Mid-wave infrared generation by difference frequency mixing of continuous wave lasers in orientation-patterned Gallium Phosphide

Shekhar Guha; Jacob O. Barnes; Peter G. Schunemann

doi:10.1364/OME.5.002911

1. Introduction

With the increasing availability of high power Nd³⁺ doped fiber lasers in the 1 to 1.3 μm range, the prospect of obtaining tunable continuous wave (CW) mid-infrared radiation by nonlinear mixing with Er³⁺ doped fiber lasers (1.5 – 1.6 μm) through difference frequency generation (DFG) becomes attractive. Cubic semiconductors such as GaAs and GaP with quasi-phase matched (QPM) structures are ideal nonlinear optical material candidates for this process as they are transparent in the wavelength range of 1 to 10 μm and because of the high value of their high d-coefficients (94 pm/V and 71 pm/V respectively [1, 2]). Using reported values of refractive index [1, 3], QPM grating period (Λ) required for generating idler (longest) wavelengths ranging from 3 to 8 μm for a signal (middle) wavelength at 1.55 μm for orientation patterned GaAs (OP-GaAs) and orientation patterned GaP (OP-GaP) crystals are plotted in Fig. 1. The values of Λ are larger for OP-GaP, making fabrication of QPM structures with 1 mm or larger thicknesses in GaP more practical than in GaAs. The calculated values of Λ for DFG of 1.064 and 1.55 μm in OP-GaAs and OP-GaP crystals (shown by the vertical line in Fig. 1 are respectively 8.7 and 17.5 μm.

Fig. 1 The calculated values of grating period in OP-GaAs and OP-GaP as a function of idler and pump wavelengths, (λ₁ and λ₃, respectively) for signal wavelength λ₂ = 1.55 μm, at temperature 295 K. The vertical line is drawn at λ₃ = 1.064 and λ₁ = 3.400 μm.

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2. Material growth and fabrication

The orientation-patterned gallium phosphide (OP-GaP) crystal used in this work was produced at BAE Systems using a unique combination of molecular beam epitaxy (MBE) and hydride vapor phase epitaxy (HVPE) reactors modified for phosphide growth [4]. The approach was based on the all-epitaxial processing technique pioneered at Stanford University [5, 6] (and independently at the University of Tokyo [7, 8]) for the growth of orientation-patterned gallium arsenide (OP-GaAs) and later extended to the growth of OP-GaP [2, 9, 10]. This method utilizes polar-on-nonpolar molecular beam epitaxy (MBE) whereby a thin Si layer (5 nm) is deposited on a GaP substrate (3-inch, (100) cut, 4° offcut toward <111B>, double-side polished) and the subsequent GaP layer - under the proper growth conditions - has an inverted orientation relative to the substrate. The resulting inverted layer is photo-lithographically patterned with the required grating spacing (based on work by Parsons and Coleman [3]), and alternate domains are etched through the inverted layer back to the original substrate by reactive ion etching (RIE). Subsequent regrowth on the patterned template - first by MBE then by HVPE - produces a thick (>500 μm) quasi-phasematched (QPM) structure for in-plane laser pumping.

The OP-GaP crystal used for these experiments was cut from a multi-grating OP-GaP wafer which was produced by using of two sequential HVPE runs on the patterned MBE template. The layer thickness produced by each run was approximately 150 μm (300 μm total) on top of a 400 μm thick GaP substrate. Unfortunately the 20.8 μm grating did not propagate past the growth interruption despite excellent domain integrity for the first 150 μm, as shown in Fig. 2.

Fig. 2 Polished and etched cross-section of OP-GaP crystal used for this work. The 20.8 μm grating propagation was limited to 150 μm due to a growth interruption.

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A 6.3-mm-wide by 16.5-mm-long sample was cut from this grating, and the end faces were polished and anti-reflection (AR) coated with side 1/side 2 reflectivities of 21/34%, 54/55%, and 0.82/0.81% at the pump (1064.6 nm), signal (1549.8 nm) and idler (3340.5nm) wavelengths respectively, as shown in Fig. 3 from measurements on a witness sample coated in the same run. This AR coating was designed for a different 2- μm-pumped experiment [4], and not for the DFG experiment described here, which is why the reflectivities are much higher than desired.

Fig. 3 The reflectivities of the two sides of the AR coated crystals shown by the blue and red dashed lines.

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3. DFG experiment

The experimental arrangement for DFG is shown in Fig. 4. The 1.0646 μm (pump) and 1.5498 μm (signal) laser beams (denoted by subscripts 3 and 2, respectively) from two CW fiber lasers were expanded by telescopes T₃ and T₂, variably attenuated by the half-wave plate- polarizer combinations (HWP_3a, P₃) and (HWP_2a, P₂), rotated in polarization by half-wave-plates HWP_3b and HWP_2b and focused by a 10 cm focal length CaF₂ lens (L₁) to be incident on the crystal, which was mounted on a custom designed oven controlled by a thermo-electric cooler (TEC) which provided both active heating and cooling. The crystal temperature was maintained at a constant value by the TEC even when it was irradiated with high power laser beams. The crystal temperature was measured using a platinum resistance temperature detector. A picture of the oven is shown in Fig. 5. The oven was mounted on a stage with three rotational and three translational motion control axes. The laser beam size at focus was 26 μm for the pump and 33 μm for the signal respectively (half-width at e⁻¹ of intensity). Due to experimental constraints, the focal planes of the pump and the signal beams were separated by approximately 3 mm in air.

Fig. 4 The set-up for the difference frequency mixing experiment.

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Fig. 5 Picture of the oven on which the OP-GaP crystal was mounted.

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4. Results

When the pump beam was incident on the sample by itself, a green beam generated by second harmonic generation of the pump could be seen at the exit of the sample. With both the pump and signal beams properly aligned through the sample, a red beam was observed in addition to the green beam, arising from sum frequency mixing (at 0.631 μm) of the pump and the signal beams. With the two incident beams (and the generated red and green beams) blocked by filters with dielectric coatings and germanium windows, the midwave infrared beam at 3.4 μm was observed on a PbSe or a pyroelectric detector. The generated infrared beam was collected by a 20 cm focal length CaF₂ lens (L₂) and two dielectric filters (BS₂) placed after the lens reflected the pump and the signal beams while transmitting the generated idler beam. An AR coated Ge wafer absorbed the residual pump and signal beams and a pyroelectric detector measured the idler beam power. The maximum idler power obtained at the crystal exit was about 152 mW with incident pump and signal power values of 47 W and 24 W, respectively. The shape of the generated idler beam, seen on an InSb infrared camera is shown in Fig. 6.

Fig. 6 The generated idler beam at 3.39 μm.

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For incident beams that are Gaussian in transverse distribution, the generated idler power P₁ at the exit plane is theoretically predicted to be [11]

P_{1} = \frac{P_{2} P_{3}}{P_{DF}} h_{1}

where

P_{DF} \equiv \frac{c ε_{0} n_{3}^{2} λ_{1} λ_{2}^{2}}{32 π^{2} d_{eff}^{2} ℓ}

and the expression for h₁ is given [11]. Using the value of 51 pm/V for d_eff, ℓ = 16.5 mm and using n₃ = 3.1044 from the work of Parsons and Coleman [3], we obtain P_DF = 15.5 Watts. Assuming the maximum value of h₁ to be 0.16 [11], Eq. (1) gives P₁ to be of the order of 10 W, so the observed power of 150 mW is approximately two orders of magnitude below the predicted value. Absorption and scattering in the crystal, unoptimized focusing of the non-Gaussian incident beams and possible inequality of grating wave vector and the phase mismatch of the interacting beams are possibly all contributing to the discrepancy between the predicted and observed power values.

5. Polarization dependence

In the DFG experiment described here, the polarization directions of the two incident pump and signal beams can be independently controlled, and the dependence of the idler power on the polarization directions of the incident beams can be studied. Polarization dependence of the three wave mixing process in cubic crystals has been described by Kuo [12] where the general expression for d_eff, the effective second order nonlinear optical coefficient, was derived. Here, in addition, the explicit expressions for the direction of the idler field for various cases of the incident beam polarizations are provided.

Since the substrate chosen was (100) oriented and the OPGaP crystal was mounted with the incident and exit faces in vertical planes, the principal dielectric X axis was vertical. To obtain the maximum frequency conversion efficiency for the cubic crystals when the incident beams are linear polarized, the propagation direction needs to be along a base diagonal, which was chosen here to be the [ $0 \bar{11}$ ] direction. The polarization directions of all the propagating fields then lie on the ( $0 \bar{11}$ ) plane, which is shown as the incident or exit face of the crystal in Fig. 7.

Fig. 7 Orientation of alternate layers in the patterned structure. The body diagonal [111̄] is perpendicular to the propagation direction [ $0 \bar{11}$ ] and lies on the incident (and exit) face of the crystal.

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Choosing the [100] and the [011̄] directions to be the coordinate axes (defined as û₂ and û₁, respectively) for vectors lying on the ( $0 \bar{11}$ ) plane, we have

{\hat{u}}_{1} = \frac{(\hat{Y} - \hat{Z})}{\sqrt{2}}

{\hat{u}}_{2} = \hat{X}

where X̂, Ŷ and Ẑ denote the unit vectors along the principal dielectric axes.

If E₃ and E₂ denote the incident pump and signal field vectors, with unit vectors ê₃ and ê₂, then for arbitrary polarized incident beams we can write (following Kuo, [12])

{\hat{e}}_{3} = e^{i β_{3}} cos ψ_{3} \hat{X} + sin ψ_{3} \frac{(\hat{Y} - \hat{Z})}{\sqrt{2}}

{\hat{e}}_{2} = e^{i β_{2}} cos ψ_{2} \hat{X} + sin ψ_{2} \frac{(\hat{Y} - \hat{Z})}{\sqrt{2}}

where (β₃, ψ₃) and (β₂, ψ₂) characterize the polarization states of the pump and the signal beams, respectively.

For a linear polarized incident beam, the parameter β = 0 and then ψ denotes the angle between the polarization direction and the X axis; for circular polarized incident beams, we have β = π/2 and ψ = π/4; and for random polarized incident beam, β is randomly varying and ψ = π/4; with appropriate subscripts (3 or 2) added to the β and ψ parameters to signify the pump or the signal beams, respectively.

The nonlinear idler polarization P₁ oscillating with frequency c/λ₁ is generated by the second order mixing of E₃ and E₂ and has components along the principal dielectric axes

\begin{array}{l} P_{1 X} & = & 4 ε_{0} d_{14} (E_{3 Y} E_{2 Z}^{*} + E_{3 Z} E_{2 Y}^{*}) \\ P_{1 Y} & = & 4 ε_{0} d_{25} (E_{3 Z} E_{2 X}^{*} + E_{3 X} E_{2 Z}^{*}) \\ P_{1 Z} & = & 4 ε_{0} d_{36} (E_{3 X} E_{2 Y}^{*} + E_{3 X} E_{2 Z}^{*}) . \end{array}

Since only the generated idler beam propagating along the pump and signal propagation direction is significant, the polarization vector of the idler beam also lies on the (

0 \bar{11}

) plane. To determine the component (denoted by say P_u) of the vector P₁ on this plane, we first find the projections of P₁ on the û₁ and û₂ axes from the dot products

\begin{array}{l} P_{1 u 1} & = & P_{1} \cdot {\hat{u}}_{1} \\ P_{1 u 2} & = & P_{1} \cdot {\hat{u}}_{2} \end{array}

and then

P_{u} = P_{1 u 1} {\hat{u}}_{1} + P_{1 u 2} {\hat{u}}_{2} .

The direction of the idler polarization is the same as that of P_u. To find this direction, we define a vector A with components

\begin{array}{l} A_{X} & = & e_{3 Y} e_{2 Z}^{*} + e_{3 Z} e_{2 Y}^{*} \\ A_{Y} & = & e_{3 Y} e_{2 Z}^{*} + e_{3 Z} e_{2 Y}^{*} \\ A_{Z} & = & e_{3 Y} e_{2 Z}^{*} + e_{3 Z} e_{2 Y}^{*} \end{array}

and find the projections

\begin{array}{l} A_{u 1} & = & A \cdot {\hat{u}}_{1} \\ A_{u 2} & = & A \cdot {\hat{u}}_{2} . \end{array}

to find the vector

A_{u} = A_{u 1} {\hat{u}}_{1} + A_{u 2} {\hat{u}}_{2}

For cubic crystals, i.e., with d₁₄ = d₂₅ = d₃₆, P_u is parallel to A_u, so we can find the unit vector for the idler polarization to be

{\hat{e}}_{1} = \frac{A_{u 1}}{\sqrt{{| A_{u 1} |}^{2} + {| A_{u 2} |}^{2}}} {\hat{u}}_{1} + \frac{A_{u 2}}{\sqrt{{| A_{u 1} |}^{2} + {| A_{u 2} |}^{2}}} {\hat{u}}_{2} .

Using Eqs. (6) and (10) we find

\begin{array}{l} A_{u 1} & = & - sin ψ_{3} cos ψ_{2} e^{- i β_{2}} - cos ψ_{3} sin ψ_{2} e^{i β_{3}} \\ A_{u 2} & = & - sin ψ_{2} sin ψ_{3} . \end{array}

The unit vector ê₁ along the generated idler polarization direction can then be shown to be given by

{\hat{e}}_{1} = - \frac{sin ψ_{3} sin ψ_{2}}{δ} \hat{X} - \frac{sin ψ_{3} cos ψ_{2} e^{- i β_{2}} + cos ψ_{3} sin ψ_{2} e^{i β_{3}}}{δ} \frac{(\hat{Y} - \hat{Z})}{\sqrt{2}}

where

δ \equiv (\frac{d_{eff}}{d_{14}}) = {{sin}^{2} ψ_{3} + {cos}^{2} ψ_{3} {sin}^{2} ψ_{2} + \frac{1}{2} sin 2 ψ_{3} sin 2 ψ_{2} cos (β_{2} + β_{3})}^{1 / 2} .

The expression for δ in Eq. (16) is identical with Eq. 6.9 obtained by Kuo [12]. From the general expressions for ê₁ and d_eff given in Eqs. (15) and (16) various special cases for incident beam polarizations can now be considered.

5.1. Pump and signal beams both linear polarized

In this case β₃ = β₂ = 0 and ψ₃ and ψ₂ denote the angles of the polarization vectors of the pump and signal fields with respect to the X axis. Then,

δ^{2} = {(\frac{d_{eff}}{d_{14}})}^{2} = {sin}^{2} (ψ_{3} + ψ_{2}) + {sin}^{2} ψ_{3} {sin}^{2} ψ_{2}

and

{\hat{e}}_{1} = - \frac{sin ψ_{3} sin ψ_{2}}{\sqrt{{sin}^{2} (ψ_{3} + ψ_{2}) + {sin}^{2} ψ_{3} {sin}^{2} ψ_{2}}} \hat{X} - \frac{sin (ψ_{3} + ψ_{2})}{\sqrt{{sin}^{2} (ψ_{3} + ψ_{2}) + {sin}^{2} ψ_{3} {sin}^{2} ψ_{2}}} \frac{(\hat{Y} - \hat{Z})}{\sqrt{2}} .

Results for various orientations of the pump and signal beam polarizations can be easily obtained from Eqs. (17) and (18). For pump beam polarization along the X axis, i.e., along the [100] direction, we have ψ₃ = 0, so that δ = sinψ₂, and the idler power, which is proportional to

d_{eff}^{2}

, is maximum when ψ₂ = 90°, i.e., with signal polarization perpendicular to the pump polarization direction.

When the pump beam polarization is along the [011̄] direction, i.e., ψ₃ = 90°, we have δ = 1, so the idler power is constant for all values of ψ₂. The idler polarization direction for this case is along

{\hat{e}}_{1} = - sin ψ_{2} \hat{X} - cos ψ_{2} \frac{(\hat{Y} - \hat{Z})}{\sqrt{2}}

which is complementary to the signal polarization direction.

From Eq. (17) we find that for the case of linear polarized pump and signal beams, the idler power is maximum when the angles ψ₂ and ψ₃ are equal to each other and to ${tan}^{- 1} \sqrt{2} (= 54.7356 °)$ , i.e., when the polarization directions are along a body diagonal. For this case the polarization direction of the idler beam is also along the same direction and the value of δ is $2 / \sqrt{3}$ .

The predicted dependence of (d_eff/d₁₄)² on the signal polarization angle ψ₂ for linear polarized pump and signal beams is shown in Fig. 8.

Fig. 8 The dependence of the direction of the idler polarization and the (d_eff/d₁₄)² values on the directions of the pump and signal polarization, when both the pump and signal beams are linear polarized.

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5.2. Pump beam circular and signal beam linear polarized

In this case, β₂ = 0, β₃ = π/2, and ψ₃ = π/4, with ψ₂ denoting the angle between the polarization vector of the signal field and the X axis. From Eqs. (15) and (16) we get

{\hat{e}}_{1} = - \frac{sin ψ_{2}}{\sqrt{1 + {sin}^{2} ψ_{2}}} \hat{X} - \frac{(cos ψ_{2} - i sin ψ_{2})}{\sqrt{1 + {sin}^{2} ψ_{2}}} \frac{(\hat{Y} - \hat{Z})}{\sqrt{2}} .

and

δ^{2} = {(\frac{d_{eff}}{d_{14}})}^{2} = \frac{1 + {sin}^{2} ψ_{2}}{2} .

If the pump beam is linear and signal beam is circular polarized, the unit vector and d_eff values are obtained from Eqs. (20) and (21) by replacing ψ₂ by ψ₃.

We find from Eq. (20) that when ψ₂ = 0 (i.e., signal beam is along X̂), the idler beam is linear polarized and perpendicular to the signal beam. When ψ₂ = 90°, the idler beam is circular polarized, rotating in the opposite sense from the pump beam. And when ψ₂ is not equal to 0 or 90°, the idler beam is elliptically polarized, and rotating in the opposite sense from the pump beam.

5.3. Pump beam random polarized and signal beam linear polarized

Since output of commercial fiber lasers are often random polarized, we consider the cases of random polarized incident beams in this and two later subsections. If the pump beam is random polarized and the signal beam is linear polarized, we have β₂ = 0, ψ₃ = π/4 and β₃ is randomly changing. From Eqs. (16) and (15) we then get

{\hat{e}}_{1} = - \frac{sin ψ_{2}}{\sqrt{1 + {sin}^{2} ψ_{2}}} \hat{X} - \frac{(cos ψ_{2} - i sin ψ_{2} e^{i β_{3}})}{\sqrt{1 + {sin}^{2} ψ_{2}}} \frac{(\hat{Y} - \hat{Z})}{\sqrt{2}} .

and

δ^{2} = \frac{1 + {sin}^{2} ψ_{2}}{2} .

The time-averaged squared amplitudes of the orthogonal components of the unit vector ê₁ of the generated idler field are

{| {\hat{e}}_{1 u 1} |}^{2} = \frac{{sin}^{2} ψ_{2}}{1 + {sin}^{2} ψ_{2}}

{| {\hat{e}}_{1 u 2} |}^{2} = \frac{1}{1 + {sin}^{2} ψ_{2}}

i,e., the generated beam is randomly elliptically polarized in general. However, if the signal beam is polarized is along [100], i.e., for ψ₂ = 0, the idler beam is linear polarized perpendicular to it (along [011̄]) and δ² is equal to 0.5. If the polarization direction of the signal beam is along [011̄], i.e., with ψ₂ = 90°, δ² is equal to 1, and the idler beam is random polarized with equal components in all directions.

The predicted idler beam directions and values of (d_eff/d₁₄)² for the cases of circular or random polarized pump and linear polarized signal beams are tabulated in Fig. 9.

Fig. 9 The direction of the idler polarization and the (d_eff/d₁₄)² values for circular or random polarized pump beam and linear polarized signal beam.

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5.4. Pump and signal beams both circular polarized, rotating in opposite sense

In this case, β₂ = −β₃ = π/2 and ψ₂ = ψ₃ = π/4, From Eqs. (15) and (16) we get

δ^{2} = 1.25

and

{\hat{e}}_{1} = - \frac{1}{2 δ} \hat{X} - \frac{i}{δ} \frac{(\hat{Y} - \hat{Z})}{\sqrt{2}} .

The squared amplitudes of the orthogonal components of the unit vector ê₁ of the generated idler field

{| {\hat{e}}_{1 u 1} |}^{2} = \frac{1}{δ^{2}} = \frac{4}{5}

{| {\hat{e}}_{1 u 2} |}^{2} = \frac{1}{4 δ^{2}} = \frac{1}{5}

are i,e., the generated beam is elliptically polarized and rotating in opposite sense from the pump beam.

5.5. Pump and signal beams both circular polarized and rotating in same sense

In this case, β₂ = β₃ = π/2, and ψ₂ = ψ₃ = π/4, From Eqs. (15) and (16) we get

δ^{2} = 0.25

and

{\hat{e}}_{1} = \hat{X}

the generated idler beam is linear polarized in the X direction.

5.6. Pump beam random polarized and signal beam circular polarized

If the pump beam is random polarized and the signal beam is circular polarized, we have β₂ = π/2, ψ₂ = π/4, ψ₃ = π/4 and β₃ is randomly changing. From Eqs. (16) and (15) we then get

δ^{2} = 0.75

and

{\hat{e}}_{1} = - \frac{1}{2 δ} \hat{X} - \frac{e^{i β_{3}} - i}{2 δ} \frac{(\hat{Y} - \hat{Z})}{\sqrt{2}} .

The time-averaged squared amplitudes of the orthogonal components of the unit vector ê₁ of the generated idler field are

{| {\hat{e}}_{1 u 1} |}^{2} = \frac{2}{4 δ^{2}} = \frac{2}{3}

{| {\hat{e}}_{1 u 2} |}^{2} = \frac{1}{4 δ^{2}} = \frac{1}{3}

i,e., the generated beam is elliptically polarized with a randomly oscillating component.

5.7. Pump and signal beams both random polarized

If both the pump and the signal beams are random polarized, we have ψ₂ = ψ₃ = π/4 and β₂, β₃ are randomly changing. From Eqs. (16) and (15) we then get

δ^{2} = 0.75

and

{\hat{e}}_{1} = - \frac{1}{2 δ} \hat{X} - \frac{e^{i β_{3}} + e^{- i β_{2}}}{2 δ} \frac{(\hat{Y} - \hat{Z})}{\sqrt{2}} .

The time-averaged squared amplitudes of the orthogonal components of the unit vector ê₁ of the generated idler field are

{| {\hat{e}}_{1 u 1} |}^{2} = \frac{2}{4 δ^{2}} = \frac{2}{3}

{| {\hat{e}}_{1 u 2} |}^{2} = \frac{1}{4 δ^{2}} = \frac{1}{3}

i,e., the generated beam is elliptically polarized, with a randomly oscillating component. The predicted values of (d_eff/d₁₄)² for the different cases of circular or random polarized pump and signal beams are tabulated in Fig. 10.

Fig. 10 The direction of the idler polarization and the (d_eff/d₁₄)² values for circular or random polarized pump and signal beams.

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5.8. Experimental verification of polarization dependence

Experimentally, the pump polarization angle ψ₃ was set at three values (0, 90° and 54.7356°) by the half-wave plate HWP_3b in Fig. 4, and circular polarized pump beam was obtained by replacing HWP_3b by a quarter wave plate. Experimental results obtained for the measured idler power for three cases linear polarized pump beam and the case of circular polarized pump beam, all for linear polarized signal beam, are shown in Fig. 11. The match between the experimental results and the theoretical predictions was found to be very good.

Fig. 11 Experimentally measured idler beam power as a function of ψ₂, the angle between the signal beam and the [100] direction, for different polarization states of the pump beam. (a) Linear polarized pump, withψ₃ = 0; (b) Linear polarized pump, with $ψ_{3} = {tan}^{- 1} \sqrt{2}$ ; (c) Linear polarized pump, with ψ₃ = 90°; (d) Circular polarized pump. In each case, the solid lines show the theoretically predicted dependence of the idler beam power on ψ₂.

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6. Conclusion

First demonstration of continuous wave frequency mixing in OP-GaP is reported. About 150 mW was generated at 3.4 μm by mixing of 1.064 μm and 1.55 μm beams. With improved grating dimensions, optimized antireflection coatings and better quality of incident beams, higher levels of power in the midwave infrared are expected. Idler beam direction and relative values of d_eff were theoretically determined for various polarization states of the incident beams. Some of the theoretical predictions were experimentally verified.

Acknowledgments

We thank an anonymous reviewer for very careful reading of the manuscript, for making several suggestions for improvement, and especially for pointing out previous work [12] on this topic. The authors also thank Douglas M. Krein and Dr. Joel M. Murray of Air Force Research Laboratory, Wright Patterson Air Force Base, OH for their help with sample polishing and manuscript preparation.

References and links

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Mid-wave infrared generation by difference frequency mixing of continuous wave lasers in orientation-patterned Gallium Phosphide

Abstract

1. Introduction

2. Material growth and fabrication

3. DFG experiment

4. Results

5. Polarization dependence

5.1. Pump and signal beams both linear polarized

5.2. Pump beam circular and signal beam linear polarized

5.3. Pump beam random polarized and signal beam linear polarized

5.4. Pump and signal beams both circular polarized, rotating in opposite sense

5.5. Pump and signal beams both circular polarized and rotating in same sense

5.6. Pump beam random polarized and signal beam circular polarized

5.7. Pump and signal beams both random polarized

5.8. Experimental verification of polarization dependence

6. Conclusion

Acknowledgments

References and links

Cited By

Figures (11)

Equations (39)

Optical Materials Express