett. 25, 402–404 (2000).
    [Crossref]
  2. B. A. Cumberland, S. V. Popov, J. R. Taylor, O. I. Medvedkov, S. A. Vasiliev, and E. M. Dianov, “2.1 μm continuous-wave Raman laser in GeO2 fiber”, Opt. Lett. 32, 1848–1850 (2007).
    [Crossref] [PubMed]
  3. Y.-G. Han, C.-S. Kim, J. U. Kang, U.-C. Paek, and Y. Chung, “Multiwavelength Raman fiber-ring laser based on tunable cascaded long-period fiber gratings”, IEEE Photon. Technol. Lett. 15, 383–385 (2003).
    [Crossref]
  4. P. C. Reeves-Hall and J. R. Taylor, “Wavelength tunable CW Raman fibre ring laser operating at 1486-1551 nm”, Electron. Lett. 37, 491–492 (2001).
    [Crossref]
  5. S. A. Babin, D. V. Churkin, S. I. Kablukov, M. A. Rybakov, and A. A. Vlasov, “All-fiber widely tunable Raman fiber laser with controlled output spectrum”, Opt. Express 15, 8438–8443 (2007).
    [Crossref] [PubMed]
  6. N. S. Kim, M. Prabhu, C. Li, J. Song, and K. Ueda, “1239/1484 nm cascaded phosphosilicate Raman fiber laser with CW output power of 1.36 W at 1484 nm pumped by CW Yb-doped double-clad fiber laser at 1064 nm and spectral continuum generation”, Opt. Commun. 176, 219–222 (2000).
    [Crossref]
  7. M. Higashihata, K. Tochigi, Y. Nakata, and T. Okada “Application to the optical coherent tomography of fiber Raman laser”, 5th CLEO/Pacific Rim 2003 (15-19 Dec. 2003),  1, 183 (2003).
  8. W. Hackenberg, D. Bonaccini, and D. Werner, “Fiber Raman laser development for multiple sodium laser guide star adaptive optics”, Proc. SPIE 4839, 421–428 (2003).
    [Crossref]
  9. Y. Feng, S. Huang, A. Shirakawa, and K.-I. Ueda, “Multiple-color cw visible lasers by frequency sum-mixing in a cascading Raman fiber laser,” Opt. Express 12, 1843–1847 (2004).
    [Crossref] [PubMed]
  10. D. Georgiev, V. P. Gapontsev, A. G. Dronov, M. Y. Vyatkin, A. B. Rulkov, S. V. Popov, and J. R. Taylor, “Watts-level frequency doubling of a narrow line linearly polarized Raman fiber laser to 589 nm”, Opt. Express 13, 6772–6776 (2005).
    [Crossref] [PubMed]
  11. Y. Feng, L. Taylor, and D. Bonaccini Calia, “20W CW, 4 MHz linewidth Raman fiber amplifier with SHG to 589 nm”, Photonics West 2009, San Jose (postdeadline paper 7195–101).
  12. V. I. Karpov, W. R. L. Clements, E. M. Dianov, and S. B. Parenyi “High-power 1.24 μm phosphosilicate-fiber-based laser pumped by laser diodes”, Can. J. Phys. 78, 407–413 (2000).
    [Crossref]
  13. S. A. Babin, D. V. Churkin, A. E. Ismagulov, S. I. Kablukov, and E. V. Podivilov, “Spectral broadening in Raman fiber lasers”, Opt. Lett. 31, 3007–3009 (2006).
    [Crossref] [PubMed]
  14. S. A. Babin, D. V. Churkin, A. E. Ismagulov, S. I. Kablukov, and E. V. Podivilov, “Four-wave-mixing-induced turbulent spectral broadening in a long Raman fiber laser”, J. Opt. Soc. Am. B 24, 1729–1738 (2007).
    [Crossref]
  15. J. Hagen, R. Engelbrecht, O. Welzel, A. Siekiera, and B. Schmauss, “Numerical modeling of intracavity spectral broadening of Raman fiber lasers”, IEEE Photon. Technol. Lett. 19, 1759–1761 (2007).
    [Crossref]
  16. V. G. Dmitriev and L. V. Tarasov, Applied nonlinear optics (M., Radio i svyaz’, 1982) [in Russian].
  17. V. G. Dmitriev and Yu.V. Yur’ev, “Equations for second-harmonic generation under quasi-phase-matched interaction conditions in nonlinear crystals with a regular domain structure,” Quantum Electron. 28, 1007–1010 (1998).
    [Crossref]
  18. G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams”, J. Appl. Phys. 39, 3597 (1968).
    [Crossref]
  19. S. D. Smith, H. D. Riccius, and R. P. Edwin, “Refractive indices of lithium niobate,” Opt. Commun. 17, 332(1976) and  20, 188 (1977) (errata).
    [Crossref]
  20. F. J. Kontur, I. Dajani, Y. Lu, and R. J. Knize, “Frequency-doubling of a CW fiber laser using PPKTP, PMgSLT, and PPMgLN,” Opt. Express 15, 12882–12889 (2007).
    [Crossref] [PubMed]
  21. J. Ducuing and N. Bloembergen, “Static fluctuations in nonlinear optical processes,” Phys. Rev. 133, A1493–1502 (1964).
    [Crossref]

2007 (5)

2006 (1)

2005 (1)

2004 (1)

2003 (3)

M. Higashihata, K. Tochigi, Y. Nakata, and T. Okada “Application to the optical coherent tomography of fiber Raman laser”, 5th CLEO/Pacific Rim 2003 (15-19 Dec. 2003),  1, 183 (2003).

W. Hackenberg, D. Bonaccini, and D. Werner, “Fiber Raman laser development for multiple sodium laser guide star adaptive optics”, Proc. SPIE 4839, 421–428 (2003).
[Crossref]

Y.-G. Han, C.-S. Kim, J. U. Kang, U.-C. Paek, and Y. Chung, “Multiwavelength Raman fiber-ring laser based on tunable cascaded long-period fiber gratings”, IEEE Photon. Technol. Lett. 15, 383–385 (2003).
[Crossref]

2001 (1)

P. C. Reeves-Hall and J. R. Taylor, “Wavelength tunable CW Raman fibre ring laser operating at 1486-1551 nm”, Electron. Lett. 37, 491–492 (2001).
[Crossref]

2000 (3)

N. S. Kim, M. Prabhu, C. Li, J. Song, and K. Ueda, “1239/1484 nm cascaded phosphosilicate Raman fiber laser with CW output power of 1.36 W at 1484 nm pumped by CW Yb-doped double-clad fiber laser at 1064 nm and spectral continuum generation”, Opt. Commun. 176, 219–222 (2000).
[Crossref]

E. M. Dianov, I. A. Bufetov, M. M. Bubnov, M. V. Grekov, S. A. Vasiliev, and O. I. Medvedkov, “Three-cascaded 1407-nm Raman laser based on phosphorus-doped silica fiber”, Opt. Lett. 25, 402–404 (2000).
[Crossref]

V. I. Karpov, W. R. L. Clements, E. M. Dianov, and S. B. Parenyi “High-power 1.24 μm phosphosilicate-fiber-based laser pumped by laser diodes”, Can. J. Phys. 78, 407–413 (2000).
[Crossref]

1998 (1)

V. G. Dmitriev and Yu.V. Yur’ev, “Equations for second-harmonic generation under quasi-phase-matched interaction conditions in nonlinear crystals with a regular domain structure,” Quantum Electron. 28, 1007–1010 (1998).
[Crossref]

1982 (1)

V. G. Dmitriev and L. V. Tarasov, Applied nonlinear optics (M., Radio i svyaz’, 1982) [in Russian].

1976 (1)

S. D. Smith, H. D. Riccius, and R. P. Edwin, “Refractive indices of lithium niobate,” Opt. Commun. 17, 332(1976) and  20, 188 (1977) (errata).
[Crossref]

1968 (1)

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams”, J. Appl. Phys. 39, 3597 (1968).
[Crossref]

1964 (1)

J. Ducuing and N. Bloembergen, “Static fluctuations in nonlinear optical processes,” Phys. Rev. 133, A1493–1502 (1964).
[Crossref]

Babin, S. A.

Bloembergen, N.

J. Ducuing and N. Bloembergen, “Static fluctuations in nonlinear optical processes,” Phys. Rev. 133, A1493–1502 (1964).
[Crossref]

Bonaccini, D.

W. Hackenberg, D. Bonaccini, and D. Werner, “Fiber Raman laser development for multiple sodium laser guide star adaptive optics”, Proc. SPIE 4839, 421–428 (2003).
[Crossref]

Boyd, G. D.

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams”, J. Appl. Phys. 39, 3597 (1968).
[Crossref]

Bubnov, M. M.

Bufetov, I. A.

Calia, D. Bonaccini

Y. Feng, L. Taylor, and D. Bonaccini Calia, “20W CW, 4 MHz linewidth Raman fiber amplifier with SHG to 589 nm”, Photonics West 2009, San Jose (postdeadline paper 7195–101).

Chung, Y.

Y.-G. Han, C.-S. Kim, J. U. Kang, U.-C. Paek, and Y. Chung, “Multiwavelength Raman fiber-ring laser based on tunable cascaded long-period fiber gratings”, IEEE Photon. Technol. Lett. 15, 383–385 (2003).
[Crossref]

Churkin, D. V.

Clements, W. R. L.

V. I. Karpov, W. R. L. Clements, E. M. Dianov, and S. B. Parenyi “High-power 1.24 μm phosphosilicate-fiber-based laser pumped by laser diodes”, Can. J. Phys. 78, 407–413 (2000).
[Crossref]

Cumberland, B. A.

Dajani, I.

Dianov, E. M.

Dmitriev, V. G.

V. G. Dmitriev and Yu.V. Yur’ev, “Equations for second-harmonic generation under quasi-phase-matched interaction conditions in nonlinear crystals with a regular domain structure,” Quantum Electron. 28, 1007–1010 (1998).
[Crossref]

V. G. Dmitriev and L. V. Tarasov, Applied nonlinear optics (M., Radio i svyaz’, 1982) [in Russian].

Dronov, A. G.

Ducuing, J.

J. Ducuing and N. Bloembergen, “Static fluctuations in nonlinear optical processes,” Phys. Rev. 133, A1493–1502 (1964).
[Crossref]

Edwin, R. P.

S. D. Smith, H. D. Riccius, and R. P. Edwin, “Refractive indices of lithium niobate,” Opt. Commun. 17, 332(1976) and  20, 188 (1977) (errata).
[Crossref]

Engelbrecht, R.

J. Hagen, R. Engelbrecht, O. Welzel, A. Siekiera, and B. Schmauss, “Numerical modeling of intracavity spectral broadening of Raman fiber lasers”, IEEE Photon. Technol. Lett. 19, 1759–1761 (2007).
[Crossref]

Feng, Y.

Y. Feng, S. Huang, A. Shirakawa, and K.-I. Ueda, “Multiple-color cw visible lasers by frequency sum-mixing in a cascading Raman fiber laser,” Opt. Express 12, 1843–1847 (2004).
[Crossref] [PubMed]

Y. Feng, L. Taylor, and D. Bonaccini Calia, “20W CW, 4 MHz linewidth Raman fiber amplifier with SHG to 589 nm”, Photonics West 2009, San Jose (postdeadline paper 7195–101).

Gapontsev, V. P.

Georgiev, D.

Grekov, M. V.

Hackenberg, W.

W. Hackenberg, D. Bonaccini, and D. Werner, “Fiber Raman laser development for multiple sodium laser guide star adaptive optics”, Proc. SPIE 4839, 421–428 (2003).
[Crossref]

Hagen, J.

J. Hagen, R. Engelbrecht, O. Welzel, A. Siekiera, and B. Schmauss, “Numerical modeling of intracavity spectral broadening of Raman fiber lasers”, IEEE Photon. Technol. Lett. 19, 1759–1761 (2007).
[Crossref]

Han, Y.-G.

Y.-G. Han, C.-S. Kim, J. U. Kang, U.-C. Paek, and Y. Chung, “Multiwavelength Raman fiber-ring laser based on tunable cascaded long-period fiber gratings”, IEEE Photon. Technol. Lett. 15, 383–385 (2003).
[Crossref]

Higashihata, M.

M. Higashihata, K. Tochigi, Y. Nakata, and T. Okada “Application to the optical coherent tomography of fiber Raman laser”, 5th CLEO/Pacific Rim 2003 (15-19 Dec. 2003),  1, 183 (2003).

Huang, S.

Ismagulov, A. E.

Kablukov, S. I.

Kang, J. U.

Y.-G. Han, C.-S. Kim, J. U. Kang, U.-C. Paek, and Y. Chung, “Multiwavelength Raman fiber-ring laser based on tunable cascaded long-period fiber gratings”, IEEE Photon. Technol. Lett. 15, 383–385 (2003).
[Crossref]

Karpov, V. I.

V. I. Karpov, W. R. L. Clements, E. M. Dianov, and S. B. Parenyi “High-power 1.24 μm phosphosilicate-fiber-based laser pumped by laser diodes”, Can. J. Phys. 78, 407–413 (2000).
[Crossref]

Kim, C.-S.

Y.-G. Han, C.-S. Kim, J. U. Kang, U.-C. Paek, and Y. Chung, “Multiwavelength Raman fiber-ring laser based on tunable cascaded long-period fiber gratings”, IEEE Photon. Technol. Lett. 15, 383–385 (2003).
[Crossref]

Kim, N. S.

N. S. Kim, M. Prabhu, C. Li, J. Song, and K. Ueda, “1239/1484 nm cascaded phosphosilicate Raman fiber laser with CW output power of 1.36 W at 1484 nm pumped by CW Yb-doped double-clad fiber laser at 1064 nm and spectral continuum generation”, Opt. Commun. 176, 219–222 (2000).
[Crossref]

Kleinman, D. A.

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams”, J. Appl. Phys. 39, 3597 (1968).
[Crossref]

Knize, R. J.

Kontur, F. J.

Li, C.

N. S. Kim, M. Prabhu, C. Li, J. Song, and K. Ueda, “1239/1484 nm cascaded phosphosilicate Raman fiber laser with CW output power of 1.36 W at 1484 nm pumped by CW Yb-doped double-clad fiber laser at 1064 nm and spectral continuum generation”, Opt. Commun. 176, 219–222 (2000).
[Crossref]

Lu, Y.

Medvedkov, O. I.

Nakata, Y.

M. Higashihata, K. Tochigi, Y. Nakata, and T. Okada “Application to the optical coherent tomography of fiber Raman laser”, 5th CLEO/Pacific Rim 2003 (15-19 Dec. 2003),  1, 183 (2003).

Okada, T.

M. Higashihata, K. Tochigi, Y. Nakata, and T. Okada “Application to the optical coherent tomography of fiber Raman laser”, 5th CLEO/Pacific Rim 2003 (15-19 Dec. 2003),  1, 183 (2003).

Paek, U.-C.

Y.-G. Han, C.-S. Kim, J. U. Kang, U.-C. Paek, and Y. Chung, “Multiwavelength Raman fiber-ring laser based on tunable cascaded long-period fiber gratings”, IEEE Photon. Technol. Lett. 15, 383–385 (2003).
[Crossref]

Parenyi, S. B.

V. I. Karpov, W. R. L. Clements, E. M. Dianov, and S. B. Parenyi “High-power 1.24 μm phosphosilicate-fiber-based laser pumped by laser diodes”, Can. J. Phys. 78, 407–413 (2000).
[Crossref]

Podivilov, E. V.

Popov, S. V.

Prabhu, M.

N. S. Kim, M. Prabhu, C. Li, J. Song, and K. Ueda, “1239/1484 nm cascaded phosphosilicate Raman fiber laser with CW output power of 1.36 W at 1484 nm pumped by CW Yb-doped double-clad fiber laser at 1064 nm and spectral continuum generation”, Opt. Commun. 176, 219–222 (2000).
[Crossref]

Reeves-Hall, P. C.

P. C. Reeves-Hall and J. R. Taylor, “Wavelength tunable CW Raman fibre ring laser operating at 1486-1551 nm”, Electron. Lett. 37, 491–492 (2001).
[Crossref]

Riccius, H. D.

S. D. Smith, H. D. Riccius, and R. P. Edwin, “Refractive indices of lithium niobate,” Opt. Commun. 17, 332(1976) and  20, 188 (1977) (errata).
[Crossref]

Rulkov, A. B.

Rybakov, M. A.

Schmauss, B.

J. Hagen, R. Engelbrecht, O. Welzel, A. Siekiera, and B. Schmauss, “Numerical modeling of intracavity spectral broadening of Raman fiber lasers”, IEEE Photon. Technol. Lett. 19, 1759–1761 (2007).
[Crossref]

Shirakawa, A.

Siekiera, A.

J. Hagen, R. Engelbrecht, O. Welzel, A. Siekiera, and B. Schmauss, “Numerical modeling of intracavity spectral broadening of Raman fiber lasers”, IEEE Photon. Technol. Lett. 19, 1759–1761 (2007).
[Crossref]

Smith, S. D.

S. D. Smith, H. D. Riccius, and R. P. Edwin, “Refractive indices of lithium niobate,” Opt. Commun. 17, 332(1976) and  20, 188 (1977) (errata).
[Crossref]

Song, J.

N. S. Kim, M. Prabhu, C. Li, J. Song, and K. Ueda, “1239/1484 nm cascaded phosphosilicate Raman fiber laser with CW output power of 1.36 W at 1484 nm pumped by CW Yb-doped double-clad fiber laser at 1064 nm and spectral continuum generation”, Opt. Commun. 176, 219–222 (2000).
[Crossref]

Tarasov, L. V.

V. G. Dmitriev and L. V. Tarasov, Applied nonlinear optics (M., Radio i svyaz’, 1982) [in Russian].

Taylor, J. R.

Taylor, L.

Y. Feng, L. Taylor, and D. Bonaccini Calia, “20W CW, 4 MHz linewidth Raman fiber amplifier with SHG to 589 nm”, Photonics West 2009, San Jose (postdeadline paper 7195–101).

Tochigi, K.

M. Higashihata, K. Tochigi, Y. Nakata, and T. Okada “Application to the optical coherent tomography of fiber Raman laser”, 5th CLEO/Pacific Rim 2003 (15-19 Dec. 2003),  1, 183 (2003).

Ueda, K.

N. S. Kim, M. Prabhu, C. Li, J. Song, and K. Ueda, “1239/1484 nm cascaded phosphosilicate Raman fiber laser with CW output power of 1.36 W at 1484 nm pumped by CW Yb-doped double-clad fiber laser at 1064 nm and spectral continuum generation”, Opt. Commun. 176, 219–222 (2000).
[Crossref]

Ueda, K.-I.

Vasiliev, S. A.

Vlasov, A. A.

Vyatkin, M. Y.

Welzel, O.

J. Hagen, R. Engelbrecht, O. Welzel, A. Siekiera, and B. Schmauss, “Numerical modeling of intracavity spectral broadening of Raman fiber lasers”, IEEE Photon. Technol. Lett. 19, 1759–1761 (2007).
[Crossref]

Werner, D.

W. Hackenberg, D. Bonaccini, and D. Werner, “Fiber Raman laser development for multiple sodium laser guide star adaptive optics”, Proc. SPIE 4839, 421–428 (2003).
[Crossref]

Yur’ev, Yu.V.

V. G. Dmitriev and Yu.V. Yur’ev, “Equations for second-harmonic generation under quasi-phase-matched interaction conditions in nonlinear crystals with a regular domain structure,” Quantum Electron. 28, 1007–1010 (1998).
[Crossref]

Can. J. Phys. (1)

V. I. Karpov, W. R. L. Clements, E. M. Dianov, and S. B. Parenyi “High-power 1.24 μm phosphosilicate-fiber-based laser pumped by laser diodes”, Can. J. Phys. 78, 407–413 (2000).
[Crossref]

Electron. Lett. (1)

P. C. Reeves-Hall and J. R. Taylor, “Wavelength tunable CW Raman fibre ring laser operating at 1486-1551 nm”, Electron. Lett. 37, 491–492 (2001).
[Crossref]

IEEE Photon. Technol. Lett. (2)

Y.-G. Han, C.-S. Kim, J. U. Kang, U.-C. Paek, and Y. Chung, “Multiwavelength Raman fiber-ring laser based on tunable cascaded long-period fiber gratings”, IEEE Photon. Technol. Lett. 15, 383–385 (2003).
[Crossref]

J. Hagen, R. Engelbrecht, O. Welzel, A. Siekiera, and B. Schmauss, “Numerical modeling of intracavity spectral broadening of Raman fiber lasers”, IEEE Photon. Technol. Lett. 19, 1759–1761 (2007).
[Crossref]

J. Appl. Phys. (1)

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams”, J. Appl. Phys. 39, 3597 (1968).
[Crossref]

J. Opt. Soc. Am. B (1)

Opt. Commun. (2)

N. S. Kim, M. Prabhu, C. Li, J. Song, and K. Ueda, “1239/1484 nm cascaded phosphosilicate Raman fiber laser with CW output power of 1.36 W at 1484 nm pumped by CW Yb-doped double-clad fiber laser at 1064 nm and spectral continuum generation”, Opt. Commun. 176, 219–222 (2000).
[Crossref]

S. D. Smith, H. D. Riccius, and R. P. Edwin, “Refractive indices of lithium niobate,” Opt. Commun. 17, 332(1976) and  20, 188 (1977) (errata).
[Crossref]

Opt. Express (4)

Opt. Lett. (3)

Phys. Rev. (1)

J. Ducuing and N. Bloembergen, “Static fluctuations in nonlinear optical processes,” Phys. Rev. 133, A1493–1502 (1964).
[Crossref]

Proc. SPIE (1)

W. Hackenberg, D. Bonaccini, and D. Werner, “Fiber Raman laser development for multiple sodium laser guide star adaptive optics”, Proc. SPIE 4839, 421–428 (2003).
[Crossref]

Quantum Electron. (1)

V. G. Dmitriev and Yu.V. Yur’ev, “Equations for second-harmonic generation under quasi-phase-matched interaction conditions in nonlinear crystals with a regular domain structure,” Quantum Electron. 28, 1007–1010 (1998).
[Crossref]

Other (3)

V. G. Dmitriev and L. V. Tarasov, Applied nonlinear optics (M., Radio i svyaz’, 1982) [in Russian].

Y. Feng, L. Taylor, and D. Bonaccini Calia, “20W CW, 4 MHz linewidth Raman fiber amplifier with SHG to 589 nm”, Photonics West 2009, San Jose (postdeadline paper 7195–101).

M. Higashihata, K. Tochigi, Y. Nakata, and T. Okada “Application to the optical coherent tomography of fiber Raman laser”, 5th CLEO/Pacific Rim 2003 (15-19 Dec. 2003),  1, 183 (2003).

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1. Experimental setup.
Fig. 2.
Fig. 2. Fundamental wave (a) and SH (b) output spectra measured at different RFL powers. (c) Fundamental wave (boxes) and SH (circles) spectral widths together with SH width calculated from Eqs. (4),(5) (line).
Fig. 3.
Fig. 3. Experimental data (points) and calculated SHG power P versus Pω =PRFL for single frequency (dashed line) and multiple frequency (solid line) fundamental wave. Inset: corresponding SHG efficiency P /Pω .
Fig. 4.
Fig. 4. Second harmonic spectrum: experiment at Pω ≈7.1 W (dots), calculation from Eqs. 4, 5 for direct frequency doubling (dashed line) and the same with sum-frequency mixing (solid line). Inset: an example of SHG for N=4.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

A 2 n z + 1 u A 2 n t = i σ 2 ( A 1 m 2 ξ n + j + k = n + 1 j k A 1 j A 1 k ) m = ( n + 1 ) 2 ξ n = [ ( 1 ) n + 1 + 1 ] 2 ,
I 2 n = ( σ 2 z ) 2 [ ( a 1 m 4 + 2 a 1 m 2 j + k = n + 1 j k a 1 j a 1 k × cos ( 2 φ 1 m φ 1 j φ 1 k ) ) ξ n +
+ 2 j k ( a 1 j a 1 k ) 2 + 2 j k p q a 1 j a 1 k a 1 p a 1 q × cos ( φ 1 j + φ 1 k φ 1 p φ 1 q ) ]
I 2 n = ( σ 2 z ) 2 [ a 1 m 4 ξ n + 2 j k ( a 1 j a 1 k ) 2 ]
I 2 n = ( σ 2 z ) 2 [ a 1 m 4 ξ n sinc 2 ( Δ k mm z / 2 ) + 2 j k ( a 1 j a 1 k sinc ( Δ k jk z / 2 ) ) 2 ] ,
z 2 π z , Δk ( Δk 2 π Λ ) π 2 ,
η = P 2 ω ( P ω ) 2 = 16 π 2 d eff 2 L λ ω 3 n ω n 2 ω ε 0 c h ,

Metrics

Select as filters


Select Topics Cancel
© Copyright 2022 | Optica Publishing Group. All Rights Reserved