Electronic band-gap modified passive silicon optical modulator at telecommunications wavelengths

The silicon optical modulator is considered to be the workhorse of a revolution in communications. In recent years, the capabilities of externally driven active silicon optical modulators have dramatically improved. Self-driven passive modulators, especially passive silicon modulators, possess advantages in compactness, integration, low-cost, etc. Constrained by a large indirect band-gap and sensitivity-related loss, the passive silicon optical modulator is scarce and has been not advancing, especially at telecommunications wavelengths. Here, a passive silicon optical modulator is fabricated by introducing an impurity band in the electronic band-gap, and its nonlinear optics and applications in the telecommunications-wavelength lasers are investigated. The saturable absorption properties at the wavelength of 1.55 μm was measured and indicates that the sample is quite sensitive to light intensity and has negligible absorption loss. With a passive silicon modulator, pulsed lasers were constructed at wavelengths at 1.34 and 1.42 μm. It is concluded that the sensitive self-driven passive silicon optical modulator is a viable candidate for photonics applications out to 2.5 μm.

susceptibility and the latter is related to the imaginary part 10 . Compared with the Kerr effect, saturable absorption is a modulation of the absorption and has advantages in some aspects, such as tunable and large modulation depth. However, besides the loss generated during saturable absorption process which is determined by the sensitivity of the absorption to light intensity, the 1.12 eV indirect band-gap of silicon constrains its application in passive modulators, especially at telecommunications wavelengths e.g. 1.3 (0.95 eV) and 1.5 μ m (0.8 eV) 7 . Modifying the electronic band structure of silicon represents the challenge in the development of passive silicon modulators 7,10 . Recently, theoretical calculations indicated that a dopant-induced impurity electronic band located within the silicon band-gap could be generated and controlled by supersaturated doping with chalcogen elements 17 . The linear infrared photoresponse of supersaturated implanted silicon was experimentally investigated and showed much stronger absorption than intrinsic germanium 18,19 . Here, we address the third-order optical nonlinear response, saturable absorption, of crystalline silicon supersaturated doped with sulfur and its application as a passive optical modulator at telecommunications wavelengths. Exploiting the unique nonlinear optical response of sulfur-doped silicon, we have found that it possesses quite sensitive nonlinear saturable absorption and broadband response out to 2.5 μ m. Moreover, modulated pulses at the telecommunications wavelengths were also produced using the fabricated silicon sample as the optical modulator.

Results and Discussion
The silicon crystal sample was cut along the < 100> direction with a thickness of 381 μ m and polished on opposite faces perpendicular to this direction. The 32 S + ion was implanted into the silicon crystal at 95 keV to a dose of 3 × 10 15 cm −2 at room temperature. Based on theoretical calculation 17 , it is assumed that sulfur is substitutional in the silicon crystal since the formation energy of the substitutional positioning process is 2.84 eV per sulfur ion, which is lower than interstitial implantation. An intermediate band generated by the sulfur impurities appears, as shown in Fig. 1a, with a bandwidth of 0.22 eV, 0.39 eV above the valence band maximum and 0.51 eV below the conduction band minimum. The impurity band is fully occupied and the transfer of electrons from the impurity to the conduction band is dominant for absorption in the telecommunication wavelength band with an absorption peak at 0.8 eV corresponding to the wavelength of 1.54 μ m 17,18 . Therefore, we can assume that with irradiation under light with photon energy greater than 0.51 eV, electrons in the impurity band are transferred to the conduction band with the absorption of the light.
In order to verify that electron transfer from the impurity to the conduction band occurs, the absorption spectrum of the silicon samples was measured with a V-570 JASCO UV/VIS/NIR spectrophotometer, and the results are shown in Fig. 2a. For comparison, the spectrum of an undoped silicon sample is also presented in this figure. From the figure, it is seen that the difference between the absorption bands of sulfur doped silicon and undoped silicon samples is indistinguishable in wavelength range from 2.0 to about 2.5 μ m corresponding to 0.51 to 0.62 eV jump from the impurity to the conduction band, as shown in Fig. 1a in agreement with theoretical calculations and previous experimental results 17,19 . The absorption band covers the telecommunications wavelengths of 1.3 and 1.5 μ m. From the band-gap structure and absorption spectrum shown in Fig. 1, it is seen that when the sulfur-doped silicon sample is irradiated by light with photon energy greater than 0.51 eV, electrons are transferred from the impurity band to the conduction band. It can also be theoretically predicted that under strong excitation, photogenerated carriers fill the states in the conduction and impurity bands, blocking further absorption and thus producing saturable absorption, as shown in Fig. 1b,c. The result represents a third order nonlinear response of the silicon sample to incident light, and allows the sample to be used as an optical modulator.
In order to investigate the saturable absorption properties of the sulfur-doped silicon sample, the Z-scan technique was applied. A mode-locked fiber laser with a wavelength of 1.55 μ m was used as the pump source. The fiber laser has a pulse duration and repetition rate of 565 fs and 20.13 kHz, respectively. Through a focusing lens, the minimum focus point had a radius of 30 μ m. The Z-scan experiment data of the sulfur-doped silicon sample are shown in Fig. 2b. According to the theoretical calculation 20 , the Z-scan data was fitted with the following equation: where T is the normalized transmittance, β is nonlinear absorption coefficient, I 0 is peak intensity at the focus point z = 0, is the effective length, L is the length of sample, α 0 is linear absorption coefficient, z is the position of the sample and z 0 is the Rayleigh length. The fitting result shows that the nonlinear absorption coefficient β of the sample is determined to be − 0.834 cm/MW. The saturable intensity, the irradiation intensity reducing the linear absorption coefficient to be 0.5α 0 , of the sample is calculated to be 3.19 MW/cm 2 , which is larger than graphene (0.71 to 0.61 MW/cm 2 ) but about three orders smaller than MoS 2 (2.45 GW/cm 2 or 413 GW/cm 2 ) [21][22][23][24] , which indicates that the prepared sample has strong three-order nonlinear response and large three-order nonlinear absorption coefficient inversely proportional to the saturation intensity, is a material that is considered to be a promising optical modulator at telecommunications wavelengths. The much smaller saturation intensity also indicates that the sulfur-doped silicon sample is easily saturate, and is quite sensitive to incident light. It can be predicted that the absorption loss for bleaching the sample is much small, especially for short-pulse and high peak power lasers at telecommunications wavelengths, and as a result, the fabricated sample should be a promising loss-negligible optical modulator, especially at telecommunications wavelengths.
In order to exclude the burnt effect of the sample in the Z-scan experimental process, the experiments about the laser-induced damage threshold has been implemented. A mode-locked fiber laser with a wavelength of 1.55 μ m was used as the source. The laser has a pulse width and repetition of 602 fs and 21 MHz, respectively. With a focus system, the laser beam was focused to be 13 μ m in the radius. The silicon sample was put at the focus of the beam. However, no damage was observed in the sample at the peak intensity of 2.24 GW/cm 2 much larger than maximum incident intensity 43.9 MW/cm 2 used in the Z-scan experiments. The result indicates that prepared sample has a laser-induced damage threshold larger than 2.24 GW/cm 2 and nonlinear response measured in Z-scan experiments was generated by the saturable absorption.
To investigate the optical modulation properties of the sulfur-doped silicon sample, it was used as a pulse modulator in two solid-state lasers operating at wavelengths of 1.34 and 1.42 μ m employing Nd:GdVO 4 and Nd:Y 3 Ga 5 O 12 (Nd:YGG) crystals, respectively. A detailed description of the experimental configuration is shown in the Method section. With a digital oscilloscope, the pulse width and repetition rate of the pulsed lasers modulated by the prepared silicon sample were recorded. The average output power and repetition rate are shown in Fig. 3a,b at wavelengths of 1.34 and 1.42 μ m, respectively. From the output power, repetition rate and pulse width measurement, the pulse energy and peak power of the lasers was determined. It was found that the average output power and repetition rate for both lasers increased with incident pump power, in good agreement with Q-switching theory under modulation by a passive optical modulator 25,26 . The maximum output power and repetition rate are 50 mW and 245.5 kHz, respectively, at an operating wavelength of 1.34 μ m, with maximum output energy of 0.21 μ J. The pulse width of the Nd:GdVO 4 pulsed laser decreased from 681 to 402 ns with increase in incident pump power. Figure 4a-c present the operating wavelength spectrum, pulse train with a repetition rate of 245.5 kHz, and single pulse profile with a pulse width of 402 ns of the passively modulated Nd:GdVO 4 laser, respectively. In the Nd:YGG laser operating at 1.42 μ m, the maximum output power is 16 mW with a maximum repetition rate of 75.76 kHz with a minimum pulse width of 167 ns and a maximum pulse energy of 0.22 μ J. The laser wavelength spectrum, pulse train with repetition rate of 75.76 kHz and a single pulse profile with pulse width of 167 ns are shown in Fig. 4e-g, respectively. All the laser experiments demonstrated that the sulfur-doped silicon sample exhibits saturable absorption properties and can be applied as a broadband passive modulator at telecommunications wavelengths. Combining the ease of integration and low cost of silicon crystals, it is concluded that the prepared silicon sample has promising applications as an optical modulator.
In conclusion, with the aim of constructing a loss-negligible passive optical modulator for application at telecommunications wavelengths, a silicon optical modulator was fabricated. By implanting sulfur ions in the silicon crystal, an impurity band was generated which is located between the valence and conduction bands, with a gap in the range of 0.51 ~ 0.62 eV between impurity and conduction bands. Under irradiation by high-intensity light, the third-order nonlinear optical response, saturable absorption, was generated by photogenerated carriers that move between the impurity and conduction bands. Saturable absorption of the prepared samples at 1.5 μ m was demonstrated and shows that the sample has a strong third-order nonlinear response to light. Passive pulsed lasers at 1.3 and 1.4 μ m were produced in standard solid-state lasers modified with the prepared silicon sample as a passive pulse modulator. All the results show that the sulfur-doped silicon sample holds promise as a pulse modulator with negligible loss and may play a valuable role in enhancing connectivity especially in computing fields at telecommunications wavelengths band 15,26,27 .

Methods
Lasers configuration with silicon optical modulator. For the pulsed laser experiments modulated by the sulfur-doped silicon sample, we used a two-mirror resonator. The detailed description of the experimental configuration is shown in the Supplementary Information. The pump source was a fiber-coupled diode at an emission wavelength of 808 nm, with a numerical aperture of 0.22 and a 400 μ m core diameter. The prepared silicon sample was inserted into the resonator between the gain material and output coupler. With a focusing system, pump power was focused through the front input mirror, antireflection (AR) coated at the pump wavelength and highly reflective (HR) at the laser wavelength into the laser crystal. The laser transmission surfaces of all the crystals were polished and uncoated. All laser crystals were mounted in Cu holders with cooling water operating at 15 °C.
In the 1.3 μ m laser, a Nd:GdVO 4 crystal with the dimensions of 3 mm × 3 mm × 10 mm (b × c × a) was used as the gain material. The doped Nd 3+ ion concentration was 0.5 at%. The front mirror was concave with a 200 mm radius of curvature and AR coated at 1.06 μ m. The output coupler was a plane mirror AR coated at 1.06 μ m with a transmission of 5% at 1.3 μ m. The AR coating is intended to inhibit oscillation at 1.06 μ m. For the 1.42 μ m laser, a Nd:YGG crystal with dimensions of 2 mm × 2 mm × 6 mm cut along the < 111> direction was used as the gain material. The doped Nd 3+ concentration in the YGG crystal was 1 at%. In the cavity, both the front and output mirrors were AR coated at 1.06 μ m and 1.3 μ m in order to inhibit oscillation at these two wavelengths. The front mirror was planar and the output mirror had a radius of curvature of 50 mm with a transmission of 5% at 1.42 μ m. The length between the front and output mirrors was 45 mm.