RF intensity modulated mid-IR light source based on dual-frequency optical parametric oscillation

Kun Li; Suhui Yang; Xin Wang; Zhuo Li; Jinying Zhang

doi:10.1364/OE.27.004907

1. Introduction

Atmosphere has a transmission window in 3-5 μm since light waves in this spectrum experience low absorption by nitrogen and oxygen. Therefore, 3-5 μm laser has been applied in infrared laser missile guidance, infrared Ladar, infrared laser communication, infrared laser directional interference [1–4]. In addition, there are many molecular vibration spectral lines in 3-5 μm, which makes 3-5 μm light source an ideal candidate in the field of molecule spectroscopy and environment monitoring [5,6].

Ladar-radar used intensity modulated laser as the transmitter. The phase of the back scattered light is used to resolve the range and velocity of the detected objects. Ladar-radar has high spatial resolution as Ladar, at the same time, the modulated beam is less affected by atmospheric turbulence and scattering from molecules and smog in the air [7–9]. Intensity modulation combined with coherent detection had been used in a differential absorption Ladar system for CO₂ sensing to improve the sensitivity and accuracy [10,11]. Nevertheless, Ladar-radar have been better developed in visible and near infrared spectra due to the maturity of intensity modulated light sources and photo detectors in visible to near infrared spectra [12–15]. The development of broadband mid-infrared detectors has made mid-IR Ladar-radar more attractive. Naturally, RF intensity modulated mid-IR light source is another necessity for the development of mid-IR Ladar-radar. Optical parametric oscillator (OPO) is the most practical way to generate mid-IR laser output [16,17]. OPO has advantages of high output power, wide frequency tenability and good beam quality [18,19]. Output coupling of single resonate oscillator (SRO) signal has enabled the generation 8.6 W of total signal and idler output with single-frequency spectra at both wavelengths for 14.5 W of pump power [20]. Reference [21] reported the generation of 17.5 W of total power (9.8 W signal, 7.7 W idler) from an out-coupled cw SRO at 61% extraction efficiency. Nevertheless, direct intensity modulation of mid-IR light usually requires high-voltage driving electronics which can be an obstacle for high speed modulation. Therefore, we need to look for other approaches. Interference between two single frequency beams can generate stable beat note which have been used to realize intensity modulation of visible and Near-IR lasers [22–24]. In this paper, we extended the concept to mid-IR via dual-frequency pumped OPO. A dual-frequency laser at 1064 nm is used to pump a MgO:PPLN OPO. Since the two frequencies of the pump laser beam are very close to each other, they can stimulate optical parametric oscillations respectively. Therefore, the output signal and idler waves also contain two-frequency components, respectively. Intensity modulated light waves at both signal and idler wavelengths are realized due to interferences. By varying the beat note frequency of the pump, the modulation frequency of the signal and idler are tuned respectively. In this paper, we aim on generation of RF intensity modulated mid-IR light wave, we focus on the study of the idler light. When the pump power is 13 W, 2.38 W idler output power is obtained, corresponding to a conversion efficiency from pump to idler of 19.4%. The wavelength of the idler is tuned from 3.1 to 3.8 μm by changing the temperature. High harmonic modulation frequencies can be observed when the pump power exceeds 7 W, the modulation power spectrum of the idler wave is discussed.

2. Theories of dual-frequency OPO

Optical parametric oscillation is a second-order nonlinear process involving the interaction of three optical fields at frequencies $ω_{3}$ , $ω_{2}$ , and $ω_{1}$ , such that

ω_{3} = ω_{1} + ω_{2}

The field at $ω_{3}$ corresponds to an intense input optical pump field. The generated field at the higher frequency— $ω_{2}$ , is usually referred to as the signal, while the field at the lower frequency $ω_{1}$ is termed the idler.

We consider a total field $E$ comprising three waves representing the pump, signal, and idler. To simplify the discussion, we also assume that the optical fields are infinite uniform plane waves propagating in the z-direction, and define dual-frequency pump field as

E_{3} (z) = A_{31} e^{i (k_{3} z - ω_{3} t)} + A_{32} e^{i [k_{3}^{'} z - (ω_{3} + Δ ω) t]}

where

A_{31}

,

A_{32}

represent the field amplitudes of dual-frequency pump light, respectively.

k_{j} = ω_{j} n_{j} / c

, with

j = 1, 2, 3

,

n_{j}

is the refractive index. Since

ω_{j}

approximates to

ω_{j} + m \cdot Δ ω

, with

m = 1, 2, 3 \dots

, we can take

k_{j}^{'} = k_{j}

.

Define the initial signal field as

E_{2} (z) = A_{2} e^{i (k_{2} z - ω_{2} t)}

where

A_{2}

represents the field amplitude of the signal light.

The wave equations are [25]:

\frac{\partial E_{1} (z)}{\partial z} = i K_{1} E_{3} (z) E_{2}^{*} (z) e^{i Δ k z}

\frac{\partial E_{2} (z)}{\partial z} = i K_{2} E_{3} (z) E_{1}^{*} (z) e^{i Δ k z}

\frac{\partial E_{3} (z)}{\partial z} = i K_{3} E_{1} (z) E_{2} (z) e^{- i Δ k z}

where

K_{1}

,

K_{2}

,

K_{3}

are the coupling coefficients,

Δ k = k_{3} - k_{1} - k_{2}

is the phase mismatch, consider the perfect phase matching condition,

Δ k = 0

, submit (2), (3) to formula (4a), we arrive

\begin{matrix} \frac{\partial E_{1} (z)}{\partial z} = i K_{1} {A_{31} e^{i (k_{3} z - ω_{3} t)} + A_{32} e^{i [k_{3} z - (ω_{3} + Δ ω) t]}} A_{2} e^{- i (k_{2} z - ω_{2} t)} \\ = i K_{1} A_{2} {A_{31} e^{i (k_{1} z - ω_{1} t)} + A_{32} e^{i [k_{1} z - (ω_{1} + Δ ω) t]}} \end{matrix}

Suppose $A_{2}$ is slowly varying with respect to z, apply integration on Eq. (5), we reach

E_{11} (z) = A_{2} \frac{K_{1}}{k_{1}} {A_{31} e^{i (k_{1} z - ω_{1} t)} + A_{32} e^{i [k_{1} z - (ω_{1} + Δ ω) t]}}

Similarly, submit (6), (3) to formula (4c), we reach

E_{3}^{'} (z) = A_{2}^{2} \frac{K_{1} K_{3}}{k_{1} k_{3}} {A_{31} e^{i (k_{3} z - ω_{3} t)} + A_{32} e^{i [k_{3} z - (ω_{3} + Δ ω) t]}}

Submit (6), (2) to formula (4b), we obtain

E_{21} (z) = A_{2} \frac{K_{1} K_{2}}{k_{1} k_{2}} {\begin{cases} (A_{31}^{2} + A_{32}^{2}) e^{i (k_{2} z - ω_{2} t)} \\ + A_{31} A_{32} e^{i [k_{2} z - (ω_{2} - Δ ω) t]} + A_{31} A_{32} e^{i [k_{2} z - (ω_{2} + Δ ω) t]} \end{cases}}

Equation (8) tells us that pump light $ω_{3}$ , $ω_{3} + Δ ω$ and signal light $ω_{2}$ are coupled to generate idler light $ω_{1}$ , $ω_{1} + Δ ω$ . This idler with frequencies of $ω_{1}$ , $ω_{1} + Δ ω$ couples with the pump light $ω_{3}$ , $ω_{3} + Δ ω$ again and generate signal light $ω_{2}$ , $ω_{2} - Δ ω$ , $ω_{2} + Δ ω$ .

The side bands of the signal light $ω_{2} - Δ ω$ ; $ω_{2} + Δ ω$ is coupled to the pump $ω_{3}$ , $ω_{3} + Δ ω$ light,then two idler fields are generated as following:

E_{1}^{'} (z) = A_{2} A_{31} A_{32} \frac{K_{1}^{2} K_{2}}{k_{1}^{2} k_{2}} {A_{31} e^{i [k_{1} z - (ω_{1} + Δ ω) t]} + A_{32} e^{i [k_{1} z - (ω_{1} + 2 Δ ω) t]}}

E_{1}^{' ​'} (z) = A_{2} A_{31} A_{32} \frac{K_{1}^{2} K_{2}}{k_{1}^{2} k_{2}} {A_{31} e^{i [k_{1} z - (ω_{1} - Δ ω) t]} + A_{32} e^{i (k_{1} z - ω_{1} t)}}

The total field reads

E_{12} = E_{1}^{'} + E_{1}^{' ​'}

Submit (9a)/(9b), (2) to formula (4b), we get

E_{2}^{' ​'} (z) = A_{2} A_{31} A_{32} \frac{K_{1}^{2} K_{2}^{2}}{k_{1}^{2} k_{2}^{2}} {\begin{cases} (A_{31}^{2} + A_{32}^{2}) e^{i [k_{2} z - (ω_{2} - Δ ω) t]} \\ + A_{31} A_{32} e^{i (k_{2} z - ω_{2} t)} + A_{31} A_{32} e^{i [k_{2} z - (ω_{2} - 2 Δ ω) t]} \end{cases}}

E_{2}^{' ​' ​'} (z) = A_{2} A_{31} A_{32} \frac{K_{1}^{2} K_{2}^{2}}{k_{1}^{2} k_{2}^{2}} {\begin{cases} (A_{31}^{2} + A_{32}^{2}) e^{i [k_{2} z - (ω_{2} + Δ ω) t]} \\ + A_{31} A_{32} e^{i (k_{2} z - ω_{2} t)} + A_{31} A_{32} e^{i [k_{2} z - (ω_{2} + 2 Δ ω) t]} \end{cases}}

E_{22} = E_{2}^{' ​'} + E_{2}^{' ​' ​'}

Similarly, we can deduce that

E_{1}^{' ​' ​'} (z) = A_{2} A_{31}^{2} A_{32}^{2} \frac{K_{1}^{3} K_{2}^{2}}{k_{1}^{3} k_{2}^{2}} {A_{31} e^{i [k_{1} z - (ω_{1} +2 Δ ω) t]} + A_{32} e^{i [k_{1} z - (ω_{1} + 3 Δ ω) t]}}

E_{13} = E_{1}^{' ​' ​'} + E_{1} {^{' ​'}}^{' ​'}

If we repeat this process, we will reach similar expressions for even higher order side bands for both the signal and idler fields. The power in the side bands drops with the order because in each step only a fraction of the idler and signal fields are coupled with the pump and generate one order higher sidebands, therefore, the sidebands signal and idler fields are getting weaker and weaker with respect to the order. The process is illustrated in Fig. 1.

Fig. 1 Illustration of the generation of high order signal and idler sidebands.

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The total idler field can be described as

E_{1} = E_{11} + E_{12} + E_{13} + \dots + E_{1 N} + \dots

The intensity of the idler field is proportional to ${| E_{1} |}^{2}$ , substitute (12)the into ${| E_{1} |}^{2}$ , the interferences between different order side bands will produce modulation frequency at $Δ ω$ , $2 Δ ω$ , $3 Δ ω$ and so on. The strength of the modulated signal decreases with the modulation frequency.

3. Experimental setup

Figure 2 shows the experimental setup. The pump laser is a dual-frequency master oscillator power amplifier (MOPA) system. The dual-frequency seed laser is formed by frequency-shifted-and-recombined method. The output from a non-planar ring oscillator (NPRO) single frequency laser is frequency shifted via an acousto-optic modulator (AOM) (Isomet Corp., M1324-T150), the shifted and unshifted beams are recombined in a fiber coupler. The NPRO is pumped by a 2 W 808 nm laser diode (LD) (Hi-Tech optoelectronics Co., Ltd.) and the maximum single frequency output power from the NPRO is 376 mW. The insertion loss of the AOM is 2 dB. The power ration of the two beams is controlled via changing the RF power added to the AOM. The beat note frequency can be tuned from 140 to 160 MHz via changing the radio frequency added to the AOM. The dual-frequency seed laser is amplified via a two-stage LD pumped ytterbium doped fiber amplifier (YDFA). A polarization beam splitter (PBS) and a half wave plate are used to adjust the polarization direction of the dual-frequency pump to match the polarization direction of MgO:PPLN crystal.

Fig. 2 Diagram of the experimental setup of the dual-frequency OPO.

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The OPO resonator is formed with two concave mirrors M₁ and M₂ and two plane mirrors M₃ and M₄. The radius of curvature of both concave mirrors are 150 mm. The length of the OPO cavity is 720 mm, the distance between M₁ and M₂ is 220 mm, and the distance between M₃ and M₄ is 130 mm. The MgO:PPLN crystal is placed in the middle of M₁ and M₂. All four cavity mirrors are coated with anti-reflection coating at both pump and idler wavelengths and high-reflection coating at signal wavelength (R>99.8%), so that the pump only pass the ring cavity once to avoid the pump form resonance in the cavity and cause decrease of the conversion efficiency and output instability.

The linewidth of the pump is 20 kHz if we do not take into account that there are two frequency components in the pump. The narrow linewidth of the pump ensures both the signal and the idler have only one longitudinal mode oscillating. The Free Spectral Range (FSR) and finesse of the ring cavity for the idler wave are 386 MHz and 785, respectively. Thus, the spectral width of the cavity for the idler is approximately 0.5 MHz. The beat-note frequency of the dual-frequency idler is 140-160 MHz, which is within one FSR of the cavity but much bigger than its spectral resolution, therefore the two frequency components of the idler can be resolved without ambiguity.

The MgO:PPLN crystal (HC Photonics Corp.) is $50 \times 8.7 \times 1$ mm³ slab with four different poling periods. Both ends of the crystal are coated with anti-reflection coating at three wavelengths, the pump, signal and idler. (1064 nm (R<1%)/1400-1750nm (R<1%)/2800-4300 nm (R<10%)). The MgO:PPLN crystal is wrapped with indium foil and mounted in a copper heat sink. The thermal sensor is attached on the heat sink. The whole piece is put into an oven with a precise temperature controller. The accuracy of the temperature control is 0.1 $° C$ . The oven is placed on a three-axis adjustable stage. Different poling period of the crystal in use is chosen via adjusting the position of the oven with respect to the optical axis of the cavity.

The pump light is the output of the fiber amplifier. The diameter of the fiber core is 25 μm and the numerical aperture of the fiber is 0.065. A lens f₁ with focal length of 80 mm is used to collimate the pump, then two lenses f₂ and lens f₃ focus the pump to the nonlinear crystal. The pump spot has a diameter of 180 μm at the center of the crystal.

4. Experimental results and discussions

4.1 Wavelength tunability

By changing the temperature of the nonlinear crystal, the output wavelength of both the signal and the idler can be tuned. An optical spectrometer (Zolix omni- $λ 3$ 00i, covering wavelength from 2500 to 8000 nm) is used to measure the wavelength of the idler. By changing the temperature and the poling period, the wavelength of the idler can be tuned. Figure 3(a) shows the spectra of the idler at different temperatures. The wide linewidths of the curves are due to low resolution bandwidths we use when the curves are measured, but one can see that the peak wavelength decreases when the temperature increases. Figure 3(b) shows the dependence of wavelength to temperature of the crystal at different poling periods. Wavelength tuning from 3.1 to 3.8 $μm$ is realized.

Fig. 3 (a) Spectra of the idler at different temperatures (The crystal poling period is 31 μm.); (b) Wavelength of the idler versus temperature of the crystal at different poling periods.

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4.2 Output power

When the beat note frequency of the pump is fixed at 150 MHz, the power ratio is 1:1, total pump power is 10 W. We measure the output power of the idler at different wavelengths. Figure 4 shows the results. The maximum output power is obtained with poling period of 30.5 μm at wavelength of 3385 nm.

Fig. 4 Output power of the idler at different wavelengths and poling periods.

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We test the efficiency of different poling periods at their phase matching temperatures. The output power of the idler and conversion efficiencies are shown in Fig. 5. When the poling period is 30.5 μm, pump power is 13 W, we obtained the maximum output power 2.22 W of the idler. At the maximum output power, we measure the stability of the output within 30 minutes. The standard deviation of the output power is 1.3%. Figure 5(b) shows the results. When the poling period is 30 μm, pump power is 9 W, we obtain the highest conversion efficiency of 17.2% from the pump to the idler.

Fig. 5 (a)Output powers and conversion efficiencies from pump to idler versus pump power at different poling period of crystal; (b)Power stability of the idler within 30 minutes.

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In order to see the influence of the frequency difference of the two waves to the output power of the idler, we used the 30 μm poling period at its optimized temperature, 75 $° C$ . The power ratio is set to 1:1, we plot the output power and conversion efficiencies of the idler at different beat note frequencies. The results are shown in Fig. 6. As the difference of the two frequencies is smaller, the two components have almost the same gain and same loss in the cavity. So, the impact on the output of the idler is not very big, although there is some small drop of the output power at low pump power when the beat note frequency is increased. This is due to the fact that one of the pump frequencies gets out of the optimum phase matching condition.

Fig. 6 Output powers and efficiencies of the idler versus the pump powers at different beat-note frequencies.

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4.3 Power spectra of the modulation of the idler

A fast HgCdTe detector is used to obtain beat note spectra of the idler light. We fix the beat note frequency at 150 MHz, and the pump power at 4 W. Figure 7 shows the spectra of modulation of the idler light at different power ratio of the pump. When the pump power is at a low level, only 150 MHz modulation frequency can be seen, as the ratio of two powers get larger, the modulation signal is getting stronger but no higher resonance is observed.

Fig. 7 Modulation spectrum of the idler at different pump power radio.

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Figure 8 shows the spectra of the modulation of the idler light at different beat note frequency of the pump. The beat-note frequency of idler light is always the same as that of the pump light.

Fig. 8 Modulation tunability of the idler (The beat note frequency of the idler is the same as the pump, which is presented with dashed line.).

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The stabilities of the beat note of both the pump and idler are measured with a frequency counter. The stabilities of the bump and idler are 3 Hz and 4.1 Hz, respectively as shown in Fig. 9. The stability of the idler is not as good as the pump but in the same order. The slightly degradation might be caused by the mechanical and thermal noise from the OPO.

Fig. 9 (a)Frequency stability of pump beat-note; (b)Frequency stability of idler beat-note.

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In order to see the higher resonance of the modulation spectrum, we increase the pump power but fix the power ratio to 1:1. As the pump power increases, more and more higher resonances can be seen in the modulation spectrum as shown in Fig. 10. Higher resonances contain less power, the experimental results are consistent to our theoretical predictions.

Fig. 10 (a), (b), (c), (d), (e)Modulation spectra of the idler at different pump power levels; (f)Modulation spectra of the signal at 12W of pump power.

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The signal has similar behaviors on the modulation spectra as the idler. When the pump power is 12 W, we observe four modulation sidebands as shown in Fig. 10(f). Both the number and the relative intensity of sidebands are the same for the signal and idler spectra. This is easy to be predicted since the idler and the signal are generated in pair from the OPO.

5. Conclusion

High power, high efficiency intensity modulated mid-IR light have been obtained via dual-frequency optical parametric oscillator. MgO:PPLN crystal with four poling periods is used to optimize the efficiency and output power of the idler light. When the pump power is 13 W, the idler output power at mid-IR is 2.38 W, corresponding to a pump-idler conversion efficiency of 19.4%. The wavelength of the idler light is tuned from 3.1 to 3.8 μm. The power spectrum of the modulation of the idler wave is studied. The modulation frequency can be tuned from 140 to 160 MHz. The beat note stability of the mid-IR light is measured to be 4.1 Hz. The influence of the pump power and power ratio to the modulation spectrum of the idler light is discussed. This stable RF intensity modulated mid-IR light source has potential applications in differential absorption lidar (DIAL) and mid-IR Ladar-radar.

Funding

National Natural Science Foundation of China (61741502, 61835001, 61875011, 61205116).

References

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RF intensity modulated mid-IR light source based on dual-frequency optical parametric oscillation

Abstract

1. Introduction

2. Theories of dual-frequency OPO

3. Experimental setup

4. Experimental results and discussions

4.1 Wavelength tunability

4.2 Output power

4.3 Power spectra of the modulation of the idler

5. Conclusion

Funding

References

Cited By

Figures (10)

Equations (19)

Optics Express