A distributed feedback (DFB) semiconductor laser with equivalent phase shifts and chirps is proposed for the first time to our knowledge and is investigated numerically. As an example, it is shown that the desired λ/4 phase shift in a phase-shifted laser can be obtained equivalently by a specially designed sampling structure instead of an actual phase shift, while the external characteristics are unchanged. This novel DFB structure is advantageous in that it can be fabricated by standard holographic technology. Hence, the proposed scheme is expected to provide a low-cost method for fabricating a high-performance DFB semiconductor laser with complex structures.
©2007 Optical Society of America
A distributed feedback (DFB) semiconductor laser is one of the most widely used laser sources in fiber-optic communications for its excellent performance and compact size. Because of mode degeneracy in the uniform grating structure quarter-wave λ/4) shift , multiple phase shifts or chirps are usually used to achieve stable single-longitude-mode (SLM) operation. A number of methods can be applied to form the above-mentioned phase shifts and chirps. Electron-beam (E-beam) lithography is mature and reliable for the production of exact phase shifts or complex chirps in the DFB structure. However, it is still expensive for mass production. From a commercial point of view, holographic exposure may be the cheapest way to fabricate DFB structures directly on the diode chip. Some improved holographic methods, including varying the stripe width  or using a special photoresist , were introduced. Compared with E-beam technology, these methods are still difficult and complicated for producing both complex phase shifts and chirps during real fabrication. A technology wherein the fabrication is simple, as is E-beam technology, and where the cost is cheap, as is standard holographic technology, is required and necessary for high-end DFB laser diodes with very low cost.
In this study we propose a novel DFB semiconductor laser where the equivalent phase shift and chirp can be fabricated by the conventional holographic technique. The proposed DFB structure is based on a uniform grating that is sampled with unequal spacing, and a SLM lasing can be obtained at the wavelength corresponding to the -1st-order channel of the sampled structure. As an example, it is shown numerically that a λ/4 shift can be obtained equivalently by a special unequally spaced sampling, which makes the proposed DFB laser act the same as one with an actual π-phase shift, including the threshold, the P-I characteristics, the light intensity distribution, and the side-mode suppression ratio (SMSR). Because there is no actual phase shift in the novel DFB laser, its sampling structure can be fabricated by conventional holographic technology.
Sampling is usually used to achieve multiwavelength lasing in a DFB structure. However, it acts in a completely different way in this study. The proposed special unequally spaced sampling allows an effective control of the main lasing peak position relative to the Bragg wavelength, i.e., it acts the same as actual phase shifts. This equivalent technique comes from reconstruction-equivalent-chirp (REC) technology and has been used successfully in fiber Bragg gratings (FBGs) . Many relevant devices, such as the fiber DFB laser (which contains a single equivalent π-phase shift)  and the phase en/de-coder for optical code division multiple access system (which contains numerous equivalent π-phase shifts) , have been experimentally demonstrated based on REC technology. REC technology has greatly simplified the fabrication of phase shifts and chirps by realizing precise optical phase control using only μm-level precision. On the other hand, nm-level precision is required for achieving precise opticalphase control during conventional fabrication. In this study, REC technology is applied, for the first time to our knowledge, to the design of DFB semiconductor lasers and is expected to mitigate the fabrication difficulties of high-quality DFB semiconductor lasers.
A schematic of the proposed DFB structure is shown in Fig. 1(a) compared with the conventional phase-shift structure shown in Fig. 1(b). The novel structure is a uniform Bragg grating sampled with period P (6 μm in this study). The length of each sample (containing tens of grating pitches) equals P/2, corresponding to a duty cycle of 0.5. However, the sample length at the center is extended to D.
There are many channels for the sampled structure illustrated in Fig. 1(a). Based on REC technology, an equivalent phase shift θ will be introduced into the -1st-order channel (hereinafter referred to as the resonant channel, for convenience) by D as follows :
Then, by changing D, one can control the position of the low-threshold mode (the so-called gap mode) within the stop-band of the resonant channel. For example, if D=P, an equivalent λ/4 (71-phase) shift is obtained, and it is possible to achieve SLM lasing at the center of the resonant channel.
However, the possibility of lasing in channels of other orders should be considered carefully. Usually the 3dB bandwidth of the semiconductor laser gain spectrum is about 50 nm. To obtain good dynamic performance, the lasing wavelength is selected at 15–20 nm shorter than the wavelength that corresponds to peak gain. In the DFB laser proposed here, the lasing wavelength falls within the resonant channel. For possible lasing at other wavelengths, only a zero-order channel and a -2nd-order channel should be considered, as shown schematically in Fig. 2. Other nonzero-order channels have much less gain or effective index modulation (i.e., κL) than the resonant channel and can be completely neglected. When the duty cycle is 0.5, the index modulation of the -2nd-order channel is, from Fourier analysis, almost zero. Thus the -2nd-order channel is much weaker than the resonant channel, as shown in Fig. 2 (the thicker it is, the stronger it is in index modulation). As a result, only the possibility of lasing in the zero-order channel (less gain but larger κL) should be considered. Because the channel spacing is large (about 50 nm in this study, corresponding to P=6 μm), the optical gain decreases greatly in the zero-order channel Therefore, it is expected that the threshold in the zero-order channel is much higher than that in the resonant channel.
In this study, lasing operation in both the resonant and the zero-order channels is analyzed by simulation. We will see that: first, the threshold margin (difference in lasing threshold between resonant and zero-order channels) is large enough to maintain SLM operation even at high output; and second, external characteristics of the proposed structure are the same as those of the conventional phase-shifted DFB semiconductor lasers.
A spectral domain model developed in Refs. [8, 9] is used in our simulation. Using this model, static characteristics of the proposed DFB with equivalent λ/4 shifts are studied, while the conventional λ/-shifted DFB laser is also analyzed for comparison. Parameters used for the simulation are listed in Table 1 except for the index modulation, which is 50 cm-1 and 150 cm-1 for the lasers with actual and equivalent λ/4 shift, respectively. (As the Fourier coefficient in the -2nd-order is 1/3, in order to get the same characteristics, the index modulation required by the DFB structure using REC technique is usually three times the conventional one.)
The left part of Fig. 3(a) shows the calculated P-I curve of a DFB semiconductor laser with an actual λ/4 shift (dotted line) or an equivalent λ/4 shift (solid line). The corresponding thresholds are 15.7 mA and 15.8 mA, respectively, while their lasing wavelengths are both around 1550 nm. When the injection current=17.5 mA (corresponding to 8 mW output power for both lasers), light intensity distribution along the lasers are plotted in Fig. 3(b). Unsmooth intensity distribution in the equivalent λ/4-shifted DFB laser results from the sampled structure.
The spectrum of the DFB semiconductor laser can be obtained based on the model in Ref. , as shown in Fig. 4. It can be seen that both lasers have the same excellent SMSR (about 75 dB). Obviously, Figs. 3 and 4 show that the DFB laser with an equivalent λ/4 shift acts almost the same as the laser with an actual λ/4 shift.
Since the wavelength difference between the zero-order and the resonant channels is as large as ~50 nm, gain in the former case is much less than that in the latter case, and it is assumed to be 1:6 in this study. The spectrum corresponding to the zero-order channel is calculated and plotted in Fig. 4, where it shows no increase in the SMSR (the side mode induced by the zero-order channel has lower intensity than that of the resonant channel). It can be seen that the spectrum generated by the spontaneous emission in the zero-order channel is similar to that of a DFB laser with uniform grating . This is because there is no equivalent phase shift or chirp in the zero-order channel, and the two symmetrical gap-modes in the zero-order channel are out of the stop-band, which significantly restrains the possible lasing in the zero-order channel. If the injection current is large enough, lasing will occur in the zero-order channel. The calculated threshold of one of the gap-modes in the zero-order channel is about 36 mA, which is much higher than that in the resonant channel (15.8 mA) and shows a wide-enough threshold margin. The calculated P-I curve of the gap-mode is plotted in the right half of Fig. 3(a).
Based on the above analysis, one can conclude that the sampled structure, which generates multi-wavelength operation traditionally, shows no impact on the characteristics of the DFB laser with an equivalent λ/4 shift, especially on the SMSR.
Based on the REC technique, various equivalent phase shifts or chirps (which may be more complicated than the DFB laser mentioned above with only one phase shift) can be obtained simply by adjusting the sampling period of the sampled structure. This is quite useful for high-quality DFB semiconductor lasers. For example, the DFB structure with only one phase shift has some disadvantages such as heavy spatial hole-burning, and more complex structures like multi-phase-shifts  or even chirped DFB structures have been proposed to solve this problem. With a specially-designed sampled structure, almost all of the semiconductor lasers with a complex DFB structure can be obtained without any actual phase shifts or chirps. Figure 5 shows an example with two equivalent phase shifts: 0.5 π occurs at z=0.33 L and z=0.66 L, respectively. The threshold is 16.5 mA. Figure 5(a) shows the master mode P-I curve of this DFB laser diode, while Fig. 5(b) indicates the corresponding intensity distributions along the cavity under an output power of 9.03 mW. Compared with Fig. 3, the maximum intensity decreases a lot under similar output power. Additionally, since the DFB structure in the zero-order channel is always a uniform one, a large threshold margin will then confirm the equivalence between the characteristics of the DFB laser with actual and equivalent phase shifts or chirps.
In our design, the magnitude of the sampling period is 6 μm and the minimum line width is 3 μm, so it is possible to use the conventional holographic technology to fabricate DFB semiconductor lasers with equivalent phase shifts and chirps. For example, a specially designed sampling structure corresponding to a certain phase shift and chirp profile can be first encoded into a photomask, and then the DFB structure is fabricated by holographic technology based on this photomask. In fact, a minimum line-width of 1 μm and a sampling period of 2 μm are very common for photomasks. In terms of the technology we proposed, the fundamental grating (zero-order channel) provides only a basic feedback, and the lasing is actually determined by the resonant channel. Because the characteristics of the resonant channel can be varied by adjusting the sampling period (2–6μm) and duty cycle in each sample, the lasing wavelength and some lasing performance can be controlled easily. With a decreasing sampling period, the lasing wavelength will increase in terms of the Fourier theory. Hence, precise control of the lasing wavelength can be realized by carefully adjusting the sampling period. For example, as shown in the dashed plot H of Fig. 2, we can decrease the sampling period and the duty cycle so that (1) lasing occurs at the gain peak, and (2) the resonant channel can be weakened a little. That is to say, when the corresponding pattern is encoded in the photomask, tens of thousands of laser diodes on a laser chip can have different lasing wavelengths and performances, even between two neighboring laser diodes. It should be mentioned again that standard holographic technology can provide such great flexibilities. Thus the proposed technology may provide a lower-cost and highly flexible method for fabricating high-end DFB semiconductor lasers with complicated structures.
A novel DFB semiconductor laser with equivalent phase shifts and chirps based on REC technology is proposed and numerically studied in this research. The equivalent phase shifts or chirps can be obtained by a specially designed sampling structure so that no actual phase shifts or chirps are required. Simulation results show that DFB lasers with equivalent phase shifts and chirps may have the same external characteristics as traditional DFB lasers. However, the novel structure shows great advantage in fabrication easiness, requiring only conventional holographic techniques and photomasks, even for very complex structures.
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