Open Access
Add to BibSonomy
Abstract
We demonstrate a synchronously-pumped optical parametric oscillator (OPO) with a cavity formed from high refractive index inverted prisms, also known as Brewster mirrors. Exploiting a single total internal reflection, this is the simplest device capable of deviating a laser beam by $180^\circ$. The OPO produced a chirped signal output tunable from 1060 - 1570 nm with a maximum power of 114 mW. We investigate the geometric properties of ideal and imperfect Brewster mirror prisms and find the latter can provide ∼1000 × finer control of the signal wavelength when compared to cavity length tuning.
Published by Optica Publishing Group under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
1. Introduction
Sources of widely tunable ultrashort pulses are required for such diverse applications as deep-tissue multi-photon imaging [1], stand-off spectroscopy [2], and material characterisation [3]. Synchronously-pumped optical parametric oscillators (OPOs) are versatile platforms for the generation of wavelengths not readily accessible from laser gain media [4–7], using a resonant cavity to enhance weak single-pass parametric down-conversion in a nonlinear crystal and convert a high frequency pump wave into lower frequency signal and idler waves in an energy conserving process. For a fixed pump, tuning the signal is primarily achieved by altering the phase-matching properties of the crystal, or by adjusting the cavity length [8]. The synchronous nature of the OPO constrains its operation such that the cavity group delay is fixed, expressed as:
where $k$ is a constant. A small change in cavity length $L$ must be reflected by a change in group delay such that $\tau (\omega ) + \frac {\Delta L(\omega )}{c} = k$. Differentiating to find group delay dispersion (GDD) gives:In previous work [10] we described an OPO cavity formed from a pair of N-BK7 Pellin-Broca prisms acting as retroreflectors, with a ${\sim }45$ mm path length inside each prism. Despite this large amount of glass the cavity length tuning rate was almost 2000 nm/mm, and the system exhibited dual-wavelength signal operation driven by a minimum in the cavity group delay around $1.34~\mu$m. Here we demonstrate a synchronously-pumped OPO formed by a pair of high refractive index inverted triangular prisms, or Brewster mirrors, as first proposed by Moosmüller [11]. Operating in an all-normal dispersion regime, the OPO is tunable across 500 nm in the near-infrared and produces sub-picosecond chirped pulses with up to 114 mW of average power. We examine the geometric properties of these prisms, and report low sensitivity to misalignment and sub-nm/mm signal tuning rates.
2. Properties of a Brewster mirror prism
Figure 1 illustrates the operation of a Brewster mirror prism. The prism is composed of a homogeneous glass of refractive index $n(\lambda )$, with apex angle $\alpha$ and side length $\overline {AB} = S$. A beam entering $\overline {AB}$ at Brewster’s angle $\theta _B$ is refracted at angle $\theta _n (\lambda )$ and undergoes total internal reflection (TIR) at face $\overline {BC}$ a distance $y$ from vertex B. The reflected beam exits through $\overline {AC}$, travelling parallel to the input with separation $x$ without inversion or reversal of the beam profile.
Fig. 1. Left: angles and beam path within a Brewster mirror prism. Right: translation of the prism base orthogonal to the input beam does not change the beam separation.
2.1 Requirements for total internal reflection
In his paper Moosmüller noted that the refractive index of the prism must exceed $n = 1.84$ to enable total internal reflection at the prism base. While this value is correct, the inequality was given without derivation and contained a typographical error. Here we fully derive the lower bound limitation on the refractive index, including a wavelength dependence not discussed in [11].
We assume the input beam strikes face $\overline {AB}$ at angle $\theta _B$, as shown in Fig. 1. Using simple laws of triangles, we can see that the angle of incidence at the base of the prism is given by $\theta _B - \theta _n(\lambda )$. For total internal reflection to occur the angle of incidence must be greater than critical angle $\theta _C$, where $\theta _C = \sin ^{-1}\left ({\frac {1}{n(\lambda )}}\right )$. This condition is satisfied when:
For the specific case of a monochromatic wave entering at Brewster’s angle, prism apex $\alpha$ is selected such that $\theta _B = 90 - \frac {\alpha }{2} = 90 - \theta _n= \tan ^{-1}(n)$, with Eq. (3) becoming:
which is satisfied when $n > 1.83929$. This limits the choice of prism to a small group of dense flint or lanthanum dense flint optical glasses, or some crystalline materials. For a polychromatic beam entering at a fixed Brewster’s angle defined by prism apex $\alpha$, Eq. (3) becomes: an inequality that varies with wavelength. Figure 2(a) shows the wavelength-dependent refractive index of CDGM glass H-ZLaF68C, along with the calculated solution to Eq. (5) for an apex angle of $\alpha = 56.6^{\circ }$ ($\theta _B(\lambda =1.1~\mu {\rm m}) = 61.7^{\circ }$). The refractive index drops below the monochromatic TIR cutoff ($n \approx 1.83929$) at $2.21~\mu$m, however the wavelength dependence of the inequality increases the cutoff to $2.44~\mu$m.Fig. 2. Calculated properties of a H-ZLaF68C prism with $\alpha = 56.6^\circ$ and $S = 25$ mm. (a) Refractive index and total internal reflection limit. (b) Internal path length.
2.2 Geometric path
We take the simplified case where the refracted ray strikes face $\overline {BC}$ opposite the apex. We define distance $y$ from vertex $B$ such that $y = \frac {\overline {BC}}{2} = S\sin {\left (\frac {\alpha }{2}\right )}$. Using the laws of sines, we can write:
Substituting in $y = S\sin {\left (\frac {\alpha }{2}\right )}$ and rearranging for $z$, we get:
Due to our symmetry condition, the total path length as a function of wavelength is therefore:
This function is plotted in Fig. 2(b) for a H-ZLaF68C prism with $\alpha = 56.6^\circ$ and $S = 25$ mm.
2.3 Beam separation upon prism exit
As the separation between the input and exit beams is often an experimental limitation, we derive an expression for distance $x$. Employing the same symmetry argument used above and the diagram shown in Fig. 1, it is simple to show that:
Substituting in the expression for total path length $2z$ in Eq. (9), we find beam separation:
The refractive index dependence of $x$ results in a spatially dispersed output of parallel propagating wavelengths. This spatial dispersion can be reversed with a second prism.
We note that both Eq. (9) and Eq. (11) are independent of the position of the input beam along face $\overline {AB}$, allowing the prism to be translated parallel to the base without changing the path length or beam separation, as illustrated on the right of Fig. 1. This feature of the Brewster mirror prism contrasts with the operation of a right-angled prism or hollow roof mirror which produce a varying beam separation under translation.
3. Experiment and results
A schematic of the Brewster-mirror OPO is shown in Fig. 3. The pump source was a 333-MHz Ti:sapphire laser (Gigajet, Laser Quantum) producing 30-fs pulses with 1.25 W of average power at a centre wavelength of 806 nm. The pump was coupled into the OPO cavity with a 950 nm long-pass dichroic mirror (87-039, Edmund Optics) and focused into a 3-mm-long PPLN crystal (periodically-poled lithium niobate, FOPMIR-FA, HCP) using a 20 mm lens (38-409, Edmund Optics), with a second 20 mm lens collimating the beam after the crystal. Mode-matching optics and the focusing lens increase the pump pulse duration to ${\sim }$100 fs at the crystal plane. The PPLN crystal was held at $60^\circ$C and contained a fan-out grating structure with $\Lambda =20.5-23.5~\mu$m. The calculated pump focus in the crystal was $12~\mu$m, producing a Gaussian focusing parameter of $\xi \approx 1.22$ [12]. The cavity was formed with a pair of H-ZLaF68C Brewster mirror prisms with $\alpha = 56.6^\circ$, $S = 25$ mm and a height of 10 mm (Haisong Optoelectronic Technology Ltd. (Dongguan)), with the refractive index and internal path length previously shown in Fig. 2. The dimensions were selected to minimise the internal path while providing a beam separation of $x\approx 13$ mm, allowing the reflected beam to cleanly pass the lens and crystal. Approximately $13{\%}$ output coupling was achieved using the Fresnel reflection from the uncoated surface of a 2-mm-thick lithium niobate plate, with the rear side having the same anti-reflection coating as the crystal.
The net cavity transmission function is shown in the top of Fig. 4 in blue, along with contributions from the coated optics, Fresnel output coupler, and transmittance of the bulk prism material [13]. Additional losses from wavelengths entering and exiting the prisms away from Brewster’s angle, along with scattering from the TIR surface, are assumed to be negligible. The transmission of the N-BK7 lens falls sharply above $2.7~\mu$m, and significant idler absorption occurs before the output coupler, with any remaining idler absorbed in the prism bulk or refracting out the prism base. Manufacturer data were unavailable above $2~\mu$m for some components and so we omit longer wavelengths from this plot.
Fig. 3. Schematic of the Brewster mirror OPO, not to scale. Each prism could be translated both parallel and orthorgonally to the base. LPF; low pass filter. OC; output coupler. PPLN; periodically-poled lithium niobate.
Fig. 4. Top: Cavity transmission function for the Brewster mirror OPO. The output coupler operates in reflection, with the transmitted component shown here. Bottom: Normalised spectra and output powers recorded at increasing cavity length increments of $\Delta L = 40~\mu$m.
Signal spectra were obtained as the cavity length was tuned by moving a micrometer stage orthogonal to the prism base, with results shown in the bottom of Fig. 4. Signal outputs with centre wavelengths ranging from 1060 - 1570 nm were measured over $600~\mu$m of length change, with a maximum observed power of 114 mW recorded after a 1000 nm long-pass filter (FELH1000, Thorlabs) and 0.17% RMS stability over 1 hour. The threshold was 650 mW and the slope efficiency was $26{\%}$.
The net dispersion of the OPO cavity was dominated by contributions from the prisms and is normal until reaching 1660 nm, with GDD decreasing from 6000 fs$^2$ at 1000 nm to 600 fs$^2$ at 1600 nm. Intensity autocorrelation measurements revealed chirped signal pulses with durations ranging from 300 - 600 fs. Our prior investigation of a Pellin-Broca prism OPO would suggest these pulses should be externally compressible to sub-150-fs durations [10].
4. Discussion
As detailed in $\$$2.3, the geometry of the Brewster mirror indicates that translating the prism parallel to the base should not change the beam separation or the internal beam path, and therefore should not alter the round trip synchronicity condition of the OPO which would result in a shift in the signal wavelength. We tested this property by independently translating each prism with a micrometer stage aligned parallel to the base, with the results shown in Fig. 5. We observed a linear change in signal wavelength of $\pm 1.6$ nm when translating the first prism by $\pm 2.5$ mm relative to the point opposite the prism apex, with a $\pm 7.3$ nm wavelength shift observed when moving prism 2. Tuning rates of 0.64 nm/mm and 2.91 nm/mm were observed for prism 1 and 2 respectively. These wavelength shifts were reversible by translating the prisms back to their original positions and could be replicated with different initial wavelengths.
We explain this wavelength shift by considering a Brewster mirror which has been imperfectly manufactured, such that the base of the prism is not orthogonal to the bisector of apex $\alpha$ but instead is offset by $d\theta$, as shown in Fig. 6. We assume that the apex angle has been manufactured as expected, and that the prism is oriented such that the input beam meets $\overline {AB}$ at $\theta _B$. We define the prism angles as:
As the symmetry condition considered in §2 no longer exists, path lengths $z_1$ and $z_2$ now depend on where the input beam meets $\overline {AB}$, which we define here as $S'$, the distance from vertex $B$. To find $z_1$ we first define angle $\delta = \theta _n + \frac {\alpha }{2} + d\theta$. From the law of sines we have:
Assuming the TIR condition has been met, the length of second internal path $z_2$ is dependent on the position at which the beam strikes $\overline {BC}$. We therefore define expressions for $\overline {BC}$ and $y$, the length along this face from apex $B$, as:
Equations (14) and (17) show that the path length varies linearly with position along the input face, while still varying with wavelength. Figure 7 shows an example of this variation over a 5 mm prism base translation for $d\theta = 0.1^\circ$, $\alpha = 56.6^\circ$ and $S = 25$ mm. A similar analysis, not detailed here, shows that an otherwise ideal Brewster mirror angled such that the prism base is not orthogonal to the input beam does not display a path length variation as the base is translated. Further analysis of Fig. 6 shows that the angle at which the reflected beam meets face $\overline {AC}$ is:
and therefore the refracted beam exits at angle:This has implications for a resonator built using a pair of Brewster mirror prisms with poorly specified tolerance as the beam will not exit at Brewster’s angle and will incur additional loss, and will also no longer travel parallel to the input beam, potentially missing a second prism.
Fig. 7. (a) Calculated path length at $1.2~\mu$m in a H-ZLaF68C prism as the base is translated orthogonally to the input beam $\left (\alpha = 56.6^\circ,~S = 25~{\rm mm,}~d\theta = 0.1^\circ \right )$. (b) Wavelength dependent path length change.
The geometry and signal tuning behavior of our OPO allowed us to determine the manufacturing error in each Brewster mirror prism. The prism separation illustrated in Fig. 3 was 400 mm, producing a cavity length that matched the 333 MHz repetition rate of the pump laser and placing an upper limit of $d\theta = 0.06^\circ$ due to Eq. (19). Translating the prism base alters the internal path, changing the round-trip group delay and therefore the resonant signal wavelength. Figure 8 shows the relative cavity group delay for three entry positions across input face $\overline {AB}$ of prism 2, for an error of $d\theta = 0.031^\circ$. Translating the prism by $\pm$2.5 mm alters the relative group delay and shifts the signal wavelength by $\mp 7.3$ nm, which can be recovered by adjusting the cavity length by $\pm 11~\mu$m. A similar analysis of the tuning behavior for prism 1 produces an error of $d\theta = 0.007^\circ$. The tuning behavior shown in Fig. 8 is advantageous for fine control of the central signal wavelength. Cavity length adjustment of the OPO has a tuning rate of 850 nm/mm, while moving the base of prism 1 results in a rate of 0.64 nm/mm, three orders of magnitude improvement in sensitivity. In theory a desirable tuning rate could be selected by specifying the base angle error, provided the strict manufacturing tolerances could be met.
Fig. 8. Signal wavelength shift for prism 2 as the prism base and cavity length are adjusted. The net group delay change implies that $d\theta = 0.031^\circ$.
5. Conclusions
We have demonstrated an OPO cavity based on high refractive index inverted prisms, a compact and low-loss approach for achieving $180^\circ$ beam deviation using Brewster’s angle and total internal reflection. Pumped at 800 nm, the OPO produced chirped signal pulses tunable across the near-infrared. Our approach can be readily translated to picosecond pumping with amplified fiber sources, provided that the total internal reflection cut-off limit of $n \approx 1.83929$ is satisfied at the resonant wavelength. Our investigation into the behavior of the Brewster mirror prisms revealed three orders of magnitude increase in the wavelength tuning sensitivity when compared to cavity length tuning. This secondary tuning mechanism should improve OPO cavity stabilization, required for carrier-envelope phase control in OPO-based frequency combs [14–16].
Funding
Science and Technology Facilities Council (ST/T000651/1, ST/T003242/1).
Acknowledgments
The authors thank Prof. Derryck Reid for use of the Ti:sapphire laser.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. D. Kobat, M. E. Durst, N. Nishimura, et al., “Deep tissue multiphoton microscopy using longer wavelength excitation,” Opt. Express 17(16), 13354–13364 (2009). [CrossRef]
2. O. Kara, F. Sweeney, M. Rutkauskas, et al., “Open-path multi-species remote sensing with a broadband optical parametric oscillator,” Opt. Express 27(15), 21358–21366 (2019). [CrossRef]
3. P. Mehta, M. Krishnamurthi, N. Healy, et al., “Mid-infrared transmission properties of amorphous germanium optical fibers,” Appl. Phys. Lett. 97(7), 071117 (2010). [CrossRef]
4. J. Fan, C. Gu, C. Wang, et al., “Extended femtosecond laser wavelength range to 330 nm in a high power LBO based optical parametric oscillator,” Opt. Express 24(12), 13250–13257 (2016). [CrossRef]
5. N. Coluccelli, D. Viola, V. Kumar, et al., “Tunable 30-fs light pulses at 1-W power level from a Yb-pumped optical parametric oscillator,” Opt. Lett. 42(21), 4545–4548 (2017). [CrossRef]
6. S. C. Kumar, J. Krauth, A. Steinmann, et al., “High-power femtosecond mid-infrared optical parametric oscillator at 7 µm based on CdSiP2,” Opt. Lett. 40(7), 1398–1401 (2015). [CrossRef]
7. L. Maidment, P. G. Schunemann, and D. T. Reid, “Molecular fingerprint-region spectroscopy from 5 to 12 µm using an orientation-patterned gallium phosphide optical parametric oscillator,” Opt. Lett. 41(18), 4261–4264 (2016). [CrossRef]
8. D. C. Edelstein, E. S. Wachman, and C. L. Tang, “Broadly tunable high repetition rate femtosecond optical parametric oscillator,” Appl. Phys. Lett. 54(18), 1728–1730 (1989). [CrossRef]
9. T. Beddard, M. Ebrahimzadeh, T. D. Reid, et al., “Five-optical-cycle pulse generation in the mid infrared from an optical parametric oscillator based on aperiodically poled lithium niobate,” Opt. Lett. 25(14), 1052–1054 (2000). [CrossRef]
10. D. E. Hunter and R. A. McCracken, “Ultrashort-pulsed optical parametric oscillator employing Brewster angle prism retroreflectors,” Opt. Express 29(23), 37013–37020 (2021). [CrossRef]
11. M. Moosmüller, “Brewster’s angle Porro prism: a different use for a Pellin-Broca prism,” Appl. Opt. 37(34), 8140–8141 (1998). [CrossRef]
12. G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39(8), 3597–3639 (1968). [CrossRef]
13. “H-ZLaF68C material properties,” http://www.cdgmgd.com/webapp/pdf/H-ZLaF68C.pdf [retrieved 16 Sep 2023].
14. K. Balskus, M. Fleming, R. A. McCracken, et al., “Carrier-envelope offset frequency stabilization in a femtosecond optical parametric oscillator without nonlinear interferometry,” Opt. Lett. 41(5), 966–969 (2016). [CrossRef]
15. M. Vainio and L. Halonen, “Stabilization of femtosecond optical parametric oscillators for infrared frequency comb generation,” Opt. Lett. 42(14), 2722–2725 (2017). [CrossRef]
16. Y. Kobayashi, K. Torizuka, A. Marandi, et al., “Femtosecond optical parametric oscillator frequency combs,” J. Opt. 17(9), 094010 (2015). [CrossRef]
