DEVICES AND METHODS FOR PROVIDING STIMULATED RAMAN LASING

Abstract

Devices and methods for providing stimulated Raman lasing are provided. In some embodiments, devices include a photonic crystal that includes a layer of silicon having a lattice of holes and a linear defect that forms a waveguide configured to receive pump light and output Stokes light through Raman scattering, wherein the thickness of the layer of silicon, the spacing of the lattice of holes, and the size of the holes are dimensioned to provide Raman lasing. In some embodiments, methods include forming a layer of silicon, and etching the layer of silicon to form a lattice of holes with a linear defect that forms a waveguide configured to receive pump light and output Stokes light through Raman scattering, wherein the thickness of the layer of silicon, the spacing of the lattice of holes, and the size of the holes are dimensioned to provide Raman lasing.

Description

FIELD OF THE INVENTION

This invention relates to Raman microlasers using photonic crystal waveguides made from silicon to achieve Raman lasing.

BACKGROUND OF THE INVENTION

Stimulated Raman scattering (SRS) has a rich and evolving history since the development of the laser. In 1962, Woodbury and Ng discovered the SRS effect at infrared frequencies. [E. J. Woodbury and W. K. Ng, Proc. IRE 50, 2347 (1962)] Hellwarth quickly described this observation as a two-photon process with a full quantum mechanical calculation. [R. W. Hellwarth, Theory of Stimulated Raman Scattering, Phys. Rev. 130, 1850 (1963)] To account for anti-Stokes generation and higher-order Raman effects, however, Garmire et al. and Bloembergen and Shen then adopted the coupled-wave formalism to describe the stimulated Raman effect. [E. Garmire, E. Pandarese, and C. H. Townes, Coherently Driven Molecular Vibrations and Light Modulation, Phys. Rev. Lett. 11, 160 (1963); N. Bloembergen and Y. R. Shen, Coupling Between Vibrations and Light Waves in Raman Laser Media, Phys. Rev. Lett. 12, 504 (1964); Y. R. Shen and N. Bloembergen, Theory of Stimulated Brillouin and Raman Scattering, Phys. Rev. 137, A1787 (1965)] These understandings were later improved by the inclusion of self-focusing to account for the much larger gain observed in SRS.

Recent developments include coupling a high Q (“Q” is a quality factor) silica microsphere to an optical fiber to achieve a minimum threshold of 62 μW, an example of which is illustrated in FIG. 1A. [S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, Ultralow-threshold Raman laser using a spherical dielectric microcavity, Nature 415, 621 (2002)] Higher-order Raman modes were observed in addition to other nonlinearities such as four-wave mixing and stimulated Brillouin scattering.

In a different line of researches that does not use SRS, various researches have demonstrated that a laser-reflowed silicon oxide microresonator with additional Er³⁺ doping can achieve low-threshold lasing. [A. Polman, B. Min, J. Kalkman, T. J. Kippenberg, and K. J. Vahala, Ultralow-threshold erbium-implanted toroidal microlaser on silicon, App. Phys. Lett. 84 (7), 1037, 2004)] Concurrently, Claps et al. have demonstrated a small but first-ever Raman amplification in silicon on-chip waveguides for photonic integrated circuit applications. [R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, Observation of stimulated Raman amplification in silicon waveguides, Optics Express 11 (15), 0.1731 (2003)] FIG. 1B illustrates an example of such a waveguide that is a centimeter long.

However, presently, the development of sizable gain in silicon photonic integrated circuits has yet to be demonstrated. This is suspected due to un-optimized phase matching design of the optical structures. [R. H. Stolen and E. P. Ippen, Raman gain in glass optical waveguides, App. Phys. Lett. 22 (6), 276 (1973)]

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the present invention will be best understood when read in reference to the accompanying figures wherein:

FIG. 1A is a magnified view of a conventional microsphere made from silica;

FIG. 1B is a magnified view of a conventional waveguide having its modal area of approximately 2-4 μm² and the length of approximately 10,000 μm;

FIG. 2 is a magnified view of an example photonic crystal with a waveguide manufactured in accordance with various embodiments of the present invention;

FIG. 3 is a graphical illustration of a relationship between pump light, Stokes light, and phonons in Raman scattering for various embodiments of the present invention;

FIGS. 4 and 5 are graphical illustrations of a calculated band structure depicting possible guided modes for various embodiments of the present invention;

FIGS. 4A and 5A are magnified views of portions of FIG. 4 and FIG. 5, respectively;

FIG. 6 is illustrations of electric and magnetic field intensity distributions for various embodiments of the present invention;

FIGS. 7( a)-(c) are SEM pictures of an example slow-light PhC waveguide fabricated in accordance with various embodiments of the present invention;

FIG. 8 are pictures showing an example fiber coupling setup in accordance with various embodiments of the present invention;

FIG. 9 is a graphical illustration of transition spectrum of an example of PhC waveguide fabricated in accordance with various embodiments of the present invention; and

FIG. 10 is a block diagram illustrating various components for using pulsed pump light in various embodiments of the present invention.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE PRESENT INVENTION

SRS is a linear inelastic two-photon process, where an incident photon interacts with an excited state of the material. In various embodiments of the present invention, which include the use of photonic crystals made of silicon, the excited state of the material refers to the longitudinal optical (LO) and transversal optical (TO) phonons of crystal silicon. In such embodiments, the strongest Stokes peak arises from single first-order Raman-phonon (threefold degenerate) at the Brillouin zone center of silicon. A microscopic description that depicts the change in the average number of photons n_s at the Stokes wavelength ω_s with respect to the longitudinal distance z is:

$\begin{array}{cc}\frac{n_s}{z}=\left(G_R·{\alpha }_s\right)n_s,G_R=\frac{W_{\mathrm{fi}}}{{\omega }_s}\left({\rho }_i·{\rho }_f\right)\frac{1}{{\mu }^{1/2}n_s},& \left(1\right)\end{array}$

where G_R is the Raman gain, α_s an attenuation coefficient, μ the permeability,

$\frac{W_{\mathrm{fi}}}{{\omega }_s}$

the transition rate, and ρ_i and ρ_f the initial and final state populations, respectively. For n_s and n_p (the average number of photons at ω_p) significantly greater than 1,

$\frac{W_{\mathrm{fi}}}{{\omega }_s}\propto n_sn_p$

and thus the Raman gain G_R is ∝n_p. For large n_s and n_p, a mesoscopic classical description with Maxwell equations using nonlinear polarizations P⁽³⁾ can also be used. The wave equations describing the interactions are:

$\begin{array}{cc}\nabla \times \left(\nabla \times E_s\right)+\frac{1}{c^2}\frac{{\partial }^2}{\partial t^2}\left({\varepsilon }_sE_s\right)=-\frac{1}{c^2}\frac{{\partial }^2}{\partial t^2}\left(P_s^{\left(3\right)}\right)& \left(2\right)\\ \nabla \times \left(\nabla \times E_p\right)+\frac{1}{c^2}\frac{{\partial }^2}{\partial t^2}\left({\varepsilon }_pE_p\right)=-\frac{1}{c^2}\frac{{\partial }^2}{\partial t^2}\left(P_p^{\left(3\right)}\right).& \left(3\right)\end{array}$

Specifically,

$P_s^{\left(3\right)}={\chi }^{\stackrel{\left(3\right)}{\mathrm{jkmn}}}E_pE_p^{*}E_s,$

where

${\chi }^{\stackrel{\left(3\right)}{\mathrm{jkmn}}}$

is the third-order fourth-rank Raman susceptibility with {j,k,m,n}={x,y,z}. The resonant terms in P_s⁽³⁾ give rise to SRS, while the non-resonant terms add to self-focusing and field-induced birefringence. The E_p and E_s are the electric fields at the pump and Stokes wavelengths, respectively. With

${\chi }^{\stackrel{\left(3\right)}{\mathrm{jkmn}}}$

obtained from bulk material properties, Equations (2) and (3) can be turned into discrete forms in the time-domain for direct ab initio numerical calculations of the nonlinear response.

As an approximation to the direct solution of this wave interpretation, the coupled-mode theory can be used to estimate the stimulated Raman gain. In particular, under the assumption of weak coupling between the pump and Stokes waves, the mode amplitudes can be given as:

$\begin{array}{cc}\frac{\partial E_p}{\partial \underset{\_}{z}}=-{\beta }_{\mathrm{pp}}I_pE_p& \left(4\right)\\ \frac{\partial E_s}{\partial \underset{\_}{z}}=-\left({\beta }_{ps}\left({\omega }_s\right)+{\kappa }_{ps}\left({\omega }_s\right)\right)I_pE_s-\left({\beta }_{pa}\left({\omega }_s\right)+{\kappa }_{pa}\left({\omega }_s\right)\right)E_p^2E_a^{*}{}^{-\Delta \mathrm{kz}}& \left(5\right)\\ \frac{\partial E_a}{\partial \underset{\_}{z}}=-\left({\beta }_{pa}\left({\omega }_a\right)+{\kappa }_{pa}\left({\omega }_a\right)\right)I_pE_a-\left({\beta }_{ps}\left({\omega }_a\right)+{\kappa }_{ps}\left({\omega }_a\right)\right)E_p^2E_s^{*}{}^{-\Delta \mathrm{kz}}& \left(6\right)\end{array}$

where the self-coupling terms are neglected, E_p, E_s and E_a denote the pump, and Stokes and anti-Stokes field amplitudes are denoted, respectively, as I_p=|E_p|², I_s=|E_p|². β_ab denotes the non-resonant terms and resonant terms with no frequency dependence. κ_ab denotes the resonant overall coupling coefficients (integrated spatially) between the modes. By determining κ_ps(ω_s), Equations (4) and (5) can be employed to determine the SRS gain. Intrinsic loss due to two-photon absorption (TPA) is assumed to be small based on the measured TPA coefficients in silicon and at pump powers on the order of 1 W. The role of TPA-induced free carrier absorption is also reduced in sub-wavelength silicon-on-insulator (SOI) waveguides of various embodiments of the present invention due to significantly shorter lifetime (compared to the recombination lifetime). This results in lower overall carrier densities.

Dimitropoulos et al. have derived a specialized form of Equations (5) to determine the Raman gain G_R in waveguides. [D. Dimitropoulos, B. Houshmand, R. Claps, and B. Jalali, Coupled-mode theory of the Raman effect in silicon-on-insulator waveguides, Optics Lett. 28 (20), 1954 (2003)] In particular, G_R has an approximate 1/(modal area)^3/4 dependence; that is, the SRS gain increases with decreasing modal areas, such as from high-index contrast waveguide structures. In various embodiments of the present invention, as will be described in detail later, enhancements through smaller modal areas A_m and length scales x, Purcell enhancements and/or slow group velocities afforded by photonic crystal structures permit increased amplification with significantly smaller device length scales.

An example photonic crystal 201 manufactured in accordance with various embodiments of the present invention is illustrated in FIG. 2. In particular, the photonic crystal 201 is formed from a layer of silicon on an insulator layer (e.g., a layer of oxide, SiO₂) (not shown). The layer of silicon can be formed by any known semiconductor fabrication method. For example, the layer of silicon can be deposited or grown on the layer underneath it. In another example, a prefabricated wafer that has a silicon layer already formed on an oxide layer can be used. A lattice of air-holes 203 is formed by etching the silicon layer. Although FIG. 2 illustrates the air-holes having a cylindrical shape, the air-holes can be in other shapes (e.g., rectangular, ellipsoidal, etc.) for some embodiments. The air-holes are not required to form perfect cylindrical shapes. The air-holes can have rough edges typically introduced during fabrication processes. The depth of the air-holes can be substantially equal to the thickness of the silicon layer (e.g., 300 nm). However, the air-holes can be shallower or deeper than the silicon layer. The etching of the silicon layer can be achieved by any known method (e.g., plasma etching, wet etching, etc.).

The lattice of air-holes also forms basic patterns 205. The example in FIG. 2 illustrates the basic lattice as having a triangular shape. However, the lattice can be formed using other basic patterns (e.g., squares, rectangles, pentagons, etc.). The etching step also creates defects (e.g., areas with no air-holes) in the lattice. In FIG. 2, the defects form a line of air-hole free region that is a pathway, which is an optical waveguide 207. Typically, a waveguide means optically transparent or low attenuation material that is used for the transmission of signals with light waves. As used in connection with various embodiments of the present invention, a waveguide is also capable of lasing using Raman scattering.

The Raman scattering is further described using the example waveguide 207 shown in FIG. 2. A light pump (not shown) coupled to the waveguide 207 supplies a beam of light (hereinafter the pump light) to an input port 209 of the waveguide 207. The pump light has a certain frequency and a corresponding wavelength. As the pump light enters and travels to an output port 211 of the waveguide 207, the pump light is downshifted to become Stokes light, as well as causing phonons to appear. The production of Stokes light and phonons from the pump light is referred to as Raman scattering. The relationship between the pump light, Stokes light, and phonons is graphically illustrated in FIG. 3.

FIG. 2 is a magnified view of an example photonic crystal. In fact, photonic crystals of various embodiments of the present invention have lengths on order of micrometers. For instance, the length can be between 2-3 micrometers. In some embodiments, the length can be 2.5 micrometers. However, the length can be shorter or longer than these example ranges depending on the overall design of each photonic crystal. Regarding the waveguide 207, its length (i.e., the distance between the input port 209 and output port 211) can be as co-extensive as that of the photonic crystal 201. A rectangular cross-sectional area 213 of the waveguide 207 perpendicular to the propagation direction of light in the waveguide 207 (i.e., from the input port 209 to the output port 211) is preferably on order of sub-wavelength. Such a cross-sectional area is also referred to as a model area. Here, sub-wavelength refers to lengths shorter than the wavelength of a light beam (either the pump light or the Stokes light), which is approximately 1.5 micrometers. In other words, each side of the rectangular cross-section 213 of the waveguide 207 is shorter than the wavelength of a light beam. In some embodiments, the rectangular cross-sectional area is on order of sub-microns. This means each side of the rectangular cross-section of the waveguide is shorter than a micron.

The small cross-sectional area of the waveguide 207 causes optical field densities to increase and causes the gain of the Raman scattering and lasing to increase as well. In addition to this enhancement, various embodiments of the present invention take advantage of slow light phenomena. That is, at the photonic band edge, photons experience multiple reflections and move very slowly through the material structure. In photonic crystal structures, line-defects in the periodic lattice permit guided-mode bands within the band gap, as shown in FIGS. 4 and 5. In various embodiments of the present invention, these bands are designed to be as flat as possible (v_g≡dω/dk) to achieve slow-light behavior, shown in FIGS. 4A and 5A. Group velocities as low as 10⁻² c can be obtained (“c” is the speed of light). Alternatively, coupled resonator optical waveguides can also permit control on the group velocity dispersion.

With slow group velocities, it is possible to reduce the interaction length by (v_g/c)². In particular, for group velocities on order of 10⁻² c, interaction lengths—between the Stokes and pump modes, for example—on order of 10⁴ times smaller than conventional lasers can be obtained. For the same operation power, the same gain can be obtained by the time-averaged Poynting power density P (˜v_g∈|E|²) incident on the photonic crystal structure. A decrease in v_g leads to a corresponding increase in ∈|E|² and in the Raman gain coefficient. These line-defect waveguides can be designed for two modes (i.e., the pump and Stokes modes) to be supported within the band gap of various embodiments of the present invention.

The small group velocity at the band edge in a 2D PhC lattice could further be employed in photonic band edge lasers. Without requiring a resonant cavity, the photonic band edge is a 2D analog of the distributed feedback laser. The lasing threshold is estimated to be proportional to v_g² for operation at slow group velocity regions, arising from the enhanced stimulated emission and the increase in the reflection coefficient for small v_g. This raises the possibility of a photonic band edge Raman laser when optically pumped.

PhC Waveguide Modes Design

An example structure is an air-bridge triangular lattice photonic crystal slab (e.g., 201) with thickness of 0.6a and the radius of air holes r is 0.29a, where a is the lattice period. The photonic band gap in this slab for TE-like modes is around 0.25˜0.32 [c/a] in frequency. The PhC waveguide is created by filling a row of air holes. FIG. 5 shows the projected band diagram of a PhC waveguide calculated by MIT Photonic Bands (MPB) package. Two defect waveguide modes (0^th order and 1^st order) exist in the bandgap of the 2D PhC, and these waveguide modes show high density states and zero group velocities at the band edge due to the Bragg condition. The 1^st order and the 0^th order waveguide modes at the band edge are considered to be pump mode and Stokes mode respectively. By tuning the geometry of PhC waveguide, such as the size of airholes, the waveguide width, and the slab thickness, the frequencies of the two modes can be shifted to match the pump-Stokes frequency spacing of 15.6 THz, corresponding to the optical phonon frequency of stimulated Raman scattering (SRS) in monolithic silicon.

The numerical design process is as following: (1) Fine-tune the PhC waveguide geometry; (2) Calculate resonant frequencies f_pump and f_Stokes with MPB; (3) Calculate the lattice constant a based on the frequencies (f_pump−f_Stokes)(c/a)=15.6 Hz and calculate the wavelength=λ_pump=a/f_pump, λ_Stokes=a/f_Stakes. For example, when a=420 nm, (f_pump−f_Stakes)=0.02184, with λ_pump=1550 nm, λ_Stokes=1686 nm. FIG. 2 shows the electric field intensity |E|² and the magnetic field intensity |H|² at the middle of the slab for pump mode (1^st order waveguide mode) and Stokes mode (0^th order waveguide mode) respectively.

Fabrication and Measurements

FIG. 7 shows the SEM pictures of PhC waveguide fabricated using a silicon-on-insulator (SOI) substrate with top silicon thickness of 320 nm. The pump-Stokes frequency spacing can be obtained by active trimming of PhC thickness. A potential issue for small v_g modes is the impedance and mode mismatch when coupling into these waveguides. In order to decrease the coupling loss between the conventional ridge waveguide and the PhC waveguide, the taper structure for adiabatic mode transformation is designed, as shown in FIG. 7 (c).

UWS-1000 Supercontinuum laser is used to provide a measurement window from 1200 to 2000 nm. A polarization controller and a fiber-coupled lens assembly were used to couple light into the structure. A second lensed fiber collects the waveguide output that is sent to the optical spectrum analyzer. The fiber coupling setup is shown in FIG. 8. The measured transmission spectrum of PhC waveguide is given in FIG. 9.

The amplification gain improved by the waveguides is further enhanced by integrating a p-i-n (p-type, intrinsic, n-type) junction diode with the photonic crystal. In such a configuration, the strong electrical field created by the diode removes free carriers (electrons and holes). These free carriers, which are induced by two-photon absorption, can reduce, if not removed, the amplification gain factor in the photonic crystal. The p-i-n diode can be fabricated using any known semiconductor fabrication method. In operation, the diode is biased by a constant voltage.

For various embodiments of the present invention, in order to provide a net Raman gain, TPA induced the free-carrier absorption phenomenon can also be addressed using pulsed operations, where the carrier lifetime is much larger than the pulse width and much less than the pulse period. In particular, as shown in FIG. 10, a photonic crystal 1001 with one or more microcavities is coupled to a multiplexer (MUX) 1003. The MUX 1003 receives its input from a polarization controller 1005 that combines inputs from a pulsed pump laser 1007 and a continuous wave (CW) Stokes laser 1009. The output from the photonic crystal 1001 is then input to an optical spectrum analyzer (e.g., a detector) 1011.

Various embodiments of the present invention relate to methods of manufacturing a laser device. The methods may include the acts of forming a layer of silicon; and etching the silicon layer to form a lattice of regularly spaced air-holes with a linear defect created by a row of missing air-holes. The linear defect forms a waveguide that receives pump light and outputs Stokes light through Raman scattering. The methods may further include acts of selecting frequencies of the pump light and the Stokes light from slow group velocity modes of the pump light and Stokes light in the waveguide. The slow group velocity is about 1/100 of the speed of light. A distance between two regularly spaced air-holes is approximately 420 nm.

Various embodiments of the present invention relate to devices for generating a laser beam. The devices may include a layer of photonic crystal having a lattice of regularly spaced air-holes with a linear defect created by a row of missing air-holes. The linear defect forms a waveguide that receives pump light and outputs Stokes light-through Raman scattering. The frequencies of the pump light and the Stokes light are selected from slow group velocity modes of the pump light and Stokes light in the waveguide. The slow group velocity is about 1/100 of the speed of light.

Various embodiments and advantages of the present invention are apparent from the detailed specification, and, thus, it is intended by the appended claims to cover all such features and advantages of the invention which fall within the true spirit and scope of the invention. Further, since numerous modifications and variations will readily occur to those skilled in the art, it is not desired to limit the invention to the exact construction and operation illustrated and described, and, accordingly, all suitable modifications and equivalents may be resorted to falling within the scope of the invention. The foregoing invention has been described in detail by way of illustration and example of various embodiments, numerous modifications, substitutions, and alterations are possible without departing from the scope of the invention.

Claims

1. A device for providing stimulated Raman lasing, comprising: a photonic crystal that includes a layer of silicon having a lattice of holes and a linear defect that forms a waveguide configured to receive pump light and output Stokes light through Raman scattering, wherein the thickness of the layer of silicon, the spacing of the lattice of holes, and the size of the holes are dimensioned to cause the photonic crystal to provide Raman lasing.

2. The device of claim 1, wherein the thickness of the layer of silicon is within a range of about 240 nm to about 265 nm, the spacing of the holes is within a range of about 399 mm to about 441 nm, and the size of the holes is within a range of about 166 nm to about 122 nm.

3. The device of claim 1, wherein the thickness of the layer of silicon is within a range of about 216 nm to about 238 nm, the spacing of the holes is within a range of about 360 nm to about 400 nm, and the size of the holes is within a range of about 79 nm to about 87 nm.

4. The device of claim 1, wherein the waveguide is configured to cause the pump light to be in a slow group velocity mode.

5. The device of claim 1, wherein the slow group velocity mode has a slow group velocity as low as about 1/1000 the speed of light.

6. The device of claim 5, wherein the waveguide is configured to receive pump light with a wavelength of about 1550 nm.

7. The device of claim 1, wherein the holes are regularly spaced and arranged in a repeating triangular pattern.

8. The device of claim 1, further comprising forming an adiabatic coupling region between an input waveguide and the lattice of holes forming a waveguide.

9. The device of claim 1, further comprising a p-i-n diode coupled to the waveguide that removes free carriers in the waveguide.

10. A method of manufacturing a photonic crystal waveguide for providing stimulated Raman lasing, comprising: forming a layer of silicon; andetching the layer of silicon to form a lattice of holes with a linear defect, such that the lattice of holes forms a waveguide configured to receive pump light and output Stokes light through Raman scattering, wherein the thickness of the layer of silicon, the spacing of the lattice of holes, and the size of the holes are dimensioned to cause the photonic crystal to provide Raman lasing.

11. The method of claim 10, wherein the thickness of the layer of silicon is within a range of about 240 nm to about 265 nm, the spacing of the holes is within a range of about 399 nm to about 441 nm, and the size of the holes is within a range of about 166 nm to about 122 nm.

12. The device of claim 10, wherein the thickness of the layer of silicon is within a range of about 216 nm to about 238 nm, the spacing of the holes is within a range of about 360 nm to about 400 nm, and the size of the holes is within a range of about 79 nm to about 87 nm.

13. The method of claim 10, wherein the waveguide is configured so that pump light of a chosen frequency will be in a slow group velocity mode of the waveguide.

14. The method of claim 10, wherein the slow group velocity mode has a slow group velocity as low as about 1/1000 the speed of light.

15. The method of claim 14, wherein the wavelength of the selected frequency is about 1550 nm

16. The method of claim 10, further comprising etching the lattice of holes, such that a triangular pattern is formed.

17. The method of claim 10, further comprising trimming the photonic crystal using etching techniques.

18. The method of claim 10, further comprising forming an adiabatic coupling region between an input waveguide and the lattice of holes forming a waveguide.