JP3767299B2 - Parameter determination method for solid-state laser - Google Patents

Description

【００１６】
【数２】

【００１７】
曲面が逆のときはＲが−Ｒになる。ここで球欠的面内と子午的面内を区別するために添え字ｓとｔを用いている。この添え字の使い方は以下でも同様である。
【００１８】
屈折率ｎの媒体を距離Ｌだけ伝播するときのＡＢＣＤ行列は（数３）で与えられる。
【００１９】
【数３】

【００２０】
ＡＢＣＤ行列で記述される複数の光学系が直列に並んでいる場合は光線が進行する順番に各ＡＢＣＤ行列を掛け合わせれば良い。ＦＩＧ．３Ａに示す屈折率ｎ₂の媒体のレンズ３００は屈折曲面、自由空間、屈折平面の３つの光学的要素からなりそれらを表すＡＢＣＤ行列の積を取ればよい。球欠的面内における屈折曲面のＡＢＣＤ行列は（数１）で与えられる。但し、図２と図３を見比べれば分かるように曲面の向きが逆なので（数１）においてＲが−Ｒになる。屈折平面は（数１）においてＲ＝０であり、またｎ _１ とｎ _２ が逆になる。自由空間は一般的には（数３）になるが、ここの計算ではｎ＝１になる。これはＡＢＣＤ行列の傾きに関する定義で上記の一つ目の定義を採用したために、レンズを構成する媒体の屈折率ｎ _２ の効果が屈折曲面及び屈折平面を表すＡＢＣＤ行列に含まれているためである。以上のことを考慮してｔ_f をレンズの厚さ、Ｌ_f をレンズ中の伝播距離とすれば、図３（Ａ）のレンズのＡＢＣＤ行列は（数４）で与えられる。
【００２１】
【数４】

【００２２】
焦点距離ｆの極薄レンズのＡＢＣＤ行列が（数５）で表わされることを考慮すれば（数４）はＦＩＧ．３Ｂに示す焦点距離ｆ_sの薄型レンズ３１１と空間長ｔ_sの空間３１２の合成
【００２３】
【数５】

【００２４】
ＡＢＣＤ行列と等価になり、ｆ _s とｔ _s は（数６）、（数７）で与えられる。
【００２５】
【数６】

【００２６】
【数７】

【００２７】
子午的面内に対しても同様で（数８）、（数９）及び（数１０）に示すようになる。
【００２８】
【数８】

【００２９】
【数９】

【００３０】
【数１０】

【００３１】
前記と同様な議論を、ＦＩＧ．４Ａに示す屈折率ｎ₂＝１．４４９６３（波長１０６４ｎｍに対して）の合成石英からなる凹レンズ４００に当てはめれば、ＦＩＧ．４Ｂに示すように、焦点距離ｆ_sあるいはｆ_tの薄型レンズ４１１と空間長ｔ_sあるいはｔ_tの空間４１２で表現することができ、それぞれ、ｆ_s＝−２１７ｍｍ，ｔ_s＝４．０１ｍｍ，ｆ_t＝−２０３ｍｍ，ｔ_t＝３．８６ｍｍになる。計算上の注意点は、図３と図４では光線の向きが逆になっていることである。
【００３２】
ＦＩＧ．１に示す固体レーザーの構成から励起光に関係した要素のみを抜き出したものをＦＩＧ．５に示す。これから主要な要素である励起光源１１、収束レンズ３１、凹レンズ２２および利得結晶１４のみを取り出して簡単化し、さらに一直線状に書き直したものがＦＩＧ．６である。本質的影響のないアイソレータ１２、半波長板１３、及びビーム軸調整用のプレート３２は省略してある。また、収束レンズ３１および凹レンズ２２については、ＦＩＧ．３Ｂ、４Ｂに示した薄型レンズと空間長の等価的表現を併記した。
【００３３】
励起光源１１の励起光の出口面１から利得結晶内の任意の面７への経路の合成ＡＢＣＤ行列は各光学要素のＡＢＣＤ行列の積を取って球欠的面内Ｍ_17Sに対して（数１１）で与えられる。
【００３４】
【数１１】

【００３５】
ここでｆ_1s，ｔ_1sに現れる添え字１は収束レンズ３１に対応し、ｆ_2s，ｔ_2sに現れる添え字２は凹レンズ２２に対応する。Ｌ_ij（Ｌ₁₂，Ｌ₃₄，Ｌ₅₆，Ｌ₆₇）は面ｉと面ｊの間の等価的距離を表わす。ｎ_YAGは利得結晶１４の屈折率で、Ｃｒ：ＹＡＧ結晶を用いた場合、ｎ_YAG＝１．８２（波長１０６４ｎｍに対して）である。子午的面内に対しては（数１１）において添え字ｓをｔに置き換え、ｎ_YAGを（ｎ_YAG）³に置き換えれば良い。後者の置き換えをする理由は利得結晶１４がブリュスタ角に研磨してあることに由来し、（数８）においてＲ＝∞とブリュスタ角の条件であるｔａｎθ₁＝ｎ₂（ｎ₁＝１）を代入すれば（数１２）を得ることから理解される。
【００３６】
【数１２】

【００３７】
励起光の出口面１での初期条件が分かれば利得結晶１４中の任意の面７におけるビーム径は合成ＡＢＣＤ行列を用いて計算可能であり、ここでその方法を述べる。
【００３８】
任意の面ｉでのビームパラメタｑ_iを（数１３）で定義する。
【００３９】
【数１３】

【００４０】
ここで、Ｒ_iは面ｉでの波面の曲率半径、ｗ_iは面ｉでのビーム径、λは波長、ｊは虚数単位を表わす。励起光の出口面１は励起光源１１の出射口なのでＲ₁＝∞で、ｗ₁には用いる励起光源のビーム径を代入すれば良い。出口面１でのビームパラメタｑ₁が決まれば利得結晶１４中の任意の面７でのビームパラメタは（数１４）により計算できる（例えば、 A.E. Siegman, Lasers, University Science Books, Mill Valley, California (1986)p784）。
【００４１】
【数１４】

【００４２】
利得結晶内の共振器モードの焦点に励起光の焦点を一致させるために（数１４）を用いて収束レンズ３１の傾き角θと位置を求める。θは（数４）、（数８）においてはθ _１ に対応する。集束レンズ３１の位置は距離Ｌ _１２ により表現される。励起光源１１、凹レンズ２２、利得結晶１４を固定すれば、面７でのビームパラメータｑ _７ は３つの独立変数θ、Ｌ _１２ ，Ｌ _６７ の関数ｑ _７ （θ、Ｌ _１２ ，Ｌ _６７ ）になる。球欠的面内の励起光の面７を球欠的面内における利得結晶内の共振器モードの焦点の位置（面 7s 、このとき L ₆₇ = L _67s 、 q ₇ = q _7s ）に、子午的面内の励起光の面７を子午的面内における利得結晶内の共振器モードの焦点の位置（面 7t 、このとき L ₆₇ = L _67t 、 q ₇ = q _7t ）に設定する。励起光は球欠的面内においては面７ｓで、子午的面内においては面７ｔで焦点を結べばよく、焦点では波面の曲率半径が∞になることを利用すれば（数１３）の定義によりビームパラメータ q _7s 及び q _7t の実成分が０になって、（数１５）、（数１６）と書ける。
Re ［ q _7s (L ₁₂ , θ , L _67s ) ］ = 0 （数１５）
Re ［ q _7t (L ₁₂ , θ , L _67t ) ］ = 0 （数１６）
L _67s と L _67t は共振器モードで決まる既知量なので未知のパラメータは L ₁₂ 及びθのみとなって、（数１５）と（数１６）の連立方程式を解けば L ₁₂ 及びθが求まる。これが求めるべき収束レンズの傾き角と位置である。
【００４３】
例として対称型のＣｒ：ＹＡＧレーザー（利得結晶の長さ２０ｍｍ）の共振器を考え、利得結晶１４の中心に焦点を結ぶとし、Ｌ＝Ｌ₁₂＋Ｌ₃₄＝７７０ｍｍ、Ｌ₅₆＝４９．４ｍｍ、励起光源１１のビーム径ｗ₁＝０．１５ｍｍ，励起光源１１の出射口でＲ₁＝∞とし、励起光源１１として発振波長１０６４ｎｍのＮｄ：ＹＶＯ₄レーザーを用い、凹レンズ２２に合成石英からなるＦＩＧ．４に示す寸法のものを用い、収束レンズ３１に合成石英からなる曲率半径Ｒ＝３３．７ｍｍ、厚さｔ_f＝５．０ｍｍのものを用いた場合、収束レンズ３１の傾き角は１０．９°になる。実験的にはこの角度を中心に±３°程度に亙ってモード同期動作が得られるが、１０．９°からずれるにしたがい発振特性は悪くなる。
【００４４】
傾き角の１０．９°は理想的な状態での計算値であり、実際にはこの角度の周辺で微調整する必要がある。理想的な状態からずれる原因は色々とあり、
（１）共振器が対称型でない場合、あるいは対称型であっても利得結晶が共振器の中心からずれている場合等は、共振器モードのビームの利得結晶内の球欠的面内と子午的面内の焦点が一致せず非点収差が残る。この場合には、その非点収差に合うように励起光の非点収差を残す必要がある。計算方法は、共振器モードの球欠的面内と子午的面内の収束点が決まれば上記に示した通りで（数１５）と（数１６）を用いる。
【００４５】
（２）励起光の吸収による発熱に基づく非線型効果、利得結晶のカー効果に基づく自己収束効果や自己導波効果、励起光が利得結晶内を吸収されながら進行するために生ずる励起の場所依存効果、共振器モードのビームと励起光ビームの重なりに不具合がある場合に発生する共振器モードの補正効果、等の種々の非線型効果のために共振器モードのビームは利得結晶内で正確に焦点を結んでいない。励起光の非点収差の補償はこの共振器モードのビームに合わせて行われる必要がある。
【００４６】
以上の効果に加えてＣｒ：ＹＡＧ結晶のように不均一な結晶ではその不均一効果も加わる。レーザー発振は非線型現象なので非常に複雑である。実際の調整では計算結果を中心に傾き角を数度振って最適値を確認するのが良い。
【００４７】
収束レンズ３１を傾けていくと励起光の光軸はそれに伴いずれていく。それを補償するためにビーム軸調整用のプレート３２を構成要素に取り入れることは、収束レンズ３１の傾き角を微調整するときにはとりわけ有効である。プレート３２の材質を収束レンズ３１と同じ物とし、厚さを収束レンズ３１の厚さｔ_fと同じにすれば、プレート３２の傾き角は理論的には収束レンズ３１の傾き角と大きさが等しく向きが逆になる。
【００４８】
固体レーザーをモード同期動作させる場合、正確なアライメントが必要であり、製品化する場合の困難さを生じて来た。特にＣｒ：ＹＡＧレーザーのようにモード同期動作し難いものでは本発明で述べた非点収差の補償は極めて有用である。
【００４９】
次に、本発明が、ＦＩＧ．１に示す実施例の利得結晶の構造およびレンズ、凹面鏡の配列構造とは異なる実施例においても有用であることを以下の二つの実施例で簡単に説明しておく。
【００５０】
(実施例２)
本実施例の構成をＦＩＧ．７に示す。共振器は利得結晶１０３、凹面鏡１０４およびリトロプリズム１０５の要素からなり、利得結晶１０３の黒く塗りつぶした面とリトロプリズム１０５の黒く塗りつぶした面とがエンドミラーを構成する
。利得結晶１０３の励起光の入射面（塗りつぶした面）は垂直研磨されている。共振器の出力光は利得結晶１０３の塗りつぶした面から取り出され凹面鏡１０２で折り返されて得られる。したがって凹面鏡１０２は出力光の波長に対しては高反射コーティング、励起光に対しては反射防止コーティングになっている。
【００５１】
本実施例では、励起光が収束レンズ１０１により利得結晶１０３の黒く塗りつぶした面に収束されるが、励起光は凹面鏡１０２（励起光に対しては凹レンズとして働く）のために非点収差を生じるのでそれを補償するために収束レンズ１０１を傾ける。
【００５２】
(実施例３)
本実施例の構成をＦＩＧ．８に示す。共振器は凹面鏡１１２、利得結晶１１３、凹面鏡１１４、プリズム１１５、エンドミラー１１６の要素からなり、凹面鏡１１２とエンドミラー１１６の黒く塗りつぶした面がエンドミラーを構成する。出力光はエンドミラー１１６から取り出される。出力光は、あるいは、凹面鏡１１２の塗りつぶした面から取り出し、破線で示す凹面鏡１１７で折り返して破線で示すように導出してもよい。
【００５３】
本実施例では、励起光は収束レンズ１１１により利得結晶１１３内部に焦点を結ばせるが、利得結晶１１３が垂直研磨でないために非点収差を生じる。それを補償するようにレンズ１１１を傾ける。
【００５４】
なお、本実施例で、凹面鏡１１２から出力光を取り出す場合は、破線で示す位置に凹面鏡１１７を配置し、これで出力光を折り返す。したがって凹面鏡１１７の凹面は出力光の波長に対しては高反射コーティング、励起光に対しては反射防止コーティングになっている。この場合は、収束レンズ１１１による非点収差の補償は利得結晶１１３が垂直研磨でないことの他に、凹面鏡１１７が傾いていることに帰因する非点収差の両者を考慮したものとすることが必要である。この場合も、前述したように、球欠的面内と子午的面内の両面内での焦点をそれぞれ独立に計算して、両者が、共振器モードのそれぞれの面内の焦点と一致するように収束レンズ１１１の傾きを決定すればよい。
【００５５】
なお、上述の実施例では、利得結晶を直角研磨としないときは、全て、ブリュスタ角に研磨したものについて説明したが、これは、必ずしもブリュスタ角に研磨しなければならないものではなく、共振器モードの設計に応じて任意の角度に研磨した場合においても同様に適用できる。例えば、非点収差を小さくしたいときにブリュスタ角よりも小さい角度に研磨する場合、あるいは、利得結晶の両面が垂直研磨の場合に多重反射による干渉を防ぐために片側もしくは両側を垂直研磨からずらす場合等がある。ＦＩＧ．１あるいはＦＩＧ．８の利得結晶１４の両面にこの考え方を適用できる。
【００５６】
【発明の効果】
本発明により固体レーザーのモード同期動作の安定性と信頼性が向上しＣｒ：ＹＡＧレーザーのようにモード同期し難いレーザーも製品化が容易になる。
【図面の簡単な説明】
【図１】 本発明に関わる実施例１の固体レーザーの構成例を示す図である。
【図２】 曲率半径Ｒの曲面を屈折する光線を表わす図である。
【図３】 (Ａ)は平凸レンズを屈折する光線を表わす図、(Ｂ)は平凸レンズを極薄凸レンズ及び空間とで表わす等価図である。
【図４】 (Ａ)は平凹レンズを屈折する光線を表わす図、(Ｂ)は平凹レンズを極薄凹レンズ及び空間とで表わす等価図である。
【図５】 図１の構成から励起光に関係した部分のみを抜き出した説明図である。
【図６】 図５の主要な構成要素を取り出し、直線状に並べ替えた説明図である。
【図７】 本発明に関わる実施例２の固体レーザーの主要部の構成例を示す図である。
【図８】 本発明に関わる実施例３の固体レーザーの主要部の構成例を示す図である。
【符号の説明】
１：励起光の出口面、２：平凸レンズの凸面、３：平凸レンズの平面、４：平凹レンズの平面、平凹レンズの凹面、６：利得結晶の入射面、７：利得結晶内の任意の面、１１：励起光源、１２：アイソレーター、１３：半波長板、１４：利得結晶、２１：ミラー、２２：ダイクロイックな凹面鏡、２３：凹面鏡、２４：ミラー、２５：ミラー、２６：ミラー、３１：平凸レンズ、３２：ビーム軸調整用のプレート、４１：ブリュスタ分散プリズム、４２：ブリュスタ分散プリズム、３００：平凸レンズ、３１１：極薄凸レンズ、３１２：空間。[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a parameter determination method for compensating astigmatism of excitation light in a solid-state laser .
[0002]
[Prior art]
In order to oscillate the solid-state laser efficiently, it is important to focus the excitation light beam in the gain crystal. This is particularly important when the solid-state laser is operated in the car lens mode synchronization. A normal car lens mode-locked laser includes a gain crystal polished at a Brewster angle and a dichroic concave mirror (which acts as a concave lens for excitation light) in the resonator, both of which are incident on the excitation light. Some angles cause astigmatism in the excitation light.
[0003]
As a result, the focal point of the excitation light beam is blurred and the car lens mode synchronization operation is not performed in the worst case. To solve this problem, for example, a solid-state laser known by the trade name “Model 3960” of Spectra Physics uses a concave mirror for converging excitation light to compensate for astigmatism generated in the gain crystal and the concave lens.
[0004]
However, adjustment of the focusing system of the excitation light using the concave mirror is difficult as compared with the case of using the lens, and a method using a simple lens is desired.
[0005]
On the other hand, it is widely practiced to construct a focusing system for excitation light using only a lens without using a concave mirror. In this case, in general, no consideration is given to astigmatism. Recently, however, it has been reported empirically that the converging lens is tilted approximately 5 degrees to optimize the overlap between the resonator mode and the excitation light beam to improve astigmatism (Y. Chang et al. Applied Physics Letters, Volume 73, Number 15, pp. 2098-2100 (1998)).
[0006]
However, the tilt of about 5 degrees shown in this paper is only an angle that has been reported in the reported laser, and does not give general design guidelines to optimize the overlap between the cavity mode and the excitation light beam in any solid state laser. Absent. Also, this angle is not theoretically indicated, so there may be a more appropriate angle.
[0007]
[Problems to be solved by the invention]
An object of the present invention is to provide a general guideline for optimally compensating for the astigmatism of pumping light when the focusing system of pumping light is composed of only a lens in a solid-state laser, and to provide a parameter determination method for the focusing lens. That is. Specifically, the astigmatism corresponding to the astigmatism of the excitation light converging system, that is, the astigmatism caused by the gain crystal or the concave lens, is intentionally generated by tilting the convex lens for converging the excitation light. By compensating both, the astigmatism of the excitation light is optimally compensated. The inclination angle of the converging lens can be determined theoretically and uniquely if the configuration of the converging system of the laser excitation light is determined.
[0008]
The converging lens, concave lens, and gain crystal are optical elements arranged in series with a common optical axis. The combined focal length of these three elements is calculated independently in the spherical and meridian planes as a function of the tilt angle of the converging lens, so that each approximately matches the focal point in each plane of the resonator mode. If the tilt angle of the converging lens is selected, excitation light compensated for astigmatism can be obtained. The present invention focuses on this.
[0009]
[Means for Solving the Problems]
A gain crystal and a dichroic concave mirror are provided in the laser resonator. The dichroic concave mirror acts as a concave mirror for the resonator mode and focuses in the gain crystal, but acts as a concave lens for the excitation light. The excitation light passes through the converging lens and its concave lens and is focused in the gain crystal, and the position and angle of the converging lens are designed so as to substantially coincide with the focal position of the resonator mode. However, if the spherical in-plane focal position of the excitation light deviates from the meridian in-plane focal position, astigmatism occurs, and the laser does not operate as a stable Kerr lens mode-locked laser. Therefore, in the present invention, the converging lens is tilted with respect to the optical axis of the excitation light, and the combined focal length of the converging lens, the concave lens, and the gain crystal is used as a function of the tilt angle of the converging lens. And the inclination angle of the converging lens is determined so that the respective focal positions substantially coincide with the focal positions in the respective planes of the resonator modes in the gain crystal.
[0010]
DETAILED DESCRIPTION OF THE INVENTION
(Example 1)
FIG. 1 represents an example of the configuration of a car lens mode-locked solid-state laser. The laser resonator includes mirror 21 and mirror 24 as end mirrors, and includes dichroic mirror 22, gain crystal 14 polished to Brewster angle, mirror 23, and Brewster dispersion prisms 41 and 42 therebetween. The light emitted from the excitation light source 11 is transmitted through the isolator 12 and the half-wave plate 13, adjusted in the traveling direction by the mirrors 25 and 26, and then passed through the beam axis adjusting plate 32, and the converging lens 31 and the concave lens (dichroic mirror). ) Is focused by 22 and focused inside the gain crystal 14. The concave lens (dichroic mirror) 22 acts as a concave lens for the excitation light, but acts as a concave mirror for the laser resonator.
[0011]
In order to synchronize the Kerr lens mode, the resonator mode beam needs to be focused in the gain crystal 14, and the resonator is designed so that the focal point in the spherical plane coincides with the focal point in the meridian plane. It is normal to do. However, in general, the focal point in the spherical plane is deviated from the focal point in the meridian plane.
[0012]
The pump light also needs to be focused in the gain crystal 14 in accordance with the focus of the resonator mode, but the pump light is subjected to astigmatism due to refraction on the Brewster surface of the gain crystal 14 and the tilted concave lens 22. The focal point in each plane of the resonator mode cannot be matched in both the spherical plane and the meridian plane. Therefore, the converging lens 31 is tilted in the same direction as or opposite to the tilt direction of the concave lens 22 with respect to the optical axis of the pumping light to compensate for astigmatism generated in the gain crystal 14 and the concave lens 22, and the focal point of the resonator mode and the pumping light The focal point is matched in both the spherical and meridian planes.
[0013]
In order to determine the tilt angle of the convergent lens 31, it is first necessary to obtain a general formula that gives the astigmatism of the lens. In the following example, explanation is given by a theory using an ABCD matrix (for example, AE Siegman, Lasers, University Science Books, Mill Valley, California (1986) pp. 581-584). The ABCD matrix represents the input / output relationship of an arbitrary optical system under paraxial approximation, and can be applied to both geometrical optics (ray optics) and wave optics (Gaussian beams). Input and output parameters in ray optics are the distance from the central axis of each ray and the slope of that ray. There are two definitions for tilt, the first is purely using the tilt of the ray itself, and the second is the product of the tilt of the ray multiplied by the refractive index of the medium on the input and output sides. To define. If the refractive indexes of the media on both sides of the input and output are equal, there is no difference in the ABCD matrix in either definition. This embodiment will be described below according to the first definition. (However, the cited definition of Siegman's work adopts the second definition.)
[0014]
FIG. 2, a medium having a refractive index n _{1 and} a medium having a refractive index n ₂ are in contact with each other at a radius of curvature R, and light incident at an incident angle θ ₁ from the medium side having a refractive index n ₁ has a refractive angle θ ₂ . When the refractive index n ₂ is refracted toward the medium side, the ABCD matrix representing the refraction is given by (Equation 1) and (Equation 2) in the spherical plane and the meridian plane, respectively (for example, J.-P Tache, Applied Optics, Vol. 26, No. 3, pp. 427-429 (1987)).
[0015]
[Expression 1]

[0016]
[Expression 2]

[0017]
When the curved surface is reversed, R becomes -R. Here, the subscripts s and t are used to distinguish between a spherical surface and a meridian surface. The usage of this subscript is the same in the following.
[0018]
The ABCD matrix when propagating through a medium having a refractive index n by a distance L is given by (Equation 3).
[0019]
[Equation 3]

[0020]
When a plurality of optical systems described by ABCD matrices are arranged in series, each ABCD matrix may be multiplied in the order in which light rays travel. FIG. The lens 300 of the medium having the refractive index n ₂ shown in 3A is composed of three optical elements, ie, a refractive surface, a free space, and a refractive plane, and an ABCD matrix representing them can be taken. ABCD matrix refractive curved definitive in sagittal plane is given by equation (1). However, as can be seen by comparing FIG. 2 and FIG. 3, since the direction of the curved surface is reversed, R is −R in (Equation 1). The refractive plane is R = 0 in (Equation 1), and n ₁ and n ₂ are reversed. The free space is generally (Equation 3), but in this calculation, n = 1. This is because the effect of the refractive index n ₂ of the medium constituting the lens is included in the ABCD matrix representing the refraction curved surface and the refraction plane because the first definition is adopted for the definition of the ABCD matrix. is there. Considering the above, if t _f is the thickness of the lens and L _f is the propagation distance in the lens, the ABCD matrix of the lens in FIG. 3A is given by (Equation 4).
[0021]
[Expression 4]

[0022]
Considering that the ABCD matrix of the ultrathin lens with the focal length f is expressed by (Equation 5), (Equation 4) can be expressed as FIG. Synthesis of the focal length f _s of thin lenses 311 and spatial length t _s of the space 312 shown in 3B [0023]
[Equation 5]

[0024]
It becomes equivalent to an ABCD matrix, and f _s and t _s are given by (Equation 6) and (Equation 7).
[0025]
[Formula 6]

[0026]
[Expression 7]

[0027]
The same applies to the meridian plane as shown in (Equation 8), (Equation 9), and (Equation 10).
[0028]
[Equation 8]

[0029]
[Equation 9]

[0030]
[Expression 10]

[0031]
The same discussion as above is shown in FIG. When applied to a concave lens 400 made of synthetic quartz having a refractive index n ₂ = 1.44963 (for a wavelength of 1064 nm) shown in FIG. As shown in 4B, it can be represented in the spatial 412 of focal length f _s or f thin lenses 411 and spatial length of _t t _s or t _{t, respectively, f s = -217mm, t s} = 4.01mm, f _t = −203 mm, t _t = 3.86 mm. The point to be noted in the calculation is that the directions of the light beams are reversed in FIGS.
[0032]
FIG. 1 in which only elements related to excitation light are extracted from the configuration of the solid-state laser shown in FIG. As shown in FIG. Only the excitation light source 11, the converging lens 31, the concave lens 22 and the gain crystal 14 which are main elements will be taken out, simplified, and rewritten in a straight line. 6. The isolator 12, the half-wave plate 13, and the beam axis adjusting plate 32, which have no substantial influence, are omitted. For the converging lens 31 and the concave lens 22, FIG. The thin lens shown in 3B and 4B and the equivalent expression of the space length are shown together.
[0033]
(Number Synthesis ABCD matrix routes to any surface 7 with respect to the sagittal plane M _17S taking the product of ABCD matrix of each optical element in the gain in the crystal from the outlet face 1 of the excitation light of the excitation light source 11 11).
[0034]
[Expression 11]

[0035]
Here, the subscript 1 appearing at f _1s and t _1s corresponds to the converging lens 31, and the subscript 2 appearing at f _2s and t _2s corresponds to the concave lens 22. L _ij (L ₁₂ , L ₃₄ , L ₅₆ , L ₆₇ ) represents an equivalent distance between the surface i and the surface j. n _YAG is the refractive index of the gain crystal 14, and when using a Cr: YAG crystal, n _YAG = 1.82 (for a wavelength of 1064 nm). For the meridian plane, the subscript s may be replaced with t in (Equation 11) and n _YAG may be replaced with (n _YAG ) ³ . The reason for replacing the latter is that the gain crystal 14 is polished to the Brewster angle. In (Equation 8), R = ∞ and the condition of the Brewster angle tan θ ₁ = n ₂ (n ₁ = 1) are set. It can be understood from substituting (Equation 12).
[0036]
[Expression 12]

[0037]
If the initial conditions at the exit surface 1 of the pumping light are known, the beam diameter at an arbitrary surface 7 in the gain crystal 14 can be calculated using the synthesized ABCD matrix, and the method will be described here.
[0038]
The beam parameter q _i on an arbitrary plane i is defined by (Equation 13).
[0039]
[Formula 13]

[0040]
Here, R _i is the radius of curvature of the wavefront at the surface i, w _i is the beam diameter at the surface i, λ is the wavelength , and j is the imaginary unit . Since the exit surface 1 of the excitation light is the exit of the excitation light source 11, R ₁ = ∞, and the beam diameter of the excitation light source used may be substituted for w ₁ . Beam parameters at arbitrary plane 7 in the gain crystal 14 once the beam parameters q ₁ of the outlet face 1 can be calculated by (Equation 14) (e.g., AE Siegman, Lasers, University Science Books, Mill Valley, California ( 1986) p784).
[0041]
[Expression 14]

[0042]
In order to make the focal point of the excitation light coincide with the focal point of the resonator mode in the gain crystal, the inclination angle θ and the position of the converging lens 31 are obtained using (Equation 14). θ corresponds to θ ₁ in (Equation 4) and (Equation 8) . Position of the focusing lens 31 is represented by the distance _{L 12.} Excitation light source 11, the concave lens 22, if secure the gain crystal 14, the beam parameters _{q 7} in terms 7 is a function _{q 7} of three independent variables _{θ, L 12, L 67 (} θ, L 12, L 67) . The surface 7 of the excitation light in the _spherical plane is placed in the meridian at the position of the focal point of the resonator mode in the gain crystal in the _spherical plane (plane 7s , where L ₆₇ = L _67s , q ₇ = q _7s ). The plane 7 of the excitation light in the target plane is set to the position of the focal point of the resonator mode in the gain crystal in the meridian plane (plane 7t , where L ₆₇ = L _67t and q ₇ = q _7t ). The excitation light may be focused on the surface 7s in the spherical plane and on the surface 7t in the meridian plane, and if the fact that the curvature radius of the wave front becomes ∞ at the focal point is used, the definition of (Equation 13) is given. Thus, the real components of the beam parameters q _7s and q _7t become 0, and can be written as (Equation 15) and (Equation 16).
_{Re [q 7s (L 12,} θ, L 67s)] = 0 ( equation 15)
_{Re [q 7t (L 12,} θ, L 67t)] = 0 ( Equation 16)
L _67s And L _67t Since L is a known amount determined by the resonator mode, the only unknown parameters are L ₁₂ and θ, and L ₁₂ and θ can be obtained by solving the simultaneous equations of (Equation 15) and (Equation 16) . This is the inclination angle and position of the convergent lens to be obtained.
[0043]
As an example, consider a resonator of a symmetric Cr: YAG laser (gain crystal length 20 mm), and focus on the center of the gain crystal 14, and L = L ₁₂ + L ₃₄ = 770 mm, L ₅₆ = 49.4 mm, The beam diameter w _{1 of} the excitation light source 11 is 0.15 mm, R ₁ = ∞ at the exit of the excitation light source 11, an Nd: YVO ₄ laser with an oscillation wavelength of 1064 nm is used as the excitation light source 11, and the concave lens 22 is made of FIG. . 4 having the radius of curvature R = 33.7 mm made of synthetic quartz and the thickness t _f = 5.0 mm, the tilt angle of the convergent lens 31 is 10.9. It becomes °. Experimentally, mode-locked operation can be obtained over about ± 3 ° around this angle, but the oscillation characteristics become worse as it deviates from 10.9 °.
[0044]
The tilt angle of 10.9 ° is a calculated value in an ideal state, and actually it is necessary to finely adjust around this angle. There are various causes that deviate from the ideal state.
(1) When the resonator is not symmetric, or even if it is symmetric, the gain crystal is displaced from the center of the resonator, etc. Astigmatism remains because the focal points in the target plane do not match. In this case, it is necessary to leave the astigmatism of the excitation light so as to match the astigmatism. The calculation method uses (Equation 15) and (Equation 16) as shown above if the convergence points in the spherical plane and the meridian plane of the resonator mode are determined.
[0045]
(2) Nonlinear effects based on heat generation due to absorption of excitation light, self-convergence effects and self-waveguide effects based on Kerr effect of gain crystal, and location dependence of excitation that occurs because excitation light travels while being absorbed in gain crystal Because of various nonlinear effects such as the effect, the correction effect of the resonator mode that occurs when there is a defect in the overlap between the resonator mode beam and the excitation light beam, the resonator mode beam is precisely in the gain crystal. Not focused. Compensation for the astigmatism of the excitation light needs to be performed in accordance with this resonator mode beam.
[0046]
In addition to the above effects, the non-uniform crystal such as Cr: YAG crystal also has the non-uniform effect. Since laser oscillation is a non-linear phenomenon, it is very complicated. In actual adjustment, it is preferable to check the optimum value by shifting the tilt angle several degrees around the calculation result.
[0047]
As the converging lens 31 is tilted, the optical axis of the excitation light accompanies it. In order to compensate for this, incorporating the beam axis adjusting plate 32 as a component is particularly effective when the tilt angle of the converging lens 31 is finely adjusted. The material of the plate 32 as same as the converging lens 31, when the thickness equal to the thickness t _f of the converging lens 31, the tilt angle of the plate 32 is the inclination angle and the magnitude of the converging lens 31 is theoretically The direction is equally reversed.
[0048]
When a solid-state laser is operated in a mode-locked manner, accurate alignment is required, which has caused difficulty in commercialization. In particular, the compensation for astigmatism described in the present invention is extremely useful for a laser that is difficult to perform mode-locking operation, such as a Cr: YAG laser.
[0049]
Next, the present invention relates to FIG. It will be briefly described in the following two embodiments that the gain crystal structure and the lens / concave mirror arrangement shown in FIG.
[0050]
(Example 2)
The configuration of this example is shown in FIG. 7 shows. The resonator includes elements of a gain crystal 103, a concave mirror 104, and a retro prism 105, and the black painted surface of the gain crystal 103 and the black painted surface of the retro prism 105 constitute an end mirror. The incident surface (filled surface) of the excitation light of the gain crystal 103 is vertically polished. The output light of the resonator is obtained by being taken out from the painted surface of the gain crystal 103 and folded back by the concave mirror 102. Therefore, the concave mirror 102 is a highly reflective coating for the wavelength of the output light and an antireflection coating for the excitation light.
[0051]
In this embodiment, the excitation light is converged on the black-filled surface of the gain crystal 103 by the converging lens 101. However, the excitation light causes astigmatism due to the concave mirror 102 (acting as a concave lens for the excitation light). Therefore, the converging lens 101 is tilted to compensate for it.
[0052]
Example 3
The configuration of this example is shown in FIG. It is shown in FIG. The resonator includes elements of a concave mirror 112, a gain crystal 113, a concave mirror 114, a prism 115, and an end mirror 116. The black surfaces of the concave mirror 112 and the end mirror 116 constitute an end mirror. Output light is extracted from the end mirror 116. Alternatively, the output light may be extracted from the painted surface of the concave mirror 112, and returned by the concave mirror 117 indicated by a broken line, as indicated by the broken line.
[0053]
In this embodiment, the excitation light is focused inside the gain crystal 113 by the converging lens 111, but astigmatism occurs because the gain crystal 113 is not vertically polished. The lens 111 is tilted to compensate for this.
[0054]
In this embodiment, when the output light is extracted from the concave mirror 112, the concave mirror 117 is disposed at the position indicated by the broken line, and the output light is folded back. Therefore, the concave surface of the concave mirror 117 is a highly reflective coating for the wavelength of the output light and an antireflection coating for the excitation light. In this case, the astigmatism compensation by the converging lens 111 may take into account both astigmatism caused by the tilt of the concave mirror 117 in addition to the fact that the gain crystal 113 is not vertically polished. is necessary. Also in this case, as described above, the focal points in both the spherical surface and the meridian surface are calculated independently so that both coincide with the focal points in the respective planes of the resonator mode. The inclination of the converging lens 111 may be determined.
[0055]
In the above-described embodiments, when the gain crystal is not right-angle polished, all of the gain crystals have been described to be polished to the Brewster angle. However, this is not necessarily required to be polished to the Brewster angle. The same applies to the case of polishing at an arbitrary angle according to the design. For example, when you want to reduce astigmatism, when polishing to an angle smaller than the Brewster angle, or when shifting both sides of the gain crystal from vertical polishing to prevent interference due to multiple reflection when both sides of the gain crystal are vertical polishing There is. FIG. 1 or FIG. This concept can be applied to both sides of the eight gain crystals 14.
[0056]
【The invention's effect】
According to the present invention, the stability and reliability of the mode-locking operation of the solid-state laser is improved, and a laser that is difficult to mode-lock like a Cr: YAG laser can be easily commercialized.
[Brief description of the drawings]
FIG. 1 is a diagram showing a configuration example of a solid-state laser of Example 1 according to the present invention.
FIG. 2 is a diagram illustrating a light beam that refracts a curved surface having a radius of curvature R;
FIG. 3A is a diagram showing light rays refracting a plano-convex lens, and FIG. 3B is an equivalent diagram showing the plano-convex lens by an ultrathin convex lens and a space.
4A is a diagram showing a light beam refracting a plano-concave lens, and FIG. 4B is an equivalent diagram showing the plano-concave lens with an ultrathin concave lens and a space.
FIG. 5 is an explanatory diagram in which only a portion related to excitation light is extracted from the configuration of FIG.
6 is an explanatory diagram in which the main components in FIG. 5 are taken out and rearranged linearly.
FIG. 7 is a diagram illustrating a configuration example of a main part of a solid-state laser according to a second embodiment related to the present invention.
FIG. 8 is a diagram illustrating a configuration example of a main part of a solid-state laser according to a third embodiment related to the present invention.
[Explanation of symbols]
1: exit surface of excitation light, 2: convex surface of plano-convex lens, 3: plane of plano-convex lens, 4: plane of plano-concave lens, concave surface of plano-concave lens, 6: incident surface of gain crystal, 7: arbitrary surface in gain crystal 11: excitation light source, 12: isolator, 13: half-wave plate, 14: gain crystal, 21: mirror, 22: dichroic concave mirror, 23: concave mirror, 24: mirror, 25: mirror, 26: mirror, 31: Plano-convex lens, 32: Beam axis adjusting plate, 41: Brewster dispersion prism, 42: Brewster dispersion prism, 300: Plano-convex lens, 311: Ultrathin convex lens, 312: Space.

Claims (7)

Excitation light source,
A focusing lens that converges the excitation light from the excitation light source and enters the resonator;
A dichroic concave mirror that transmits excitation light and reflects resonator mode light,
And an optical system having a resonator having a gain crystal as one of its constituent elements,
In a laser resonator that introduces excitation light into a gain crystal through a converging lens and a dichroic concave mirror,
The converging lens so that the respective focal points in the spherical and meridional planes of the excitation light in the gain crystal substantially coincide with the focal points in the respective planes in the gain crystal in a resonator mode; A parameter determination method for a solid-state laser tilted with respect to the optical axis of the excitation light,
A solid laser parameter determination method, wherein the tilt angle and position of the convergent lens are determined in the following process.
(1) Fix the position of the excitation light source, dichroic concave mirror, gain crystal,
The tilt angle (θ) of the converging lens, the distance (L ₁₂ ) from the output coupler section (surface 1) of the excitation light source to the surface (surface 2) on the excitation light source side of the focusing lens, and the end surface of the gain crystal on the excitation light source side ( The ABCD matrix from the output coupler of the excitation light source to the plane 7 is expressed in the spherical plane and the meridian plane with the distance (L ₆₇ ) from the plane 6) to an arbitrary plane (plane 7) in the gain crystal as a variable. Ask for each one.
(2) By using the beam parameter q ₁ on the surface 1 which is a known amount given by the excitation light source and the ABCD matrix from the surface 1 to the surface 7, the beam parameter on the surface 7 is Calculate for each in-plane and meridian plane.
Here, the beam parameter of light of wavelength λ on the surface i is defined by (Equation 13) using the curvature radius R _i of the wave front and the beam radius w _i (where j is an imaginary unit).

(3) In order to make the focal point of the pumping light coincide with the focal point of the resonator mode in the gain crystal, the surface 7 of the pumping light in the spherical surface is aligned with the focal point of the resonator mode in the gain crystal in the spherical surface. The position of the resonator mode focal point in the gain crystal in the meridian plane (plane _7s ), the plane 7 of the excitation light in the meridian plane at the position (plane 7s, in this case L ₆₇ = L _67s , q ₇ = q _7s ) 7t, L ₆₇ = L _67t and q ₇ = q _7t ), and L ₁₂ and θ are obtained by solving the following two simultaneous equations.
Re [q _7s (L ₁₂ , θ, L _67s )] = 0
Re [q _7t (L ₁₂ , θ, L _67t )] = 0   2. The solid laser parameter determination method according to claim 1, wherein the surface is polished with a Brewster angle or a right angle with respect to the optical axis of the resonator mode.   2. The solid-state laser parameter determination method according to claim 1, wherein the surface is polished at right angles to the optical axis of the resonator mode.   The angle of inclination (θ) with respect to the optical axis of the converging lens is determined by the respective planes in the gain crystal where the focal points of the excitation light in the spherical crystal and the meridian plane in the gain crystal are in the resonator mode. 2. A method for determining a parameter of a solid-state laser according to claim 1, further comprising a step of changing within a predetermined angle range from an inclination angle substantially coincident with the focal point.   The angle of inclination (θ) with respect to the optical axis of the converging lens is determined by the respective planes in the gain crystal where the focal points of the excitation light in the spherical crystal and the meridian plane in the gain crystal are in the resonator mode. 3. The method for determining a parameter of a solid-state laser according to claim 2, further comprising a step of changing within a predetermined angle range from an inclination angle substantially coincident with the focal point.   The angle of inclination (θ) with respect to the optical axis of the converging lens is determined by the respective planes in the gain crystal where the focal points of the excitation light in the spherical crystal and the meridian plane in the gain crystal are in the resonator mode. 4. The method for determining a parameter of a solid-state laser according to claim 3, further comprising a step of changing within a range of a predetermined angle from an inclination angle substantially coincident with the focal point.   The solid laser parameter determination method according to claim 1, further comprising a beam axis adjusting plate between the excitation light source and the converging lens.

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