In this paper, we introduce a concept of phase matching bandwidth of broadband sources by using the retracing behavior of collinear quasi-phase-matching (CQPM) optical parametric generation (OPG) in periodically poled lithium niobate (PPLN). By comparing various pump wavelengths we derive the pumping condition and parameters of PPLN to realize a broadband source near 1550 nm in the CQPM-OPG. We predict the optimum pump wavelength and the maximum ideal bandwidth range to be 940.75 nm and 1475–1681 nm respectively. Experimentally we have demonstrated a 946 nm Nd:YAG laser which serves as the pumping source of CQPM-OPG.
©2006 Optical Society of America
Broadband optical sources are employed for optical signal generation and amplification in many fields such as wavelength-division multiplexing (WDM) fiber communications, optical coherence tomography (OCT) and spectroscopy. For WDM communications, conventional erbium-doped fiber amplification and stimulated Raman scattering in fiber are usually used to realize broadband optical sources. By using the retracing behavior of birefringence phase-matching (BPM) in different nonlinear crystals, broadband sources have also been developed [1,2]. With the rapid development of periodically poled crystals and successful applications of quasi-phase matching (QPM) [3–5], using QPM technology to realize broadband sources in periodically poled crystals has become a research focus.
Nowadays, there are two main methods in using periodically poled lithium niobate (PPLN) to develop broadband sources: 1) broadband generation operating near the degenerate point and, 2) broadband generation based on a fan QPM structure. So far, very few studies have been carried by using the retracing behavior of a QPM optical parametric generator (OPG) in PPLN as a broadband source , and there are a number of issues which need to be solved in this research area.
Firstly, in previous studies, no theoretical basis of bandwidth confirmation is produced and only the bandwidth concept is presented qualitatively from the tendency of tuning curve variation. It is considered that the broadband generation can be only obtained when the phase matching condition is strictly satisfied. In fact, the broadband generation has a tolerance band. From the concept of phase-matching band we produce condition of phase-matching band confirmation. Secondly the previous studies have considered that the broadband generation near 1550 nm can not be obtained by using collinear quasi-phase-matching (CQPM) and noncollinear QPM (NCQPM) must be used to achieve the range required. NCQPM has the advantages such as increased angle-tuning range, extended bandwidth, and tuning flexibility. However, the walk-off problem which decreases the nonlinear conversion efficiency can not be avoided. The conversion efficiency of CQPM can be increased with the increase of the crystal length without suffering the walk-off problem.
In this paper, we report a theoretical analysis of broadband sources near 1550 nm by using the retracing behavior [6–9] of CQPM-OPG in PPLN. Our research indicates that near the break point of 946 nm laser pumped CQPM tuning curve QPM period is insensitive to the variation of the signal wavelength centered at 1550 nm. Therefore near the break point only one period can contribute to the broadband generation. The signal wavelength in this range can approximately satisfy the phase-matching condition. Experimentally we have obtained continuous-wave (CW) and quasi-continuous-wave (QCW) 946 nm Nd:YAG lasers which serve as the pump sources for the CQPM-OPG.
2. The confirmation of bandwidth of a broadband source
In CQPM, the crystal is generally periodically poled along the crystal z-axis and the three wave vectors are collinear along the crystal x-axis. Under the phase-matching condition ∆k=0 we can obtain the relationship between the signal wavelength and the grating period Λ at different pump wavelengths. We find that at some pump wavelengths the QPM tuning curves are very flat. Therefore, the change of phase mismatch is small when the signal wavelength varies in a certain range. Although the output power at the wavelength which approximately satisfies the phase-matching condition is not the maximum, the wavelength which makes the phase mismatch ∆k satisfy the condition of ∆k<π/L (L is the crystal length) can be obtained. We can draw a conclusion that a broad bandwidth for the signal wavelength can be obtained.
In QPM, assuming that λp<λs<λi, the energy conservation condition can be expressed as
In CQPM, the phase mismatch ∆k which is described in the form of wavelength is
where λp, λs and λi are the pump wavelength, the signal wavelength and the idle wavelength respectively; np, ns and ni are the refractive indexes of pump, signal and idle respectively; Λ is the grating period of the crystal.
The concept of phase-matching bandwidth is the range of wavelength which makes the phase mismatch ∆k satisfy the condition of |∆k|<π/L. Phase mismatch ∆k is a function of QPM signal wavelength λ s in Eq. (2), and it can be expanded in a Taylor series about λs,
where L is the crystal length. The first item in Eq. (3) is zero at the condition of λ=λs. We usually neglect the higher-order terms in the expansion. The bandwidth, denoted by ∆λ, can be written as
3. Design of a broadband source by using CQPM-OPG in PPLN
According to the above conclusion we designed a broadband source by using CQPM-OPG in PPLN. In the design, we assumed that the temperature of the PPLN crystal is in a range of 373–473 K. Here we fixed the temperature to 410 K. The range of signal wavelength we would like to achieve is from 1500 nm to 1600 nm.
We made the prime selection of pump wavelengths by comparing the QPM tuning curves at different pump wavelengths of commercially available semiconductor lasers (808 nm and 980 nm) and Nd:YAG lasers (946 nm and 1064 nm). As shown in Fig. 1, when the pump wavelength is 1064 nm, near 1550 nm the QPM period is sensitive to the variation of the signal wavelength. It can not satisfy the condition for broadband sources. When the pump wavelength is 808 nm, 946 nm and 980 nm respectively, the signal range becomes broader. Therefore it is obvious that the QPM periods are insensitive to the variation of the signal wavelength in this range.
Further we calculated the sensitivities of the QPM period (∂Λ/∂λs) versus the signal wavelength under different pump wavelengths of 808 nm, 946 nm and 980 nm, as shown in Fig. 2. It can be seen that 946 nm is more suitable for our design because the sensitivity at this wavelength is smaller than that at 808 nm or 980 nm.
Using 1550 nm as the central wavelength of the signal range, we calculated the QPM period as 27.01 µm (27.06 µm at 410 K) at room temperature when the pump wavelength is 946 nm. For 980 nm the grating period is 28.20 µm (28.25 µm at 410 K) and for 808 nm it is 20.31 µm (20.35 µm, 410 K).
Next we calculated the normalized phase mismatch ∆k versus the signal wavelength under the different pump wavelengths of 946 nm, 808 nm and 980 nm at 410 K, as shown in Fig. 3. Here the length of PPLN is 20 mm. From Fig. 3 we can see that the phase mismatch corresponding to a signal range of 1500–1600 nm can satisfy the condition of |∆k|<π/L when the pump wavelength is 946 nm. However, when the pump wavelength is 808 nm or 980 nm the signal range reduces to 1530–1580 nm and 1540–1560 nm respectively. Furthermore it is indicated that 946 nm lasers would be a better choice for pump source in our design.
Figure 4 shows the normalized phase mismatches at different signal wavelengths under different crystal lengths. When the PPLN length is 50 mm, the lower limit value of the signal wavelength which satisfies the phase-matching condition increases to 1520 nm and the bandwidth reduces. From Eq. (5) we can also know that the bandwidth decreases as a consequence of the increase in crystal length.
In general we can draw a conclusion that when the pump wavelength is 946 nm we can realize 1500–1600 nm broadband sources by using CQPM-OPG in a 20 mm-long PPLN crystal with a grating period of 27.06 µm at 410 K.
4. Optimal pump wavelength and ideal bandwidth
An optimal pump wavelength can be obtained if we only consider whether we can achieve the maximum broadband source near 1550 nm. The theoretical optimal pump wavelength is 940.75 nm. Figure 5 shows the sensitivity of QPM period (∂Λ/∂λs) versus the signal wavelength with 940.75 nm and 946 nm pumps. Near 1550 nm the sensitivity at 940.75 nm is zero. We also calculated the QPM period for a 940.75 nm pump as 26.81 µm at room temperature (26.86 µm at 410 K). The normalized phase mismatch at 940.75 nm versus the signal wavelength is shown in Fig. 6 in comparison with that of 946 nm. The maximum ideal bandwidth range is 1475–1681 nm when the crystal length and the pump wavelength is 20 mm and 940.75 nm respectively. If we only want to realize a broadband source in the range of 1500–1600 nm pumped by a 940.75 nm laser, the phase mismatch is still in the phase-matching bandwidth even if the crystal length is 50 mm (Fig. 7).
5. Experiments with a 946 nm Nd:YAG laser
Here we report the efficient low-temperature operation of a laser diode (LD) pumped Nd:YAG laser at 946 nm. A 400 µm diameter, 0.22 numerical aperture (NA) fiber-coupled LD (50W, LIMO Co., Germany) operating at the maximum absorption wavelength (807.5 nm) of Nd:YAG was used for CW pumping in an end-pumping geometry. With a collimating and focusing lens the end-face of the fiber was imaged into the medium in an about 350 µm diameter spot. A power meter (Molectron EPM1000) was used to measure the powers of the pump laser and the 946 nm output.
A conventional Nd:YAG crystal (4 mm in diameter, 4 mm in length, and 1.1 at.%) was first polished with a high accuracy to obtain parallel flat surfaces, and then AR coated for 808 nm (R<5%) and HR coated for 946 nm (R>99.8%) on the flat front surface which serves as one of the resonator mirrors. The flat exit surface of the crystal was also AR coated for 946 nm (R<0.2%). The length of the Nd:YAG crystal was chosen to be 4 mm to increase the overall efficiency of the laser system, to reduce the reabsorption losses, to absorb a proper fraction of the pump power, and to keep a low pump threshold. To obtain efficient lasing operation at 946 nm, heat effects must be minimized. We used a water-cooling system in our experiments. The Nd:YAG crystal was placed in a brass heat sink and an indium foil was used to improve the thermal contact between the Nd:YAG crystal and the brass mount.
In order to suppress the parasitic oscillation at 1064 nm, the output mirrors were coated with high-transmission coatings at this wavelength. However, the practical coatings were not ideal and the transmission at 1064 nm was about 50%.
A schematic diagram of the LD end-pumped Nd:YAG laser operating on the 4F3/2–4I9/2 transition at 946 nm is shown in Fig. 8.
When the working temperature of the Nd:YAG crystal was 273 K, we achieved a maximum CW output of 6 W with an output mirror of 5% transmission at 946 nm for 19.9 W absorbed pump power, leading to optical-to-optical efficiency of 30.2% with respect to the absorbed pump power (or 25% with respect to the incident pump power). The output coupler was a concave mirror with a curvature radius of 150 mm. The cavity length was set to be 7.8 mm. The threshold (in term of the absorbed pump power) was 1.05 W when the slope efficiency with respect to the absorbed pump power was 31.8% (or 26.5% with respect to the incident pump power). Figure 9 shows the CW 946 nm output power versus the incident pump power.
The laser spectrum shown in Fig. 10(a), which was measured with an optical spectrum analyzer (Aligent 86142B) with a resolution of 0.01 nm, has a central wavelength of 946.220 nm. Fig. 10(b) shows the 946 nm laser spectrum in the range of 900–1100 nm, indicating that suppression of the parasitic oscillation at 1064 nm was very successful.
We also demonstrated a QCW 946 nm laser of 2.46 W by inserting an acousto-optic (AO) Q-switch (QSGSU-1Q) in the cavity (Fig. 8) when the incident pump power was 13.33 W. The concave out-coupling mirror had a transmission of 10% with a curvature radius of 60 mm. The length of the cavity was 40 mm. The working temperature of the Nd:YAG crystal was 280 K. Repetition frequency of the AO Q-switch was 19.57 kHz with the QCW 946 nm laser pulse duration of 132 ns (Fig. 12). The optical-to-optical efficiency with respect to the absorbed pump power was 23.1% (or 18.5% with respect to the incident pump power). The threshold for the absorbed pump power was 1.5 W with a slope efficiency of 26.8% (or 21.7% with respect to the incident pump power). Figure 11 shows the QCW 946 nm output power versus the incident pump power. The transverse beam profile of the 2.46 W QCW 946 nm laser was investigated by imaging the laser beam onto a CCD detector (Fig. 13).
We have theoretically predicted the generation of broadband optical signals near 1550 nm by using the retracing behavior of CQPM in PPLN. We introduce the concept of phase-matching bandwidth and obtain the pump condition and parameters of PPLN. From our theoretical analysis we found that the optimum pump wavelength and the maximum ideal bandwidth range to be 940.75 nm and 1475–1681nm respectively. Experimentally we obtained CW and QCW 946 nm laser outputs which will serve as the pump sources of the CQPM-OPG to realize broadband sources. To the best of our knowledge, the 2.46 W QCW 946 nm laser (132 ns, 19.57 kHz) we demonstrated, could be the best result so far.
In the future experiments with the broadband source, we need to consider the coupling between the broadband source and the fiber communication system. This issue can be solved by using a PPLN waveguide structure. We also need to reduce the threshold and increase the OPG conversion efficiency to avoid damaging the crystal at high power intensities. The fabrication of PPLN crystals is also important. The deviation of the PPLN period can be compensated by tuning the crystal temperature in certain extent. Finally, the spectral flatness of a broadband source is also important for fiber communication applications. The spectrum of a broadband source can be flattened by using the well developed techniques such as fiber Bragg gratings.
This project is supported by the National Natural Science Foundation of China (Grant No.10474071) and the PhD. Programs Foundation of Ministry of Education of China (Grant No.20040056010). The authors appreciate the HC Photonics Corp. for providing the PPLN crystal.
References and links
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